url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://metanumbers.com/96944 | 1,638,899,147,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363405.77/warc/CC-MAIN-20211207170825-20211207200825-00469.warc.gz | 461,242,041 | 7,423 | # 96944 (number)
96,944 (ninety-six thousand nine hundred forty-four) is an even five-digits composite number following 96943 and preceding 96945. In scientific notation, it is written as 9.6944 × 104. The sum of its digits is 32. It has a total of 6 prime factors and 20 positive divisors. There are 47,232 positive integers (up to 96944) that are relatively prime to 96944.
## Basic properties
• Is Prime? No
• Number parity Even
• Number length 5
• Sum of Digits 32
• Digital Root 5
## Name
Short name 96 thousand 944 ninety-six thousand nine hundred forty-four
## Notation
Scientific notation 9.6944 × 104 96.944 × 103
## Prime Factorization of 96944
Prime Factorization 24 × 73 × 83
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 6 Total number of prime factors rad(n) 12118 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 96,944 is 24 × 73 × 83. Since it has a total of 6 prime factors, 96,944 is a composite number.
## Divisors of 96944
1, 2, 4, 8, 16, 73, 83, 146, 166, 292, 332, 584, 664, 1168, 1328, 6059, 12118, 24236, 48472, 96944
20 divisors
Even divisors 16 4 2 2
Total Divisors Sum of Divisors Aliquot Sum τ(n) 20 Total number of the positive divisors of n σ(n) 192696 Sum of all the positive divisors of n s(n) 95752 Sum of the proper positive divisors of n A(n) 9634.8 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 311.358 Returns the nth root of the product of n divisors H(n) 10.0619 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 96,944 can be divided by 20 positive divisors (out of which 16 are even, and 4 are odd). The sum of these divisors (counting 96,944) is 192,696, the average is 963,4.8.
## Other Arithmetic Functions (n = 96944)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 47232 Total number of positive integers not greater than n that are coprime to n λ(n) 2952 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 9316 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 47,232 positive integers (less than 96,944) that are coprime with 96,944. And there are approximately 9,316 prime numbers less than or equal to 96,944.
## Divisibility of 96944
m n mod m 2 3 4 5 6 7 8 9 0 2 0 4 2 1 0 5
The number 96,944 is divisible by 2, 4 and 8.
• Deficient
• Polite
## Base conversion (96944)
Base System Value
2 Binary 10111101010110000
3 Ternary 11220222112
4 Quaternary 113222300
5 Quinary 11100234
6 Senary 2024452
8 Octal 275260
10 Decimal 96944
12 Duodecimal 48128
20 Vigesimal c274
36 Base36 22sw
## Basic calculations (n = 96944)
### Multiplication
n×y
n×2 193888 290832 387776 484720
### Division
n÷y
n÷2 48472 32314.7 24236 19388.8
### Exponentiation
ny
n2 9398139136 911093200400384 88325019219614826496 8562580663226339739828224
### Nth Root
y√n
2√n 311.358 45.9382 17.6453 9.93812
## 96944 as geometric shapes
### Circle
Diameter 193888 609117 2.95251e+10
### Sphere
Volume 3.81638e+15 1.181e+11 609117
### Square
Length = n
Perimeter 387776 9.39814e+09 137100
### Cube
Length = n
Surface area 5.63888e+10 9.11093e+14 167912
### Equilateral Triangle
Length = n
Perimeter 290832 4.06951e+09 83956
### Triangular Pyramid
Length = n
Surface area 1.62781e+10 1.07373e+14 79154.4
## Cryptographic Hash Functions
md5 27ef2e87221c355f517e2824b19f7ca6 46e66a4bee61b27ded545a9974211b81db5b08fb c9b4dea3f2a854da20179cee5ae347928ad06892b08e65d0b7dd0006bb311d93 3af8224d32923fcc896c98f98ac1374a8674012c8499a1f401ba8494b31021c7612b1c29669b3f5499f1efd6990cdcb978d95b82d6eedbf283fa6fda857bf6d1 08577c2b988ba2296acedaa376c757d5abbeb8ed | 1,478 | 4,149 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2021-49 | latest | en | 0.801641 |
https://www.abcteach.com/search.php?category=0&q=4&search_type=1&match_words=2&limit_search=1&_form_action=&search_form1_form_visited=1 | 1,571,137,772,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986658566.9/warc/CC-MAIN-20191015104838-20191015132338-00198.warc.gz | 799,972,189 | 24,082 | You are an abcteach Member, but you are logged in to the Free Site. To access all member features, log into the Member Site.
SEARCH RESULTS: 4
Clip Art:
= Member Site Document
There are 2486 documents matching your search.
• Updated: A one page biography of Olympic Gold Medal swimmer, Michael Phelps, with multiple choice and short response questions.
Common Core:
RI.3.1, RI 3.2, RI 3.3, RI. 3.6, RI. 3.8
RI 4.1, RI 4.2, RI 4.3, RI 4.5, RI.4.6, RI.4.8
• Use this 'Spelling Level 4, unit 1' printable worksheet in the classroom or at home. Your students will love this 'Spelling Level 4, unit 1'. First of a complete set on our member site.
• Use this 'High Frequency Spelling: Primary, Unit 4' printable worksheet in the classroom or at home. Your students will love this 'High Frequency Spelling: Primary, Unit 4'. Review of high frequency primary level spelling units 1-3
• Eight pages of Math practice investigating Chichen Itza. Common Core: Geometry 6.G.A1, 5.G.B3, 4.MD.3
• This Magic Squares 4 x 4 (set 3) Worksheet is perfect to practice addition skills. Your elementary grade students will love this Magic Squares 4 x 4 (set 3) Worksheet. Not really magic-- just math fun! Numbers should be inserted so that rows, columns, and diagonals all add up to the same sum. Solve the two squares 4 different ways
• Use this 'Book Unit: The Magic School Bus Explores the Senses' printable worksheet in the classroom or at home. Your students will love this 'Book Unit: The Magic School Bus Explores the Senses'. This unit contains vocabulary, comprehension and writing activities for the book; The Magic School Bus: Explores the Senses by Joanna Cole. Common Core: RL.4.1, RL.4.4, W.4.1, RL5.4, W.5.1
• This Circle04 4/4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle04 4/4 B&W clipart is provided in jpeg format.
• This Rectangle04 4/4 Color clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Rectangle04 4/4 Color clipart is provided in jpeg format.
• This Polygon 04 4/4 Color clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Polygon 04 4/4 Color clipart is provided in jpeg format.
• This Circle04 Color 4/4 clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle04 Color 4/4 clipart is provided in jpeg format.
• This Polygon04 4/4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Polygon04 4/4 B&W clipart is provided in jpeg format.
• This Pinwheel: 4 Blades 4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Pinwheel: 4 Blades 4 B&W clipart is provided in jpeg format.
• This Pinwheel: 4 Blades 4 Color 1 clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Pinwheel: 4 Blades 4 Color 1 clipart is provided in jpeg format.
• Use this 'Game: Search a Word 4 x 4 (horse)' printable worksheet in the classroom or at home. Your students will love this 'Game: Search a Word 4 x 4 (horse)'. A horse peeks out from behind this game board. More game boards are available on our member site.
• This Labeled Fractions: 04 4/4 Four Fourths Grayscale clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Labeled Fractions: 04 4/4 Four Fourths Grayscale clipart is provided in jpeg format.
• This Labeled Fractions: 04 4/4 Four Fourths Color clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Labeled Fractions: 04 4/4 Four Fourths Color clipart is provided in jpeg format.
• This Numerical 04 4/4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Numerical 04 4/4 B&W clipart is provided in jpeg format.
• This Math Lesson Planner - Number, Operations and Fractions (grade 4) Common Core is perfect to practice fractions and number operations skills. Your elementary grade students will love this Math Lesson Planner - Number, Operations and Fractions (grade 4) Common Core. PowerPoint Template. Type or print these lesson planner pages. Each page has the standard, the link to the detailed standard and space for you to jot down your lessons. Great for those who need to identify the standards to their lesson plans. CC: 4.NF.A.1, 4.NF.B.1-4, 4.NF.C.1-2
• This Multiplication (by 4) Math Wheels is perfect to practice multiplication skills. Your elementary grade students will love this Multiplication (by 4) Math Wheels. Our math "machines" make multiplication drills fun. Cut out the two shapes and practice simple multiplication. With multiples up to 4.
• Use this 'Interactive Flipchart: Phonics Dolch Set 4 Cloze Story' printable worksheet in the classroom or at home. Your students will love this 'Interactive Flipchart: Phonics Dolch Set 4 Cloze Story'. Cloze Story for Dolch Set 4. (and, blue, many, they, before, put, went, must, read, because). Promethean ActivInspire .flipchart files. Includes related printable worksheet.
• Use this 'Interactive Flipchart: Phonics Dolch Set 4 Crossword' printable worksheet in the classroom or at home. Your students will love this 'Interactive Flipchart: Phonics Dolch Set 4 Crossword'. Crossword for Dolch Set 4. (and, blue, many, they, before, put, went, must, read, because). Promethean ActivInspire .flipchart files. Includes related printable worksheet.
• Use this 'Interactive Flipchart: Phonics Dolch Set 4 Spelling (with audio)' printable worksheet in the classroom or at home. Your students will love this 'Interactive Flipchart: Phonics Dolch Set 4 Spelling (with audio)'. Audio spelling exercises for Dolch Set 4. (and, blue, many, they, before, put, went, must, read, because). Promethean ActivInspire .flipchart files. Includes related printable worksheet.
• Use this 'Flashcards: Places (set 4)' printable worksheet in the classroom or at home. Your students will love this 'Flashcards: Places (set 4)'. Bedroom, bathroom, kitchen, living room. Colorfully illustrated.
• This Multiplication (2 digits, set 4) Worksheet is perfect to practice multiplication skills. Your elementary grade students will love this Multiplication (2 digits, set 4) Worksheet. 5 pages of worksheets to practice 2-digit multiplication, plus answers.
• This Addition Grids - Integers 4 Worksheet is perfect to practice addition skills. Your elementary grade students will love this Addition Grids - Integers 4 Worksheet. Add positive and negative numbers vertically and horizontally to complete ten by nine square grids.
• This Jack-o-Lantern 4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Jack-o-Lantern 4 B&W clipart is provided in jpeg format.
• This Jack-o-Lantern 4 color clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Jack-o-Lantern 4 color clipart is provided in jpeg format.
• This Praise Notes 4 Color clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Praise Notes 4 Color clipart is provided in jpeg format.
• This Kids: Boy 4 Color clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Kids: Boy 4 Color clipart is provided in jpeg format.
• This Kids: Girl 4 Color clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Kids: Girl 4 Color clipart is provided in jpeg format.
• Use this 'Crossword: Little House in the Big Woods Ch. 3 & 4' printable worksheet in the classroom or at home. Your students will love this 'Crossword: Little House in the Big Woods Ch. 3 & 4'. This sample was made with the abcteach crossword puzzle tool.
• This Kids: Back to School 4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Kids: Back to School 4 B&W clipart is provided in jpeg format.
• This Circle08 4/8 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle08 4/8 B&W clipart is provided in jpeg format.
• This Circle05 4/5 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle05 4/5 B&W clipart is provided in jpeg format.
• This Circle04 3/4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle04 3/4 B&W clipart is provided in jpeg format.
• This Circle04 2/4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle04 2/4 B&W clipart is provided in jpeg format.
• This Circle04 1/4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle04 1/4 B&W clipart is provided in jpeg format.
• This Circle04 0/4 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle04 0/4 B&W clipart is provided in jpeg format.
• This Circle06 4/6 B&W clipart is great to illustrate your teaching materials. As an abcteach member you have unlimited access to our 22,000+ clipart illustrations and can use them for commercial use. This Circle06 4/6 B&W clipart is provided in jpeg format. | 2,780 | 11,206 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2019-43 | latest | en | 0.835123 |
http://blogs.yis.ac.jp/18bhattacharjeer/2014/01/ | 1,534,496,921,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221211935.42/warc/CC-MAIN-20180817084620-20180817104620-00222.warc.gz | 61,305,025 | 12,079 | # Using Standard Form in Measurement- Math
In Math, we have been learning how to convert basic numerals into ‘Standard Form’.
Standard form is also known as ‘Scientific Notations’.
Today in Math class, we went outside to look for 4 objects in the school.
We then measured each objects so we could convert them into ‘standard form measurements’ later.
My partner (Marina) and I measured the following things:
Bench (3rd floor)
Printer (3rd floor)
Water Fountain (2nd floor)
TV (Foyer)
Changing units of measurements:
1. Bench-
Length: 154cm (1.54m)
Length in kilometers: 0.00154km
Length in nanometers: 1,540,000,000nm
2. Printer-
Length: 110.6cm (1.106m)
Length in kilometers: 0.001106km
Length in nanometers: 1,106,000,000nm
3. Water Fountain-
Length: 89cm (0.89m)
Length in kilometers: 0.00089km
Length in nanometers: 890,000,000nm
4. Television-
Length: 74.8cm (0.748m)
Length in kilometers: 0.000748km
Length in nanometers: 748,000,000nm
Problems with converting units of measurements
Converting units of measurements can just be difficult to understand in general.
People are used to measuring things in cm/inches but not in km. You know how much a centimeter is by heart since you’re so used to measuring things in that unit but when it comes to converting them into kilometers, you aren’t exactly sure how much a kilometer is. It’s hard to decide whether that object is big or small, long or short when you aren’t too familiar with the unit.
Same with converting centimeters/inches into nanometers/micrometers, you aren’t familiar with these unit, therefore it is hard to understand how big or small the object is when first glancing at the measurement.
Standard form are mainly used for writing really big numbers. Eg; 10 million trillion. Using standard form can minimize the time you spend writing such big numbers down and it saves time 🙂
It becomes really complicated once you start adding and subtracting the 2 or more measurements written in standard form since you have to convert one of them into the same power of 10 as the other measurement.
# Chapitre 9: Mise En Train
Activity 1:Â Tu as compris?
It was fine but she didn’t do much.
2. Did Magali have a good weekend? Why? Why not?
Yes, she did. She had fun with Florent and Ahmed c:
3. Do you think Magali likes Ahmed? How can you tell?
Yes, Magali likes Ahmed 🙂 She said Ahmed was cute and nice and she was also really happy when Ahmed gave his phone number to her.
4. Why does Magali have to hang up?
She hangs up because her dad wants to use the phone.
Qui a fait ça, Magali ou Hélène?
1. Aller aux Baux: Magali
4. Aller au théâtre antique: Magali
Activity 3:Â Mets en ordre
Put Magali’s activities in order according to Un week-end spécial.
1.Elle a rencontré un garçon sympa.
3. Elle est allée aux Baux-de-Provence.
Activity 4: C’est qui?
A quelle personne correspond chaque phrase?
2. Cette personne a passé un bon week-end- Magali
3. Cette personne est super gentille- Ahmed
4. Pendant le week-end, cette personne n’a rien fait de spécial- Hélène
Activity 5:Â Cherche les expressions
According to Un week-end spécial, what do you say in French?
AllĂ´?
2. To identify yourself on the phone?
C’est… à l’appareil.
Tu as passé un bon week-end?
4. To ask what someone did?
Qu’est-ce que tu as fait?
5. To tell someone to hold?
Attends une seconde.
Â
# Allez, viens en Arles!
Avant d’explorer
A. Some of your friends are going on a vacation to Arles. They’ve asked you to help them plan their trip. They would like to visit a monument and a museum and go to a festival. Think of a keyword in French for each piece of information you need to search on the Internet, and write your keywords below.
Keywords: Festives, Les Arenes Romains, La Camargue, Les Alyscamps, Obélisque.
En ligne!
B. Now, explore the Internet for the information you need to find and fill the chart below with the name of each place or event your friends could visit and its location, and briefly describe what there is to see and do there.
Musee RĂ©attu- Located near the Roman Baths in Arles. The Reattu museum is a modern art museum and it features various drawings by Picasso.
Les Arenes Romaines- France Arles. Arenes Romaines is an arena where you can enjoy plays, concerts and bullfighting 🙂
Les Rencontres Arles- 34 Rue du Docteur Fanton, 13200 Arles. Rencontres Arles is a festival which displays photographies.
Write the name and URL of each site you visited to complete Activity B:
www.museereatu.arles.fr, arlesfrance.ca/attractions/reattu-museum.html
www.rencontres-arles.com/A11/Home
C. You have a passion for regional cuisine, and you’d love to know what’s cooking in Arles. List three dishes mentioned on the Web sites you find and their main ingredients.
1. Filets de rougets á la creme d’olive et marjolaine
Main Ingredients:
• Red Mullet
• Marjoram
• Olive
• Butter
2. Gigot d’agneau de lait braise aux petits oignons
Main Ingredients:
• Lamb
• Onions
• White Wine
• Butter
• Milk
3. Soupe au Pistou
Main Ingredients:
• Green beans
• Zucchini
• Tomatoes
• Carrots
• Potatoes
• Pasta
Sources:
www.provenceweb.fr/f/mag/cooking/clasilva1/html, www.provenceweb.fr/f/mag/cooking/recettes/marie/pistou.htm
D. Explore l’Internet et trouve des informations sur une personne cĂ©lèbre qui a habitĂ© en Arles ou en Provence.
1. Son nom: Vincent Van Gogh
2. Ou il/elle a habité: Netherlands, Paris, Arles, etc.
3. Quand il/elle y a habité: Netherlands from 1853 to 1886, Paris from 1886 to 1888, Arles from 1888 to 1889, Saint Rémy from 1889 to 1890 and Auvers-Sur-Oise 1890 May to 1890 July.
4. La raison de sa célèbrité: He became famous for his artwork and influence ib Expressionism and Fauvism.
Sources:
WemMuseum Paris
www.ibiblio.org/wm/paint/auth/gogh
Wikipedia
en/wikipedia.org/wiki/Vincent_Van_Gogh#Bibliography
Faisons le bilan
E. List five new French words that you learned while doing the previous activities and explain what each word means.
1. Agneau- Lamg
2. Fermes- Farm
3. Thermes- Bath
4. Rougets- Red Mullet
5. Courgette- Zucchini
 | 1,756 | 6,129 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.46875 | 4 | CC-MAIN-2018-34 | longest | en | 0.917027 |
http://forums.xkcd.com/viewtopic.php?f=3&t=113255&p=3898305 | 1,556,268,001,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578762045.99/warc/CC-MAIN-20190426073513-20190426095513-00379.warc.gz | 63,030,036 | 8,236 | ## Eight by eight matrix, flip a coin.
A forum for good logic/math puzzles.
Moderators: jestingrabbit, Moderators General, Prelates
mathocean149
Posts: 2
Joined: Fri Dec 25, 2015 8:13 am UTC
### Eight by eight matrix, flip a coin.
Say we have an eight by eight matrix, and each entry has a coin, heads or tails, determined by Randall Monroe. Randall Monroe points at a coin he deems "worthy." Then, we must flip exactly 1 coin. A partner with whom I have conspired with before must be able to tell which coin is "worthy." Is this possible or not?
emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.
### Re: Eight by eight matrix, flip a coin.
So there's an 8x8 matrix of values, heads or tails, and you can look at the entire matrix before Randall selects a coin and flips it over. Can't you just memorise the entire matrix, tell it to your partner, and leave them to determine which coin was flipped? If not, then they can't know any prior knowledge about the matrix, just what methods could be used. None, as it happens, as if this isn't a lateral thinking problem, you're partner's just looking at a 8x8 array of coins, with no idea which to turn.
For instance, all of the coins could be heads, except for the one Randall deems worthy, which is then also flipped to be heads. your partner now has to pick the worthy coin from 64 heads, with nothing to distinguish between them. Either it's impossible, a memory task, requires lateral thinking, or I've misunderstood the problem.
"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."
curiosityspoon
Posts: 35
Joined: Wed Sep 24, 2014 5:01 pm UTC
### Re: Eight by eight matrix, flip a coin.
Randall sets the initial array of heads and tails and selects a coin, then based on that choice, you select any coin (not necessarily the same one) and flip it over, then the partner (who has not looked at the initial array of coins, and has not communicated with you since you were first able to see it) gets to look at the array as it exists after you flipped a coin over. From that information, the partner has to determine which coin is the one Randall chose.
Spoiler:
A success rate of at least 64/67 is definitely possible: treat the array not as a square, but as a linear string of 64 binary digits. The numbers 2^0, 2^1, ... , 2^63 all fall into different residue classes mod-67, so flipping each individual bit to add or subtract the appropriate power of 2 will result in a different value for the mod-67 of the overall number, and if the starting array is all tails for 00000, the only values that cannot be reached with exactly one heads are 0, 17, and 34. 65 is unfortunately not prime, and there are only 13 values that get repeated across all the coins, so 67 is the smallest number of buckets you can have under this scheme that's still enough to disambiguate at least 64 values.
If necessary for obfuscation, you and the partner can agree on a secret constant beforehand that you'll add to the actual binary value derived from the 64 coins, and if possible, you flip over a coin that will make that adjusted value, mod-67, equal to the index number of the coin you want to point to.
Nitrodon
Posts: 497
Joined: Wed Dec 19, 2007 5:11 pm UTC
### Re: Eight by eight matrix, flip a coin.
Spoiler:
Number the coins 0-63. Take the bitwise XOR of all coins showing heads, and XOR the result with the position of the worthy coin. This will give you the coin you should flip. In the new configuration, the worthy coin will be the one corresponding to the bitwise XOR of all heads. | 926 | 3,793 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2019-18 | latest | en | 0.95008 |
https://edurev.in/studytube/Sample-Solution-Paper-3-Physics--Class-11/6d8ac28b-d6f1-4c6c-9a82-80440a132a91_p | 1,709,480,409,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476396.49/warc/CC-MAIN-20240303142747-20240303172747-00106.warc.gz | 229,747,851 | 56,789 | Sample Solution Paper 3: Physics, Class 11
``` Page 1
CBSE | Physics
Sample Paper 3 Solution
CBSE Board
Class XI Physics
Sample Paper-3 Solution
1.
Yes. Example is angle
2.
Motion of a body thrown vertically/obliquely under constant g
3.
- x-axis
4.
Work
5.
Since ? ? ? rF , larger arm means larger r which requires less F for same ? .
6.
3
7.
8.
No process is possible whose sole result is the absorption of heat from a reservoir and the
conversion of all of this heat into work.
Page 2
CBSE | Physics
Sample Paper 3 Solution
CBSE Board
Class XI Physics
Sample Paper-3 Solution
1.
Yes. Example is angle
2.
Motion of a body thrown vertically/obliquely under constant g
3.
- x-axis
4.
Work
5.
Since ? ? ? rF , larger arm means larger r which requires less F for same ? .
6.
3
7.
8.
No process is possible whose sole result is the absorption of heat from a reservoir and the
conversion of all of this heat into work.
CBSE | Physics
Sample Paper 3 Solution
9.
Systematic Errors Random Errors
1. Errors in which the deviation
from true value tends to have
fixed size and sign.
2. They can be attributed to a
fixed cause and can be
eliminated.
Deviation from true value is
irregular in size as well as sign.
Irregular pattern does not allow
them to be attributed to any fixed
cause and hence cannot be
eliminated, only minimized.
10.
For 3 kg:
F – F 32 = m 3a (i)
For 2 kg:
F 23 = m 2a (ii)
But from Newton’s third law
23 32
FF ??
Therefore, from (i) and (ii), F – m 2a = m 3a
F = (m 2 + m 3)a
2
5
a 1 m/s
5
? ? ?
Therefore, F 32 = m 2a = 2.1 = 2N (1/2)
Page 3
CBSE | Physics
Sample Paper 3 Solution
CBSE Board
Class XI Physics
Sample Paper-3 Solution
1.
Yes. Example is angle
2.
Motion of a body thrown vertically/obliquely under constant g
3.
- x-axis
4.
Work
5.
Since ? ? ? rF , larger arm means larger r which requires less F for same ? .
6.
3
7.
8.
No process is possible whose sole result is the absorption of heat from a reservoir and the
conversion of all of this heat into work.
CBSE | Physics
Sample Paper 3 Solution
9.
Systematic Errors Random Errors
1. Errors in which the deviation
from true value tends to have
fixed size and sign.
2. They can be attributed to a
fixed cause and can be
eliminated.
Deviation from true value is
irregular in size as well as sign.
Irregular pattern does not allow
them to be attributed to any fixed
cause and hence cannot be
eliminated, only minimized.
10.
For 3 kg:
F – F 32 = m 3a (i)
For 2 kg:
F 23 = m 2a (ii)
But from Newton’s third law
23 32
FF ??
Therefore, from (i) and (ii), F – m 2a = m 3a
F = (m 2 + m 3)a
2
5
a 1 m/s
5
? ? ?
Therefore, F 32 = m 2a = 2.1 = 2N (1/2)
CBSE | Physics
Sample Paper 3 Solution
OR
The two ways are:
1. Friction adjusts its direction to be always opposite to applied force.
2. Friction adjusts its magnitude up to a certain limit, to be equal to the applied force.
F ms = ?
s
N = ? ? ? ? ?
s
mg 0.2 2 10 4N
Since, applied force < F ms, the static friction acting = f s = 2 N.
11.
We know that
p 2mk ?
??
? ? ? ? ?
??
??
21 11 11
and p' 2mk' 2m k k 2mk p
100 10 10
Therefore,
11
pp
p1
10
p p 10
?
?
??
p
100 10%
p
?
??
12.
? ? ? rpsin mv
Direction of ? rp ? direction of
13.
Polar satellites - Their orbit is perpendicular to the orbit of geostationary satellites. These
are used for communication purpose. Also, the height above the Earth’s surface is lower.
Negative sign of total energy indicates attractive nature of force between the satellite and
the Earth.
Page 4
CBSE | Physics
Sample Paper 3 Solution
CBSE Board
Class XI Physics
Sample Paper-3 Solution
1.
Yes. Example is angle
2.
Motion of a body thrown vertically/obliquely under constant g
3.
- x-axis
4.
Work
5.
Since ? ? ? rF , larger arm means larger r which requires less F for same ? .
6.
3
7.
8.
No process is possible whose sole result is the absorption of heat from a reservoir and the
conversion of all of this heat into work.
CBSE | Physics
Sample Paper 3 Solution
9.
Systematic Errors Random Errors
1. Errors in which the deviation
from true value tends to have
fixed size and sign.
2. They can be attributed to a
fixed cause and can be
eliminated.
Deviation from true value is
irregular in size as well as sign.
Irregular pattern does not allow
them to be attributed to any fixed
cause and hence cannot be
eliminated, only minimized.
10.
For 3 kg:
F – F 32 = m 3a (i)
For 2 kg:
F 23 = m 2a (ii)
But from Newton’s third law
23 32
FF ??
Therefore, from (i) and (ii), F – m 2a = m 3a
F = (m 2 + m 3)a
2
5
a 1 m/s
5
? ? ?
Therefore, F 32 = m 2a = 2.1 = 2N (1/2)
CBSE | Physics
Sample Paper 3 Solution
OR
The two ways are:
1. Friction adjusts its direction to be always opposite to applied force.
2. Friction adjusts its magnitude up to a certain limit, to be equal to the applied force.
F ms = ?
s
N = ? ? ? ? ?
s
mg 0.2 2 10 4N
Since, applied force < F ms, the static friction acting = f s = 2 N.
11.
We know that
p 2mk ?
??
? ? ? ? ?
??
??
21 11 11
and p' 2mk' 2m k k 2mk p
100 10 10
Therefore,
11
pp
p1
10
p p 10
?
?
??
p
100 10%
p
?
??
12.
? ? ? rpsin mv
Direction of ? rp ? direction of
13.
Polar satellites - Their orbit is perpendicular to the orbit of geostationary satellites. These
are used for communication purpose. Also, the height above the Earth’s surface is lower.
Negative sign of total energy indicates attractive nature of force between the satellite and
the Earth.
CBSE | Physics
Sample Paper 3 Solution
14.
The stress required to fracture a material whether by compression, tension, or shear is
called breaking stress.
Yes, the wire is under stress as its own weight acts as load.
15.
?
= const.
Therefore, PV
?
= '' PV
?
?
5/3 5/3 5 5/3
1600 '(8 ) 2 ' V P V PV ??
Or ??
a
1600
P' 50P
32
Therefore, fall in pressure = 1600 – 500 = 1550 P a
16.
(i) For isothermal expansion ?T = 0, hence ?U = 0
(ii) For adiabatic expansion ?U = ?Q – ?W = - ?W = -P ?V as ?Q = 0.
17.
?
? ? ? ?
?
A
36 1000
36 km/h 10 m/s
60 60
AC
54 km/h 15 m/s ? ? ? ? ?
BA B A
15 10 5 m/s ? ? ? ? ? ? ? ?
CA C A
15 ( 10) 25 m/s ? ? ? ? ? ? ? ? ?
Time taken by C to cover 1 km = ?
1000
40s
25
To avoid accident, B should cover 1 km is less than 40s.
??
2
1
s ut at
2
2
1
1000 5 40 a.(40)
2
? ? ? ?
200 800a ??
800a = 1000 – 200 = 800
? a = 1 m/s
2
Page 5
CBSE | Physics
Sample Paper 3 Solution
CBSE Board
Class XI Physics
Sample Paper-3 Solution
1.
Yes. Example is angle
2.
Motion of a body thrown vertically/obliquely under constant g
3.
- x-axis
4.
Work
5.
Since ? ? ? rF , larger arm means larger r which requires less F for same ? .
6.
3
7.
8.
No process is possible whose sole result is the absorption of heat from a reservoir and the
conversion of all of this heat into work.
CBSE | Physics
Sample Paper 3 Solution
9.
Systematic Errors Random Errors
1. Errors in which the deviation
from true value tends to have
fixed size and sign.
2. They can be attributed to a
fixed cause and can be
eliminated.
Deviation from true value is
irregular in size as well as sign.
Irregular pattern does not allow
them to be attributed to any fixed
cause and hence cannot be
eliminated, only minimized.
10.
For 3 kg:
F – F 32 = m 3a (i)
For 2 kg:
F 23 = m 2a (ii)
But from Newton’s third law
23 32
FF ??
Therefore, from (i) and (ii), F – m 2a = m 3a
F = (m 2 + m 3)a
2
5
a 1 m/s
5
? ? ?
Therefore, F 32 = m 2a = 2.1 = 2N (1/2)
CBSE | Physics
Sample Paper 3 Solution
OR
The two ways are:
1. Friction adjusts its direction to be always opposite to applied force.
2. Friction adjusts its magnitude up to a certain limit, to be equal to the applied force.
F ms = ?
s
N = ? ? ? ? ?
s
mg 0.2 2 10 4N
Since, applied force < F ms, the static friction acting = f s = 2 N.
11.
We know that
p 2mk ?
??
? ? ? ? ?
??
??
21 11 11
and p' 2mk' 2m k k 2mk p
100 10 10
Therefore,
11
pp
p1
10
p p 10
?
?
??
p
100 10%
p
?
??
12.
? ? ? rpsin mv
Direction of ? rp ? direction of
13.
Polar satellites - Their orbit is perpendicular to the orbit of geostationary satellites. These
are used for communication purpose. Also, the height above the Earth’s surface is lower.
Negative sign of total energy indicates attractive nature of force between the satellite and
the Earth.
CBSE | Physics
Sample Paper 3 Solution
14.
The stress required to fracture a material whether by compression, tension, or shear is
called breaking stress.
Yes, the wire is under stress as its own weight acts as load.
15.
?
= const.
Therefore, PV
?
= '' PV
?
?
5/3 5/3 5 5/3
1600 '(8 ) 2 ' V P V PV ??
Or ??
a
1600
P' 50P
32
Therefore, fall in pressure = 1600 – 500 = 1550 P a
16.
(i) For isothermal expansion ?T = 0, hence ?U = 0
(ii) For adiabatic expansion ?U = ?Q – ?W = - ?W = -P ?V as ?Q = 0.
17.
?
? ? ? ?
?
A
36 1000
36 km/h 10 m/s
60 60
AC
54 km/h 15 m/s ? ? ? ? ?
BA B A
15 10 5 m/s ? ? ? ? ? ? ? ?
CA C A
15 ( 10) 25 m/s ? ? ? ? ? ? ? ? ?
Time taken by C to cover 1 km = ?
1000
40s
25
To avoid accident, B should cover 1 km is less than 40s.
??
2
1
s ut at
2
2
1
1000 5 40 a.(40)
2
? ? ? ?
200 800a ??
800a = 1000 – 200 = 800
? a = 1 m/s
2
CBSE | Physics
Sample Paper 3 Solution
18.
a = -kx
dv
a kx
dx
? ? ? ?
dv kx dx ? ? ?
Integrating both sides, we get
x
uo
dv kx dx
?
? ? ?
??
2 2 2
11
( u ) kx
22
? ? ? ?
or
2 2 2
11
m( u ) m kx
22
? ? ? ?
Therefore, loss in K.E. =
2
1
m kx
2
19.
(a) During free fall acceleration of thief = g = acceleration of load
So that load is unable to apply any force.
Let the force by load be N.
mg – N ? N = 0 = force applied by load on man
(b) Along horizontal direction, ?
? ext
F0 . Net linear momentum is conserved.
Before firing, the system is at rest.
Therefore, 0 =
b b g g
mm ? ? ?
b
gb
g
m
m
? ? ? ?
So, to conserve linear momentum, the gun recoils.
(c) The sand yields but the cemented floor doesn’t.
Hence, the time taken by man to come to rest increases in case of sand.
Since,
p
F
t
?
?
?
, force on man is less.
20.
We know that
12
KA(T T )t
Q
x
?
?
A = area of 6 faces = 6 × (3 × 10
-1
)
2
= 54 × 10
-3
m L =
12
KA(T T )t
x
?
or
12
KA(T T )t
m
xL
?
?
```
### Top Courses for Grade 11
Explore Courses for Grade 11 exam
### Top Courses for Grade 11
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
; | 3,511 | 10,648 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2024-10 | latest | en | 0.859324 |
https://www.kilomegabyte.com/1-mibit-to-tb | 1,701,328,939,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100172.28/warc/CC-MAIN-20231130062948-20231130092948-00854.warc.gz | 939,712,245 | 5,863 | #### Data Units Calculator
###### Mebibit to Terabyte
Online data storage unit conversion calculator:
From:
To:
The smallest unit of measurement used for measuring data is a bit. A single bit can have a value of either zero(0) or one(1). It may contain a binary value (such as True/False or On/Off or 1/0) and nothing more. Therefore, a byte, or eight bits, is used as the fundamental unit of measurement for data storage. A byte can store 256 different values, which is sufficient to represent standard ASCII table, such as all numbers, letters and control symbols.
Since most files contain thousands of bytes, file sizes are often measured in kilobytes. Larger files, such as images, videos, and audio files, contain millions of bytes and therefore are measured in megabytes. Modern storage devices can store thousands of these files, which is why storage capacity is typically measured in gigabytes or even terabytes.
# 1 mibit to tb result:
1 (one) mebibit(s) is equal 0.000000131072 (zero point zero × 6 one hundred and thirty-one thousand and seventy-two) terabyte(s)
#### What is mebibit?
The mebibit is a multiple of the bit, a unit of information, prefixed by the standards-based multiplier "mebi" (symbol Mi), a binary prefix meaning 2^20. The unit symbol of the mebibit is Mibit. 1 mebibit = 2^20 bits = 1048576 bits = 1024 kibibits
#### What is terabyte?
The terabyte is a multiple of the unit byte for digital information. The prefix tera represents the fourth power of 1000, and means 10^12 in the International System of Units (SI), and therefore one terabyte is one trillion (short scale) bytes. The unit symbol for the terabyte is TB.
#### How calculate mibit. to tb.?
1 Mebibit is equal to 0.000000131072 Terabyte (zero point zero × 6 one hundred and thirty-one thousand and seventy-two tb)
1 Terabyte is equal to 7629394.53125 Mebibit (seven million six hundred and twenty-nine thousand three hundred and ninety-four point fifty-three thousand one hundred and twenty-five mibit)
1 Mebibit is equal to 1048576.000000000 bits (one million forty-eight thousand five hundred and seventy-six point zero × 9 zero bits)
1 Terabyte is equal to 8000000000000 bits (eight trillion bits)
1 Mebibit is equal to 1048576 Bit (one million forty-eight thousand five hundred and seventy-six bit)
Terabyte is greater than Mebibit
Multiplication factor is 7629394.53125.
1 / 7629394.53125 = 0.000000131072.
Maybe you mean Megabit?
1 Mebibit is equal to 1.048576 Megabit (one point zero × 1 forty-eight thousand five hundred and seventy-six mbit) convert to mbit
### Powers of 2
mibit tb (Terabyte) Description
1 mibit 0.000000131072 tb 1 mebibit (one) is equal to 0.000000131072 terabyte (zero point zero × 6 one hundred and thirty-one thousand and seventy-two)
2 mibit 0.000000262144 tb 2 mebibit (two) is equal to 0.000000262144 terabyte (zero point zero × 6 two hundred and sixty-two thousand one hundred and forty-four)
4 mibit 0.000000524288 tb 4 mebibit (four) is equal to 0.000000524288 terabyte (zero point zero × 6 five hundred and twenty-four thousand two hundred and eighty-eight)
8 mibit 0.000001048576 tb 8 mebibit (eight) is equal to 0.000001048576 terabyte (zero point zero × 5 one million forty-eight thousand five hundred and seventy-six)
16 mibit 0.000002097152 tb 16 mebibit (sixteen) is equal to 0.000002097152 terabyte (zero point zero × 5 two million ninety-seven thousand one hundred and fifty-two)
32 mibit 0.000004194304 tb 32 mebibit (thirty-two) is equal to 0.000004194304 terabyte (zero point zero × 5 four million one hundred and ninety-four thousand three hundred and four)
64 mibit 0.000008388608 tb 64 mebibit (sixty-four) is equal to 0.000008388608 terabyte (zero point zero × 5 eight million three hundred and eighty-eight thousand six hundred and eight)
128 mibit 0.000016777216 tb 128 mebibit (one hundred and twenty-eight) is equal to 0.000016777216 terabyte (zero point zero × 4 sixteen million seven hundred and seventy-seven thousand two hundred and sixteen)
256 mibit 0.000033554432 tb 256 mebibit (two hundred and fifty-six) is equal to 0.000033554432 terabyte (zero point zero × 4 thirty-three million five hundred and fifty-four thousand four hundred and thirty-two)
512 mibit 0.000067108864 tb 512 mebibit (five hundred and twelve) is equal to 0.000067108864 terabyte (zero point zero × 4 sixty-seven million one hundred and eight thousand eight hundred and sixty-four)
1024 mibit 0.000134217728 tb 1024 mebibit (one thousand and twenty-four) is equal to 0.000134217728 terabyte (zero point zero × 3 one hundred and thirty-four million two hundred and seventeen thousand seven hundred and twenty-eight)
2048 mibit 0.000268435456 tb 2048 mebibit (two thousand and forty-eight) is equal to 0.000268435456 terabyte (zero point zero × 3 two hundred and sixty-eight million four hundred and thirty-five thousand four hundred and fifty-six)
4096 mibit 0.000536870912 tb 4096 mebibit (four thousand and ninety-six) is equal to 0.000536870912 terabyte (zero point zero × 3 five hundred and thirty-six million eight hundred and seventy thousand nine hundred and twelve)
8192 mibit 0.001073741824 tb 8192 mebibit (eight thousand one hundred and ninety-two) is equal to 0.001073741824 terabyte (zero point zero × 2 one billion seventy-three million seven hundred and forty-one thousand eight hundred and twenty-four)
### Convert Mebibit to other units
mibit System Description
1 mibit 1048576 bit 1 mebibit (one) is equal to 1048576 bit (one million forty-eight thousand five hundred and seventy-six)
1 mibit 131072 b 1 mebibit (one) is equal to 131072 byte (one hundred and thirty-one thousand and seventy-two)
1 mibit 131.072 kb 1 mebibit (one) is equal to 131.072 kilobyte (one hundred and thirty-one point zero × 1 seventy-two)
1 mibit 0.131072 mb 1 mebibit (one) is equal to 0.131072 megabyte (zero point one hundred and thirty-one thousand and seventy-two)
1 mibit 0.000131072 gb 1 mebibit (one) is equal to 0.000131072 gigabyte (zero point zero × 3 one hundred and thirty-one thousand and seventy-two)
1 mibit 0.000000131072 tb 1 mebibit (one) is equal to 0.000000131072 terabyte (zero point zero × 6 one hundred and thirty-one thousand and seventy-two)
1 mibit 128 kib 1 mebibit (one) is equal to 128 kibibyte (one hundred and twenty-eight)
1 mibit 0.125 mib 1 mebibit (one) is equal to 0.125 mebibyte (zero point one hundred and twenty-five)
1 mibit 0.0001220703125 gib 1 mebibit (one) is equal to 0.0001220703125 gibibyte (zero point zero × 3 one billion two hundred and twenty million seven hundred and three thousand one hundred and twenty-five)
1 mibit 0.00000011920928955078125 tib 1 mebibit (one) is equal to 0.00000011920928955078125 tebibyte (zero point zero × 6 eleven quadrillion nine hundred and twenty trillion nine hundred and twenty-eight billion nine hundred and fifty-five million seventy-eight thousand one hundred and twenty-five)
1 mibit 1048.576 kbit 1 mebibit (one) is equal to 1048.576 kilobit (one thousand and forty-eight point five hundred and seventy-six)
1 mibit 1.048576 mbit 1 mebibit (one) is equal to 1.048576 megabit (one point zero × 1 forty-eight thousand five hundred and seventy-six)
1 mibit 0.001048576 gbit 1 mebibit (one) is equal to 0.001048576 gigabit (zero point zero × 2 one million forty-eight thousand five hundred and seventy-six)
1 mibit 0.000001048576 tbit 1 mebibit (one) is equal to 0.000001048576 terabit (zero point zero × 5 one million forty-eight thousand five hundred and seventy-six)
1 mibit 1024 kibit 1 mebibit (one) is equal to 1024 kibibit (one thousand and twenty-four)
1 mibit 0.0009765625 gibit 1 mebibit (one) is equal to 0.0009765625 gibibit (zero point zero × 3 nine million seven hundred and sixty-five thousand six hundred and twenty-five)
1 mibit 0.00000095367431640625 tibit 1 mebibit (one) is equal to 0.00000095367431640625 tebibit (zero point zero × 6 ninety-five trillion three hundred and sixty-seven billion four hundred and thirty-one million six hundred and forty thousand six hundred and twenty-five) | 2,273 | 8,043 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2023-50 | latest | en | 0.85845 |
http://gmatclub.com/forum/verbal-practice-og-or-bust-90822.html?fl=similar | 1,485,301,837,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560285315.77/warc/CC-MAIN-20170116095125-00320-ip-10-171-10-70.ec2.internal.warc.gz | 118,614,572 | 53,264 | Verbal Practice - OG or bust? : GMAT Verbal Section
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack
It is currently 24 Jan 2017, 15:50
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# Verbal Practice - OG or bust?
Author Message
Manager
Joined: 09 Dec 2009
Posts: 122
Followers: 4
Kudos [?]: 46 [0], given: 19
Verbal Practice - OG or bust? [#permalink]
### Show Tags
26 Feb 2010, 09:08
After studying for verbal I'm coming to the conclusion that its best to study ONLY from the OG.
Unlike the quant, which generally has an objective solution that can be backed up with proven mathmatical principles, the verbal is really subjective. I find the non-OG material is often more debatable than the OG stuff. With the subjective nature of the verbal answers I find that non-GMAT questions tend to be frustrating to solve as they either have no good answers or more than one. Whereas with the the OG verbal I find even if I cant solve it, once i find the correct answer it will make sense in hindsight.
Anyone else come to this conclusion as well?
_________________
G.T.L. - GMAT, Tanning, Laundry
Round 2: 07/10/10 - This time it's personal.
If you have any questions
New!
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 550
Kudos [?]: 3568 [0], given: 360
Re: Verbal Practice - OG or bust? [#permalink]
### Show Tags
04 Mar 2010, 05:28
I practiced LSAT CR and found this practice very useful but I should admit that it took 1 week of solving OG CR to adapt my too suspicious LSAT style to GMAT CR.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame
Senior Manager
Joined: 21 Jul 2009
Posts: 366
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Followers: 18
Kudos [?]: 164 [1] , given: 22
Re: Verbal Practice - OG or bust? [#permalink]
### Show Tags
04 Mar 2010, 06:56
1
KUDOS
You couldn't have been more right. OG is style, language and substance in one single package, just like the best of girls I like to go out with. Anyways, the point is verbal prep material outside OG is only good for pointers but not for actual improvement in your abilities with practise. You must only try to learn the nuances, the direction you must take in order to get to the answer, OG will help you better nailing it. Practise lots of non-OG material, do the kaplan and MGMAT online tests, and when you think you are adequately efficient, come back to OG, and you'll notice a stark improvement in your scores. The difference is as good as doing a doll, and doing an adult actress!!! Whad'upp!!!!
_________________
I am AWESOME and it's gonna be LEGENDARY!!!
Manager
Joined: 09 Dec 2009
Posts: 122
Followers: 4
Kudos [?]: 46 [0], given: 19
Re: Verbal Practice - OG or bust? [#permalink]
### Show Tags
05 Mar 2010, 07:56
BarneyStinson wrote:
The difference is as good as doing a doll, and doing an adult actress!!! Whad'upp!!!!
+1
_________________
G.T.L. - GMAT, Tanning, Laundry
Round 2: 07/10/10 - This time it's personal.
Re: Verbal Practice - OG or bust? [#permalink] 05 Mar 2010, 07:56
Similar topics Replies Last post
Similar
Topics:
Verbal OG 2017 and OG 2017 (Verbal Section) 2 21 Jul 2016, 18:21
What is the best souce of Verbal Qs to practice? (OG? Mnht? Ver? etc) 2 15 Apr 2016, 03:16
GMAT verbal practice test 1 05 Jul 2011, 21:10
Verbal Practice Tests 4 07 Aug 2010, 19:02
4 Verbal OG 1 25 Jan 2008, 05:28
Display posts from previous: Sort by | 1,170 | 4,166 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2017-04 | latest | en | 0.884715 |
https://www.physicsforums.com/threads/supposedly-simple-1-d-motion-question.258391/ | 1,508,539,181,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824357.3/warc/CC-MAIN-20171020211313-20171020231313-00211.warc.gz | 988,750,533 | 15,672 | # Supposedly Simple, 1-D Motion Question
1. Sep 22, 2008
### Luca169
1. The problem statement, all variables and given/known data
A man is driving at 56.0 km/h [N]. Suddenly, a boy stumbles on the road 65 m ahead of the car. After t seconds the driver finally decides to hit the brakes, which then produces an acceleration of 3.00 m/s² . What is the maximum reaction time allowed if the driver is to avoid hitting this student?
2. Relevant equations
I started off trying to use Δd = V1Δt + 1/2a(Δt)² , however I was told this won't work since acceleration is not constant, this I understand. Then, I tried using quadratic formula to solve, but for me it wouldn't work since the number I was trying to find the square root of was negative.
3. The attempt at a solution
I would write the steps I took during my quadratic formula phase, but I'm not sure I even did it correctly, any help with this would be appreciated.
2. Sep 22, 2008
### LowlyPion
Just write out your quadratic. You don't need to show the intermediate steps.
3. Sep 22, 2008
### Luca169
0 = (-1.5m/s²)(Δt)² + (16m/s)(Δt) - 65m
X1= 5.3 X2 = 5.3
That's not the answer I'm supposed to be getting.. What have I done wrong?
4. Sep 22, 2008
### LowlyPion
But perhaps a different approach might be easier?
How long does it take to slow from 15.55m/s to 0 at -3m/s2? That's your time budget to stop.
Using that time, determine how much distance you require to stop.
If it is less than 65m then then how long can you continue at 15.55m/s before you have to stop?
If it is longer than 65m, start calling 9-1-1.
5. Sep 22, 2008
### Luca169
0 m/s = 15.55 m/s + (-3.00m/s²)(Δt)
-15.55m/s/-3.00m/s=(Δt)
(Δt)=5.183
Δd=15.55m/s(5.183s)+1/2(-3.00m/s²)(5.183s)²
Δd=40.3m
65m - 40.3m = 24.7m/15.55m/s= 1.58 s?
This is about two decimal places off from the given answer (1.56) however, is the procedure correct? | 608 | 1,880 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2017-43 | longest | en | 0.955362 |
https://aviation.stackexchange.com/questions/38018/finding-strength-of-vortex-by-solving-integration-of-thin-aerofoil-theory | 1,568,968,298,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573908.70/warc/CC-MAIN-20190920071824-20190920093824-00491.warc.gz | 386,240,731 | 27,614 | # Finding strength of vortex by solving integration of thin aerofoil theory! [closed]
Can any one solve the upper equation from the image and obtain lower equation from image?
Image from J D Anderson 5th edition page no. 324
## closed as off-topic by Ralph J, SMS von der Tann, J. Hougaard, ymb1, SimonMay 16 '17 at 6:50
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "This question does not appear to be about aviation, within the scope defined in the help center." – Ralph J, SMS von der Tann, J. Hougaard, ymb1, Simon
If this question can be reworded to fit the rules in the help center, please edit the question.
• Have you tried it yourself? Can you explain where you're getting stuck? – fooot May 15 '17 at 16:22
• Of course I have tried! – user21819 May 15 '17 at 16:23
Well, there are many solutions to the first equation. We just have to find one which makes physically sense. One of the solutions to this equation has obviously* the form:
$\gamma(\theta) = 2 V_\infty \alpha \cdot\frac{\cos{\theta}-\cos{\theta_0}}{\sin{\theta}}$
Now choose a value for $\theta_0$ that satisfies the Kutta condition. The only solution is $\theta_0=\pi$. Therefore,
$\gamma(\theta) = 2 V_\infty \alpha \cdot\frac{1 + \cos{\theta}}{\sin{\theta}}$
You can check the solution substituting $\gamma(\theta)$ in the original equation. The identities
• $\int_0^\pi\frac{1}{\cos{\theta}-\cos{\theta_0}}d\theta$ = 0
and
• $\int_0^\pi \frac{\cos{\theta}}{cos{\theta}-\cos{\theta_0}}d\theta = \pi$
should be enough to do the check. This integrals are not the easiest, so you would need to find them in a book with trigonometric identities. There, the second one often appears in the general form $\frac{1}{\pi}\cdot\int_0^\pi \frac{\cos{n \theta}}{cos{\theta_0}-\cos{\theta}}d\theta = -\frac{\sin{n \theta_0}}{\sin{\theta_0}}$.
If you want a more formal solution I'd ask at https://math.stackexchange.com/.
*Integrating constants is easy. Therefore I transform the expression inside the integral into a constant. $g(\theta)*f(\theta)=C_1 \Rightarrow g(\theta) = \frac{C_1}{f(\theta)}$. In this case $f(\theta)=\frac{\sin{\theta}}{\cos{\theta}-\cos{\theta_0}}$ | 643 | 2,205 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2019-39 | latest | en | 0.871421 |
http://www.cplusplus.com/forum/general/112172/ | 1,500,842,545,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549424610.13/warc/CC-MAIN-20170723202459-20170723222459-00147.warc.gz | 402,444,565 | 4,553 | ### computing the Riemann zeta function
I am new to c++ and taking a college coarse on it. Immediately i need help on one of my labs. I'm suppose to provide an inner loop that computes the zeta function and the other loop is just press y for to continue, anything else exit.so far i got this:
``12345678910111213141516171819202122232425262728293031323334353637383940`` ``````#include #include #include using namespace std; int main() { double x, n,zeta; char flag = 'y'; while(flag=='y') { cout <<"Enter x value "; cin >> x; n=1; zeta=0 while(1/(pow(n,x))>1e-7) { zeta= 1/(pow(n,x)); zeta=+zeta; n++; } cout<<"Sum is "<>flag; } system("pause"); return 0; }``````
I can't seem to get the formula right.
Last edited on
When learning, it is extremely important to use correct indenting. It may seem trivial and something you can 'fix' later, but when your programs get to be more than 40 lines, it will become impossible to read.
But I think this is what you are looking for:
``12345678910111213141516`` ``````#include double zeta(double s) { const double precision = 1e-7; double output = 0.0; double calculation = 1.0; for (int denom = 2; abs(output - calculation) > precision; ++denom) { output += calculation; calculation = 1.0 / pow(denom, s); } return output; }``````
If you haven't learned functions yet, then just stick lines 5-13 inside of your while(flag=='y') loop. If you can't figure out where your while loops start and end, then fix your formatting.
Last edited on
i forgot to mention i must put it in a "while" loop, and my prof. has restricted the class from using break (except in switch) and constant?. Is it also possible to dumb things down to a level of a beginner, i don't want to use anything beside what i learn which is simple stuff what i just kind of did.
Topic archived. No new replies allowed. | 502 | 1,828 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2017-30 | latest | en | 0.843109 |
http://and.ultraomegaburnreview.org/proportions-math-worksheet-printable/ | 1,600,602,809,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400197946.27/warc/CC-MAIN-20200920094130-20200920124130-00195.warc.gz | 9,823,601 | 18,823 | # Proportions Math Worksheet Printable
## Proportions Worksheets Math Worksheets 4 Kids
This Series Of Printable Proportion Worksheets Are Prepared Specifically For Learners Of Grade 6 Grade 7 And Grade 8 A Variety Of Exercises Like Finding Proportions Using A Pair Of Ratios Determining Proportions In Function Tables Creating A Proportion With A Given Set Of Numbers And Solving Word Problems Are Included Here
### Proportions Worksheets Free Printable K5 Learning
Worksheets Math Grade 6 Proportions Proportions And Ratios The Use Of Proportions Is A Practical Math Skill That Students Often Struggle With Our Proportions Worksheets Review Whole Number And Decimal Proportions As Well As Provide Simple Proportion Word Problems
#### Proportions Worksheets Tutoringhour
Worksheets Math Pre Algebra Proportions Traverse Through Our All New Free Printable Proportions Worksheets To Enlighten Students About Proportion A Simple Statement That Asserts Two Ratios Are Equivalent Also Acquaint Them With The Constant Of Proportionality K And The Proportional Relationship Between Two Variables Y Kx Count On This Myriad Collection Of Exercises To Give You
##### Free Proportion Worksheets For Grades 6 7 And 8
Basic Instructions For The Worksheets Each Worksheet Is Randomly Generated And Thus Unique The Answer Key Is Automatically Generated And Is Placed On The Second Page Of The File You Can Generate The Worksheets Either In Html Or Format Both Are Easy To Print To Get The Worksheet Simply Push The Button Titled Create Or Make Worksheet
###### Ratio And Proportions Worksheets
Ratios And Proportions Worksheets What S The Difference Between A Ratio And A Proportion Many People Think They Are One And The Same The Fact Is They Are Very Different A Ratio Is S A Fraction Like 3 4 It Can Come Many Forms Such As 3 Out Of 4 Equal Parts Or 3 4 But Fundamentally It Is A Fraction
Ratio And Proportion Worksheets Helping With Math
Ratio And Proportion Worksheets The Printable Worksheets Listed Below Help Students To Identify Simplify And Compare Ratios Identifying Ratios Writing Ratios 1 Of 2 Based On Graphical Questions Writing Ratios 2 Of 2 Writing Ratios Simplifying Ratios Simplifying Ratios 1 Of 2 4 2 2 1 Includes Prompts To Divide By G C F Simplifying Ratios 2 Of 2 Identify And
Solving Proportions Worksheets
Learn How To Solve Proportions With This Set Of Printer Friendly Worksheets That Are Specially Designed For Students Of Grade 6 Through High School A Series Of Multi Level Worksheets Require Students To Solve Proportions Using The Cross Product Method And The Answers So Derived Will Be In The Form Of Whole Numbers Fractions Or Decimals Also Solve Worksheets That Contain The Variables In
Solving Proportions Worksheets Math Worksheets
Each Math Worksheet Is Accompanied By An Answer Key Is Printable And Can Be Customized To Fit Your Needs There Are Also Examples To Help You Get Started These Solving Proportions Worksheets Will Help Students Meet Common Core Standards For Expressions Equations As Well As Ratios Proportional Relationships I Would Recommend These Exercise For 6th Grade 7th Grade And 8th Grade Math
Proportion Word Problems Worksheet Dsoftschools
Some Of The Worksheets Below Are Proportion Word Problems Worksheet Definition Of Proportion Solving Proportional Problems Rates Ratios And Proportions Quiz Study Guide 35 Proportion Word Problems Once You Find Your Worksheet S You Can Either Click On The Pop Out Icon Or Download Button To Print Or Download Your Desired Worksheet S
Ratio Worksheets Ratio Worksheets For Teachers
The Ratio Worksheets Are Randomly Created And Will Never Repeat So You Have An Endless Supply Of Quality Ratio Worksheets To Use In The Classroom Or At Home Our Ratio Worksheets Are Free To Download Easy To Use And Very Flexible These Ratio Worksheets Are A Great Resource For Children In Kindergarten 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade And 8th
Proportions Math Worksheet Printable. The worksheet is an assortment of 4 intriguing pursuits that will enhance your kid's knowledge and abilities. The worksheets are offered in developmentally appropriate versions for kids of different ages. Adding and subtracting integers worksheets in many ranges including a number of choices for parentheses use.
You can begin with the uppercase cursives and after that move forward with the lowercase cursives. Handwriting for kids will also be rather simple to develop in such a fashion. If you're an adult and wish to increase your handwriting, it can be accomplished. As a result, in the event that you really wish to enhance handwriting of your kid, hurry to explore the advantages of an intelligent learning tool now!
Consider how you wish to compose your private faith statement. Sometimes letters have to be adjusted to fit in a particular space. When a letter does not have any verticals like a capital A or V, the very first diagonal stroke is regarded as the stem. The connected and slanted letters will be quite simple to form once the many shapes re learnt well. Even something as easy as guessing the beginning letter of long words can assist your child improve his phonics abilities. Proportions Math Worksheet Printable.
There isn't anything like a superb story, and nothing like being the person who started a renowned urban legend. Deciding upon the ideal approach route Cursive writing is basically joined-up handwriting. Practice reading by yourself as often as possible.
Research urban legends to obtain a concept of what's out there prior to making a new one. You are still not sure the radicals have the proper idea. Naturally, you won't use the majority of your ideas. If you've got an idea for a tool please inform us. That means you can begin right where you are no matter how little you might feel you've got to give. You are also quite suspicious of any revolutionary shift. In earlier times you've stated that the move of independence may be too early.
Each lesson in handwriting should start on a fresh new page, so the little one becomes enough room to practice. Every handwriting lesson should begin with the alphabets. Handwriting learning is just one of the most important learning needs of a kid. Learning how to read isn't just challenging, but fun too.
The use of grids The use of grids is vital in earning your child learn to Improve handwriting. Also, bear in mind that maybe your very first try at brainstorming may not bring anything relevant, but don't stop trying. Once you are able to work, you might be surprised how much you get done. Take into consideration how you feel about yourself. Getting able to modify the tracking helps fit more letters in a little space or spread out letters if they're too tight. Perhaps you must enlist the aid of another man to encourage or help you keep focused.
Proportions Math Worksheet Printable. Try to remember, you always have to care for your child with amazing care, compassion and affection to be able to help him learn. You may also ask your kid's teacher for extra worksheets. Your son or daughter is not going to just learn a different sort of font but in addition learn how to write elegantly because cursive writing is quite beautiful to check out. As a result, if a kid is already suffering from ADHD his handwriting will definitely be affected. Accordingly, to be able to accomplish this, if children are taught to form different shapes in a suitable fashion, it is going to enable them to compose the letters in a really smooth and easy method. Although it can be cute every time a youngster says he runned on the playground, students want to understand how to use past tense so as to speak and write correctly. Let say, you would like to boost your son's or daughter's handwriting, it is but obvious that you want to give your son or daughter plenty of practice, as they say, practice makes perfect.
Without phonics skills, it's almost impossible, especially for kids, to learn how to read new words. Techniques to Handle Attention Issues It is extremely essential that should you discover your kid is inattentive to his learning especially when it has to do with reading and writing issues you must begin working on various ways and to improve it. Use a student's name in every sentence so there's a single sentence for each kid. Because he or she learns at his own rate, there is some variability in the age when a child is ready to learn to read. Teaching your kid to form the alphabets is quite a complicated practice. | 1,740 | 8,534 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2020-40 | latest | en | 0.624127 |
https://wizedu.com/questions/945065/please-answer-all-crane-limited-purchased-a | 1,708,468,193,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473347.0/warc/CC-MAIN-20240220211055-20240221001055-00450.warc.gz | 645,217,734 | 10,321 | In: Accounting
# please answer all Crane Limited purchased a machine on account on April 2, 2018, at an...
Crane Limited purchased a machine on account on April 2, 2018, at an invoice price of $360,090. On April 4, it paid$1,850 for delivery of the machine. A one-year, $4,250 insurance policy on the machine was purchased on April 5. On April 18, Crane paid$8,280 for installation and testing of the machine. The machine was ready for use on April 30.
Crane estimates the machine’s useful life will be five years or 6,018 units with a residual value of $85,700. Assume the machine produces the following numbers of units each year: 859 units in 2018; 1,504 units in 2019; 1,312 units in 2020; 1,267 units in 2021; and 1,076 units in 2022. Crane has a December 31 year end. 1. determine the cost of the machine 2. calculate Depreciable Cost Depreciation Expense Accumulated Depreciation Carrying Amount using a. straight line method, b. double diminishing method, c. units of production method 3. Which method causes net income to be lower in the early years of the asset’s life? ## Solutions ##### Expert Solution a. Computation of Cost of machine$ Invoice price $3,60,090.00 Delivery charges$1,850.00 Installation and testing $8,280.00 Total cost of machine$3,70,220.00
Straight line method: Year Depreciable Cost (a) Depreciation Expense (b) Accumulated Depreciation (c ) Carrying Amount (a-c) 2018 $2,84,520$56,904 $56,904$2,27,616 2019 $2,84,520$56,904 $1,13,808$1,70,712 2020 $2,84,520$56,904 $1,70,712$1,13,808 2021 $2,84,520$56,904 $2,27,616$56,904 2022 $2,84,520$56,904 $2,84,520$0 Note Depreciable cost = Cost of Machine - Residual Value = 370220 - 85700= Depreciation Expense = 284520/5 =$56904 Double-Diminishing Balance method: Year Opening Carrying Amount (a) Depreciation Expense (b) Accumulated Depreciation ( C) Carrying Amount (a-b) 2018$3,70,220 $1,48,088$1,48,088 $2,22,132 2019$2,22,132 $88,853$2,36,941 $1,33,279 2020$1,33,279 $53,312$2,90,252 $79,968 2021$79,968 $31,987$3,22,239 $47,981 2022$47,981 $19,192$3,41,432 $28,788 Note:- depreciation Rate = 2 X 1/5= 40% Units-of-production method: Year Depreciable Cost (a) Depreciation Expense (b) Accumulated Depreciation ( C) Carrying Amount (a-c) 2018$2,84,520 =284520/6018*859=40612 $40,612$2,43,908 2019 $2,84,520 =284520/6018*1504=71106$1,11,718 $1,72,802 2020$2,84,520 =284520/6018*1312=62029 $1,73,747$1,10,773 2021 $2,84,520 =284520/6018*1267=59901$2,33,648 $50,872 2022$2,84,520 =284520/6018*1076= 50871 $2,84,519$1
3. Double diminishing Value method
## Related Solutions
##### Sandhill Limited purchased a machine on account on April 2, 2018, at an invoice price of...
Sandhill Limited purchased a machine on account on April 2, 2018, at an invoice price of $332,220. On April 4, it paid$2,170 for delivery of the machine. A one-year, $3,960 insurance policy on the machine was purchased on April 5. On April 18, Sandhill paid$7,840 for installation and testing of the machine. The machine was ready for use on April 30. Sandhill estimates the machine’s useful life will be five years or 6,153 units with a residual value...
##### Crane Limited purchased a machine on account on April 1, 2021, at an invoice price of...
Crane Limited purchased a machine on account on April 1, 2021, at an invoice price of $325,020. On April 2, it paid$1,820 for delivery of the machine. A one-year, $3,940 insurance policy on the machine was purchased on April 5. On April 19, Crane paid$8,150 for installation and testing of the machine. The machine was ready for use on April 30. Crane estimates the machine’s useful life will be five years or 6,326 units with a residual value...
Question 2 KOL Limited purchased a machine on 1 January 2018 at $500,000. It has an expected useful life of 5 years and an estimated salvage value of$50,000. It is also expected that the machine can run for 30,000 hours. For the year ended 31 December 2018, KOL has used the machine for 4,000 hours. KOL has another equipment with the following data on 31 December 2018. Cost $260,000 Carrying amount$200,000 Fair value less costs to sell $180,000... ##### KOL Limited purchased a machine on 1 January 2018 at$500,000. It has an expected useful...
KOL Limited purchased a machine on 1 January 2018 at $500,000. It has an expected useful life of 5 years and an estimated salvage value of$50,000. It is also expected that the machine can run for 30,000 hours. For the year ended 31 December 2018, KOL has used the machine for 4,000 hours. KOL has another equipment with the following data on 31 December 2018. Cost $260,000 Carrying amount$200,000 Fair value less costs to sell $180,000 Value-in-use$175,000...
Coyote Manufacturing bought a machine for $90,000 on April 1, 2018. To install the machine Coyote Manufacturing spent$10,000. It was estimated that the useful life be 4 years or 1,000,000 machine-hours. And the residual value at the end of the useful life be $4,000. Number of hours that the machine has been used or will be used are as follows: 2018 2019 2020 2021 2022 70,000 hours 240,000 290,000 230,000 170,000 Instructions: 1. Prepare journal entries for the purchase... ##### A business machine purchased April 10, 2017, for$98,000. On August 15, 2019, the machine was...
A business machine purchased April 10, 2017, for $98,000. On August 15, 2019, the machine was fully deprecated and sold for$67,000. a) What is the amount of the gain or loss from the sale of the machine? b) What is the nature/character of the gain or loss from the sale of the machine? | 1,711 | 5,531 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2024-10 | latest | en | 0.816553 |
www.lizardslunch.com | 1,701,293,385,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100146.5/warc/CC-MAIN-20231129204528-20231129234528-00311.warc.gz | 979,936,675 | 23,440 | # What does the dot mean in math – What does a dot mean in math?
### Dear audience, welcome to my interesting blog post in the education category. Today I am going to discus about simple question and it’s answer What does the dot mean in math or What does a dot mean in math. Let’s discuss. What does a dot in a circle in math mean? What does the symbol
Dear audience, welcome to my interesting blog post in the education category. Today I am going to discus about simple question and it’s answer What does the dot mean in math or What does a dot mean in math. Let’s discuss.
## What does a dot in a circle in math mean?
What does the symbol of a circle with a dot inside it mean in Mathematics. Shaded means including that number and not shaded means excluding it. For instance, in case it was an open speck on 5 and a bolt highlighting the left it would be all numbers under 5. in case it was concealed it would be all number not exactly and equivalent to 5. There are a lot of things can be about the answer of the question what does the dot mean in math:
1. It can mean a few things-generally it implies new activity characterized on vector space-polynomial math end.
2. This is the sign for void set in set hypothesis. Void set is the set which has no component.
3. A 2 dimensional continuous bended line where each point is a similar separation from the middle.
4. It might mean duplicate particularly on the off chance that it appears as though this:16×84=…..
5. In case it is a dab and not a “0” it mean duplicate.
6. It suggests a duplication among x and y.
## Dot Plate Cards can be used to teach young students basic Math
At the point when youngsters figure out how to count, it frequently appears as repetition or counting by memory. To assist young students with getting number and amount, this natively constructed set of speck plates or spot cards will be priceless and is something that can be utilized again and again to assist with an assortment of number ideas.
## How to make dot plates or dot cards
Utilizing paper plates or firm card stock paper use the example gave to make an assortment of speck plates or cards. Utilize a bingo dabber or stickers to address the ‘pips’ or the dabs on the plates. Attempt to organize the spots in an assortment of ways as displayed (for a three, make a line of three dabs on one plate and on another plate, orchestrate the three dabs into a three-sided design.) Where conceivable, address a number with 1-3 speck courses of action. After completing, you ought to have around 15 spot plates or cards. The dabs ought not be effectively cleared off or stripped off as you will need to utilize the plates again and again.
Contingent upon the age of the youngster or kids, you can utilize each or two plates in turn for the accompanying exercises. Every movement will make them hold up a couple of plates and posing inquiries. The objective is for the kids to perceive the state of the specks on the plate and when held up, they will perceive that it’s a five or a 9 moderately rapidly. You need the kids to move beyond balanced counting of the specks and to perceive the number by the dab plan. Consider how you perceive the number on dice, you don’t count the pips yet you know when you see a 4 and a 5 that it is 9. This is the thing that you need your kids to learn.
Hold up a couple of plates and ask what number it/they address, or the number of spots there are. Do this multiple occasions until the appropriate responses nearly become programmed.
Utilize the spot plates for fundamental expansion realities, hold up two plates and request the total. Utilize the spot plates to show anchors of 5 and 10. Hold up one plate and say, what’s 5 more or 10 more and rehash regularly until the youngsters react rapidly.
Utilize the dab plates for increase. Whichever truth you’re chipping away at, hold up a speck plate and request that they duplicate it by 4. Or on the other hand keep 4 up and continue to show an alternate plate until they figure out how to increase all numbers by 4. Present an alternate truth every month. At the point when all realities are known, hold up 2 plates arbitrarily and request that they increase the 2.
Utilize the plates for 1 more than or 1 not exactly or 2 a greater number of than or 2 not exactly. Hold up a plate and say this number less 2 or this number in addition to 2.
Actually dot plates cards are used to help students to learn number of conversation.
In the light of our discussion about the question What does the dot mean in math or What does a dot mean in math, it is clear to us that it is used to make understand the student to learn number of conversation or a dab and not a “0” it mean duplicate. | 1,069 | 4,724 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2023-50 | longest | en | 0.938675 |
https://discuss.codechef.com/t/seagcd2-editorial/12571 | 1,686,393,785,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224657169.98/warc/CC-MAIN-20230610095459-20230610125459-00492.warc.gz | 246,487,262 | 10,813 | # SEAGCD2 - Editorial
Author: Sergey Nagin
Tester: Kevin Atienza
Translators: Sergey Kulik (Russian), Team VNOI (Vietnamese) and Hu Zecong (Mandarin)
Editorialist: Kevin Atienza
Medium
### PREREQUISITES:
Dynamic programming, combinatorics, number theory
### PROBLEM:
How many arrays A[1\ldots N] are there such that 1 \le A_i \le M and \gcd(A_i,A_j) = 1 for all i < j?
### QUICK EXPLANATION:
Every number > 1 appears at most once in the sequence. Everything else is 1.
Let S be the set of values of the sequence that are > 1. Our strategy will be to enumerate all possible sets S, and then sum up all their contributions to the total answer.
The first step is to enumerate all possible S's by enumerating all subsets of \{2, 3, \ldots, 100\} that are pairwise coprime. Actually, we only need the sizes, so this can be done very efficiently with memoization and some optimizations.
The next step is to add the contribution of each set S. We only need its size, s. There are \frac{N!}{(N-s)!} ways to select the arrangements of these values in the sequence, and everything else will be 1. So the answer is the sum of \frac{N!}{(N-s)!} among all sizes s.
# For M \le 10
For any two numbers a and b, \gcd(a,b) = 1 if and only if a and b has no common prime factors. In other words, if we define P(n) as the set of prime factors of n, then \gcd(a,b) = 1 if and only if P(a)\cap P(b) = \emptyset.
Since there are only four primes \le 10, namely \{2,3,5,7\}, we can formulate a dynamic programming solution that has approximately 2^4N states. If S is a subset of \{2,3,5,7\}, define f(n,S) as the number of sequences such that:
• There are n elements.
• Each element is in [1,M].
• \gcd(A_i,A_j) = 1 for all i < j.
• The only allowed prime factors are in S.
Clearly the answer that we want is f(N,\{2,3,5,7\}). Also, we can implement a subset of \{2,3,5,7\} as a bitmask of 4 bits, which is simply an integer from 0 to 15.
To find a recurrence for f(n,S), we enumerate all possible n th elements, from 1 to M. For a value v to be a valid last element, its set of prime factors, P(v), must be a subset of S. (Using bitmasks, this can be implemented using bitwise operators.) Afterwards, the set of allowed primes for the remaining n-1 elements is S - P(v), where “-” denotes set difference. Thus, we have the following recurrence:
f(n,S) = \sum_{\substack{v=1 \\\ P(v)\subset S}}^M f(n-1,S - P(v))
For optimization, the $P(v)$s can be computed beforehand. Also, for the base case, we have f(0,S) = 1. Thus, we can now compute f(n,S) using dynamic programming! See the following pseudocode:
for n = 0..N:
for S subset of {2,3,5,7}:
if n == 0:
f[n][S] = 1
else:
f[n][S] = 0
for v = 1..M:
if P(v) is a subset of S:
f[n][S] += f[n-1][S - P(v)]
print f[N][{2,3,5,7}]
Representing these sets as bitmasks and using bitwise operators for set operations, we get the following more detailed pseudocode:
// precompute P
P[1..M]
for v = 1..M:
if v % 2 == 0: P[v] |= 1 << 0
if v % 3 == 0: P[v] |= 1 << 1
if v % 5 == 0: P[v] |= 1 << 2
if v % 7 == 0: P[v] |= 1 << 3
// compute f
f[0..N][0..15]
for n = 0..N:
for S = 0..15:
if n == 0:
f[n][S] = 1
else:
f[n][S] = 0
for v = 1..M:
if (S & P[v]) == P[v]:
f[n][S] += f[n-1][S ^ P[v]]
print f[N][15]
It’s much more obvious now how many operations this will take, so we can now see that this runs fast enough for the first subtask!
# For M > 10
Unfortunately, for the remaining subtasks, M can reach up to 100, and there are 25 primes up to 100. This means that the algorithm above will have 2^{25}N states. For subtask two, you might still be able to optimize a lot and squeeze into the time limit (though it isn’t easy), but for subtask three, there’s no way this will pass. Instead, we need to find better solutions.
## Solution 1
Let’s call a number big if it is greater than 1.
The first important insight is that every big number will appear at most once in our sequence. Otherwise, if x > 1 appears more than once, say at positions i and j, then \gcd(A_i,A_j) = x \not= 1, which violates our requirements. This automatically means that there are at most 99 big numbers in our sequence, and for large N, this means that most elements will be equal to 1!
Thus, we have two remaining tasks:
• Enumerate all sets of big numbers that are pairwise coprime, and
• For each set of big numbers, find the number of valid sequences of length N having exactly these numbers as its big numbers.
The second one is actually easy: If the set of big numbers has size s, then there are exactly {N \choose s} ways to choose the places where these big numbers will go, and then s! ways to choose which big number goes where. Everything else will be 1, thus, there are {N \choose s}s! = \frac{N!}{(N-s)!} valid sequences!
To compute N! and (N-s)!^{-1}, we need to precompute all factorials and inverse factorials up to 100000 beforehand. We can use the following simple recurrences:
\begin{aligned} N! &\equiv N(N-1)! \bmod (10^9 + 7) \\\ N!^{-1} &\equiv N^{-1}(N-1)!^{-1} \bmod (10^9 + 7) \end{aligned}
All that remains is enumerating all sets of big numbers that are pairwise coprime. Let’s call such sets big sets. To begin with, let’s try a simple recursive enumeration. Let’s create a routine called all_big_sets(m, S), where m is the maximum allowed value in the big set, and S is the set of disallowed primes. The initial call is simply all_big_sets(M, {}), where {} denotes the empty set.
A straightforward implementation is the following:
def all_big_sets(m, S):
if m == 1:
yield {}
else:
// if m is not in the set
for big_set in all_big_sets(m-1, S):
yield big_set
// if m is in the set
if P(m) and S don't intersect:
for big_set in all_big_sets(m-1, union(P(m), S)):
yield union({m}, big_set)
This yields all big sets. In most languages, you can just collect all sets called with yield in a giant list, like in the following:
def all_big_sets(m, S):
big_sets = []
if m == 1:
else:
// if m is not in the set
for big_set in all_big_sets(m-1, S):
// if m is in the set
if P(m) and S don't intersect:
for big_set in all_big_sets(m-1, union(P(m), S)):
return big_sets
Unfortunately, this doesn’t work as it is, because there are just too many big sets. So here, we will describe a few optimizations that will make things faster.
First, notice that we can do a simple optimization: instead of the sets themselves, we can just enumerate the sizes of the big sets, because the sizes are all we need.
def all_big_set_sizes(m, S):
sizes = []
if m == 1:
else:
// if m is not in the set
for size in all_big_set_sizes(m-1, S):
// if m is in the set
if P(m) and S don't intersect:
for size in all_big_set_sizes(m-1, union(P(m), S)):
return sizes
A second optimization is to collect the sizes as a list of frequency counts for each size, because the largest size of each big set is at most m:
def all_big_set_sizes(m, S):
size_counts[0..m] // initially all zero
if m == 1:
size_counts[0]++
else:
// if m is not in the set
counts = all_big_set_sizes(m-1, S)
for i = 0..m-1:
size_counts[i] += counts[i]
// if m is in the set
if P(m) and S don't intersect:
counts = all_big_set_sizes(m-1, union(P(m), S))
for i in 0..m-1:
size_counts[i + 1] += counts[i]
return size_counts
But still, this isn’t enough; even though the output list is now small, we still call all_big_set_sizes too many times. Well, that’s easy to fix. We just memoize all_big_set_sizes!
memo = {}
def all_big_set_sizes(m, S):
// check if it's in the memo
if memo has (m, S) as a key:
return memo[(m, S)]
size_counts[0..m] // initially all zero
if m == 1:
size_counts[0]++
else:
// if m is not in the set
counts = all_big_set_sizes(m-1, S)
for i = 0..m-1:
size_counts[i] += counts[i]
// if m is in the set
if P(m) and S don't intersect:
counts = all_big_set_sizes(m-1, union(P(m), S))
for i in 0..m-1:
size_counts[i + 1] += counts[i]
memo[(m, S)] = size_counts
return size_counts
But this is still not enough, because there is still too many distinct calls to all_big_set_sizes! (For instance, there are already at least 2^{25} distinct values for the parameter S, because it is a set of primes \le 100.)
At this point, there are two major optimizations that will allow all_big_set_sizes to run quickly. You can implement either one of them (or even both) to pass.
Optimization 1: Primes > 50
This optimization uses the fact that primes > 50 will appear never appear with other prime factors, because if p > 50, then 2p already exceeds 100. Thus, we can try to consider these primes separately.
The first step is to create a version of all_big_set_sizes but which only considers primes up to 50:
memo = {}
def _all_big_set_sizes(m, S):
// check if it's in the memo
if memo has (m, S) as a key:
return memo[(m, S)]
size_counts[0..m] // initially all zero
if m == 1:
size_counts[0]++
else:
// if m is not in the set
counts = _all_big_set_sizes(m-1, S)
for i = 0..m-1:
size_counts[i] += counts[i]
// if m is in the set
// Note: max_prime(m) is the largest prime factor of m
if max_prime(m) <= 50 and P(m) and S don't intersect:
counts = _all_big_set_sizes(m-1, union(P(m), S))
for i in 0..m-1:
size_counts[i + 1] += counts[i]
memo[(m, S)] = size_counts
return size_counts
The added check here is max_prime(m) <= 50, which prevents adding primes > 50. Next, we implement the real all_big_set_sizes, which takes into account these primes:
def all_big_set_sizes(m):
P = (number of primes in the range [51,m])
size_counts = [0]*(m+1)
counts = _all_big_set_sizes(m, {})
for i = 0..m:
if counts[i] != 0:
for j = 0..P:
size_counts[i+j] += counts[i] * CHOOSE(P, j)
return size_counts
Here, we initially call _all_big_set_sizes above, and then take into account primes > 50 using some combinatorics. Here, j is the number of primes > 50 that we include, and CHOOSE(P, j) is the number of ways to select these j primes out of the P possible. The function CHOOSE itself can be computed using factorials and inverse factorials, which we will need anyway in the second step above.
Using this optimization, all_big_set_sizes now runs fast enough to pass the time limit!
Optimization 2: Limiting the values of S
A different optimization involves looking at the parameter S more carefully. The purpose of this parameter is to exclude primes that have already been included before. However, we are iterating m in decreasing order, which means that the maximum prime that will possibly appear is the largest prime \le m. Thus, if there are primes in S that are greater than m, then we can safely remove them and the answer will stay the same! This reduces the number of distinct all_big_set_sizes calls drastically, and in fact is fast enough to get Python accepted in under 0.5 seconds!
memo = {}
def all_big_set_sizes(m, S):
// cleanse S of primes > m
Let X = (set of all primes <= m)
S = intersection(S, X)
// check if it's in the memo
if memo has (m, S) as a key:
return memo[(m, S)]
size_counts[0..m] // initially all zero
if m == 1:
size_counts[0]++
else:
// if m is not in the set
counts = all_big_set_sizes(m-1, S)
for i = 0..m-1:
size_counts[i] += counts[i]
// if m is in the set
if P(m) and S don't intersect:
counts = all_big_set_sizes(m-1, union(P(m), S))
for i in 0..m-1:
size_counts[i + 1] += counts[i]
memo[(m, S)] = size_counts
return size_counts
The change here is in the first few lines, where a call to intersection is done to reduce the number of elements of S.
This solution implemented in one of the tester’s solutions below. (Sets are implemented as bitmasks.)
## Solution 2
A different solution involves considering all primes > 10 specially, not just primes > 50. The insight here that we will use heavily is that each number has at most one prime factor > 10.
We will need our f(n,S) function earlier. Recall that f(n,S) is the number of valid sequences of length n where the only allowed prime factors are in S. This time, we will only precompute this table for S that is a subset of \{2, 3, 5, 7\}. (Obviously this isn’t enough because M > 10, but we will still need these values.)
The key insight here is that for every value 1 \le v < 10, the primes in the range \left(\frac{100}{v+1}, \frac{100}{v}\right] are all “functionally” identical. This is a generalization of the fact that we used earlier: that primes > 50 can be treated specially because they all appear alone. Similarly:
• Every prime p in the range (100/3,100/2] = [34,50] can only appear as p or 2p.
• Every prime p in the range (100/4,100/3] = [26,33] can only appear as p, 2p or 3p.
• etc.
Thus, really, all we care about is how many primes from each of the following ranges we take: (100/2, 100/1], (100/3, 100/2], (100/4, 100/3], etc. Afterwards, we figure out using some combinatorics where their positions will be, and which ones will appear as p, 2p, 3p, etc. And then finally, once we take care of these primes, we can now fall back to our precomputed f(n,S), because all primes > 10 have been accounted for already!
Lots of details have been skipped, but if you want to find out more, this solution is implemented in one of the tester’s solutions below, so you can check it out.
### AUTHOR’S AND TESTER’S SOLUTIONS:
3 Likes
What’s the running time for the author’s and testers solutions? Are they faster than other contestants solutions? I guess I could enter them myself under the practice section to see. But it doesn’t feel right to enter someone else’s code under my name.
1 Like
The setter’s and tester’s solutions are not of this question.
Another addition is we can enumerate only odd numbers <=50 and since there can be only at the most one even number per set from the set we can determine how many even numbers are possible and if there are k even numbers to choose from we have k sets of size i+1 and 1 set of size i. I solved it using the same method but with the even number thing . here’s the link to my C++ solution.
https://www.codechef.com/viewsolution/10070529
Here is the C++ solution for the question using the same method but with some additions.
https://www.codechef.com/viewsolution/10070529
There also exist closed-form polynomial expressions for F(N,M):
F(N,1)=1, F(N,2)=1+N, F(N,3)=1+N+N^2, F(N,4)=1+N+2N^2 , F(N,5)=1+3N-N^2+2N^3 , F(N,6) = 1+3N+2N^3
F(N,7) = 1-N+9
N^2-4N^3+2N^4 … I don’t see any pattern as such , except that F(N,M) ~ O(N^pi(M))
, where pi(M) counts no. of primes <= M.
Can anyone explain solution 2 in more depth ? Thanks in advance.
In the routine all_big_sets(m,S)
What is meant by the statement // if m is not in the set
To which set m is being referred?
Why the author’s solution is giving TLE? | 4,276 | 14,660 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2023-23 | latest | en | 0.873802 |
https://www.mathworks.com/help/fininst/finpricer.fft.price.html | 1,713,873,501,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818474.95/warc/CC-MAIN-20240423095619-20240423125619-00419.warc.gz | 823,853,172 | 21,100 | # price
Compute price for equity instrument with `FFT` pricer
Since R2020a
## Syntax
``[Price,PriceResult] = price(inpPricer,inpInstrument)``
``[Price,PriceResult] = price(___,inpSensitivity)``
## Description
example
````[Price,PriceResult] = price(inpPricer,inpInstrument)` computes the instrument price and related pricing information based on the pricing object `inpPricer` and the instrument object `inpInstrument`. ```
example
````[Price,PriceResult] = price(___,inpSensitivity)` adds an optional argument to specify sensitivities.```
## Examples
collapse all
This example shows the workflow to price a `Vanilla` instrument when you use a `Heston` model and an `FFT` pricing method.
Create `Vanilla` Instrument Object
Use `fininstrument` to create a `Vanilla` instrument object.
`VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2022,9,15),'Strike',105,'ExerciseStyle',"european",'Name',"vanilla_option")`
```VanillaOpt = Vanilla with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Strike: 105 Name: "vanilla_option" ```
Create `Heston` Model Object
Use `finmodel` to create a `Heston` model object.
`HestonModel = finmodel("Heston",'V0',0.032,'ThetaV',0.1,'Kappa',0.003,'SigmaV',0.2,'RhoSV',0.9)`
```HestonModel = Heston with properties: V0: 0.0320 ThetaV: 0.1000 Kappa: 0.0030 SigmaV: 0.2000 RhoSV: 0.9000 ```
Create `ratecurve` Object
Create a flat `ratecurve` object using `ratecurve`.
```Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)```
```myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous" ```
Create `FFT` Pricer Object
Use `finpricer` to create an `FFT` pricer object and use the `ratecurve` object for the `'DiscountCurve'` name-value pair argument.
`outPricer = finpricer("fft",'DiscountCurve',myRC,'Model',HestonModel,'SpotPrice',100,'CharacteristicFcnStep', 0.2,'NumFFT',2^13)`
```outPricer = FFT with properties: Model: [1x1 finmodel.Heston] DiscountCurve: [1x1 ratecurve] SpotPrice: 100 DividendType: "continuous" DividendValue: 0 NumFFT: 8192 CharacteristicFcnStep: 0.2000 LogStrikeStep: 0.0038 CharacteristicFcn: @characteristicFcnHeston DampingFactor: 1.5000 Quadrature: "simpson" VolRiskPremium: 0 LittleTrap: 1 ```
Price `Vanilla` Instrument
Use `price` to compute the price and sensitivities for the `Vanilla` instrument.
`[Price, outPR] = price(outPricer,VanillaOpt,["all"])`
```Price = 14.7545 ```
```outPR = priceresult with properties: Results: [1x7 table] PricerData: [] ```
`outPR.Results`
```ans=1×7 table Price Delta Gamma Theta Rho Vega VegaLT ______ _______ ________ ________ ______ ______ ______ 14.754 0.44868 0.021649 -0.20891 120.45 88.192 1.3248 ```
## Input Arguments
collapse all
Pricer object, specified as a scalar `FFT` pricer object. Use `finpricer` to create the `FFT` pricer object.
Data Types: `object`
Instrument object, specified as a scalar or vector of `Vanilla` instrument objects. Use `fininstrument` to create `Vanilla` instrument objects.
Data Types: `object`
(Optional) List of sensitivities to compute, specified as a `NOUT`-by-`1` or a `1`-by-`NOUT` cell array of character vectors or string array with possible values of `'Price'`, `'Delta'`, `'Gamma'`, `'Vega'`, `'Rho'`, `'Theta'`, `'Vegalt'`, and `'All'`.
Note
For a `Vanilla` instrument using a `Heston` model, `'Vegalt'` is not supported.
`inpSensitivity = {'All'}` or ```inpSensitivity = ["All"]``` specifies that the output is `'Delta'`, `'Gamma'`, `'Vega'`, `'Rho'`, `'Theta'`, `'Vegalt'`, and `'Price'`. This is the same as specifying `inpSensitivity` to include each sensitivity.
Example: ```inpSensitivity = {'delta','gamma','vega','rho','theta','vegalt','price'}```
Data Types: `string` | `cell`
## Output Arguments
collapse all
Instrument price, returned as a numeric.
Price result, returned as a `PriceResult` object. The object has the following fields:
• `PriceResult.Results` — Table of results that includes sensitivities (if you specify `inpSensitivity`)
• `PriceResult.PricerData` — Structure for pricer data
## Version History
Introduced in R2020a | 1,301 | 4,314 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2024-18 | latest | en | 0.544947 |
https://funslovestory.com/what-percentage-is-7-out-of-8.php | 1,623,649,649,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487611445.13/warc/CC-MAIN-20210614043833-20210614073833-00029.warc.gz | 251,915,261 | 11,683 | • 7 is what percent of 8 - step by step solution
Here are step-by-step instructions showing you how we calculated 7 out of 8 as a percentage: The first step is to divide 7 by 8 to get the answer in decimal form: 7 / 8 = Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage: * = %. We can prove that the answer is correct by. A shorter way to calculate x out of y. You can easily find 7 is out of 8, in one step, by simply dividing 7 by 8, then multiplying the result by So, 7 is out of 8 = 7 / 8 x = %. To find more examples, just choose one at the bottom of this page.
In mathematics, a percentage is a number or ratio that represents a fraction of Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values. P is the percentage, V 1 is the first value that the percentage will modify, and V 2 is the result of the percentage operating on V 1. The calculator provided automatically converts the input percentage into a decimal to compute the solution.
However, if solving for pdrcentage percentage, the value returned will be the actual percentage, not its decimal representation. If solving manually, the formula requires the percentage in decimal form, so the what are some signs of breast cancer for P needs to be multiplied by in order to convert it to a percent. This is essentially what the calculator above does, except that it accepts inputs in percent rather than decimal form.
The percentage difference between two values is calculated by dividing the absolute value of the how to do a trend analysis in excel between two numbers by the average of those two numbers. Multiplying the result by will yield the solution in percent, rather than decimal form. Refer to the equation below for clarification.
Percentage increase and decrease are calculated by computing the difference between two values and comparing that difference to the initial value. Mathematically, this involves using the absolute value of the difference between two values, and dividing the result by the initial value, essentially calculating how much the initial value has changed.
The percentage increase calculator above computes an oug or decrease of a specific percentage of the input number. It basically involves converting a percent into its decimal equivalent, and either subtracting decrease or adding increase the decimal equivalent from and to 1, respectively. Multiplying the original ehat by this value will result in either an increase or decrease of the number by the given percent.
Refer to the example below for clarification. Financial Fitness and Health Math Other.
Percentage Difference Calculator
Divide the numerator by the denominator to get fraction's value: 7/8 = 7 ? 8 = Note: / = ? = % = 1 Multiply a number by the fraction /, and its value doesn't change. Calculate the percent value: = ? / = ( ? )/ = / = %; In other words: 1) Calculate fraction's value. 7. Solution for 7 is what percent of 8 %/x%=8/7 (/x)*x=(8/7)*x - we multiply both sides of the equation by x =*x - we divide both sides of the equation by () to get x /=x =x x= now we have: 7 is % of 8. Percentage Formula. Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values. P ? V 1 = V 2. P is the percentage, V 1 is the first value that the percentage will modify, and V 2 is the result of the percentage operating on V 1. The calculator provided automatically converts the input percentage into a decimal to compute the solution.
What is out of? Using this tool you can find any percentage in three ways. Or may be: How much is 7 out of 8? If you are looking for a Discount Calculator , please click here.
You can easily find 7 is out of 8, in one step, by simply dividing 7 by 8, then multiplying the result by Please link to this page! Just right click on the above image, choose copy link address, then past it in your HTML. While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions, or for the results obtained from the use of this information. Cool Conversion.
Percentage Discount Sales Tax. See the solutions to these problems below. How to work out percentages - Step by Step Here are the solutions to the questions stated above:. This question is equivalent to: "7 is what percent of 8? To find more examples, just choose one at the bottom of this page. Sample Percent Calculations 4 percent of five-ninths- 5 percent of 85 percent of 1 percent of 5 percent of thirty-one 4 percent of Percentage Calculator Please link to this page!
Disclaimer While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions, or for the results obtained from the use of this information.
## 2 comments
• ### Sajind
What is the passqord
• ### Arashikinos
I had made a new video check out | 1,118 | 5,090 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.71875 | 5 | CC-MAIN-2021-25 | latest | en | 0.934336 |
https://math.answers.com/math-and-arithmetic/What_is_a_mathematical_language_of_symbols | 1,722,713,778,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640377613.6/warc/CC-MAIN-20240803183820-20240803213820-00566.warc.gz | 294,393,625 | 47,499 | 0
# What is a mathematical language of symbols?
Updated: 12/14/2022
Wiki User
8y ago
It is algebra.
Wiki User
8y ago
Earn +20 pts
Q: What is a mathematical language of symbols?
Submit
Still have questions?
Related questions
alberia
alberia
Algebra.
### A mathematical language of symbols including variables?
I suspect that the answer that you are looking for is algebra.
### What a mathematical language of symbols including variables?
I suspect that the answer that you are looking for is algebra.
### What is an mathematical language of symbols including variables?
It could mean algebra which fits the description given.
### What are the Latin symbols used in mathematics?
Latin was the language spoken by the Romans so the obvious Latin mathematical symbols would be the Roman numeral system. Many of our mathematical words such as addition, subtraction, division, multiplication, fraction, decimal, percentage, calculate ........ etc. come directly from the Latin language.
+ - x and =
An expression.
### What language is SuperScript written in?
Superscript is a form of writing that uses numbers, figures, or symbols. Often mathematical and scientific formulas are written in subscript or in superscript.
### What is a mathematical phrase that can include numbers variable and operational symbols?
An algebraic expression is a mathematical phrase that includes numbers, variables, and operational symbols. | 285 | 1,437 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-33 | latest | en | 0.917782 |
https://www.youtuberandom.com/?watch=-V-Y5klejSg | 1,632,785,085,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058552.54/warc/CC-MAIN-20210927211955-20210928001955-00442.warc.gz | 1,062,800,286 | 7,034 | ## Producer surplus | Consumer and producer surplus | Microeconomics | Khan Academy
Looking at the supply curve as an opportunity cost curve. Understanding the producer surplus as the area between the supply curve and the market price
Microeconomics on Khan Academy: Topics covered in a traditional college level introductory microeconomics course
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
This site provides links to random videos hosted at YouTube, with the emphasis on random.
The original idea for this site actually stemmed from another idea to provide a way of benchmarking the popularity of a video against the general population of YouTube videos. There are probably sites that do this by now, but there wasn’t when we started out. Anyway, in order to figure out how popular any one video is, you need a pretty large sample of videos to rank it against. The challenge is that the sample needs to be very random in order to properly rank a video and YouTube doesn’t appear to provide a way to obtain large numbers of random video IDs.
Even if you search on YouTube for a random string, the set of results that will be returned will still be based on popularity, so if you’re using this approach to build up your sample, you’re already in trouble. It turns out there is a multitude of ways in which the YouTube search function makes it very difficult to retrieve truly random results.
So how can we provide truly random links to YouTube videos? It turns out that the YouTube programming interface (API) provides additional functions that allow the discovery of videos which, with the right approach, are much more random. Using a number of tricks, combined some subtle manipulation of the space-time fabric, we have managed to create a process that yields something very close to 100% random links to YouTube videos.
YouTube is an American video-sharing website headquartered in San Bruno, California. YouTube allows users to upload, view, rate, share, add to playlists, report, comment on videos, and subscribe to other users. It offers a wide variety of user-generated and corporate media videos. Available content includes video clips, TV show clips, music videos, short and documentary films, audio recordings, movie trailers, live streams, and other content such as video blogging, short original videos, and educational videos. Most content on YouTube is uploaded by individuals, but media corporations including CBS, the BBC, Vevo, and Hulu offer some of their material via YouTube as part of the YouTube partnership program. Unregistered users can only watch videos on the site, while registered users are permitted to upload an unlimited number of videos and add comments to videos. Videos deemed potentially inappropriate are available only to registered users affirming themselves to be at least 18 years old.
YouTube and selected creators earn advertising revenue from Google AdSense, a program which targets ads according to site content and audience. The vast majority of its videos are free to view, but there are exceptions, including subscription-based premium channels, film rentals, as well as YouTube Music and YouTube Premium, subscription services respectively offering premium and ad-free music streaming, and ad-free access to all content, including exclusive content commissioned from notable personalities. As of February 2017, there were more than 400 hours of content uploaded to YouTube each minute, and one billion hours of content being watched on YouTube every day. As of August 2018, the website is ranked as the second-most popular site in the world, according to Alexa Internet, just behind Google. As of May 2019, more than 500 hours of video content are uploaded to YouTube every minute.
YouTube has faced criticism over aspects of its operations, including its handling of copyrighted content contained within uploaded videos, its recommendation algorithms perpetuating videos that promote conspiracy theories and falsehoods, hosting videos ostensibly targeting children but containing violent and/or sexually suggestive content involving popular characters, videos of minors attracting pedophilic activities in their comment sections, and fluctuating policies on the types of content that is eligible to be monetized with advertising. | 894 | 4,841 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2021-39 | latest | en | 0.925676 |
https://philoid.com/question/16318-find-the-number-of-cuboidal-boxes-measuring-2-cm-by-3-cm-by-10-cm-which-can-be-stored-in-a-carton-whose-dimensions-are-40-cm-36- | 1,686,054,425,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652569.73/warc/CC-MAIN-20230606114156-20230606144156-00579.warc.gz | 487,470,331 | 12,128 | ## Book: RD Sharma - Mathematics
### Chapter: 21. Mensuration-II (Volumes and Surface Areas of a Cuboid and a Cube)
#### Subject: Maths - Class 8th
##### Q. No. 13 of Exercise 21.1
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
13
##### Find the number of cuboidal boxes measuring 2 cm by 3 cm by 10 cm which can be stored in a carton whose dimensions are 40 cm, 36 cm, and 24 cm.
Given,
Dimensions of cuboidal boxes = 2cm×3 cm×10 cm
Dimesions of carton = 40cm×36cm×24cm
So,
Number of boxes can be stored in carton =
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21 | 206 | 613 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2023-23 | longest | en | 0.724755 |
https://e-answersolutions.com/mathematics/question15352534 | 1,656,199,275,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103036176.7/warc/CC-MAIN-20220625220543-20220626010543-00001.warc.gz | 274,495,355 | 15,390 | , 27.03.2020 00:27 CourtGard
# How do i solve-2x+1y=5
### Another question on Mathematics
Mathematics, 21.06.2019 18:10
What is the equation in slope-intercept form of the linear function represented by the table? y -18 -1 -8 4 2 912 o y=-2x-6 o y=-2x+6 o y=2x-6 o y = 2x+6
Mathematics, 21.06.2019 19:00
You are at a restaurant and owe \$56.20 for your meal. you want to leave an 18% tip. approximately how much is your tip? | 160 | 427 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2022-27 | latest | en | 0.883516 |
https://gmatclub.com/forum/here-s-the-next-batch-of-the-most-brutal-35-scs-posted-on-34300-200.html?sort_by_oldest=true | 1,495,603,638,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463607786.59/warc/CC-MAIN-20170524035700-20170524055700-00393.warc.gz | 752,842,435 | 59,900 | Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
It is currently 23 May 2017, 22:27
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# Here's the next batch of the most brutal 35 SCs posted on
Author Message
TAGS:
### Hide Tags
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1
Kudos [?]: 16 [0], given: 186
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 15:56
40. A group of sudents who have begun to clean up Frederick Law Olmstead's Morning Park in New York City believes that the park needs not to be redesigned but to be returned to its former condition
1)believes that the park needs not to be redesigned but to
2)believe that the park needs to not be redesigned but to
3)believes that the park needs not to be redesigned but could
4)believe that the park needs not to be redesigned but to
5)believe that the park needs not to be redesigned but that it
OA says A but can anyone please clarify why it is not D considering the 'have'?
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1
Kudos [?]: 16 [0], given: 186
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 15:59
32. A year advantage in a new computer product or process being introduced can give a company a significant edge on its competitors.
a...
b. Introducing a new computer product or process by a year earlier
c. A year's advantage to introduce a new computer product or process
d. To introduce a new computer product or process by a year earlier
e. Being a year ahead in introducing a new computer product or process
In this question,the answer is d.It somehow doesnt make sense for me.Could anyone please clarify? Shouldnt the answer be e or b?
Director
Joined: 05 Sep 2010
Posts: 833
Followers: 89
Kudos [?]: 259 [0], given: 61
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 20:45
Quote:
40. A group of sudents who have begun to clean up Frederick Law Olmstead's Morning Park in New York City believes that the park needs not to be redesigned but to be returned to its former condition
1)believes that the park needs not to be redesigned but to
2)believe that the park needs to not be redesigned but to
3)believes that the park needs not to be redesigned but could
4)believe that the park needs not to be redesigned but to
5)believe that the park needs not to be redesigned but that it
OA says A but can anyone please clarify why it is not D considering the 'have'?
kindly underline ur sentences .also hide ur doubts under a spoiler
as for ur question .the answer has to be A coz its the group (singular) that believes
Director
Joined: 05 Sep 2010
Posts: 833
Followers: 89
Kudos [?]: 259 [0], given: 61
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 20:47
Quote:
32. A year advantage in a new computer product or process being introduced can give a company a significant edge on its competitors.
a...
b. Introducing a new computer product or process by a year earlier
c. A year's advantage to introduce a new computer product or process
d. To introduce a new computer product or process by a year earlier
e. Being a year ahead in introducing a new computer product or process
In this question,the answer is d.It somehow doesnt make sense for me.Could anyone please clarify? Shouldnt the answer be e or b?
the question is not even clear .u have not written the first option !! u have not even underlined !! how is someone suppose to make out as from where the underling is starting .had u given the first option ,it wud have made some sense !!
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1
Kudos [?]: 16 [0], given: 186
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 21:12
32. A year advantage in a new computer product or process being introduced can give a company a significant edge on its competitors.
a.. A year advantage in a new computer product or process being introduced
b. Introducing a new computer product or process by a year earlier
c. A year's advantage to introduce a new computer product or process
d. To introduce a new computer product or process by a year earlier
e. Being a year ahead in introducing a new computer product or process
In this question,the answer is d.It somehow doesnt make sense for me.Could anyone please clarify? Shouldnt the answer be e or b?
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1
Kudos [?]: 16 [0], given: 186
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 21:14
Quote:
40. A group of sudents who have begun to clean up Frederick Law Olmstead's Morning Park in New York City believes that the park needs not to be redesigned but to be returned to its former condition
1)believes that the park needs not to be redesigned but to
2)believe that the park needs to not be redesigned but to
3)believes that the park needs not to be redesigned but could
4)believe that the park needs not to be redesigned but to
5)believe that the park needs not to be redesigned but that it
OA says A but can anyone please clarify why it is not D considering the 'have'?
kindly underline ur sentences .also hide ur doubts under a spoiler
as for ur question .the answer has to be A coz its the group (singular) that believes
am new to the site so not sure of spoiler and all...
yeah,but A group of students who have begun to clean up Frederick Law Olmstead's Morning Park in New York City believes..in this students who have begun is plural,so do we have to ignore the plurality and focus on the collective one,group?
Director
Joined: 05 Sep 2010
Posts: 833
Followers: 89
Kudos [?]: 259 [0], given: 61
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 21:29
Quote:
yeah,but A group of students who have begun to clean up Frederick Law Olmstead's Morning Park in New York City believes..in this students who have begun is plural,so do we have to ignore the plurality and focus on the collective one,group?
yeah its the student who have begun but its the group that believes !!
Director
Joined: 05 Sep 2010
Posts: 833
Followers: 89
Kudos [?]: 259 [0], given: 61
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 21:34
Quote:
32. A year advantage in a new computer product or process being introduced can give a company a significant edge on its competitors.
a.. A year advantage in a new computer product or process being introduced
b. Introducing a new computer product or process by a year earlier
c. A year's advantage to introduce a new computer product or process
d. To introduce a new computer product or process by a year earlier
e. Being a year ahead in introducing a new computer product or process
what is the source of this question ?
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1
Kudos [?]: 16 [0], given: 186
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 21:40
I am referring to the brutal SC list of 70 questions.(by one of the GMAT club members).Anyway,i got the correct answer, its there in one of the Manhattan's ask the expert links.(e. Being a year ahead in introducing a new computer product or process):
http://www.manhattangmat.com/forums/com ... t7284.html
Director
Joined: 05 Sep 2010
Posts: 833
Followers: 89
Kudos [?]: 259 [0], given: 61
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 21:48
Quote:
I am referring to the brutal SC list of 70 questions.(by one of the GMAT club members).Anyway,i got the correct answer, its there in one of the Manhattan's ask the expert links.(e. Being a year ahead in introducing a new computer product or process):
http://www.manhattangmat.com/forums/com ... t7284.html
thanks for forwarding this link .if RON is saying its E then its E .even i was little wary abt D as answer !! btw i seriously doubt if this brutal SC is a good source !!
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1
Kudos [?]: 16 [0], given: 186
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 22:04
True,after going through these questions, i have ended up in a low confidence and lot of confusion.Some ques are really vague
Last edited by up4gmat on 20 Mar 2013, 22:06, edited 1 time in total.
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1
Kudos [?]: 16 [0], given: 186
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
20 Mar 2013, 22:05
Intern
Joined: 24 Apr 2011
Posts: 15
Location: United States
GMAT 1: 710 Q49 V39
GPA: 3.67
Followers: 0
Kudos [?]: 7 [0], given: 3
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
05 Jun 2013, 02:18
If I want to score a 43+ verbal, any idea what % of these I should be getting correct?
Currently in the mid 40%....
GMAT Club Legend
Joined: 01 Oct 2013
Posts: 10372
Followers: 996
Kudos [?]: 224 [0], given: 0
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
21 Jun 2014, 23:38
Hello from the GMAT Club VerbalBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Current Student
Joined: 04 Mar 2014
Posts: 142
Location: India
GMAT 1: 710 Q49 V38
WE: Information Technology (Consulting)
Followers: 0
Kudos [?]: 12 [0], given: 178
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
30 Aug 2014, 09:07
aceon wrote:
If I want to score a 43+ verbal, any idea what % of these I should be getting correct?
Currently in the mid 40%....
Even I have the same query.I just completed 25 of them,got only 12 right!Pretty demoralising!
That is less than 50%.Is it good enough to crack a 40+ score in VA.
Moderator
Joined: 01 Sep 2010
Posts: 3166
Followers: 855
Kudos [?]: 7298 [0], given: 1063
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
30 Aug 2014, 09:42
It is a good set but nothing to be concerned about too much......some question is good some is flawed
_________________
GMAT Club Legend
Joined: 01 Oct 2013
Posts: 10372
Followers: 996
Kudos [?]: 224 [0], given: 0
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
30 Sep 2015, 09:16
Hello from the GMAT Club VerbalBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Intern
Joined: 22 Jan 2013
Posts: 4
Followers: 0
Kudos [?]: 0 [0], given: 1
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink]
### Show Tags
04 Jun 2016, 23:17
Fantastic. Keep it coming... The questions are great to score in the 90th percentile of the gmat
Re: Here's the next batch of the most brutal 35 SCs posted on [#permalink] 04 Jun 2016, 23:17
Go to page Previous 1 2 3 4 5 6 7 8 9 10 11 [ 218 posts ]
Similar topics Replies Last post
Similar
Topics:
1 Brutal SC Questions REVISED 1 22 Oct 2013, 10:43
Brutal SC 1 22 May 2012, 11:56
Brutal SC question 7 13 Jun 2012, 06:56
84 Just started doing the BRUTAL SC's.. Am posting the links as 12 08 Mar 2016, 05:57
16 13 Brutal SC questions(help). let collect explanations here. 21 11 Sep 2016, 09:00
Display posts from previous: Sort by | 3,560 | 12,831 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2017-22 | longest | en | 0.917595 |
https://www.rdocumentation.org/packages/car/versions/3.0-10/topics/symbox | 1,618,236,267,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038067400.24/warc/CC-MAIN-20210412113508-20210412143508-00056.warc.gz | 1,030,811,568 | 8,588 | car (version 3.0-10)
# symbox: Boxplots for transformations to symmetry
## Description
`symbox` first transforms `x` to each of a series of selected powers, with each transformation standardized to mean 0 and standard deviation 1. The results are then displayed side-by-side in boxplots, permiting a visual assessment of which power makes the distribution reasonably symmetric.
## Usage
```symbox(x, ...)
# S3 method for formula
symbox(formula, data=NULL, subset, na.action=NULL, ylab, ...)
# S3 method for default
symbox(x, powers = c(-1, -0.5, 0, 0.5, 1), start,
trans=bcPower, xlab="Powers", ylab, ...)```
## Arguments
x
a numeric vector.
formula
a one-sided formula specifying a single numeric variable.
data, subset, na.action
as for statistical modeling functions (see, e.g., `lm`).
xlab, ylab
axis labels; if `ylab` is missing, a label will be supplied.
powers
a vector of selected powers to which `x` is to be raised. For meaningful comparison of powers, `1` should be included in the vector of powers.
start
a constant to be added to `x`. If `start` is missing and `trans` is `bcPower` (the default) or `bcnPower`, then a start will be automatically generated if there are zero or negative values in `x`, and a warning will be printed; the auto-generated `start` is the absolute value of the minimum `x` plus 1 percent of the range of `x`.
trans
a transformation function whose first argument is a numeric vector and whose second argument is a transformation parameter, given by the `powers` argument; the default is `bcPower`, and another possibility is `yjPower`. `bcnPower` may also be used, in which case the `gamma` parameter is set to the value of `start`.
arguments to be passed down.
## Value
as returned by `boxplot`.
## References
Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition. Sage.
`boxplot`, `boxcox`, `bcPower`, `yjPower`
```# NOT RUN { | 499 | 1,924 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2021-17 | latest | en | 0.7604 |
https://www.calcapp.net/learn/formulas/subtraction.html | 1,726,452,504,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651668.29/warc/CC-MAIN-20240916012328-20240916042328-00101.warc.gz | 637,853,641 | 5,820 | Subtraction operator (-)
Value1 - Value2
Value1
Number or { Number }
The number to subtract from (the minuend).
Value2
Number or { Number }
The number which should be substracted from the first number (the subtrahend).
Returns
Number or { Number }
The difference between the numbers.
Subtracts one number from another and returns the result. 8 - 38 - 3 returns 5.
This operator also works with arrays. { 8, 9 } - 6{ 8; 9 } - 6 returns the array { 2, 3 }{ 2; 3 } (equivalent to { 8 - 6, 9 - 6 }{ 8 - 6; 9 - 6 }) and { 8, 9 } - { 6, 10 }{ 8; 9 } - { 6; 10 } returns the array { 2, -1 }{ 2; -1 } (equivalent to { 8 - 6, 9 - 10 }{ 8 - 6; 9 - 10 }).
Subtracting many values
The SUM function is equivalent to this operator, provided that all parameters other than the first one are negated.
These formulas both return 5:
8 - 38 - 3
SUM(8, -3)SUM(8; -3)
However, SUM can be invoked with arrays with an arbitrary number of elements. To subtract the field values of the Field2:Field4Field2:Field4 range from the value of Field1 and return the result, use this formula:
SUM(Field1, -Field2:Field4)SUM(Field1; -Field2:Field4)
(The Field2:Field4Field2:Field4 range is a short-hand way of expressing an array containing Field2 and Field4, as well as any fields that appear between them, such as Field3. If only Field3 appears between the other two fields, Field2:Field4Field2:Field4 and { Field2, Field3, Field4 }{ Field2; Field3; Field4 } are equivalent.)
Examples
8 - 38 - 3
Returns 5.
{ 8, 9 } - 6{ 8; 9 } - 6
Returns the array { 2, 3 }{ 2; 3 }, equivalent to { 8 - 6, 9 - 6 }{ 8 - 6; 9 - 6 }.
{ 8, 9 } - { 6, 10 }{ 8; 9 } - { 6; 10 }
Returns the array { 2, -1 }{ 2; -1 }, equivalent to { 8 - 6, 9 - 10 }{ 8 - 6; 9 - 10 }. | 645 | 1,738 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2024-38 | latest | en | 0.664154 |
http://dictionnaire.sensagent.leparisien.fr/LIMACON/en-en/ | 1,606,871,713,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141685797.79/warc/CC-MAIN-20201201231155-20201202021155-00315.warc.gz | 23,724,536 | 19,900 | LIMACON : définition de LIMACON et synonymes de LIMACON (anglais)
Publicité ▼
Merriam Webster
Limaçon‖Limaçon" (l�mȧsôN"), n. [F. limaçon, lit., a snail.] (Geom.) A curve of the fourth degree, invented by Pascal. Its polar equation is r = a cos θ + b.
Publicité ▼
## définition - LIMACON
voir la définition de Wikipedia
Wikipedia
# Limaçon
In geometry, a limaçon or limacon (), also known as a limaçon of Pascal, is defined as a roulette formed when a circle rolls around the outside of a circle of equal radius. It can also be defined as the roulette formed when a circle rolls around a circle with half its radius so that the smaller circle is inside the larger circle. Thus, they belong to the family of curves called centered trochoids; more specifically, they are epitrochoids. The cardioid is the special case in which the point generating the roulette lies on the rolling circle; the resulting curve has a cusp.
The term derives from the Latin word limax, which means "snail". Depending on the position of the point generating the curve, it may have inner and outer loops (giving the family its name), it may be heart-shaped, or it may be oval.
A limaçon is a bicircular rational plane algebraic curve of degree 4.
Three limaçons: dimpled, with cusp (a cardioid), and looped, respectively. Not shown: the convex limaçon
## History
The earliest formal research on limaçons is generally attributed to Étienne Pascal, father of Blaise Pascal. However, some insightful investigations regarding them had been undertaken earlier by the German Renaissance artist Albrecht Dürer. Dürer's Underweysung der Messung (Instruction in Measurement) contains specific geometric methods for producing limaçons. The curve was named by Gilles de Roberval when he used it as an example for finding tangent lines.
## Equations
The equation (up to translation and rotation) of a limaçon in polar coordinates has the form
$r = b + a \cos \theta \ .$
This can be converted to Cartesian coordinates by multiplying by r (thus introducing a point at the origin which in some cases is spurious), and substituting $r^2 = x^2+y^2$ and $r \, \cos \theta = x$ to obtain[1]
$(x^2+y^2-ax)^2=b^2(x^2+y^2). \,$
Parametrically, this becomes
$x = {a\over 2} + b \cos \theta + {a\over 2} \cos 2\theta,\, y = b \sin \theta + {a\over 2} \sin 2\theta.$
In the complex plane this takes the form
$z = {a\over 2} + b e^{i\theta} + {a\over 2} e^{2i\theta}.$
Construction of a limaçon
If we shift this horizontally by a/2 we obtain the equation in the usual form for a centered trochoid:
$z = b e^{it} + {a\over 2} e^{2it}.$
This is the equation obtained when the center of the curve (as a centered trochoid) is taken to be the origin.
### Special cases
In the special case a = b, the polar equation is $r = b(1 + \cos \theta) = 2b\cos^2 {\theta \over 2}$ or $r^{1 \over 2} = (2b)^{1 \over 2} \cos {\theta \over 2}$ making it a member of Sinusoidal spiral family of curves. This curve is the Cardioid
In the special case $a = 2b$ the centered trochoid form of the equation becomes
$z = b (e^{it} + e^{2it}) = b e^{3it\over 2} (e^{it\over 2} + e^{-it\over 2}) = 2b \cos {t\over 2} e^{3it\over 2}$,
or, in polar coordinates,
$r = 2b\cos{\theta \over 3}$
making it a member of the rose family of curves. This curve is a trisectrix, and is sometimes called the limaçon trisectrix.
## Form
When $b > a$ the limaçon is a simple closed curve. However, the origin satisfies the Cartesian equation given above so the graph of this equation has an acnode or isolated point.
When $b > 2a$ the area bounded by the curve is convex and when $a < b < 2a$ the curve has an indentation bounded by two inflection points. At $b = 2a$ the point $(-a, 0)$ is a point of 0 curvature.
As $b$ is decreased relative to $a$, the indentation becomes more pronounced until, at $b = a$, the cardioid, it becomes a cusp. For $0 < b < a$, the cusp expands to an inner loop and the curve crosses itself at the origin. As $b$ approaches 0 the loop fills up the outer curve and, in the limit, the limaçon becomes a circle traversed twice.
## Measurement
The area enclosed by the limaçon is $(b^2 + {{a^2}\over 2})\pi$. When $b < a$ this counts the area enclosed by the inner loop twice. In this case the curve crosses the origin at angles $\pi \pm \arccos {b \over a}$, the area enclosed by the inner loop is $(b^2 + {{a^2}\over 2})\arccos {b \over a} - {3\over 2} b \sqrt {{a^2} - {b^2}}$, the area enclosed by the outer loop is $(b^2 + {{a^2}\over 2})(\pi - \arccos {b \over a}) + {3\over 2} b \sqrt {{a^2} - {b^2}}$, and the area between the loops is $(b^2 + {{a^2}\over 2})(\pi - 2\arccos {b \over a}) + 3 b \sqrt {{a^2} - {b^2}}.$
## Relation to other curves
• Let P be a point and C be a circle whose center is not P. Then the envelope of those circles whose center lies on C and that pass through P is a limaçon.
Limaçon — pedal curve of a circle
• A pedal of a circle is a limaçon. In fact, the pedal with respect to the origin of the circle with radius $b$ and center $(a,0)$ has polar equation $r = b + a \cos \theta$
• The inverse with respect to the unit circle of $r = b + a \cos \theta$ is $r = {1 \over {b + a \cos \theta}}$ which is the equation of a conic section with eccentricity a/b and focus at the origin. Thus a limaçon can be defined as the inverse of a conic where the center of inversion is one of the foci. If the conic is a parabola then the inverse will be a cardioid, if the conic is a hyperbola then the corresponding limaçon will have an inner loop, and if the conic is an ellipse then the corresponding limaçon will have no loop.
• The conchoid of a circle with respect to a point on the circle is a limaçon.
• A particular special case of a Cartesian oval is a limaçon.[2]
## References
1. ^ J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. pp. 113–118. ISBN 0-486-60288-5.
2. ^
• Jane Grossman and Michael Grossman. "Dimple or no dimple", The Two-Year College Mathematics Journal, January 1982, pages 52–55.
• Howard Anton. Calculus, 2nd edition, page 708, John Wiley & Sons, 1984.
• Howard Anton. [1] pp. 725 - 726.
• Howard Eves. A Survey of Geometry, Volume 2 (pages 51,56,273), Allyn and Bacon, 1965.
Contenu de sensagent
• définitions
• synonymes
• antonymes
• encyclopédie
• definition
• synonym
Publicité ▼
dictionnaire et traducteur pour sites web
Alexandria
Une fenêtre (pop-into) d'information (contenu principal de Sensagent) est invoquée un double-clic sur n'importe quel mot de votre page web. LA fenêtre fournit des explications et des traductions contextuelles, c'est-à-dire sans obliger votre visiteur à quitter votre page web !
Essayer ici, télécharger le code;
Solution commerce électronique
Augmenter le contenu de votre site
Ajouter de nouveaux contenus Add à votre site depuis Sensagent par XML.
Parcourir les produits et les annonces
Obtenir des informations en XML pour filtrer le meilleur contenu.
Indexer des images et définir des méta-données
Fixer la signification de chaque méta-donnée (multilingue).
Renseignements suite à un email de description de votre projet.
Jeux de lettres
Les jeux de lettre français sont :
○ Anagrammes
○ jokers, mots-croisés
○ Lettris
○ Boggle.
Lettris
Lettris est un jeu de lettres gravitationnelles proche de Tetris. Chaque lettre qui apparaît descend ; il faut placer les lettres de telle manière que des mots se forment (gauche, droit, haut et bas) et que de la place soit libérée.
boggle
Il s'agit en 3 minutes de trouver le plus grand nombre de mots possibles de trois lettres et plus dans une grille de 16 lettres. Il est aussi possible de jouer avec la grille de 25 cases. Les lettres doivent être adjacentes et les mots les plus longs sont les meilleurs. Participer au concours et enregistrer votre nom dans la liste de meilleurs joueurs ! Jouer
Dictionnaire de la langue française
Principales Références
La plupart des définitions du français sont proposées par SenseGates et comportent un approfondissement avec Littré et plusieurs auteurs techniques spécialisés.
Le dictionnaire des synonymes est surtout dérivé du dictionnaire intégral (TID).
L'encyclopédie française bénéficie de la licence Wikipedia (GNU).
Changer la langue cible pour obtenir des traductions.
Astuce: parcourir les champs sémantiques du dictionnaire analogique en plusieurs langues pour mieux apprendre avec sensagent.
4276 visiteurs en ligne
calculé en 0,047s
Je voudrais signaler :
section :
une faute d'orthographe ou de grammaire
un contenu abusif (raciste, pornographique, diffamatoire) | 2,498 | 8,605 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 33, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2020-50 | latest | en | 0.848694 |
https://en.essays.club/Social-Issues/Social-Culture/Cause-Effect-Ma-Health-Insurance-Mandate-7579.html | 1,521,525,421,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647299.37/warc/CC-MAIN-20180320052712-20180320072712-00071.warc.gz | 581,364,452 | 8,923 | # Cause & Effect: Ma Health Insurance Mandate
Autor: • March 11, 2018 • 3,589 Words (15 Pages) • 3 Views
Page 1 of 15
...
The estimate of INTERACTION should give us the effect of the policy, but there are some assumptions we have to take into consideration when dealing with differences in differences. The estimate will give us an unbiased estimate if and only if the parallel trend assumption holds. The parallel trend says that if the policy had not taken place, the average change in Y would have been the same for treatment and control.
There are a few ways to measure the parallel trend. The first is called the eyeball test. Although it is not very accurate, we can plot data across time and check whether or not the control and treated groups are trending together prior to the policy effect date. After the policy is implemented, we expect to see a change in the treatment group and no longer be trending of that with the control group.
The second and more reliable way to measure parallel trend is through a placebo experiment. I will use time periods before the real policy date and create a fake treatment date. This placebo test will show us if there was any difference between the treatment group and control group. We expect the differences to be zero if parallel trend holds to be true. If the difference is non-zero, chances are that the difference in difference estimate is not a good method to find causal effect of the policy change.
Another assumption is that there may be a likelihood of a random effect that makes the control and treatment groups move together over time. If not careful, this could lead to a downward bias, or a notion that the policy has no effect at all. To control for this, I will use several pre-treatment time periods to calculate the variance of the difference in difference estimator and adjust the standard errors for it. In order to correct this, I will run my regression in Stata with the cluster command.
The last test will be for heterogeneity. Was everyone affected the same way? Did it matter if the individual was a male or female, young or old, and married or not? This analysis will concentrate on race, specifically if the individual was white or not.
4. Data
For this research I used data from the Integrated Public Use Microdata Series[3] (IPUMS) Current Population Survey (CPS). The two online resources collaborate and harmonize their data to be user friendly. It’s a popular resource for researchers and is deemed reliable. Table 1 below shows the means for the variables that will be discussed respectively:
The individual-level data I gathered was for all adults (aged 18-64) from 2002 to 2010. The treatment years are identified as 2008 and later. The control group are years 2006 and before. Although information was gathered for 2007, I dropped it from this analysis. This decision was made because the implementation of the policy was mid year, and the data used from IPUMS is gathered in March. Thus, I have no way of knowing if the data was before or after the policy for that particular year. Table 1 below shows the means for the variables that will be discussed respectively.
The second identifying statistic is the person's state of residence. In this set, I used 10 different states that had the highest population density per square mile[4] in 2012. These states (ranked from highest to lowest) are New Jersey, Rhode Island, Massachusetts, Connecticut, Maryland, Delaware, New York, Florida, Ohio, and Pennsylvania. I also used the 11th highest state, California, to account for the dropped fixed effects state.
The first dependent variable is if the individual has health insurance coverage. I acknowledge those that are insured as the treatment group. Those without insurance are marked as the control group. Being insured means having any health insurance at all, whether it’s public or private. It doesn’t take into consideration why a person doesn’t have coverage. For example, maybe the data classified the person as a resident of a state, but they moved within the 63-day grace period that the law mandated them to get covered. Maybe they were unaware of the new policy. The reform did allow individuals to petition unique situations where coverage may not have been warranted. Again, this variable doesn’t distinguish the reasons behind not being insured. It would make good data though.
The second dependent variable is if the person is healthy. Individuals were asked to conduct a self-assessment on their current health and rate it on a five-point scale, as excellent, very good, good, fair, or poor. For those that identified themselves with excellent or very good health, I made them the treatment group. For those that felt like they had only good, fair, or poor health I classified them as the control group.
The third dependent variable represents part-time or full-time work status conditional on working at all. There were a few examples in the data set that were either unemployed or had an unknown work status. Those observations were dropped accordingly. Part-time workers are my treatment group. Part-time is defined as working 34 hours a week or less on average during the previous calendar year. Full-time employment is my control group.
Finally, I will use race as an independent variable to measure for heterogeneity. In 2003, respondents to CPS could report more than one race. In this study, the treatment group is classified as only white. If the individual reported more than one race, then they would be in the control group.
5. Results
It is worth mentioning that my estimates are reported as percentage points and not just a percentage. A percentage point is the difference between two percentages. A quick example is to think about data at 5% and it increases to 10%. We can say, “The data increased by 5 percentage points.” We wouldn’t report the results in this section as saying, “The data increased by 100%.”
5.1 Effect on Health Insurance Coverage
After running the regression for equation 1, the DD estimates say that the policy increased the number of individuals insured by 6.8 percentage points. This is shown on Table 2. This estimate is statistically significant at the 1% level. While being statistically significant does not suggest the results are conclusive, it does imply that the statistic is reliable.
So what does this mean? How do we know that the reform really impacted the number of insured by 6.8 percentage points? One can argue that this increase would have happened with or without the implementation of the policy. Maybe people in Massachusetts are smarter (it does have Harvard and M.I.T after all) than other people in different states. They know the value of health insurance.
That’s
... | 1,390 | 6,759 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2018-13 | longest | en | 0.939909 |
https://de.zxc.wiki/wiki/Geographische_Breite | 1,725,826,456,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651017.43/warc/CC-MAIN-20240908181815-20240908211815-00309.warc.gz | 186,932,889 | 10,641 | # Geographic latitude
Parallels
Definition of latitude ${\ displaystyle \ phi}$
50th degree of latitude in downtown Mainz
The 49th parallel is marked with a monument in Prešov (Eperies).
The latitude (B or φ ), and geodetic latitude or latitude mentioned ( latin latitudo , English latitude ; international abbreviation Lat. , Or LAT ) is the in the square in the unit level specified northern or southern distance of a point of the surface of the earth from the equator . The latitude assumes values from −90 ° at the south pole over 0 ° at the equator to + 90 ° at the north pole. Instead of the sign , the designations N and S for north or south are also permitted. B. the latitude of the South Pole can be noted as 90 ° S.
The latitude uses ellipsoidal coordinates ; one measures the angle between the normal (perpendicular) to the earth ellipsoid and the equatorial plane of the earth. Unlike the geocentric latitude, it is not measured to the center of the earth, nor is it related to the true vertical direction , as is the case with the astronomical latitude .
## Subdivision
The latitude is traditionally given in the sexagesimal system with degrees , minutes and seconds , where a degree corresponds to 60 minutes and a minute to 60 seconds (as in the time). In decimal fractions are indicated.
There are - depending on the desired accuracy - different methods of representation, e.g. B .:
1. Degrees, minutes, seconds: 66 ° 43 ′ 12 ″
2. Degrees, minutes, decimal seconds: 66 ° 43 ′ 12.0 ″
3. Degrees, decimal minutes: 66 ° 43.1 ′
4. Decimal degrees: 66.7200 °
The distance between two circles of latitude whose latitude differs by 1 ° is always around 111 km or 60 nautical miles . However, the distance at the poles (111.694 km per degree) due to the flattening of the earth is slightly larger than at the equator (110.574 km per degree), as the curvature from the pole to the equator increases by about 1%.
If N or S is missing, positive values stand for northern latitude and negative values for southern latitude.
When specifying location coordinates , the latitude must always be entered first, then the longitude: "B before L, as in the alphabet" . The alphabetical rule also works for the English terms "Latitude" and "Longitude". This convention has its basis in history: the latitude could already be determined quite precisely centuries before the longitude.
Coordinate examples
## Determination of the geographical latitude
The width can be determined quite easily from the highest position of the sun (midday latitude ) or from the height of the culminating stars. The measurement can take place , for example, with the aid of a sextant .
In the northern hemisphere of the earth, the height of the relatively bright polar star (Polaris) above the horizon indicates the degree of latitude fairly precisely. At the equator , the North Star appears on the horizon, at the North Pole it is almost vertical in the sky. In fact, the star location of Polaris with a declination of (currently) about 89 ° 16 'does not exactly correspond to the celestial pole ; the resulting error fluctuates twice a day between 0 ° and approx. 0.75 ° due to the rotation of the earth and can be reduced by simple formulas or averaging .
Already the seafarers of the late 15th century knew how to use the width for navigation . Determining the longitude , however, was more complicated and required precise dead reckoning or the measurement of moon- star distances. Since the end of the 18th century it has been carried out with the exact time of chronometers , since the middle of the 20th century using various methods using electromagnetic waves from terrestrial transmitters, and since the 1990s with GPS satellite receivers.
## Astronomical, ellipsoidal, geodetic and geocentric latitudes
With a perfectly stable (flattened) ellipsoid of revolution (no mountains or valleys, constant density) the ellipsoidal latitude would correspond to the astronomical latitude. In addition, the geocentric latitude for each location would be numerically closest to the equator (i.e. smallest amount).
## Influence on the climate
Since the mean solar radiation on a point on the earth's surface depends on its geographical latitude, this largely determines the local climate and can be used to define the (geographical) climatic zones : The tropics lie between the tropics (23 ° 26 ′) and the polar regions above the polar circles (66 ° 34 ′), in between are the subtropical and temperate zones .
The climate also depends on other factors; so are z. B. European locations because of the North Atlantic Current are usually significantly warmer than Asian and North American locations of the same geographical latitude.
The geographical latitude also has an influence on the wind conditions . In earlier times, when ships were still mostly sailed, they were of great importance for shipping as they are today for sailing ships . From the time of the sailing ships, names such as horse widths or roaring forties have been preserved, which assign the wind conditions to corresponding widths.
## Latitude
The 48th parallel as a paving mosaic in Freiburg / Br. , 2010
The word latitude is used with different meanings. On the one hand it can mean the latitude in degrees itself, on the other hand the circle of latitude on which all places of the same latitude lie, and here sometimes only those circles of latitude whose latitude is an integer in degrees. | 1,190 | 5,469 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2024-38 | latest | en | 0.774091 |
http://www.efunda.com/forum/show_member.cfm?member=neil%20moran&start=1&thread=10894 | 1,537,524,305,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267157028.10/warc/CC-MAIN-20180921092215-20180921112615-00178.warc.gz | 315,998,327 | 7,705 | Member Info (neil moran)
• Materials • Design Center • Processes • Units & Constants • Formulas • Mathematics
Home Membership Magazines Forum Search Member Calculators
Materials Design Processes Units Formulas Math
Basic Information UserName: neil moran Name: Neil Moran Location: Suffolk UK Occupation: Structural / Mechanical Design Engineer Specialty: Theatre & Stage Engineering E-Mail: NMDesignsLtd@aol.com
Profile Summary
Posts by neil moran [ Order by Time Posted ] [ Group by Topic ] [ Topics by neil moran ] [ All Topics ] Showing Messages 1-30 (of 183) Next >> Composite beam in simple bending Hi Rob, I see your problem, but I would still tackle it the way ... Posted 05/01/09 12:11 PST Composite beam in simple bending Hi Rob, The simplest way to tackle this is to treat the beam as ... Posted 05/01/09 07:47 PST Good gear design book - any recommendations? Gear Design & Application by Nicholas P Chironis Posted 12/22/08 11:53 PST Bending stiffness Hi,I agree with Ram Bala, for problems relating to bending we use... Posted 12/21/08 14:11 PST RPM to Gear ratio Darrell,Assuming you know the weight of the boat and that it is o... Posted 12/19/08 12:57 PST calculate I value to get first natural frequency of 450Hz Hi,I may be a bit late for you here, but here goes anyway.An appr... Posted 12/19/08 09:25 PST RPM to Gear ratio Hi Darrell,1HP is equal to 550lbs.ft/sec. In other words (assumin... Posted 12/19/08 07:56 PST Scissor lift table mechanism Hi Asa,I do indeed remember my post, several years old now.The ho... Posted 11/30/07 13:54 PST PULLEY STUFF Hi all,Force x distance = constantIn other words - 200# x 2"... Posted 10/23/07 13:17 PST MEng project help: energy to lift something Hi Tom,It doesnt take any power (watts) to just hold something up... Posted 10/31/06 09:34 PST Thickness of plate Hi Jak0889, Take a look at `Roark's Formulas for Stress & Stra... Posted 10/31/03 09:29 PST Focus and arc length of a Parabola, solar trough Hi Paul, There is some information on this in `Machinery's Han... Posted 10/14/03 01:29 PST Stress Concentration Factor for Threads Hi Bmayville, Take a look in `Roark's Formulas for Stress and ... Posted 09/25/03 01:03 PST laplace transform Hello irl81, Take a look at - www.treasure-troves.com - ... Posted 07/29/03 01:10 PST Wrench Clearances Hi Chris, Try, Machinery's Handbook, its as good a place as an... Posted 07/16/03 12:07 PST Fiberglass vs sheet metal floor Hi Dalibor, In a collision, sheet metal deforms and crumples t... Posted 07/08/03 07:52 PST Fiberglass vs sheet metal floor I think Spike78 is right. On a `one off`, fibreglass is relativel... Posted 07/08/03 01:21 PST Ultimate load capabilities of M10 x 1.5 bolt I would use the min dia of thread. This may not be strictly corre... Posted 07/06/03 03:21 PST Ultimate load capabilities of M10 x 1.5 bolt Nearly right hammerpe, except you need to use the shear stress ra... Posted 07/04/03 12:00 PST CORKED BATS This is very similar to a question asked on another forum. Its al... Posted 07/02/03 08:04 PST The most basic of applications of f=ma Another way to check this is to take the square root of the ratio... Posted 06/26/03 12:04 PST The most basic of applications of f=ma Hi Manhattan, Ah, Hah, it's the Kinetic energy that you are af... Posted 06/24/03 09:52 PST The most basic of applications of f=ma Hi Manhatten, I'm not exactly sure what you are asking here, a... Posted 06/24/03 08:29 PST Rigorous Proof of Heron's Formula Hi Acroduster1, Try this - http://mathworld.wolfram.com/Her... Posted 06/23/03 11:38 PST Warping Constant Hi Acroduster1, Try "Roarks Formulas for Stress & strain" by W... Posted 06/11/03 08:27 PST converting wind spead to force Thanks acroduster1 for your kind words. Neil Moran Posted 06/05/03 05:53 PST converting wind spead to force Thanks b1ueshift, for putting me right. I forgot to convert miles... Posted 06/05/03 01:42 PST converting wind spead to force Hello jophillips, 100miles/hr = 100/3.2808 = 30.48m/sec The... Posted 06/04/03 01:34 PST I Beam Deflection Hello lito1130, If you really want to calculate the second mom... Posted 05/25/03 06:17 PST Deflection of plate... Hi Janghoon, "Roarks Formulas for Stress & Strain" by Warren C... Posted 05/22/03 01:04 PST Showing Messages 1-30 (of 183) Next >> | 1,242 | 4,295 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2018-39 | latest | en | 0.820161 |
https://link.springer.com/article/10.1007/BF02481965 | 1,531,769,558,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589417.43/warc/CC-MAIN-20180716174032-20180716194032-00514.warc.gz | 694,954,198 | 16,333 | Annals of the Institute of Statistical Mathematics
, Volume 36, Issue 1, pp 207–215
# A minimax regret estimator of a normal mean after preliminary test
Article
## Summary
This paper considers the problem of estimating a normal mean from the point of view of the estimation after preliminary test of significance. But our point of view is different from the usual one. The difference is interpretation about a null hypothesis. Let$$\bar X$$ denote the sample mean based on a sample of sizen from a normal population with unknown mean μ and known varianceσ 2. We consider the estimator that assumes the value$$\omega \bar X$$ when$$\left| {\bar X} \right|{{< C\sigma } \mathord{\left/ {\vphantom {{< C\sigma } {\sqrt n }}} \right. \kern-\nulldelimiterspace} {\sqrt n }}$$ and the value$$\bar X$$ when$$\left| {\bar X} \right|{{ \geqq C\sigma } \mathord{\left/ {\vphantom {{ \geqq C\sigma } {\sqrt n }}} \right. \kern-\nulldelimiterspace} {\sqrt n }}$$ where ω is a real number such that 0≤ω≤1 andC is some positive constant. We prove the existence of ω, satisfying the minimax regret criterion and make a numerical comparison among estimators by using the mean square error as a criterion of goodness of estimators.
## Keywords
Preliminary Test Usual Estimator Numerical Comparison Lower Semicontinuous Function Minimax Regret
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
## References
1. [1]
Akaike, H. (1973). Information theory and an extention of the maximum likelihood principle,2nd International Symposium on Information Theory (eds. B. N. Petrov and F. Csaki), Akademiai Kiado, Budapest, 267–281.Google Scholar
2. [2]
Bancroft, T. A. and Han, Chien-Pai (1977). Inference based on conditional specification: a note and a bibliography,International Statistical Review,45, 117–127.
3. [3]
Hirano, K. (1977). Estimation procedures based on preliminary test, shrinkage technique and information criterion,Ann. Inst. Statist. Math.,29, A, 21–34.
4. [4]
Meeden, G. and Arnold, B. C. (1979). The admissibility of a preliminary test estimator when the loss incorporates a complexity cost,J. Amer. Statist. Ass.,74, 872–874.
5. [5]
Ohtani, K. and Toyoda, T. (1978). Minimax regret critical values for a preliminary test in pooling variances,J. Japan Statist. Soc.,8, 15–20.
6. [6]
Sawa, T. and Hiromatsu, T. (1973). Minimax regret significance points for a preliminary test in regression analysis,Econometrica,41, 1093–1101.
7. [7]
Toyoda, T. and Wallace, T. D. (1975). Estimation of variance after a preliminary test of homogeneity and optimal levels of significance for the pre-test,J. Econometrics,3, 395–404. | 742 | 2,730 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2018-30 | latest | en | 0.727066 |
https://www.numere-romane.ro/cum_se_scrie_numarul_arab_cu_numerale_romane.php?nr_arab=50000&nr_roman=(L)&lang=en | 1,607,133,662,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141746033.87/warc/CC-MAIN-20201205013617-20201205043617-00173.warc.gz | 743,660,037 | 9,217 | # Convert number: 50,000 in Roman numerals, how to write?
## Latest conversions of Arabic numbers to Roman numerals
900,199 = (C)(M)CXCIX Dec 05 02:01 UTC (GMT) 1,741,999 = (M)(D)(C)(C)(X)(L)MCMXCIX Dec 05 02:01 UTC (GMT) 2,552,117 = (M)(M)(D)(L)MMCXVII Dec 05 02:01 UTC (GMT) 50,000 = (L) Dec 05 02:00 UTC (GMT) 138,933 = (C)(X)(X)(X)(V)MMMCMXXXIII Dec 05 02:00 UTC (GMT) 1,880,501 = (M)(D)(C)(C)(C)(L)(X)(X)(X)DI Dec 05 02:00 UTC (GMT) 345,987 = (C)(C)(C)(X)(L)(V)CMLXXXVII Dec 05 02:00 UTC (GMT) 11,820 = (X)MDCCCXX Dec 05 02:00 UTC (GMT) 18,593 = (X)(V)MMMDXCIII Dec 05 02:00 UTC (GMT) 12,388 = (X)MMCCCLXXXVIII Dec 05 02:00 UTC (GMT) 2,111,110 = (M)(M)(C)(X)MCX Dec 05 02:00 UTC (GMT) 100,338 = (C)CCCXXXVIII Dec 05 02:00 UTC (GMT) 3,531 = MMMDXXXI Dec 05 02:00 UTC (GMT) converted numbers, see more...
## The set of basic symbols of the Roman system of writing numerals
• ### (*) M = 1,000,000 or |M| = 1,000,000 (one million); see below why we prefer this notation: (M) = 1,000,000.
(*) These numbers were written with an overline (a bar above) or between two vertical lines. Instead, we prefer to write these larger numerals between brackets, ie: "(" and ")", because:
• 1) when compared to the overline - it is easier for the computer users to add brackets around a letter than to add the overline to it and
• 2) when compared to the vertical lines - it avoids any possible confusion between the vertical line "|" and the Roman numeral "I" (1).
(*) An overline (a bar over the symbol), two vertical lines or two brackets around the symbol indicate "1,000 times". See below...
Logic of the numerals written between brackets, ie: (L) = 50,000; the rule is that the initial numeral, in our case, L, was multiplied by 1,000: L = 50 => (L) = 50 × 1,000 = 50,000. Simple.
(*) At the beginning Romans did not use numbers larger than 3,999; as a result they had no symbols in their system for these larger numbers, they were added on later and for them various different notations were used, not necessarily the ones we've just seen above.
Thus, initially, the largest number that could be written using Roman numerals was:
• MMMCMXCIX = 3,999. | 737 | 2,157 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2020-50 | latest | en | 0.905656 |
http://www.ask.com/web?qsrc=3053&o=102140&oo=102140&l=dir&gc=1&q=How+Big+Is+A+Square+Foot | 1,464,311,011,000,000,000 | text/html | crawl-data/CC-MAIN-2016-22/segments/1464049276415.60/warc/CC-MAIN-20160524002116-00009-ip-10-185-217-139.ec2.internal.warc.gz | 357,374,117 | 18,519 | Web Results
Square foot
en.wikipedia.org/wiki/Square_foot
The square foot is an imperial unit and U.S. customary unit (non-SI, non-metric) of area, used mainly in the United States and partially in Canada, United ...
How to Measure Square Footage: 11 Steps (with Pictures) - wikiHow
www.wikihow.com/Measure-Square-Footage
Break down the area into manageable parts. If you're having trouble finding the square footage, then it's probably because you're not working with a neat area ...
Square Foot Calculator | How to Measure Square Feet
Calculating Square Footage. by HomeAdvisor. Large home. Calculating square footage and cubic footage of a house is important for current and prospective ...
Square Footage Calculator - Calculator Soup
www.calculatorsoup.com/calculators/construction/square-footage-calculator.php
Calculate square footage, square meters or square yardage for home or construction project. Calculate square feet, meters or yards for flooring, carpet, or tiling ...
Jan 21, 2011 ... Divide this number by 144 to get the square footage of your triangle .... I just wanna how exactly big a square foot is. lol (Or whatever.).
Square Feet to Square Inches - How many sq. inches in a sq. foot?
Square foot to inch area units conversion table and converter to find out how many square inches in square feet.
How much carpet will you need? | Bankrate.com
www.bankrate.com/calculators/home-equity/how-much-carpet-calculator.aspx
You will get two figures -- one as square yards and the other as square feet -- of how much carpet you will need. More details ... Enter measurements ...
How big is the White House? - White House Historical Association
www.whitehousehistory.org/questions/how-big-is-the-white-house
The White House is 168 feet (51.2 meters) longThe White House is 85 feet 6 inches (26.1 ... Floor area (total of 6 floors) approximately 55,000 square feet.
2 Square Feet vs. 2 Feet - Math Forum - Ask Dr. Math
mathforum.org/library/drmath/view/58411.html
What is the difference between 2 square feet and 2 feet square?
How big is a square foot? - Fine Homebuilding
www.finehomebuilding.com/1999/07/01/how-big-is-a-square-foot
Jul 1, 1999 ... Unfortunately, having this universal square-foot number doesn't by ... Generally, people selling houses want them to seem big, so a 25-ft. by ... | 550 | 2,335 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2016-22 | longest | en | 0.864771 |
http://convertit.com/Go/ConvertIt/Measurement/Converter.ASP?From=dry+barrel&To=capacity | 1,603,644,846,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107889574.66/warc/CC-MAIN-20201025154704-20201025184704-00356.warc.gz | 23,343,640 | 3,799 | Partner with ConvertIt.com
New Online Book! Handbook of Mathematical Functions (AMS55)
Conversion & Calculation Home >> Measurement Conversion
Measurement Converter
Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC.
Conversion Result: ```dry barrel = 0.115627123584 volume (volume) ``` Related Measurements: Try converting from "dry barrel" to barrel, beer gallon (English beer gallon), cc (cubic centimeters), chetvert (Russian chetvert), cord (of wood), drop, dry quart, freight ton, gallon, hogshead, jigger, last, minim, nebuchadnezzar, peck (dry peck), pipe, tablespoon, teaspoon, tou (Chinese tou), UK pint (British pint), or any combination of units which equate to "length cubed" and represent capacity, section modulus, static moment of area, or volume. Sample Conversions: dry barrel = .00009374 acre foot, 2.97 amphora (Greek amphora), .96969697 barrel, 115,627.12 cc (cubic centimeters), .55054018 chetvert (Russian chetvert), .82030487 coomb, 488.73 cup, 3,854,237.45 drop, 152.73 fifth, 3.39 firkin, 30.55 gallon, .48484848 hogshead, 15.27 methuselah, 977.45 noggin, 13.12 peck (dry peck), 4.47 Roman amphora, 1.09 sack, 25.43 UK gallon (British gallon), 101.74 UK quart (British quart), 152.61 wine bottle.
Feedback, suggestions, or additional measurement definitions?
Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks! | 460 | 1,618 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2020-45 | latest | en | 0.619852 |
https://www.jiskha.com/questions/770663/the-barrel-of-a-rifle-has-a-length-of-0-916m-a-bullet-leaves-the-muzzle-of-a-rifle-with-a | 1,624,152,100,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487653461.74/warc/CC-MAIN-20210619233720-20210620023720-00565.warc.gz | 762,056,144 | 5,024 | # Physics
The barrel of a rifle has a length of 0.916m. A bullet leaves the muzzle of a rifle with a speed of 621m/s.
What is the acceleration of the bullet while in the barrel? A bullet in a rifle barrel does not have a constant acceleration, but constant acceleration is to be assumed for this problem.
1. 👍
2. 👎
3. 👁
1. cnjewjgr
1. 👍
2. 👎
2. vgvvijhvj
1. 👍
2. 👎
3. gsy
1. 👍
2. 👎
## Similar Questions
1. ### physics
A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m. Determine the acceleration of the bullet (uniform acceleration)
2. ### physics
A 2.0 g bullet leaves the barrel of a gun at a speed of 260 m/s. (a) Find its kinetic energy. J (b) Find the average force exerted by the expanding gases on the bullet as the bullet moves the length of the 43 cm long barrel. N
3. ### K. N. Memo Academy Asarganj Munger (a student)
A bullet leaves the barrel of a rifle with a speed of 300m/s. If the length of the barrel is 0.9m, at what rate is the bullet accelerated while in the barrel?
4. ### physics
The barrel of a rifle has a length of 0.976 m. A bullet leaves the muzzle of a rifle with a speed of 561 m/s. What is the acceleration of the bullet while in the barrel? A bullet in a rifle barrel does not have constant
1. ### physics
The drawing shows an exaggerated view of a rifle that has been ‘sighted in' for a 91.4-meter target. If the muzzle speed of the bullet is v0 = 392 m/s, there are the two possible angles θ1 and θ2 between the rifle barrel and
2. ### physics
A bullet of mass 6.45 g is fired from a 66.0 cm-long rifle barrel at 237 m/s. The mass of the rifle is 4.50 kg. Determine the acceleration of the bullet as well as the recoil acceleration of the rifle
3. ### physics
a 2 kilogram rifle initially at rest fires a 0.002 kilogram bullet. as the bullet leaves the rifle with a velocity of 500 meters per second, what is the momentum of the rifle bullet system? isn't the answer one because final
4. ### physics
bull's-eye bob at a hunting range fires his rifle at a target 200 meters downrange. the bullet moves horizontally from the rifle barrel with a speed of 400 m/s? how far does the bullet drop from a straight line horizontal path bny
1. ### physics
a 15-g bullet is fired from a rifle. it takes 2.50 * 10^-3s for the bullet to travel the length of the barrel, and it exits the barrel with a speed of 715 m/s. assuming that the acceleration of the bullet is constant, find the
2. ### physics
The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v=(-5.00×10^7)t^2 + (3.00×10^5)t where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves
3. ### physics
A 30-06 caliber hunting rifle fires a bullet of mass 0.0118 kg with a velocity of 505 m/s to the right. The rifle has a mass of 6.15 kg. What is the recoil speed of the rifle as the bullet leaves the rifle? Answer in units of m/s.
4. ### Physics
A rifle with a mass of 1.2 kg fires a bullet with a mass of 6.0 (0.006kg). The bullet moves with a muzzle velocity of 600 m/s after the rifle is fired. a. What is the momentum of the bullet after the rifle is fired? b. If external | 897 | 3,272 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2021-25 | latest | en | 0.901713 |
https://scicomp.stackexchange.com/questions/1506/non-differentiable-global-optimization-problem | 1,723,676,624,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641137585.92/warc/CC-MAIN-20240814221537-20240815011537-00130.warc.gz | 386,503,188 | 43,036 | Non-differentiable global optimization problem
I am trying to solve the following test problem which is well-known in the community in different variants:
Place N = 15 points in the 3-dim. unit cube such that the minimal distance between them is maximal, e.g. like in the case of repellent but confined electrons. Here are Matlab-like non-vectorized/vectorized forms of the function to be optimized (where we assume n = 3*N):
---- non-vectorized -------------------------------------------------
function d = balls(x)
d = 2.0;
for i = 1:14
for j = (i+1):15
s = (x(i)-x(j))^2 + (x(i+15)-x(j+15))^2 + (x(i+30)-x(j+30))^2;
s = sqrt(s);
if s < d, d = s; end
end
end
d = -d;
end
---- vectorized -----------------------------------------------------
function d = balls(x)
X = reshape(x, [], 3);
d = -min(pdist(X));
end
The function is continuous, but not smooth; gradient-based methods will not work. Multi-start and stochastic approaches have a problem, too, because with 45 dimensions the search space is already quite big. The boundary is also a problem, compared for example to the problem of placing electrons on a sphere where there is no boundary.
It will have many local minima, e.g. permuting ball indices or interchanging dimensions. I guess all these local minima have the same function value, like an energy level that will always end in a similar configuration (is that true?). I am only interested in this minimal value, so calculating one local minimum exactly and reliably should be enough.
From applying Matlab' fmincon() with several restarts I know the minimum will be below -0.62... Still I would like to compute this value more accurately and with open source software only! Please no hints to powerful commercial solvers.
• You could convert it to a smooth constrained optimization problem. The constraints would be d <= s for all s and the objective is to maximize d.
– Opt
Commented Mar 3, 2012 at 18:44
• Is your boundary periodic? Commented Mar 3, 2012 at 23:25
• @Deathbreath It's the boundary of the unit cube, i.e. 0<=xi<=1; what do you mean with 'periodic'? Commented Mar 4, 2012 at 7:44
• @HansWerner: Periodic conditions would imply that your unit box was replicated indefinitely in all three dimensions. This is case in crystal structures for instance. Commented Mar 4, 2012 at 18:46
• Have you tried any genetic algorithms? Your objective function can be calculated extremely fast. Commented Jun 11, 2014 at 14:26
Smooth reformulation
As Sid points out, there's no need to treat this problem as non-smooth, since you'd just be making it harder on yourself.
Let's assume for the sake of notation that $\mathbf{x}_{1}, \ldots, \mathbf{x}_{15} \in [0,1]^{3} \subset \mathbb{R}^{3}$ are the coordinates of your 15 particles in the unit cube. A smooth formulation, as Sid suggests, presented in standard form (for nonlinear programming), would be:
\begin{alignat}{1} &\min_{\mathbf{x}_{1}, \ldots, \mathbf{x}_{15} \in [0,1]^{3}} -E \\ \mathrm{s.t.} & \quad E - \|\mathbf{x}_{i} - \mathbf{x}_{j}\|^{2} \leq 0, \,\, i, j = 1, \ldots, 15, \,\, i \neq j \end{alignat}
where $E$ is a proxy for the minimum distance, which I'm assuming is related to minimizing some sort of energy. There might be a way to reformulate this problem as an equivalent convex problem, but I don't think there is.
This formulation probably isn't convex, because the left-hand sides of the nonlinear constraints aren't convex, so you'll need to use a nonconvex nonlinear programming solver to be assured of a global optimal solution (unless you can prove convexity of the feasible set, but I doubt that). Deterministic global solvers that will work for nonconvex problems include (but aren't limited to):
• BARON (which is commercial, but you can submit jobs for free via the NEOS optimization server run by University of Wisconsin-Madison)
• LINDOGlobal (also commerical, also available through the NEOS optimization server)
• Couenne (open-source, part of the COIN-OR suite of open-source solvers)
• Bonmin (also part of COIN-OR)
• LaGO (again, part of COIN-OR)
• icos (available as open-source, or through NEOS)
It's important to note that one solver may work on your problem when others won't; BARON is generally considered the best, but it's fallible, and there are cases where, for example, Couenne will solve a problem to (epsilon) global optimality, but BARON won't (and vice versa).
Solving nonsmooth problems
Let's suppose for the sake of argument that you (like Hans) want to solve a non-smooth nonlinear programming problem. This type of problem isn't my area of expertise, but I know of a couple references.
The most famous person in the field (who, as far as I can tell, developed the most important parts of the theory early on) is Frank H. Clarke. The gist of non-smooth optimization seems to be: replace gradients with Clarke's generalized gradients. Using Clarke's generalized gradients, you're supposed to be able to formulate a non-smooth analogue of Newton's method, as well as algorithms for optimization. His textbook on the theory (Optimization and Nonsmooth Analysis by Frank H. Clarke; the link goes to Amazon) is considered a classic.
In terms of software, the best links I can find are to Napsu Karmitsa's home page; she's developed a couple non-smooth optimization solvers, and she links to other non-smooth optimization solvers. The methods I've heard of most often are called bundle methods, and should be deterministic. (I favor deterministic methods over stochastic methods.) More links to non-smooth codes can be found here; your mileage may vary, because like I said, I don't work with these methods.
I do know that just because a method is developed for non-smooth problems does not mean it will work for non-smooth, non-convex problems, so you will need to make sure that the solver you choose can handle both non-smoothness and non-convexity.
Finally, as Hans points out in the comments, non-smooth formulations regularly appear in science and engineering. However, my first instinct as someone in the optimization field is to try and find an equivalent smooth reformulation because methods for solving smooth problems are generally much faster than methods for solving non-smooth methods (a labmate uses non-smooth solvers, and has made this observation). If you can reformulate the problem as a smooth optimization problem, it generally behooves you to do so.
• I want to make it hard. I want to solve it as a non-smooth, non-convex problem. And it is still unclear (to me) if it will be sufficient to hit one local minimum. I do know COIN-OR and NEOS, but a more concrete plan would be welcome. As I said, no hints to commercial solvers. Commented Mar 4, 2012 at 7:29
• The formulation above will be equivalent; it has the same set of global optima as the original formulation you proposed, except that the formulation I proposed is smooth. If the optimal objective function value of my formulation is $-E'$, then the optimal objective function value of your formulation is $\sqrt{E'}$. There's no need to make it non-smooth, unless, of course, you still want to, in which case, I can recommend a different solver. (You'll want to look at non-smooth bundle solvers in that case.) Commented Mar 4, 2012 at 7:41
• In engineering, non-smooth problems emerge regularly, quite often because of minimax formulations, and special techniques have been developed to solve these kinds of optimization tasks, see for example Smoothing-out techniqes for min-max problems , or Non-linear minimax optimization as least pth optimization Perhaps I should set up a new question asking specifically for such approaches in free solvers. Commented Mar 4, 2012 at 9:32
• So yes, I would like to solve the function as is. I really admire your know-how in optimization theory, but sometimes I find lists of solvers a bit boring. I had hoped for answers describing some real experience with such tasks. Commented Mar 4, 2012 at 9:34
• I don't solve non-smooth optimization problems, but a labmate of mine does. I've updated my answer based on what I've seen in his presentations. Right now, the number of people involved in optimization research on scicomp is pretty small (based on the number of people who have answered questions on that tag; I have as many upvotes on the "optimization" tag as the next top 7 users on the tag), but I'm hoping that'll grow over time. Commented Mar 4, 2012 at 17:24
You might wish to try one of the (local) nonsmooth solvers at my web page http://www.mat.univie.ac.at/~neum/glopt/software_l.html#nonsm using multiple starting points to globalize the search.
I found CMA-ES quite robust in dimensions up to 50. (It gets very slow though when the dimension is large.) | 2,135 | 8,740 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2024-33 | latest | en | 0.886417 |
https://byjus.com/question-answer/let-f-x-left-begin-matrix-left-x-2-3x-right-a-0-leq-x-1/ | 1,719,070,795,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862404.32/warc/CC-MAIN-20240622144011-20240622174011-00253.warc.gz | 131,981,566 | 33,794 | 1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question
# Let f(x)=⎧⎨⎩∣∣x2−3x∣∣+a,0≤x<32−2x+3 x≥32 If f(x) has a local maximum at x =.
A
a0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a94
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
a94
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a=3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
## The correct option is B a≤−94 f(32)=0⇒limx→32∣∣x2−3x∣∣+a≤0⇒94+≤⇒a≤−94
Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Extrema
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program | 273 | 691 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-26 | latest | en | 0.763787 |
https://www.edplace.com/worksheet_info/maths/keystage3/year9/topic/965/1456/calculate-the-mean-median-and-range-of-a-dataset-2 | 1,656,665,053,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103922377.50/warc/CC-MAIN-20220701064920-20220701094920-00524.warc.gz | 788,710,193 | 11,995 | # Calculate the Mean, Median and Range of a Dataset (2)
In this worksheet, students must calculate the mean, median and range of a dataset.
Key stage: KS 3
Curriculum topic: Statistics
Curriculum subtopic: Understand Variables, Representation, Measures and Spread
Difficulty level:
#### Worksheet Overview
This worksheet is about calculating the mean, median and range of a dataset.
Remember
To find the mean, add up all the values and divide by the total number of values.
The median is the middle value, once the numbers have been put in order (lowest number to highest number). If there are two middle numbers, find the mean of these two middle numbers.
The range is the difference between the largest and smallest values.
Example
Calculate the mean, median and range of this dataset.
Minimum temperatures in oC over 1 week:
7, 3.5, 2.5, -1, -4.5, 5, -2
First find the total which is 7 + 3.5 + 2.5 - 1 - 4.5 + 5 - 2 = 10.5
Mean = total ÷ number = 10.5 ÷ 7 = 1.5 oC
For the median, place them in increasing order.
-4.5, -2, -1, 2.5, 3.5, 5, 7
The middle number is the 4th number in the list.
Median is 2.5 oC
Range = largest value - smallest value = 7 - -4.5 = 7 + 4.5 = 11 oC
### What is EdPlace?
We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.
Get started | 431 | 1,603 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2022-27 | latest | en | 0.876905 |
http://calculator.tutorcircle.com/correlation-coefficient-calculator.html | 1,537,663,478,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267158766.65/warc/CC-MAIN-20180923000827-20180923021227-00227.warc.gz | 40,298,052 | 5,947 | Sales Toll Free No: 1-855-666-7446
# Correlation Coefficient Calculator
Top
Correlation coefficients determines how two variables are associated. Correlation coefficient is denoted by "r". Correlation coefficient r ranges between 1 and -1. If r = 1, then its perfect positive correlation and when r = -1, then its perfect negative correlation. If r = 0, then there is no correlation coefficient.
Correlation Coefficient Calculator finds the correlation coefficient when you plug in the two sets of variables into the calculator.
## Steps
Step 1 : Observe and note the number of sample (n).
Step 2 : Determine the value of XY, $X^2$ and $Y^2$.
Step 3 : Find the sum($\Sigma$) of X, $X^2$, Y, $Y^2$ and XY.
Step 4 : Plug in these values into the correlation coefficient formula given below and you will get the correlation value(r).
$r = \frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n(\Sigma X^{2})-(\Sigma X)^{2}][n(\Sigma Y^{2})-(\Sigma Y)^{2}]}}$
## Problems
Given below are the problems based on correlation coefficient.
### Solved Examples
Question 1: Find the value of correlation coefficient for
X value Y value 21 65 42 75 59 81 43 98 26 79
Solution:
Solution :
Step 1 : Number of sample, n = 5
Step 2 :
X values Y values XY $X^2$ $Y^2$ 21 65 1365 441 4225 42 75 3150 1764 5625 59 81 4779 3481 6561 43 98 4214 1849 9604 26 79 2054 676 6241
Step 3 :
$\Sigma X$ = 21+42+59+43+26 = 191
$\Sigma Y$ = 65+75+81+98+79 = 398
$\Sigma XY$ = 1365+3150+4779+4214+2054 = 15562
$\Sigma X^2$ = 441+1764+3481+1849+676 = 8211
$\Sigma Y^2$ = 4225+5625+6561+9604+6241 = 32256
Step 4 :
Correlation r = $\frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n(\Sigma X^{2})-(\Sigma X)^{2}][n(\Sigma Y^{2})-(\Sigma Y)^{2}]}}$
r = $\frac{5(15562)-(191)(398)}{\sqrt{[5(8211)-(191)^{2}][5(32256)-(398)^{2}]}}$
$r = 0.4941$
Question 2: Find the value of correlation coefficient for
X value Y value 1 2 3 4 5 6 7 8 9 0
Solution:
Solution :
Step 1 : Number of sample, n = 5
Step 2 :
X values Y values XY $X^2$ $Y^2$ 1 2 2 1 4 3 4 12 9 16 5 6 30 25 36 7 8 56 49 64 9 0 0 81 0
Step 3 :
$\Sigma X$ =1+3+5+7+9 = 25
$\Sigma Y$ = 2+4+6+8+0 = 20
$\Sigma XY$ = 2+12+30+56+0 = 100
$\Sigma X^2$ = 1+9+25+49+81 = 165
$\Sigma Y^2$ = 4+16+36+64+0 =120
Step 4 :
Correlation r = $\frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n(\Sigma X^{2})-(\Sigma X)^{2}][n(\Sigma Y^{2})-(\Sigma Y)^{2}]}}$
r = $\frac{5(100)-(25)(20)}{\sqrt{[5(165)-(25)^{2}][5(120)-(20)^{2}]}}$
$r = 0$ | 976 | 2,467 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2018-39 | latest | en | 0.604509 |
https://www.teacherspayteachers.com/Store/Glitter-In-Third/Category/-hearts-Google-Drive-Math-273184?aref=gl6erlth | 1,532,149,035,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676592309.94/warc/CC-MAIN-20180721032019-20180721052019-00468.warc.gz | 1,003,402,174 | 29,913 | Glitter in Third
(4,169)
United States - Virginia
4.0
You Selected:
Category
Subject
Prices
Top Resource Types
My Products
sort by:
Best Seller
view:
These digital activities will help your students understand and practice how to measure, length, volume, weight, area, perimeter, mass, and capacity. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource
Subjects:
Types:
CCSS:
\$10.00
62 ratings
4.0
These digital resources will help your students understand and practice lines, angles, symmetry, congruency/similar, polygons, and 3D solids. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also
Subjects:
Types:
CCSS:
\$10.00
49 ratings
4.0
These digital activities will give students practice to read a clock, tell time, and read time expressions. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an answer key. Save money
Subjects:
Types:
CCSS:
\$3.00
57 ratings
4.0
These digital activities will help your students understand and practice place value, comparing numbers base ten blocks, standard form, written form, and expanded form. These resources are 100% online and can be used on Google Classroom and Google
Subjects:
Types:
CCSS:
\$7.00
36 ratings
4.0
These digital activities will help your students understand and practice creating fractions on a number line. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an answer key. Save
Subjects:
Types:
CCSS:
\$4.00
33 ratings
4.0
These digital activities will help your students understand and practice money, counting coins, and making change. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an answer key.
Subjects:
Types:
CCSS:
\$6.00
30 ratings
4.0
These digital activities will help your students understand and practice fraction comparisons with the same numerator, same denominator, and different numerators and denominators. These resources are 100% online and can be used on Google Classroom
Subjects:
Types:
CCSS:
\$3.00
28 ratings
4.0
These digital activities will help your students understand and practice how to multiply, including arrays, equal groups, number lines, repeated addition, fact families, word problems, and multiplying with zeroes. These resources are 100% online and
Subjects:
Types:
CCSS:
\$6.00
32 ratings
4.0
These digital activities and online resources will help your students learn and practice bar graphs, line plots, pictographs, and line graphs. These graph resources are 100% online and can be used on Google Classroom and Google Drive. This resource
Subjects:
Types:
CCSS:
\$7.00
26 ratings
3.9
These digital fraction activities will give students understanding and practice of fractions, parts of a whole, parts of a set, and fraction representations. These resources are 100% online and can be used on Google Classroom and Google Drive. This
Subjects:
Types:
CCSS:
\$5.00
22 ratings
4.0
This online activity puts your students in the shoes of a party planner as they utilize their measurement and budgeting skills to plan a friend’s birthday party! This digital resource is 100% online and can be used on Google Classroom and Google
Subjects:
Types:
CCSS:
\$6.00
21 ratings
4.0
These online elapsed time activities and online resources will give your students a deeper understanding of elapsed time and calendars. They are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an answer
Subjects:
Types:
CCSS:
\$6.00
22 ratings
4.0
These digital properties of multiplication activities will give your students practicd of multiplication properties, including the commutative property, identity property, zero property, and associative property. These resources are 100% online and
Subjects:
Types:
CCSS:
\$3.00
18 ratings
4.0
These digital activities will help your students learn to round. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an answer key. Save money and get 30% off by purchasing this set as
Subjects:
Types:
CCSS:
\$3.00
21 ratings
4.0
These digital activities will help your students understand and practice division, including arrays, equal groups, number lines, fact families, and word problems. These resources are 100% online and can be used on Google Classroom and Google Drive.
Subjects:
Types:
CCSS:
\$6.00
18 ratings
4.0
These digital activities will allow your students to learn and practice mixed numbers and improper fractions. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an answer key. Save
Subjects:
Types:
CCSS:
\$5.00
10 ratings
4.0
These digital activities will help your students understand and practice probability, outcomes, combinations, and tree diagrams. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an
Subjects:
Types:
\$6.00
13 ratings
4.0
These digital activities will help your students to add and subtract fractions in no time. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an answer key. Save money and get 20% off
Subjects:
Types:
CCSS:
\$3.00
10 ratings
4.0
These digital equivalent fractions activities will help your students understand and practice fractions of equal value. These resources are 100% online and can be used on Google Classroom and Google Drive. This resource also includes an answer
Subjects:
Types:
CCSS:
\$3.00
13 ratings
4.0
Subjects:
Types:
CCSS:
\$8.00
17 ratings
4.0
showing 1-20 of 25
Ratings
Digital Items
4.0
Overall Quality:
4.0
Accuracy:
4.0
Practicality:
4.0
Thoroughness:
4.0
Creativity:
4.0
Clarity:
4.0
Total:
10,434 total vote(s)
TEACHING EXPERIENCE
Third-grade teacher for four years now :-)
MY TEACHING STYLE
I believe in fostering independence and giving kids responsibility, yet maintaining a warm and safe environment in which to grow.
HONORS/AWARDS/SHINING TEACHER MOMENT
MY OWN EDUCATIONAL HISTORY
I received my undergraduate in History, and my masters in elementary education.
Stay connected! Visit me at my blog!
- Blog Lovin'
- Instagram | 1,474 | 6,350 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-30 | latest | en | 0.896743 |
http://www.zweigmedia.com/RealWorld/Calcsumm3b.html | 1,555,963,534,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578582584.59/warc/CC-MAIN-20190422195208-20190422221208-00450.warc.gz | 333,991,689 | 10,076 | Applied calculus topic summary: introduction to the derivative
Tools: Function Evaluator & Grapher | Excel Grapher | Excel First and Second Derivative Grapher
Subtopics: Average Rate of Change | Derivative | Numerical Approach | Geometric Approach | Algebraic Approach | Velocity
Average Rate of Change of f(x) over [a, b]: Difference Quotient
The average rate of change of f(x) over the interval [a, b] is
Average rate of change = ΔfΔx = f(b) - f(a)b - a .
We also call this average rate of change the difference quotient of f(x) over the interval [a, b]. Its units of measurement are units of f(x) per unit of x.
Alternative Formulation: Average Rate of Change of f(x) over [a, a+h]
(Replace b above by a+h.)
The average rate of change of f(x) over the interval [a, a+h] is
Average rate of change = f(a+h) - f(a)h .
Units: The units of the average rate of change are units of f per unit of x.
Top of Page
Example
Let f(x) = 2x2 - 4x + 1. Then the average rate of change of f(x) over the interval [2, 4] is
Average rate of change = f(4) - f(2)4 - 2
= 17 - 12 = 8
Interpretation: If, say f(x) represents the annual profit of your company (in millions of dollars) and x represents the year since January 2003, then the units of measurement of the average rate of change are millions of dollars per year. Thus, your company made an average annual profit of \$8 million per year over the period January 2005 (t = 2) to January 2007 (t = 4).
Use the handy little utility below to compute the average change of the above function f(x) over other intervals. Enter the x-coordinates (a and b in the formula), leave everything else blank, and press "Compute." (You can also change the function to anything you like, using standard technology formatting.)
f(x) = a = b = Ave. Rate of Change:
You can also use the function evaluator to compute average rates of change.
Top of Page
Instantaneous Rate of Change of f(x) at x = a: Derivative
The instantaneous rate of change of f(x) at x = a is given by taking the limit of the average rates of change (computed by the difference quotient) as h approaches 0.
Instantaneous rate of change = limh→0 f(a+h) - f(a)h .
We also call this instantaneous rate of change the derivative of f(x) evaluated at x = a, and write it as f'(a) (read "f prime of a"). Its units of measurement are units of f(x) per unit of x. Thus,
f'(a) = limh→0 f(a+h) - f(a)h .
Note:
• f'(a) = Instantaneous rate of change of f at the point a.
• f'(x) = Instantaneous rate of change of f at the point x.
Hence, the derivative f'(x) is a function of x.
Since f'(x) is a limit, it may or may not exist. That is, the quantities [f(x+h) - f(x)]/h may or may not approach a fixed number as h approaches zero. If everything works out fine and the limit exists, then we say that f is differentiable at x. Otherwise, we say that f is not differentiable at x.
On this page, we summarize three ways of obtaining the derivative of a function at a point: numerical, graphical, and algebraic.
Top of Page
Examples
Let f(x) = 2x2 - 4x + 1, as above. Then the instantaneous change of f(x) at x = 2 is
f'(2) = 4.
(We shall see where this answer came from below.)
Interpretation
If, say f(x) represents the annual profit of your company (in millions of dollars) and x represents the year since January 2003, then the units of measurement of the instantaneous rate of change are millions of dollars per year. Thus, your company's annual profit was increasing at a rate of \$4 million per year at the start of 2005 (t = 2).
Top of Page
Numerical Approach
To compute an approximate value of f'(a) (for a given value of a) numerically, one can use either:
1. A table of values
2. A quick approximation
The first approach shows better and better approximations, sometimes allowing you to guess the exact value, while the second method gives a quick estimate.
Using a Table
In a table, compute a succession of values of difference quotients
f(a+h) - f(a)h
for smaller and smaller values of h, and decide what number these values are approaching. (See the example opposite.)
A Quick Approximation
Use a single small value of h and compute the difference quotient:
f'(a) ≈ f(a + 0.0001) - f(a)0.0001 Forward Difference Quotient
Here, we chose h = 0.0001. The smaller h, the better the approximation. (See the example opposite.)
Another Quick Approximation: Balanced Difference Quotient
The following formula often gives a better estimate of the derivative
f'(a) ≈ f(a+0.0001) - f(a-0.0001)0.0002 Balanced Difference Quotient
Derivative Calculator (Balanced Difference Quotient Approximation)
Enter a function, enter the point a, adjust h as you want, and press "Compute".
f(x) = a = h = f'(a)
Top of Page
Examples
Continuing with the example f(x) = 2x2 - 4x + 1, let us compute an approximate value of f'(2).
Using a Table: The difference quotient (with a = 2) is
f(2+h) - f(2)h
=
2(2+h)2-4(2+h)+1 - (2(2)2-4(2)+1)
h
The following table shows the value of this difference quotient for several values of h.
h 1 0.1 0.01 0.001 Difference Quotient 6 4.2 4.02 4.002
As h gets smaller, we see that the value gets closer and closer to 4, so we conclude
f'(2) ≈ 4.
Using A Quick Approximation (Forward Difference Quotient): We use the formula (with a = 2)
f'(2) ≈ f(2+0.0001) - f(2)0.0001 = f(2.0001) - f(2)0.0001 = 1.00040002 - 10.0001 = 4.0002.
(You could have used the little utility at the top of the page to do this calculation.)
Notice that the "quick approximation" method does not give the exact answer, but the balanced difference quotient will in this case (see opposite).
Top of Page
Geometric Approach: The Derivative as Slope
Secant and Tangent Lines
The slope of the secant line through the points on the graph of f where x = a and x = a+h is given by the slope of the line PQ in the following diagram:
msec = Slope of secant line through P and Q = f(a+h) - f(a)h
This is also the formula for the average rate of change of f over [a,a+h]. So,
Slope of Secant = Average rate of change
The slope of the tangent line through the point on the graph of f where x = a is obtained by moving the point Q closer to P; in other words, by letting h approach 0:
mtan = slope of tangent = limh→0 f(a+h) - f(a)h = f'(a)
This is also the formula for the instantaneous rate of change of f at the point a. So,
Slope of Tangent = Instantaneous rate of change = Derivative
We can approximate the slope of the tangent through the point where x = a by using the balanced difference quotient,
mtan ≈ f(a+0.0001) - f(a0.0001)0.0002 .
Zooming In
We can also interpret the derivative, or slope of the tangent, at a given point on the graph as the slope of the (almost) straight line obtained by "zooming-in" to that point on the curve.(See opposite.)
Extra Topic: Graph of the Derivative
Press here for on-line on how to obtain the graph of f' from the graph of f.
Top of Page
Examples
Continuing with the example f(x) = 2x2 - 4x + 1,
Slope of secant line through points where x = 2 and x = 3 = Average rate of change of f(x) over [2, 3] = 6 (see calculation in the table above)
Slope of tangent line through point where x = 2 = Instantaneous rate of change of f(x) at x = 2 = 4 (see quick approximation above)
Here is the graph with these two lines shown:
Zooming In
Here is an illustration of zooming in to a point on a graph where x = 0.75.
Top of Page
Computing the Derivative Algebraically
To compute the derivative of a function algebraically, proceed as follows.
1. Write down the definition of the derivative,
f'(x) = limh→0 f(x+h) - f(x)h .
2. Substitute for f(x+h) and f(x)
You can use an actual value for x if you are asked, say, to compute f'(3), or just leave it as x if you are asked for the derivative function f'(x) .
3. Simplify the numerator in order to factor out an "h." Then cancel the "h"s and take the limit to obtain the answer.
Sometimes, you need to do more than just simplify the numerator...
Top of Page
Example
Going back to our first example, f(x) = 2x2 - 4x + 1, let us now calculate f'(x) algebraically by following the steps in the adjacent window.
f'(x) = limh→0 f(x+h) - f(x)h
= limh→0 (2(x+h)2-4(x+h)+1) - (2x2-4x+1) h
= limh→0 2x2+4xh+2h2-4x-4h+1-2x2+4x-1h
= limh→0 4xh+2h2-4hh
= limh→0 h(4x+2h-4)h
= limh→0 (4x+2h-4)
=4x-4
Thus, f'(x) = 4x-4.
Go to the tutorial on average rates of change for practice in computing average rates of change algebraically (what we did above up to the last step), or to tutorial on computing the derivative algebraically and scroll down to the box called "Computing the Derivative Algebraically." The "Help" button brings up the complete solution.
Top of Page
Velocity
For an object moving in a straight line with position s(t) at time t, the average velocity from time t to time t+h is given by the difference quotient
vaverage = s(t+h) - s(t)h .
The instantaneous velocity at time t is given by
v(t) = s'(t) = limh→0 s(t+h) - s(t)h .
Top of Page
Examples
Suppose the position of a moving object is given by
s(t) = t2 -2t+4 miles
at time t hours. Then its velocity at time t is given by
s'(t) = 2t-2 miles per hour.
Thus, for example, its velocity at time t = 3 hours is
s'(3) = 4 miles per hour.
Top of Page
Last Updated: April 2010 | 2,647 | 9,286 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2019-18 | latest | en | 0.893177 |
http://asvabpracticetest.org/register-kaplan-asvab-book-interpreting-asvab-composite-scores-asvabpracticetestorg.html | 1,542,306,672,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039742906.49/warc/CC-MAIN-20181115182450-20181115204450-00257.warc.gz | 31,203,780 | 10,852 | The Armed Services Vocational Aptitude Battery (ASVAB) is one of the most widely used multiple-aptitude test batteries in the world. It was originally designed to predict success in military occupations and is used today to help both those considering entering the military (mostly high school-aged students, but also anyone who is eligible to enlist) as well as those not interested in military service (who comprise the majority of current ASVAB test takers) what sort of career may be the best fit for them. Scores from the ASVAB can be used when enlisting in the military. Students interested in taking the ASVAB should check with their high school to find out when and if the ASVAB will be offered at their school. If it is not offered, students should meet with their guidance counselor to determine if it is possible to schedule a testing session in the future. There is no cost to take the ASVAB.
Arithmetic Reasoning tests the ability to solve basic arithmetic problems encountered in everyday life. One-step and multistep word problems require addition, subtraction, multiplication, division and choosing the correct order of operations when more than one step is necessary. The items include operations with whole numbers, operations with rational numbers, ratio and proportion, interest, percentage and measurement. Arithmetic Reasoning is one factor that helps characterize mathematics comprehension, and it also assesses logical thinking.
The way to prepare for this exam is study hard and then quiz yourself with plenty of practice ASVAB tests. Remember that the exam is identical for all branches, so an Army ASVAB practice test is exactly the same as an ASVAB practice test for the Navy. The most important components of the test are the ones that count towards the Armed Services Qualifications Test, or AFQT. These sections are Word Knowledge, Paragraph Comprehension, Arithmetic Reasoning, and Math Knowledge. For tips and strategies for success on these questions, be sure to review our article on ASVAB Test Prep.
The Ultimate ASVAB Practice Pack provides you three full-length ASVAB practice tests with answer key and unlimited access to the ASVAB Online Practice Center. Modeled After the CAT-ASVAB with over 2000 questions in the question pool – each practice test is different every time you take it. See your AFQT score and Subtest scores at the end of each practice test. Track your scores and history online to monitor your progress and watch your scores increase! 100% Satisfaction Guaranteed.
Since 1976, the multiple-choice ASVAB has been used for initial aptitude screening as well as MOS classification. The exam has changed since its inception. While some parts have remained, such as arithmetic reasoning and word knowledge, others like tool knowledge have been removed in favor of questions related to assembling objects. After nearly 20 years of research and development, a computer-adaptive version of the exam was implemented in 1996. The CAT-ASVAB is the first large-scale adaptive battery test to be administered in high-stakes environments like a Military Entrance Processing Station. The paper and pencil, or P&P version is still used at a variety of other military testing sites.
Once the ASVAB is over, participants are given a score. This score is used by recruiters to determine which branch of the military would be a good fit for a given test-taker. The most important score for the ASVAB for military purposes is the AFQT score. The AFQT score looks at results from the following sections: Arithmetic Reasoning (AR), Math Knowledge (MK), and multiplies the Verbal Composite (VE) score by two. This is because the Verbal Composite Score is composed of both the Word Knowledge and the Paragraph Comprehension scores. Each branch of the military requires a different minimum AFQT score for its members. For the army and marines, this number is 31, for the navy 35, the air force 36, and the coast guard 45. Therefore, this test is a crucial part of any military career, and can determine potential jobs and advancement opportunities. Along with advancement opportunities come higher salaries and greater benefits, which makes the ASVAB an essential element for prospective military service personnel at any level.
## The Mechanical Comprehension section of the ASVAB practice test measures your understanding of basic mechanical principles and mechanisms. You may be asked why an intake valve on a pump opens when the piston goes down, or what direction friction is going when shown a diagram of a skier. The CAT-ASVAB has 16 questions in 20 minutes; the paper-and-pencil version has 25 questions in 19 minutes.
In 1974, the first six women naval aviators earned their wings as Navy pilots. The Congressionally mandated prohibition on women in combat places limitations on the pilots' advancement,[36] but at least two retired as captains.[37] In 1989, Captain Linda L. Bray, 29, became the first woman to command American soldiers in battle during the invasion of Panama. The 1991 Gulf War proved to be the pivotal time for the role of women in the U.S. Armed Forces to come to the attention of the world media; there are many reports of women engaging enemy forces during the conflict.[38]
You’ll find a great practice test and lots of other information about the ASVAB at the Department of Defense's ASVAB Career Exploration Program site (ASVABprogram.com). Since your test scores can have an impact on your Military Occupational Specialty (MOS)—and whether or not you can attend certain special schools (like Airborne school, Sniper school and many others)—we recommend you make the most of these additional resources.
The rapid growth of movable type in the late 16th century and early 17th century saw an upsurge in private publication. Political pamphlets became popular, often lampooning military leaders for political purposes. A pamphlet directed against Prince Rupert of the Rhine is a typical example. During the 19th century, irreverence towards authority was at its height, and for every elegant military gentleman painted by the master-portraitists of the European courts, for example, Gainsborough, Goya, and Reynolds, there are the sometimes affectionate and sometimes savage caricatures of Rowland and Hogarth.
### You can take the test as a junior or senior in high school and use the score to enlist, provided that you are at least 17 years old and took the test no earlier than 2 years before you begin enlistment processing. If you are at least 17, you can take the test at a Military Processing Station (MEP) or a satellite Military Entrance Test (MET) location.
Doing poorly on the ASVAB might mean missing out on the military job that you really want- and maybe not getting in the military at all. If you’re stressed about taking the ASVAB, don’t worry- we’ve got you covered! Our free study guides for the ASVAB will give you an overview of the concepts you need to know and will help you pinpoint the areas you should spend your time studying. From Arithmetic Reasoning to Word Knowledge and every subject in between, our study guides for the ASVAB will help you get the ASVAB score that you need!
The Electronics Information section of the practice test gauges your knowledge of electrical equipment and parts, including circuits, currents, batteries, and resistors. An example may be, “Because solid state diodes have no filament, they: don’t work, are less efficient than tubes, require less operating power, or require more operating power?” The CAT-ASVAB has 16 questions in 8 minutes; the paper-and-pencil version has 20 questions in 9 minutes.
This advice, though well-intentioned, doesn’t address the needs of some new recruits who are interested in specific career fields but are worried about their test performance-especially in areas related to math comprehension. Potential recruits who feel deficient in math, language, or science skills should have a frank conversation with their recruiter to discuss possible refresher study or even supplemental classes in any self-perceived “problem areas” before taking the test.
The President, Secretary of Defense and other senior executive officials are advised by a seven-member Joint Chiefs of Staff, which is headed by the Chairman of the Joint Chiefs of Staff, the highest-ranking officer in the United States military and the Vice Chairman of the Joint Chiefs of Staff.[20] The rest of the body is composed of the heads of each of the DoD's service branches (the Chief of Staff of the Army, the Chief of Naval Operations, the Commandant of the Marine Corps and the Chief of Staff of the Air Force) as well as the Chief of the National Guard Bureau. Although commanding one of the five military branches, the Commandant of the Coast Guard is not a member of the Joint Chiefs of Staff. Despite being composed of the highest-ranking officers in each of the respective branches, the Joint Chiefs of Staff does not possess operational command authority. Rather, the Goldwater-Nichols Act charges them only with advisory power.[21]
Somewhat earlier, in medieval China, gunpowder had been invented, and was increasingly used by the military in combat. The use of gunpowder in the early vase-like mortars in Europe, and advanced versions of the long bow and cross bow, which all had armour-piercing arrowheads, that put an end to the dominance of the armoured knight. After the long bow, which required great skill and strength to use, the next most significant technological advance was the musket, which could be used effectively, with little training. In time, the successors to muskets and cannon, in the form of rifles and artillery, would become core battlefield technology.
The first recorded use of the word military in English, spelled militarie, was in 1585.[2] It comes from the Latin militaris (from Latin miles, meaning "soldier") through French, but is of uncertain etymology, one suggestion being derived from *mil-it- – going in a body or mass.[3][4] The word is now identified as denoting someone that is skilled in use of weapons, or engaged in military service, or in warfare.[5][6]
The military uses the verbal expression (VE) score to measure your communicative ability. The score goes toward computing the AFQT score as well as many of the military’s line scores. The military brass determine your VE score by first adding the value of your Word Knowledge (WK) raw score to your Paragraph Comprehension (PC) raw score. The result is then converted to a scaled score ranging from 20 to 62.
## A military recruiter determines if the candidate is a possible recruit. A recruiter will ask about marital status, health, education, drug use, and arrest record. It is important for the candidate to be upfront and truthful when answering questions. Once the recruiter has determined the individual is qualified for additional processing, the ASVAB is scheduled. A physical examination may also be conducted at the time of the test.
The underlying model used for the ASVAB is a three-parameter logistic (3PL) model. This model represents the probability that an examinee at a given level of ability will respond correctly to an individual item with given characteristics. The characteristics used are difficulty, discrimination and guessing (this refers to the likelihood that a very low ability examinee would respond correctly simply by guessing).
ASVAB CEP test results are sent to students’ schools so they can explore career options with counselors. The scores show how well the student did on each subject, and how they compare with others who took the test. There are three composite scores in Verbal, Math, and Science and Technical skills, and the Armed Forces Qualification Test (AFQT) score is also reported.
The Armed Forces Qualification Test (AFQT) is used by all of the Services to determine if an applicant is eligible for the military. Four of the ASVAB subtests are combined to form the AFQT. It measures general cognitive ability and is composed of verbal and mathematics subtests. AFQT scores are grouped into categories for reporting purposes. The table below shows the AFQT categories and the percentile score ranges corresponding to the categories. Applicants that score in AFQT category IIIA or higher may qualify for enlistment incentives.
#### Since then, the advances made by human societies, and that of weapons, has been irretrievably linked. Stone weapons gave way to Bronze Age weapons, and later, the Iron Age weapons. With each technological change, was realised some tangible increase in military capability, such as through greater effectiveness of a sharper edge in defeating leather armour, or improved density of materials used in manufacture of weapons.
The President of the United States is the Commander in Chief, who is responsible for all final decisions. The Secretary of the Department of Defense (DoD) has control over the military and each branch - except the Coast Guard, which is under the Dept. of Homeland Security. With over 2 million civilian and military employees, the DoD is the world's largest "company."
Using the right ASVAB study guide is an important factor in determining how well you will do on the exam. Each branch of the U.S. Military requires you take an ASVAB (Armed Services Vocational Aptitude Battery) exam. Your scores on the ASVAB determine not only your entrance into the military, but also your job, advancement opportunities, and potential salary. The ASVAB exam consists of questions in ten different areas, but in general, the exam is measuring your aptitude in four key areas: Math, Verbal, Science and Technical, and Spatial. To efficiently prepare for your ASVAB exam, check out our recommended study guides, our free practice exams, our ASVAB flash cards, and our ASVAB study tips.
Your success on ASVAB test day depends not only on how many hours you put into preparing, but also on whether you prepared the right way. It’s good to check along the way to see whether your studying is paying off. One of the most effective ways to do this is by taking ASVAB practice tests to evaluate your progress. Practice tests are useful because they show exactly where you need to improve. Every time you take a ASVAB practice test, pay special attention to these three groups of questions:
You often hear people say something like, "I got a 70 on the ASVAB." What they are talking about is the ASVAB AFQT score or Armed Forces Qualification Test Score. Many people think the AFQT score is the overall ASVAB score, but that's not correct. In fact, the AFQT score is derived from only four of the nine ASVAB subtests: Paragraph Comprehension (PC), Word Knowledge (WK), Mathematics Knowlege (MK), and Arithmetic Reasoning (AR).
Test scores provide only one measure of your skills and abilities. Test scores and grades, combined with information about your interests, values, skills, and achievements may help you select appropriate occupations for career exploration. As you explore careers, you can compare your skills with the skill requirements of occupations in which you are interested.
After a candidate has completed the ASVAB they must wait one calendar month before retaking the exam. An additional calendar month must pass before retesting a second time. Six calendar months must pass before retaking the test a third time. The scores received from the ASVAB may be used for enlistment for up to two years from the initial test date.
A good score on the ASVAB is different than a minimum required score. Each of the military branches will have their own minimum required scores (see below). In practice, however, each branch will be more selective in their recruiting. A score of 50 on the ASVAB implies that you scored as well or better than 50% of comparable test-takers. Since ASVAB scores are used for many purposes (e.g., enlistment eligibility, military job placements, and career exploration), it is important that you score well on the ASVAB. A score of 60 or better should be your minimum target.
## Achieving the minimum required AFQT score established by an individual branch gets your foot in the door, but the higher you score, the better. For example, if you need a medical or criminal history waiver in order to enlist, the military personnel who make those decisions are more likely to take a chance on you if they think you’re a pretty smart cookie.
SEPTEMBER 27, 2018 – The Army’s most important weapons system is the Soldier. To overmatch the enemy in multi-domain operations, Soldiers must demonstrate physical fitness levels required for combat. The Army Combat Fitness Test ensures that Soldiers are physically conditioned for that fight. The ACFT will improve lethality, transform the Army’s physical fitness culture, reduce […]
Sergeant Leigh Ann Hester became the first woman to receive the Silver Star, the third-highest U.S. decoration for valor, for direct participation in combat. In Afghanistan, Monica Lin Brown was presented the Silver Star for shielding wounded soldiers with her body.[45] In March 2012, the U.S. military had two women, Ann E. Dunwoody and Janet C. Wolfenbarger, with the rank of four-star general.[46][47] In 2016, Air Force General Lori Robinson became the first female officer to command a major Unified Combatant Command (USNORTHCOM) in the history of the United States Armed Forces.[48]
NOVEMBER 9, 2018 – The U.S. Small Business Administration (SBA) is celebrating the accomplishments of veteran, service member and military spouse small business owners nationwide during National Veterans Small Business Week (NVSBW), Nov. 5-9. SBA offers a Boots to Business (B2B) entrepreneurship training program as one of the Department of Defense’s (DoD) Transition Assistance Program […]
Including U.S. territories and ships afloat within territorial waters As of 31 December 2009, a total of 1,137,568 personnel were on active duty within the United States and its territories (including 84,461 afloat).[31] The vast majority (941,629 personnel) were stationed at bases within the contiguous United States. There were an additional 37,245 in Hawaii and 20,450 in Alaska while 84,461 were at sea, 2,972 in Guam and 179 in Puerto Rico.
If you are pressed for time, it may be worthwhile to look into future ASVAB test dates in order to plan ahead in case you get a poor score on your upcoming ASVAB test. You can check with your high school counselor or your military recruiter to make sure that you will be eligible to take future tests along with your planned upcoming test date in the event that you get a bad ASVAB score.
In order to perform well on the ASVAB, you should take a practice test to get an idea of what you’ll encounter on the actual test. Also, completing a practice test will help you to feel more at ease on test day. Reading the test instructions and focusing your full attention on each question are both important steps to take. As you work through the test, avoid spending too much time on a single question. The test has a time limit and you don’t want to fall into the trap of running out of time before you arrive at the end of the test. Taking the time to provide thoughtful answers to test questions allows you to offer a clear picture of your skills and capabilities. Earning a high score on the ASVAB may give you more options when it comes to choosing a specialty.
The U.S. Armed Forces are one of the largest militaries in terms of the number of personnel. It draws its personnel from a large pool of paid volunteers. Although conscription has been used in the past in various times of both war and peace, it has not been used since 1972, but the Selective Service System retains the power to conscript males, and requires that all male citizens and residents residing in the U.S. between the ages of 18–25 register with the service.[11]
The CAT-ASVAB is an adaptive test which means the test adapts to the ability of the test-taker. It is possible to administer a shorter test this way than with the pencil and paper test. When you complete a subsection of the test, you can then move onto the next section of the test without having to wait for an administrator. Subsections are still timed however and on average it takes about 1 ½ hours to complete the computer ASVAB.
The Armed Services Vocational Aptitude Battery (ASVAB) is a comprehensive test that helps determine students’ eligibility and suitability for careers in the military. Students who score in the 31st percentile are eligible for a wide variety of careers (combined with standards such as physical condition and personal conduct). Students and schools are also encouraged to take advantage of a free career exploration program that links personal interests with demonstrated aptitudes from the 9 ASVAB subtests, half of which relate to vocational skills, in addition to math and verbal skills. | 4,363 | 20,885 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2018-47 | latest | en | 0.939985 |
https://gist.github.com/endolith/114336?permalink_comment_id=2921104 | 1,722,726,444,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640380725.7/warc/CC-MAIN-20240803214957-20240804004957-00386.warc.gz | 216,568,563 | 25,591 | Instantly share code, notes, and snippets.
# endolith/gcd_and_lcm.py
Last active June 22, 2022 23:33
Show Gist options
• Save endolith/114336 to your computer and use it in GitHub Desktop.
GCD and LCM functions in Python for several numbers
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode characters
# Greatest common divisor of 1 or more numbers. from functools import reduce def gcd(*numbers): """ Return the greatest common divisor of 1 or more integers Examples -------- >>> gcd(5) 5 >>> gcd(30, 40) 10 >>> gcd(120, 40, 60) 20 """ # Am I terrible for doing it this way? from math import gcd return reduce(gcd, numbers) # Least common multiple is not in standard libraries? It's in gmpy, but this # is simple enough: def lcm(*numbers): """ Return lowest common multiple of 1 or more integers. Examples -------- >>> lcm(5) 5 >>> lcm(30, 40) 120 >>> lcm(120, 40, 60) 120 """ def lcm(a, b): return (a * b) // gcd(a, b) return reduce(lcm, numbers, 1) # Assuming numbers are positive integers...
### vloddos commented May 19, 2019
I think there should be floordiv instead of truediv in your lcm
```import math
def lcm(a, b):
return int(a * b / math.gcd(a, b))
print(lcm(2, 6))```
### yegane-AI commented Jul 23, 2019
Great code! Can you plz explain me how does GCD works in your program?
### VisionOra commented Jun 13, 2020
Use this line of code to take LCM. Its fast and give you LCM of multiple numbers
``````import numpy as np
divisor_list = [3,4,5,6,7,2]
int(np.lcm.reduce(divisor_list))
``````
### yegane-AI commented Jun 13, 2020
Use this line of code to take LCM. Its fast and give you LCM of multiple numbers
``````import numpy as np
divisor_list = [3,4,5,6,7,2]
int(np.lcm.reduce(divisor_list))
``````
Thanks alot
### astrojuanlu commented Jun 9, 2021
It's not mentioned here, but this is the Euclidean algorithm for computing the GCD: https://en.wikipedia.org/wiki/Euclidean_algorithm
Love how short the code is!
### naemazam commented Sep 26, 2021
def find_gcd(a,b):
gcd = 1
for i in range(1,a+1):
if a%i==0 and b%i==0:
gcd = i
return gcd
first = int(input('Enter first number: '))
second = int(input('Enter second number: '))
print('HCD of %d and %d is %d' %(first, second, find_gcd(first, second)))
lcm = first * second / find_gcd(first, second)
print('MCM of %d and %d is %d' %(first, second, lcm))
print("azam") | 743 | 2,537 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2024-33 | latest | en | 0.845174 |
https://latex2e.org/_005cmultiput.html | 1,721,269,858,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514816.43/warc/CC-MAIN-20240718003641-20240718033641-00098.warc.gz | 294,451,336 | 3,010 | 8.19.2 \multiput ¶
Synopsis:
\multiput(x,y)(delta_x,delta_y){num-copies}{obj}
Copy obj a total of num-copies times, with an increment of delta_x,delta_y. The obj first appears at position (x,y), then at (x+\delta_x,y+\delta_y), and so on.
This draws a simple grid with every fifth line in bold (see also \graphpaper).
\begin{picture}(10,10)
\linethickness{0.05mm}
\multiput(0,0)(1,0){10}{\line(0,1){10}}
\multiput(0,0)(0,1){10}{\line(1,0){10}}
\linethickness{0.5mm}
\multiput(0,0)(5,0){3}{\line(0,1){10}}
\multiput(0,0)(0,5){3}{\line(1,0){10}}
\end{picture} | 221 | 563 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2024-30 | latest | en | 0.509384 |
https://www.coursehero.com/file/85664/chap42/ | 1,495,600,364,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463607786.59/warc/CC-MAIN-20170524035700-20170524055700-00337.warc.gz | 894,488,962 | 24,811 | # chap42 - 42.1 a K J 10 38 1 3 eV J 10 60 1 eV 10 9 7 2 3 2...
This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: 42.1: a) K) J 10 38 . 1 ( 3 ) eV J 10 60 . 1 )( eV 10 9 . 7 ( 2 3 2 2 3 23 19 4--- × × × = = ⇒ = k K T kT K K 1 . 6 = ⇒ T b) K. 600 , 34 ) K J 10 38 . 1 ( 3 ) eV J 10 60 . 1 ( ) eV 48 . 4 ( 2 23 19 = × × =-- T c) The thermal energy associated with room temperature (300 K) is much greater than the bond energy of 2 He (calculated in part (a)), so the typical collision at room temperature will be more than enough to break up . He 2 However, the thermal energy at 300 K is much less than the bond energy of 2 H , so we would expect it to remain intact at room temperature. 42.2: a) . eV . 5 4 1 2- =- = r e πε U b) . eV 2 . 4 ) eV 5 . 3 eV 3 . 4 ( eV . 5- =- +- 42.3: Let 1 refer to C and 2 to O. nm 1128 . , kg 10 656 . 2 , kg 10 993 . 1 26 2 26 1 = × = × =-- r m m ) carbon ( nm 0644 . 2 1 2 1 = + = r m m m r ) carbon ( nm 0484 . 2 1 1 2 = + = r m m m r b) ; m kg 10 45 . 1 2 46 2 2 2 2 1 1 ⋅ × = + =- r m r m I yes, this agrees with Example 42.2. 42.4: The energy of the emitted photon is , eV 10 01 . 1 5- × and so its frequency and wavelength are GHz 44 . 2 ) s J 10 63 . 6 ( ) eV J 10 60 . 1 )( eV 10 01 . 1 ( 34 19 5 = ⋅ × × × = =--- h E f . m 123 . Hz) 10 44 . 2 ( ) s m 10 00 . 3 ( λ 9 8 = × × = = f c This frequency corresponds to that given for a microwave oven. 42.5: a) From Example 42.2, 2 46 23 1 m kg 10 449 . 1 and J 10 674 . 7 meV 479 . ⋅ × = × = =-- I E s rad 10 03 . 1 2 gives and 12 1 2 2 1 × = = = = I E ω E K Iω K b) (carbon) s m 3 . 66 ) s rad 10 03 . 1 )( m 10 0644 . ( 12 9 1 1 1 = × × = =- ω r v (oxygen) s m 8 . 49 ) s rad 10 03 . 1 )( m 10 0484 . ( 12 9 2 2 2 = × × = =- ω r v c) s 10 6.10 2 12- × = = ω π T 42.6: a) J 10 083 . 2 ) eV 2690 . ( 2 1 2 1 20- × = = = ω E K s m 10 91 . 1 kg 10 139 . 1 ) J 10 083 . 2 ( 2 2 gives 2 1 3 26 2 r max 2 max r × = × × = = =-- m E v v m E b) According the Eq. 42.7 the spacing between adjacent vibrational energy levels is twice the ground state energy: . , ) 2 1 ( 1 hf ω E E E ω n E n n n = =- = ∆ + = + Thus, using the E ∆ specified in Example 42.3, it follows that its vibrational period is s. 10 54 . 1 ) eV J 10 60 . 1 )( eV 2690 . ( ) s J 10 63 . 6 ( 1 14 19 34--- × = × ⋅ × = ∆ = = E h f T c) The vibrational period is shorter than the rotational period. 42.7: a) 2 H Li H Li 2 r r m m m m r m I + = = eV. 10 53 . 7 J 10 20 . 1 m kg 10 69 . 3 ) s J 10 054 . 1 ( 4 4 )) 1 3 ( ) 3 ( ) 1 4 ( 4 ( 2 m kg 10 69 . 3 ) kg 10 67 . 1 kg 10 17 . 1 ( ) m 10 59 . 1 )( kg 10 67 . 1 )( kg 10 17 . 1 ( 3 21 2 47 2 34 2 2 3 4 2 47 27 26 2 10 27 26---------- × = × = ∆ ⇒ ⋅ × ⋅ × = ∆ ⇒ = +- + =- = ∆ ⋅ × = × + × × × × = E E I I E E E K K b) . m 10 66 . 1 λ J 10 20 . 1 s) m 10 00 . 3 )( s J 10 63 . 6 ( λ 4 21 8 34--- × = ⇒ × × ⋅ × = ∆ = E hc 42.8: Each atom has a mass m and is at a distance 2 L from the center, so the moment of inertia is . m kg...
View Full Document
## This homework help was uploaded on 04/08/2008 for the course PHY 205 taught by Professor Nearing during the Fall '07 term at University of Miami.
### Page1 / 21
chap42 - 42.1 a K J 10 38 1 3 eV J 10 60 1 eV 10 9 7 2 3 2...
This preview shows document pages 1 - 4. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online | 1,619 | 3,640 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2017-22 | longest | en | 0.788587 |
https://www.bath.ac.uk/announcements/having-your-christmas-cake-and-eating-it-fairly/ | 1,721,502,708,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517515.18/warc/CC-MAIN-20240720174732-20240720204732-00325.warc.gz | 561,214,884 | 6,562 | Christmas day and family tiffs. They belong together like baubles and spruces, or crackers and bad jokes. The remote control, the washing-up bowl, the PlayStation console – the trigger points for an intergenerational meltdown are as plentiful as raisins in a Christmas cake.
Talking of cake. Can this at least be a source of goodwill over the festive season, or are we destined to be divided into camps here too: the gluttons who swipe the fattest slices pitted against the martyrs who are left with the (marzipan-free) crumbs?
The University of Bath brings good tidings on this front. Mathematician Professor Chris Budd OBE is keen to spread the word that the cherished Christmas cake can be cut into perfectly equal pieces, bringing hope that harmony can spread in households across the land.
Traditionally, the “you cut, I choose” algorithm has been seen as the fairest method of slicing a cake if you have two people. The way this works is that one person slices the cake as fairly as they can, and the second person gets first dibs. The reasoning behind this technique is that it’s clearly in the interests of the first person to cut the cake as fairly as possible, so that no matter how the second person chooses, the remaining piece will be as close as possible to half of the original. Though this may sound fair, Professor Budd points out that it gives overwhelming advantage to the person who has the first choice.
“Suppose that the cake cutter is blind,” said Professor Budd. “Despite their best efforts to cut the cake fairly, it is very unlikely the slices they cut will be equal. The chooser will then take the largest piece.
“This situation will always arise if the ability of the chooser to decide which piece is larger, is greater than the ability of the cutter to divide the cake into two equal pieces.”
The only fair way to cut Christmas cake
This is how we can do better: The first person makes a cut across the cake. There are now two portions of cake. Assuming the cutter is not an expert, one piece will be smaller than the other. By placing the two slices side-by-side, the smaller one will be easy to spot. Keeping them together, it will be simple to trim the larger slice so the two match in size. This leaves two pieces that are exactly the same size, plus a new small piece. Each person then takes one of the two identical slices of cake. Now they have a much smaller slice of cake to divide. By repeating the process on the new piece, they will be left with two (much smaller) identical pieces plus an even smaller trimmed piece.
“Then all they have to do is keep repeating this process until only crumbs are left – bingo!”
This slicing technique can easily be extended if there are more than two people wanting to eat the cake, as is usually the case, said Professor Budd, who specialises in bringing creative mathematical solutions to problems arising in industry (and dessert-loving households).
How to cut your Christmas cake fairly
The maths of Christmas
Christmas cake is just one of the topics that feature in Professor Budd’s seasonal talk, A Mathematical Christmas Stocking, delivered this week to a large online audience in an event organised by the International Centre for the Mathematical Sciences (ICMS) in Edinburgh. And apparently there is more to good cake etiquette than fair slicing.
“This year, I’m particularly concerned about the way people dry out their cake by exposing the soft interior to the drying air,” he said, “This too comes down to poor cutting technique.”
The ordinary way of attacking a Christmas cake is to cut out a wedge and then divide this into smaller chunks, but this method is clearly flawed, as the remaining cake is left open to the elements.
A far better technique – first proposed in 1906 by polymath Sir Francis Galton in the highly respected journal Nature and now promoted in Professor Budd’s Christmas talk – involves removing a long, narrow wedge of cake from near the middle of the cake by making two straight cuts across the cake, close to (and equidistant from) the centre. Once this rectangular wedge has been removed, it can be cut into smaller rectangles and shared around. The two remaining segments of cake can then be pressed together and sealed with an elastic band around the perimeter. With no exposed surfaces, the cake can then be stored exactly as it is.
The next time cake is called for, a similar (but smaller) wedge can be removed by slicing the cake in two places at a right angle to the first two cuts. Again, the two remaining segments can be pressed together, maintaining the round-ish shape of the original cake, thereby sealing it.
“And so the slicing should continue, with about one-third of the cake being removed on each occasion until you are left with crumbs,” said Professor Budd.
He added: “Of course, you’ll be back to the problem we started with of cutting each wedge into even slices to keep it fair, but at least you won’t find yourself munching through dried-out cake two months after Christmas.”
How to cut your cake to keep it moist | 1,036 | 5,070 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.484375 | 3 | CC-MAIN-2024-30 | latest | en | 0.961253 |
https://studysoup.com/tsg/18315/discrete-mathematics-and-its-applications-7-edition-chapter-4-4-problem-1e | 1,653,286,664,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662555558.23/warc/CC-MAIN-20220523041156-20220523071156-00623.warc.gz | 602,809,599 | 11,895 | ×
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.4 - Problem 1e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.4 - Problem 1e
×
# Show that 15 is an inverse of 7 modulo 26.
ISBN: 9780073383095 37
## Solution for problem 1E Chapter 4.4
Discrete Mathematics and Its Applications | 7th Edition
• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants
Discrete Mathematics and Its Applications | 7th Edition
4 5 1 350 Reviews
22
4
Problem 1E
Show that 15 is an inverse of 7 modulo 26.
Step-by-Step Solution:
Step 1 of 2
In this question we have to show that 15 is an inverse of 7 modulo 26 .
Let $$\mathrm{a}$$ and $$\mathrm{b}$$ be the two integers such that
Such that $$\mathrm{a}$$ and $$\mathrm{b}$$ are inverses of each other
That is, $$a b=1(\bmod m)$$
Step 2 of 2
#### Related chapters
Unlock Textbook Solution | 295 | 1,001 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2022-21 | latest | en | 0.742776 |
https://www.cpalms.org/Public/PreviewStandard/Preview/1840 | 1,723,438,435,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641028735.71/warc/CC-MAIN-20240812030550-20240812060550-00050.warc.gz | 548,052,463 | 19,522 | # SC.8.P.8.2
Differentiate between weight and mass recognizing that weight is the amount of gravitational pull on an object and is distinct from, though proportional to, mass.
General Information
Subject Area: Science
Body of Knowledge: Physical Science
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: Properties of Matter - A. All objects and substances in the world are made of matter. Matter has two fundamental properties: matter takes up space and matter has mass which gives it inertia.
B. Objects and substances can be classified by their physical and chemical properties. Mass is the amount of matter (or "stuff") in an object. Weight, on the other hand, is the measure of force of attraction (gravitational force) between an object and Earth.
The concepts of mass and weight are complicated and potentially confusing to elementary students. Hence, the more familiar term of "weight" is recommended for use to stand for both mass and weight in grades K-5. By grades 6-8, students are expected to understand the distinction between mass and weight, and use them appropriately.
Clarification for grades K-2: The use of the more familiar term ‘weight’ instead of the term “mass” is recommended for grades K-2.
Clarification for grades 3-5: In grade 3, introduce the term mass as compared to the term weight. In grade 4, investigate the concept of weight versus mass of objects. In grade 5, discuss why mass (not weight) is used to compare properties of solids, liquids and gases.
Date of Last Rating: 05/08
Status: State Board Approved
Assessed: Yes
## Related Courses
This benchmark is part of these courses.
2002100: M/J Comprehensive Science 3 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002110: M/J Comprehensive Science 3, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2003010: M/J Physical Science (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2003020: M/J Physical Science, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7820017: Access M/J Comprehensive Science 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2023, 2023 and beyond (current))
2002055: M/J Comprehensive Science 1 Accelerated Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
## Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
SC.8.P.8.In.2: Recognize that the weight of an object is related to the pull of gravity.
SC.8.P.8.Su.2: Compare the weight of different sized objects.
SC.8.P.8.Pa.2: Recognize the heavier of two objects.
## Related Resources
Vetted resources educators can use to teach the concepts and skills in this benchmark.
## Educational Software / Tool
Density: Sea Water Mixing & Sinking:
This is an excellent resource for teachers and students that provides student sheets, data graphs, vocabulary, and teacher notes as well as Big Ideas, Essential Questions, Data Tables, Formative Assessment questions - extremely teacher friendly who need assistance on this Big Idea and Concept. (The Preconceptions were helpful to my students.)
Type: Educational Software / Tool
## Lesson Plans
Scout Robot: Mass, Density, Volume, Weight:
In this MEA, students must select which material to use in the development of an advanced military scout robot. Students must analyze data about each material’s individual properties that would make it a valid choice for military or police service. Students must complete calculations to determine material density as well as the overall mass and weight of the robot. This lesson focuses on the characteristic properties of density, unit conversion, and differentiating between mass and weight.
Type: Lesson Plan
Edible Mass vs. Weight:
Students will experiment with edibles (fun size Snickers candy bar, Oreo cookie, and Peppermint Puff candy) to measure their mass and calculate their weight on different planets. Students will be able to differentiate between weight and mass recognizing that weight is the amount of gravitational pull on an object and is distinct from, though proportional to, mass.
Type: Lesson Plan
"Weight! What's the Mass?":
The lesson will teach students the difference between mass and weight with a hands-on activity and instruction. Students will simulate a reduction in gravity (i.e. a reduction in an object's weight) using water's buoyancy. The research question that the students will address is: "Will an object's mass and weight differ in and out of water?"
Teachers Note: Prior to the lesson be sure that the balances that are to be used can be submerged in water and that they balance to horizontal or zero out while in water. Different manufacturers and materials may prohibit the use of certain balances underwater since different materials may have different buoyancies that may impact the use of the balance underwater. Please note that there is an optional variation of the activity that uses a 1000 mL beaker instead and does not require the balance to be submerged.
Type: Lesson Plan
NASA: Roving for the right wheel! 3D + MEA:
In this Model-Eliciting Activity (MEA), students will evaluate wheel designs from different companies to determine which wheel is appropriate for the mission. Further 3D printing is integrated by 3D printing different wheel models which can be directly tested using a LEGO Mindstorms Robot or Simple Rubber Band Powered Sled and different Regolith Simulants for the Moon and Titan.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
Type: Lesson Plan
Glider Challenge:
In this Model-Eliciting Activity (MEA), students will select a glider model that will meet the needs of a Summer Space Camp program.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
Type: Lesson Plan
Force (Weight versus Mass): Newton's 2nd Law:
Students will examine the relationships between mass, force and acceleration, applying Newton's 2nd Law.
This is part 2 of a two-part lab. It is recommended that the teacher cover the first lesson (, ID 51003) prior to completing this lesson.
Type: Lesson Plan
Mass/Weight Connection:
Students will recognize that the mass of an object is a measure that is independent of gravity. If they can effectively complete the guided inquiry activity as well as the short writing summary to reinforce what they learned, they will gain a foundation for understanding the difference between mass and weight.
Type: Lesson Plan
## Original Student Tutorial
Mass and Weight: What's the Difference?:
Differentiate between weight and mass, recognizing that weight is the amount of gravitational pull on an object and is distinct though proportional to mass. In this interactive tutorial you'll help a curious chicken learn more about this important topic.
Type: Original Student Tutorial
## Tutorial
Mass and Weight Clarification:
This tutorial covers the difference between mass and weight.
Type: Tutorial
## Unit/Lesson Sequence
Middle School Chemistry Unit | Chapter 3 | Density:
Students experiment with objects that have the same volume but different mass and other objects that have the same mass but different volume to develop a meaning of density. Students also experiment with density in the context of sinking and floating and look at substances on the molecular level to discover why one substance is more or less dense than another.
Type: Unit/Lesson Sequence
## Virtual Manipulative
Using this online calculator, students enter their weight on Earth. Their "weight" on other planets is calculated.
Type: Virtual Manipulative
## Worksheet
Mass vs. Weight:
This laboratory activity worksheet engages students in an exploration of mass and weight. Students use a balance and spring scale to measure the masses and weights of a several of objects. Students will analyze the data and determine the the relationship between mass and weight using graphing skills. An answer key is attached to assist the use of this resource.
Type: Worksheet
## STEM Lessons - Model Eliciting Activity
Glider Challenge:
In this Model-Eliciting Activity (MEA), students will select a glider model that will meet the needs of a Summer Space Camp program.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
NASA: Roving for the right wheel! 3D + MEA:
In this Model-Eliciting Activity (MEA), students will evaluate wheel designs from different companies to determine which wheel is appropriate for the mission. Further 3D printing is integrated by 3D printing different wheel models which can be directly tested using a LEGO Mindstorms Robot or Simple Rubber Band Powered Sled and different Regolith Simulants for the Moon and Titan.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
Scout Robot: Mass, Density, Volume, Weight:
In this MEA, students must select which material to use in the development of an advanced military scout robot. Students must analyze data about each material’s individual properties that would make it a valid choice for military or police service. Students must complete calculations to determine material density as well as the overall mass and weight of the robot. This lesson focuses on the characteristic properties of density, unit conversion, and differentiating between mass and weight.
## Original Student Tutorials Science - Grades K-8
Mass and Weight: What's the Difference?:
Differentiate between weight and mass, recognizing that weight is the amount of gravitational pull on an object and is distinct though proportional to mass. In this interactive tutorial you'll help a curious chicken learn more about this important topic.
## Student Resources
Vetted resources students can use to learn the concepts and skills in this benchmark.
## Original Student Tutorial
Mass and Weight: What's the Difference?:
Differentiate between weight and mass, recognizing that weight is the amount of gravitational pull on an object and is distinct though proportional to mass. In this interactive tutorial you'll help a curious chicken learn more about this important topic.
Type: Original Student Tutorial
## Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.
## Tutorial
Mass and Weight Clarification:
This tutorial covers the difference between mass and weight.
Type: Tutorial | 2,770 | 13,506 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2024-33 | latest | en | 0.921293 |
https://www.eurocode.us/seismic-analysis/tzz.html | 1,558,756,171,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232257847.56/warc/CC-MAIN-20190525024710-20190525050710-00450.warc.gz | 767,241,722 | 5,569 | ## Tzz
Red flow
Hypothetical flow m
Figure 2.10: Displacement thickness in boundary layer
The motivation for using displacement thickness is to permit the use of a displaced body in place of the actual body, such that the frictionless mass flow around the displaced body is the same as the actual mass flow around the real body. Use is made of the displacement thickness in the design of wind tunnels, air intakes for airplane jet engine.
As the boundary layer thickness growth, the fluid is pushed away from the plate, which means that the velocity has also a component in the y direction , vy. we would expect that vy ^ vx because the boundary layer thickness is small compared to any significant body dimension. The boundary layer thickness, that is the value of y for which vx = 0.99v^, can be obtained as following:
0 0 | 180 | 830 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2019-22 | latest | en | 0.914153 |
https://answerofmath.com/solved-understanding-hypothesis-testing-kruskal-wallis-mann-whitney-when-there-are-tied-values/ | 1,680,012,804,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948867.32/warc/CC-MAIN-20230328135732-20230328165732-00122.warc.gz | 127,278,244 | 21,201 | # Solved – Understanding hypothesis testing (Kruskal Wallis, Mann-Whitney) when there are tied values
tldr: In Python's Scipy stats modules, the `kruskal` and `mannwhitneyu` functions will both raise an error if called with only identical values. Why?
Context: I'm evaluating results obtained using stochastic algorithms. To do so, I use Kruskal Wallace tests to determine whether two sets of results are significantly different at a certain confidence level, and if they are, I use Mann-Whitney U tests to determine which group is significantly greater.
I'm using `scipy.stats.kruskal` and `scipy.stats.mannwhitneyu` in Python to do this for me. Now, one of the algorithms has a very high chance of returning 0, so I have many groups of results that consist entirely of 0s. When I run `kruskal` on two groups that consist entirely of 0s, the function raises an error like `All numbers are identical in kruskal`. MWU does the same.
In my context, I think I can safely assume that two groups consisting only of zeros are not significantly different. I would, in fact, expect the test to tell me that they are from the same population with a 100% confidence level. But before I act on my assumption and write a bypass into my script, I would like to understand why the functions are designed to behave in this way. Why are two groups, both only consisting of a single value, considered invalid input for a Kruskal or MWU test? In what scenarios would it be erroneous to conclude that the two groups are identical?
Contents
The Wilcoxon Signed-Rank (Mann-Whitney U) test two-sample test and the Kruskal-Wallis test for comparing \$k > 2\$ samples, are both based on ranks. That is, the numerical values you input are reduced to ranks.
For a single sample, ranking goes like this (output from R):
``x = c(1, 4, 7, 3, 11, 6); x [1] 1 4 7 3 11 6 rank(x) [1] 1 3 5 2 6 4 ``
If there are ties in the data, then ranking is not quite so straightforward:
``y = c(1, 4, 6, 2, 4, 6, 11); y [1] 1 4 6 2 4 6 11 rank(y) [1] 1.0 3.5 5.5 2.0 3.5 5.5 7.0 ``
Various texts and software packages treat ties differently. In order to find a p-value for the test, all of them begin with with distribution theory based on ranks from data without ties. Some have approximate distribution theory for the less-tidy ranks that result from ties. (When more than one sample is involved, not only duplicated values within a sample count as ties, but duplicated value anywhere among the groups also count.)
If there are only a few ties in a dataset, then printed warnings about ties can often be ignored. If there are many ties, then either no p-value will be given, or the p-value provided may be essentially useless.
An unofficial trick can be used to assess how serious ties are in any one analysis. You can artificially jitter the data with just enough random noise to break ties and see if the p-value changes by enough to matter. (Best to do this a couple of times with different jittering.)
Example:
``x = c(1, 2, 2, 4, 5, 3, 0); y = c(4, 6, 3, 8, 11, 11) wilcox.test(x, y) Wilcoxon rank sum test with continuity correction data: x and y W = 4, p-value = 0.01778 alternative hypothesis: true location shift is not equal to 0 Warning message: In wilcox.test.default(x, y) : cannot compute exact p-value with ties ``
.
``# Jittering jx = runif(length(x), -.01, .01); jy = runif(length(y), -.01, .01) wilcox.test(x+jx, y+jy) Wilcoxon rank sum test data: x + jx and y + jy W = 4, p-value = 0.01399 alternative hypothesis: true location shift is not equal to 0 ``
The original and jittered \$x\$s look like this:
``x; rank(x) [1] 1 2 2 4 5 3 0 [1] 2.0 3.5 3.5 6.0 7.0 5.0 1.0 round(x+jx, 4); rank(x+jx) [1] 0.9958 1.9900 2.0035 3.9945 5.0093 2.9995 -0.0095 [1] 2 3 4 6 7 5 1 ``
Another run with different random jittering also gave P-value about 0.014. So if we are working at the 5% level, is seems safe to say that the original version of the test (with warnings about ties) gave a useful result.
If there is any doubt or if the result is for review or publication, then you must do a formal test on the data. My first choice would be a simulated permutation test. One elementary review of permutation tests is Eudey, et al.. (Sect. 3 is most relevant to this discussion.) Also, perhaps see this Q&A. Permutation tests do not use ranks and can handle ties without difficulty.
Finally, I don't know exactly how your groups with all 0's should be treated because I don't know what process is producing the 0's. Clearly not with rank-based tests. You are correct that two groups with all 0's can't be distinguished from one another by hypothesis testing. If one group has a few 0's and another has mostly 0's, a binomial test (0's vs non-0's) or permutation test should help to judge whether they came from different populations.
Rate this post | 1,378 | 4,879 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2023-14 | latest | en | 0.902961 |
https://askworksheet.com/adding-mixed-numbers-worksheet/ | 1,686,058,259,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652569.73/warc/CC-MAIN-20230606114156-20230606144156-00523.warc.gz | 130,779,333 | 21,429 | In this exercise your class will add like fractions using a three step process using number lines. More adding mixed numbers and improper fractions on a number line help your students practice adding mixed numbers and improper fractions with this printable worksheet.
### Adding mixed numbers unlike denominators below are six versions of our grade 5 math worksheet on adding mixed numbers where the fractional parts of the numbers have different denominators.
Adding mixed numbers worksheet. The arithmetic in these questions is kept simple and students can try to formulate the answers mentally without writing down calculations. 2 1 2 2 3 6 add the fractions. Adding and subtracting mixed numbers adding and subtracting mixed numbers can be daunting but this worksheet helps by breaking the process down step by step.
First add the fractions. Our adding and subtracting fractions and mixed numbers worksheets are designed to supplement our adding and subtracting fractions and mixed numbers lessons. 3 1 5 4 3 5 example 3.
1 4 6 7 2 1 7 2 1. Adding mixed numbers worksheets. Read the lesson on adding mixed numbers if you need help on how to add mixed numbers.
Basic arithmetic skill adding mixed numbers find each sum. 1 1 2 3 1 4 3 2 5 3 1 2 5 2 4. Grade 5 number operations.
Answers to adding mixed numbers 1 7 2 1 1 3 3 2 4 1 2 3 5 5 6 2. Adding mixed numbers example 1. Adding fractions with different denominators adding mixed numbers reducing fractions common core standards.
With this exciting myriad collection of pdf adding mixed fractions worksheets you re sure to become more than just competent at adding mixed numbers and mixed numbers with proper and improper fractions. Be sure to check out the fun interactive fraction activities and additional worksheets below. 1 2 5 add the whole numbers.
Use the hint button to get a free letter if an answer is giving you trouble. These worksheets are pdf files. 2 1 4 2.
Add and reduce to lowest terms. These math worksheets are pdf files. Fill in all the gaps then press check to check your answers.
Adding mixed numbers with like denominators below are six versions of our grade 4 fractions worksheet on adding mixed numbers which have the same denominators. 1 2 3 1 4 6 1 add the whole numbers. You can also click on the button to get a clue.
6 1 5 3. These ready to use printable worksheets help assess student learning. 3 7 6 4 6 regroup so that the fraction is less than 1.
Write fractions with a common denominator.
Adding Subtracting Mixed Numbers Worksheet Fractions Worksheets Mathematics Worksheets Kids Math Worksheets
Adding Mixed Numbers Worksheet In 2020 Adding Mixed Number Fractions Worksheets Mixed Numbers
Worksheets Adding Mixed Numbers And Fractions In 2020 Math Multiplication Worksheets Multiplication Worksheets Fractions Worksheets
Subtracting Mixed Numbers Fractions Worksheets Fractions Worksheets Fractions Mixed Fractions Worksheets
Subtract Mixed Numbers With Like Unlike Denominators Solve The Riddle Fractions Practice Fractions Worksheets Math Fractions Worksheets Math Fractions
Adding Mixed Numbers With Like Denominators Worksheets Adding Mixed Numbers With Like Denominators Worksheets Free Adding Mixed Number Mixed Numbers Worksheets
5 Adding And Subtracting Mixed Numbers With Like Denominators Worksheet In 2020 Fractions Worksheets Free Fraction Worksheets Free Math Worksheets
Adding And Subtracting Mixed Fractions B Fractions Worksheets Fractions Mixed Fractions
Image Result For Adding Mixed Fractions With Different Denominators Worksheets Fractions Worksheets Adding Mixed Fractions Mixed Fractions
Fraction Worksheets Have Fun Adding Mixed Number Fractions Worksheets Mixed Numbers
3 Worksheet Free Math Worksheets Third Grade 3 Fractions And Decimals Adding Mixed Numbers Li In 2020 Fractions Worksheets Adding Mixed Number Adding Mixed Fractions
Adding Subtracting Mixed Numbers Worksheet Subtract Mixed Numbers Mixed Numbers Grade 5 Math Worksheets
Adding Mixed Fractions With Unlike Denominators Worksheet Education Com Adding Mixed Fractions Mixed Fractions Fractions
Addition Of Mixed Fractions Math Fractions Worksheets Fractions Worksheets Fractions
Subtracting Mixed Numbers Same Denominators Fractions Worksheets Addition Of Fractions Adding Improper Fractions
Mixed Numbers Packet
Adding And Subtracting Mixed Numbers Worksheet Education Com Subtract Mixed Numbers Fractions Worksheets Fractions
Adding And Subtracting Mixed Numbers Worksheet Education Com Fractions Worksheets Printable Math Worksheets Subtract Mixed Numbers | 928 | 4,575 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2023-23 | latest | en | 0.826887 |
http://xavieranguera.com/wordpress/?p=25 | 1,695,947,876,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510462.75/warc/CC-MAIN-20230928230810-20230929020810-00308.warc.gz | 94,215,192 | 6,929 | # Measuring the speed of the Santiago train
Yesterday night a tragic accident occurred in the outskirts of Santiago de Compostela (Spain) when an AVE (Alta Velocidad Española, equivalent to the french TGV) derailed while in a pronounced curve. Many people were killed (latest reports talk about 65 people) and many more were injured.
The driver, while trapped in the cockpit, talked in the radio with the managing post and said that he was going at 190Km/h (approx. 120mph). Authorities have still to analyze the data in the black box to certify what the speed was and what where the causes of such accident.
While we should wait for the forensic analysis to find about the exact speed and the causes of this tragic event, I measured, with some simple reasoning, that the actual speed should be around 150 Km/h. This is still much higher that than the speed limit (80 Km/h) set for this area.
Here is how I came up with the approximated speed.
One big piece of information is the video that was published today that shows exactly how the crash happened. You can find it in http://www.youtube.com/watch?v=_I6OpvWWSR0
Given the video and listening to some descriptions that say that the crash was right outside of Santiago de Compostela, I think I was able to locate the the exact place where the accident happened https://www.google.com/maps/preview#!data=!1m4!1m3!1d3755!2d-8.5295832!3d42.8585075
We can see that far back in the image there is a big highway, and that the camera is placed right after a bridge crossing the railroad, being this bridge the first one found after the highway, once the curve started. This corresponds perfectly to the image we can see from google maps or google earth. Note that I found this location by matching the description given by media and looking at the major landmarks seen in the video above, so it might not be correct after all.
In google maps we can see that if we place a camera right after the first bridge and look towards the highway in the far back, whenever we start seeing the train coming it should be approximately underneath the highway. Considering this approximate hypothesis, I computed in google earth the distance between the bridge and the highway as the approximate distance that the train will run while being filmed by the camera. As it can be seen in the image below, this distance is approx. 239 meters.
Approximate calculation of the distance between the highway and the first crossing bridge
Next, I downloaded the video of the crash and played it in very slow motion. I saw that the video is in real time (the cars in the back might seem a bit slow, but this is an optic effect due to the cars being about 250m from the observer). Still, I decided to rely instead on the time that appears in the bottom-right of the image to measure how long it takes the train to run the 239 meters that separate the point when the train appears in sight and when the train crosses the bridge. After playing the video in very slow motion several times I estimate that the train appears at 20:43:59,689 and crosses the bridge at 20:44:05,714. The two images below show the approximate snapshots when the train starts appearing and when I consider it passes under the bridge.
Approximate moment when the train appears in the far (the actual frame I used is an earlier one, when the train just starts to appear in the horizon)
Approximate moment when the train passes under the bridge
Given that distances are approximate (as well as everything else) we will say that the train takes approximately 6 seconds to go from the highway to the first bridge. With these informations we have everything we need to compute the speed of the train, which is speed = 239(m) * 3600(s/h)/(6(s) * 1000(m/Km)) = 143 Km/h.
Some might say that the train significantly slowed down after it started derailing and was sliding down the railroad towards the bridge. To take this into account I took another (very inexact) measure by considering that the train started to derail right when the side wall starts, and did again the computation. The number now accounts for approx. 4.6 seconds to travel 187 meters, which means a speed of approx. 146 Km/h.
Both these speeds are far from the 190 Km/h that the driver claims, but much higher than the maximum for that area of the railroad system, considered a very dangerous one. This, in my opinion, would explain the fact that the train derailed and thus the accident.
Finally, it is possible to think that the driver started applying the brakes right after crossing the highway and getting into the curve, but the train could not stop soon enough. This would explain why the driver claims he was going at 190Km/h while the measurements while applying the brakes account for less. In conclusion, we will have to wait for the forensic analysis to find out.
You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site. | 1,089 | 4,973 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2023-40 | latest | en | 0.953383 |
https://brilliant.org/problems/magnetic-field-6/ | 1,511,587,915,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934809419.96/warc/CC-MAIN-20171125051513-20171125071513-00428.warc.gz | 586,808,870 | 18,092 | # Magnetic field
A square wire loop having side length $$a$$, mass $$m$$, and resistance $$R$$ is moving along the positive $$x$$-axis at a speed of $$v_0$$. It enters a uniform, steady magnetic field $$\vec B = B_0 \big(-\widehat k \big)$$ at $$t = 0$$ seconds, as shown in the figure.
Find the total amount of heat loss in the resistance.
Details and Assumptions:
• The magnitude of $$v_0$$ is sufficient that the loop comes out of the region of magnetic field with some speed.
• Neglect any type of energy loss other than the heat loss in resistance of the wires of the square.
• Take $$v_0 = \dfrac{3B^2 a^3}{mR}$$.
× | 178 | 628 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2017-47 | longest | en | 0.869246 |
https://archinfos.com/library/lecture/read/106164-what-graph-do-you-use-for-standard-deviation | 1,670,300,704,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711069.79/warc/CC-MAIN-20221206024911-20221206054911-00449.warc.gz | 137,878,528 | 5,686 | # What graph do you use for standard deviation?
## What graph do you use for standard deviation?
The bell curve (what statisticians call a “normal distribution“) is commonly seen in statistics as a tool to understand standard deviation. The following graph of a normal distribution represents a great deal of data in real life. The mean, or average, is represented by the Greek letter μ, in the center.
## How do you show standard deviation on a graph in Excel?
To use your calculated standard deviation (or standard error) values for your error bars, click on the “Custom” button under “Error Amount” and click on the “Specify Value” button. The small “Custom Error Bars” dialog box will then appear, asking you to specify the value(s) of your error bars.
## How do you graph average and standard deviation in Excel?
Format Data
1. Open a new Excel spreadsheet. Enter your raw data in a logical manner. ...
2. Click the cell where you want to display the average of your data. Type "=AVERAGE(B1:B10)" (without quotes). ...
3. Click the cell where you want to display the standard deviation of your data. Type "=STDEV(B1:B10)" (without quotes).
## How do I add error bars in Excel 2020?
1. Click anywhere in the chart.
2. Click the Chart Elements button. next to the chart, and then check the Error Bars box. ...
3. To change the error amount shown, click the arrow next to Error Bars, and then pick an option.
## How do I add error bars in sheets?
Add error bars to a chart
2. To open the editor panel, double-click the chart.
3. Click Customize. Series.
4. Check the box next to “Error bars.”
5. Choose the type and value.
## What are standard deviation error bars?
They give a general idea of how precise a measurement is, or conversely, how far from the reported value the true (error free) value might be. Error bars often represent one standard deviation of uncertainty, one standard error, or a particular confidence interval (e.g., a 95% interval).
## How do you calculate SEM?
SEM is calculated by taking the standard deviation and dividing it by the square root of the sample size.
## How do you find the standard deviation of a sheet?
STDEV calculates standard deviation for a sample. To calculate standard deviation across an entire population, use STDEVP . STDEV is equivalent to the square root of the variance, or SQRT(VAR(...)) using the same dataset.
## What is the shortcut to find standard deviation?
If i=1∑9(xi−5)=9 and i=1∑9(xi−5)2=45, then the standard deviation of the 9 times x1,x2,.....,x9 is.
## What is the shortcut for getting the standard deviation in Excel?
The Excel STDEV function returns the standard deviation for data that represents a sample. To calculate the standard deviation for an entire population, use STDEVP or STDEV. P. number1 - First number or reference in the sample.
## How do you calculate weighted standard deviation in Excel?
Calculate the weighted standard deviation
1. Choose Calc > Calculator.
2. In Store result in variable, enter Weighted SD .
3. In Expression, copy and paste, or enter SQRT(SUM(C2*(C1-C3)^2 )/((SUM(C2/C2)-1)*SUM(C2)/SUM(C2/C2))) Note. If the Weights column contains a 0, you will get an error because you can't divide by 0.
4. Click OK.
## How do you calculate variance and standard deviation in Excel?
What to Know
1. To calculate variance based on the entire population in Excel, use the VAR. P function. The syntax is VAR. P(number1,[number2],...)
2. To calculate standard deviation based on the entire population given as arguments, use the STDEV. P function.
## How do you find the percentage standard deviation in Excel?
How to calculate the percentage deviation in Excel. The percentage of deviation is calculated by subtracting the old value from the new value, and then dividing the result by the old one. The result of calculating this formula in Excel should be displayed in the percentage format of the cell.
## How do you find the percentage of a standard deviation?
The relative standard deviation (RSD) is often times more convenient. It is expressed in percent and is obtained by multiplying the standard deviation by 100 and dividing this product by the average. Example: Here are 4 measurements: 51.
## Is there a standard deviation IF function in Excel?
The Excel DSTDEV function gets the standard deviation of sample data extracted from records matching criteria. Essentially, this function calculates standard deviation on a subset of data, like a "standard deviation IF" formula.
## What is the difference between Stdevp and Stdev in Excel?
STDEVP assumes that its arguments are the entire population. If your data represents a sample of the population, then compute the standard deviation using STDEV. For large sample sizes, STDEV and STDEVP return approximately equal values. The standard deviation is calculated using the "n" method.
## How do I use the IFS function in Excel?
How to use the IFS Function in Excel? The formula used is: IFS(A2>80,”A”,A2>70,”B”,A2>60,”C”,A2>50,”D”,A2>40,”E”,A2>30,”F”), which says that if cell A2 is greater than 80 then return an “A” and so on.
## How do I calculate standard error in Excel?
The formula for standard error = standard deviation / sqrt(n), where “n” is the number of items in your data set. | 1,225 | 5,288 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2022-49 | latest | en | 0.825372 |
http://mathhelpforum.com/advanced-algebra/183897-compute-hom-q-q-z.html | 1,555,822,012,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578530176.6/warc/CC-MAIN-20190421040427-20190421061402-00026.warc.gz | 114,138,915 | 9,910 | 1. ## Compute Hom(q,q/z)
Hom(z,q/z)=?
Hom(q,q/z)=?
and also please prove that Q is an injective Z-module.
2. ## Re: Compute Hom(q,q/z)
$\displaystyle Hom (\mathbb{Z} , \mathbb{Q} / \mathbb{Z} )$ is trivially isomorphic to $\displaystyle \mathbb{Q} / \mathbb{Z}$ since any morphism is determined by where it sends $\displaystyle 1$. To prove that $\displaystyle \mathbb{Q}$ is injective take any morphism $\displaystyle f: n\mathbb{Z} \rightarrow \mathbb{Q}$ with $\displaystyle f(n)=a$ then, since $\displaystyle \mathbb{Q}$ is divisible there exists $\displaystyle b\in \mathbb{Q}$ with $\displaystyle nb=a$ take $\displaystyle g: \mathbb{Z} \rightarrow \mathbb{Q}$ with $\displaystyle g(1)=b$ then $\displaystyle gi=f$ where $\displaystyle i :n\mathbb{Z} \rightarrow \mathbb{Z}$ is the inclusion, conclude by Baer's criterion. I don't have the answer to the second but maybe the fact that $\displaystyle \mathbb{Q} / \mathbb{Z} \cong \oplus_{p \ prime } \mathbb{Z}_{p^\infty}$ is of use.
3. ## Re: Compute Hom(q,q/z)
thank you jose i got it. I will try for the others.
,
,
,
# www.sawudareb.hom.q
Click on a term to search for related topics. | 366 | 1,155 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2019-18 | latest | en | 0.70479 |
https://tlu.tarilabs.com/cryptography/bulletproofs-and-mimblewimble/MainReport.html | 1,624,301,021,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488289268.76/warc/CC-MAIN-20210621181810-20210621211810-00391.warc.gz | 513,602,011 | 30,302 | # Bulletproofs and Mimblewimble
## Introduction
### Bulletproofs
Bulletproofs form part of the family of distinct Zero-knowledge Proofdef systems, such as Zero-Knowledge Succinct Non-Interactive ARguments of Knowledge (zk-SNARK); Succinct Transparent ARgument of Knowledge (STARK); and Zero Knowledge Prover and Verifier for Boolean Circuits (ZKBoo). Zero-knowledge proofs are designed so that a prover is able to indirectly verify that a statement is true without having to provide any information beyond the verification of the statement, e.g. to prove that a number is found that solves a cryptographic puzzle and fits the hash value without having to reveal the Noncedef ([2], [4]).
The Bulletproofs technology is a Non-interactive Zero-knowledge (NIZK) proof protocol for general Arithmetic Circuitsdef with very short proofs (Arguments of Knowledge Systemsdef) and without requiring a trusted setup. They rely on the Discrete Logarithmdef (DL) assumption and are made non-interactive using the Fiat-Shamir Heuristicdef. The name "Bulletproof" originated from a non-technical summary from one of the original authors of the scheme's properties: "Short like a bullet with bulletproof security assumptions" ([1], [29]).
Bulletproofs also implement a Multi-party Computation (MPC) protocol, whereby distributed proofs of multiple provers with secret committed values are aggregated into a single proof before the Fiat-Shamir challenge is calculated and sent to the verifier, thereby minimizing rounds of communication. Secret committed values will stay secret ([1], [6]).
The essence of Bulletproofs is its inner-product algorithm originally presented by Groth [13] and then further refined by Bootle et al. [12]. The latter development provided a proof (argument of knowledge) for two independent (not related) bindingdef vector Pedersen Commitmentsdef that satisfied the given inner-product relation. Bulletproofs build on these techniques, which yield communication-efficient, zero-knowledge proofs, but offer a further replacement for the inner product argument that reduces overall communication by a factor of three ([1], [29]).
### Mimblewimble
Mimblewimble is a blockchain protocol designed for confidential transactions. The essence is that a Pedersen Commitment to $0$ can be viewed as an Elliptic Curve Digital Signature Algorithm (ECDSA) public key, and that for a valid confidential transaction, the difference between outputs, inputs and transaction fees must be $0$. A prover constructing a confidential transaction can therefore sign the transaction with the difference of the outputs and inputs as the public key. This enables a greatly simplified blockchain in which all spent transactions can be pruned, and new nodes can efficiently validate the entire blockchain without downloading any old and spent transactions. The blockchain consists only of block-headers, remaining Unspent Transaction Outputs (UTXO) with their range proofs and an unprunable transaction kernel per transaction. Mimblewimble also allows transactions to be aggregated before being committed to the blockchain ([1], [20]).
## How do Bulletproofs Work?
The basis of confidential transactions is to replace the input and output amounts with Pedersen Commitmentsdef. It is then publicly verifiable that the transactions balance (the sum of the committed inputs is greater than the sum of the committed outputs, and all outputs are positive), while keeping the specific committed amounts hidden. This makes it a zero-knowledge transaction. The transaction amounts must be encoded as $integers \mod q $, which can overflow, but are prevented from doing so by making use of range proofs. This is where Bulletproofs come in. The essence of Bulletproofs is its ability to calculate proofs, including range proofs, from inner-products.
The prover must convince the verifier that commitment $C(x,r) = xH + rG$ contains a number such that $x \in [0,2^n - 1]$. If $\mathbf {a} = (a_1 \mspace{3mu} , \mspace{3mu} ... \mspace{3mu} , \mspace{3mu} a_n) \in {0,1}^n$ is the vector containing the bits of $x$, the basic idea is to hide all the bits of the amount in a single vector Pedersen Commitment. It must then be proven that each bit satisfies $\omega(\omega-1) = 0$, i.e. each $\omega$ is either $0$ or $1$, and that they sum to $x$. As part of the ensuing protocol, the verifier sends random linear combinations of constraints and challenges $\in \mathbb{Z_p}$ to the prover. The prover is then able to construct a vectorized inner product relation containing the elements of $\mathbf {a}$, the constraints and challenges $\in \mathbb{Z_p}$, and appropriate blinding vectors $\in \mathbb Z_p^n$.
These inner product vectors have size $n $ that would require many expensive exponentiations. The Pedersen Commitment scheme, shown in Figure 1, allows for a vector to be cut in half, and for the two halves to be compressed together, each time calculating a new set of Pedersen Commitment generators. Applying the same trick repeatedly, $\log _2 n $ times, produces a single value. This is applied to the inner product vectors; they are reduced interactively with a logarithmic number of rounds by the prover and verifier into a single multi-exponentiation of size $2n + 2 \log_2(n) + 1 $. This single multi-exponentiation can then be calculated much faster than $n $ separate ones. All of this is made non-interactive using the Fiat-Shamir Heuristicdef.
Figure 1: Vector Pedersen Commitment Cut and Half ([12], [63])
Bulletproofs only rely on the discrete logarithm assumption. In practice, this means that Bulletproofs are compatible with any secure elliptic curve, making them extremely versatile. The proof sizes are short; only $[2 \log_2(n) + 9] $ elements are required for the range proofs and $[\log_2(n) + 13] $ elements for arithmetic circuit proofs, with $n $ denoting the multiplicative complexity. Additionally, the logarithmic proof size enables the prover to aggregate multiple range proofs into a single short proof, as well as to aggregate multiple range proofs from different parties into one proof (refer to Figure 2) ([1], [3], [5]).
Figure 2: Logarithmic Aggregate Bulletproofs Proof Sizes [3]
If all Bitcoin transactions were confidential, approximately 50 million UTXOs from approximately 22 million transactions would result in roughly 160GB range proof data, when using current/linear proof systems and assuming use of 52 bits to represent any value from 1 satoshi up to 21 million bitcoins. Aggregated Bulletproofs would reduce the data storage requirement to less than 17GB [[1]].
In Mimblewimble, the blockchain grows with the size of the UTXO set. Using Bulletproofs as a drop-in replacement for range proofs in confidential transactions, the size of the blockchain would only grow with the number of transactions that have unspent outputs. This is much smaller than the size of the UTXO set [1].
The recent implementation of Bulletproofs in Monero on 18 October 2018 saw the average data size on the blockchain per payment reduce by ~73% and the average USD-based fees reduce by ~94.5% for the period 30 August 2018 to 28 November 2018 (refer to Figure 3).
Figure 3: Monero Payment, Block and Data Size Statistics
## Applications for Bulletproofs
Bulletproofs were designed for range proofs. However, they also generalize to arbitrary arithmetic circuits. In practice, this means that Bulletproofs have wide application and can be efficiently used for many types of proofs. Use cases of Bulletproofs are listed in this section, but this list may not be exhaustive, as use cases for Bulletproofs continue to evolve ([1], [2], [3], [5], [6], [59]).
1. Range proofs
Range proofs are proofs that a secret value, which has been encrypted or committed to, lies in a certain interval. It prevents any numbers coming near the magnitude of a large prime, say $2^{256}$, that can cause wraparound when adding a small number, e.g. proof that $x \in [0,2^{52} - 1] $.
2. Merkle proofs
Hash preimages in a Merkle tree [7] can be leveraged to create zero-knowledge Merkle proofs using Bulletproofs, to create efficient proofs of inclusion in massive data sets.
3. Proof of solvency
Proofs of solvency are a specialized application of Merkle proofs; coins can be added into a giant Merkle tree. It can then be proven that some outputs are in the Merkle tree and that those outputs add up to some amount that the cryptocurrency exchange claims they have control over without revealing any private information. A Bitcoin exchange with 2 million customers needs approximately 18GB to prove solvency in a confidential manner using the Provisions protocol [58]. Using Bulletproofs and its variant protocols proposed in [1], this size could be reduced to approximately 62MB.
4. Multi-signatures with deterministic nonces
With Bulletproofs, every signatory can prove that their nonce was generated deterministically. A SHA256 arithmetic circuit could be used in a deterministic way to show that the de-randomized nonces were generated deterministically. This would still work if one signatory were to leave the conversation and rejoin later, with no memory of interacting with the other parties they were previously interacting with.
5. Scriptless scripts
Scriptless scripts is a way to do smart contracts exploiting the linear property of Schnorr signatures, using an older form of zero-knowledge proofs called a Sigma protocol. This can all be done with Bulletproofs, which could be extended to allow assets that are functions of other assets, i.e. crypto derivatives.
6. Smart contracts and crypto derivatives
Traditionally, a new trusted setup is needed for each smart contract when verifying privacy-preserving smart contracts, but with Bulletproofs, no trusted setup is needed. Verification time, however, is linear, and it might be too complex to prove every step in a smart contract. The Refereed Delegation Model [33] has been proposed as an efficient protocol to verify smart contracts with public verifiability in the off-line stage, by making use of a specific verification circuit linked to a smart contract.
A challenger will input the proof to the verification circuit and get a binary response as to the validity of the proof. The challenger can then complain to the smart contract, claim the proof is invalid and send the proof, together with the output from a chosen gate in the verification circuit, to the smart contract. Interactive binary searches are then used to identify the gate where the proof turns invalid. Hence the smart contract must only check a single gate in the verification procedure to decide whether the challenger or prover was correct. The cost is logarithmic in the number of rounds and amount of communications, with the smart contract only doing one computation. A Bulletproof can be calculated as a short proof for the arbitrary computation in the smart contract, thereby creating privacy-preserving smart contracts (refer to Figure 4).
Figure 4: Bulletproofs for Refereed Delegation Model [5]
1. Verifiable shuffles
Alice has some computation and wants to prove to Bob that she has done it correctly and has some secret inputs to this computation. It is possible to create a complex function that either evaluates to 1 if all secret inputs are correct and to 0 otherwise. Such a function can be encoded in an arithmetic circuit and can be implemented with Bulletproofs to prove that the transaction is valid.
When a proof is needed that one list of values $[x_1, ... , x_n]$ is a permutation of a second list of values $[y_1, ... , y_n]$, it is called a verifiable shuffle. It has many applications, e.g. voting, blind signatures for untraceable payments and solvency proofs. Currently, the most efficient shuffle has size $O \sqrt{n}$. Bulletproofs can be used very efficiently to prove verifiable shuffles of size $O \log(n)$, as shown in Figure 5.
Another potential use case is to verify that two nodes executed the same list of independent instructions $[x1,x4,x3,x2]$ and $[x1,x2,x3,x4]$, which may be in different order, to arrive at the same next state $N$. The nodes do not need to share the actual instructions with a verifier, but the verifier can show that they executed the same set without having knowledge of the instructions.
Figure 5: Bulletproofs for Verifiable Shuffles [5]
1. Batch verifications
Batch verifications can be done using one of the Bulletproofs derivative protocols. This has application where the verifier needs to verify multiple (separate) range proofs at once, e.g. a blockchain full node receiving a block of transactions needs to verify all transactions as well as range proofs. This batch verification is then implemented as one large multi-exponentiation; it is applied to reduce the number of expensive exponentiations.
## Comparison to other Zero-knowledge Proof Systems
Table 1 ([2], [5]) shows a high-level comparison between Sigma protocols (i.e. interactive public-coin protocols) and the different Zero-knowledge proof systems mentioned in this report. (The most desirable outcomes for each measurement are shown in bold italics.) The aim will be to have a proof system that is not interactive, has short proof sizes, has linear prover runtime scalability, has efficient (sub-linear) verifier runtime scalability, has no trusted setup, is practical and is at least DL secure. Bulletproofs are unique in that they are not interactive, have a short proof size, do not require a trusted setup, have very fast execution times and are practical to implement. These attributes make Bulletproofs extremely desirable to use as range proofs in cryptocurrencies.
Table 1: Comparison to other Zero-knowledge Proof Systems
Proof SystemSigma Protocolszk-SNARKSTARKZKBooBulletproofs
Interactiveyesnononono
Proof Sizelongshortshortishlongshort
Prover Runtime Scalabilitylinearquasilinearquasilinear (big memory requirement)linearlinear
Verifier Runtime Scalabilitylinearefficientefficient (poly-logarithmically)efficientlinear
Trusted Setupnorequirednonono
Practicalyesyesnot quitesomewhatyes
Security AssumptionsDLnon-falsifiable, but not on par with DLquantum secure One-way Function (OWF) [50], which is better than DLsimilar to STARKsDL
## Interesting Bulletproofs Implementation Snippets
Bulletproofs development is currently still evolving, as can be seen when following the different community development projects. Different implementations of Bulletproofs also offer different levels of efficiency, security and functionality. This section describes some of these aspects.
### Current and Past Efforts
The initial prototype Bulletproofs' implementation was done by Benedikt Bünz in Java located at GitHub:bbuenz/BulletProofLib [27].
The initial work that provided cryptographic support for a Mimblewimble implementation was mainly done by Pieter Wuille, Gregory Maxwell and Andrew Poelstra in C located at GitHub:ElementsProject/secp256k1-zkp [25]. This effort was forked as GitHub:apoelstra/secp256k1-mw [26] with main contributors being Andrew Poelstra, Pieter Wuille, and Gregory Maxwell where Mimblewimble primitives and support for many of the Bulletproof protocols (e.g. zero knowledge proofs, range proofs and arithmetic circuits) were added. Current effort also involves MuSig [48] support.
The Grin project (an open source Mimblewimble implementation in Rust) subsequently forked GitHub:ElementsProject/secp256k1-zkp [25] as GitHub:mimblewimble/secp256k1-zkp [30] and has added Rust wrappers to it as mimblewimble/rust-secp256k1-zkp [45] for use in its blockchain. The Beam project (another open source Mimblewimble implementation in C++) links directly to GitHub:ElementsProject/secp256k1-zkp [25] as its cryptographic sub-module. Refer to Mimblewimble-Grin Blockchain Protocol Overview and Grin vs. BEAM, a Comparison for more information about the Mimblewimble implementation of Grin and Beam.
An independent implementation for Bulletproof range proofs was done for the Monero project (an open source CryptoNote implementation in C++) by Sarang Noether [49] in Java as the precursor and moneromooo-monero [46] in C++ as the final implementation. Its implementation supports single and aggregate range proofs.
Adjoint, Inc. has also done an independent open source implementation of Bulletproofs in Haskell at GitHub: adjoint-io/bulletproofs [29]. It has an open source implementation of a private permissioned blockchain with multiparty workflow aimed at the financial industry.
Chain/Interstellar has done another independent open source implementation of Bulletproofs in Rust from the ground up at GitHub:dalek-cryptography/bulletproofs [28]. It has implemented parallel Edwards formulas [39] using Intel® Advanced Vector Extensions 2 (AVX2) to accelerate curve operations. Initial testing suggests approximately 50% speedup (twice as fast) over the original libsecp256k1-based Bulletproofs implementation.
### Security Considerations
Real-world implementation of Elliptic-curve Cryptography (ECC) is largely based on official standards that govern the selection of curves in order to try and make the Elliptic-curve Discrete-logarithm Problem (ECDLP) hard to solve, i.e. finding an ECC user's secret key given the user's public key. Many attacks break real-world ECC without solving ECDLP due to problems in ECC security, where implementations can produce incorrect results and also leak secret data. Some implementation considerations also favor efficiency over security. Secure implementations of the standards-based curves are theoretically possible, but highly unlikely ([14], [32]).
Grin, Beam and Adjoint use ECC curve secp256k1 [24] for their Bulletproofs implementation, which fails one out of the four ECDLP security criteria and three out of the four ECC security criteria. Monero and Chain/Interstellar use the ECC curve Curve25519 [38] for their Bulletproofs implementation, which passes all ECDLP and ECC security criteria [32].
Chain/Interstellar goes one step further with its use of Ristretto, a technique for constructing prime order elliptic curve groups with non-malleable encodings, which allows an existing Curve25519 library to implement a prime-order group with only a thin abstraction layer. This makes it possible for systems using Ed25519 signatures to be safely extended with zero-knowledge protocols, with no additional cryptographic assumptions and minimal code changes [31].
The Monero project has also had security audits done on its Bulletproofs' implementation, which resulted in a number of serious and critical bug fixes as well as some other code improvements ([8], [9], [11]).
### Wallet Reconstruction and Switch Commitment - Grin
Grin implemented a switch commitment [43] as part of a transaction output to be ready for the age of quantum adversaries and to pose as a defense mechanism. It had an original implementation that was discarded (completely removed) due to it being complex, using a lot of space in the blockchain and allowing inclusion of arbitrary data. Grin also employed a complex scheme to embed the transaction amount inside a Bulletproof range proof for wallet reconstruction, which was linked to the original switch commitment hash implementation. The latest implementation improved on all those aspects and uses a much simpler method to regain the transaction amount from a Bulletproof range proof.
#### Initial Implementation
The initial Grin implementation ([21], [34]. [35], [54]) hides two things in the Bulletproof range proof: a transaction amount for wallet reconstruction and an optional switch commitment hash to make the transaction perfectly bindingdef later on, as opposed to currently being perfectly hidingdef. Perfect in this sense means that a quantum adversary (an attacker with infinite computing power) cannot tell what amount has been committed to and is also unable to produce fake commitments. Computational means that no efficient algorithm running in a practical amount of time can reveal the commitment amount or produce fake commitments, except with small probability. The Bulletproof range proofs are stored in the transaction kernel and will thus remain persistent in the blockchain.
In this implementation, a Grin transaction output contains the original (Elliptic Curve) Pedersen Commitmentdef as well as the optional switch commitment hash. The switch commitment hash takes the resultant blinding factor $b$, a third cyclic group random generator $J$ and a wallet-seed derived random value $r$ as input. The transaction output has the following form:
$$(vG + bH \mspace{3mu} , \mspace{3mu} \mathrm{H_{B2}}(bJ \mspace{3mu} , \mspace{3mu} r)) \tag{1}$$
where $\mathrm{H_{B2}}$ is the BLAKE2 hash function [44] and $\mathrm{H_{B2}}(bJ \mspace{3mu} , \mspace{3mu} r)$ the switch commitment hash. In order for such an amount to be spent, the owner needs to reveal $b , r$ so that the verifier can check the opening of $\mathrm{H_{B2}}(bJ \mspace{3mu} , \mspace{3mu} r)$ by confirming that it matches the value stored in the switch commitment hash portion of the transaction output. Grin implemented the BLAKE2 hash function, which outperforms all mainstream hash function implementations in terms of hashing speed with similar security to the latest Secure Hash Algorithm 3 (SHA-3) standard [44].
In the event of quantum adversaries, the owner of an output can choose to stay anonymous and not claim ownership or reveal $bJ$ and $r$, whereupon the amount can be moved to the then hopefully forked quantum resistant blockchain.
In the Bulletproof range proof protocol, two 32-byte scalar nonces $\tau_1 , \alpha$ (not important to know what they are) are generated with a secure random number generator. If the seed for the random number generator is known, the scalar values $\tau_1 , \alpha$ can be recalculated when needed. Sixty-four (64) bytes worth of message space (out of 674 bytes worth of range proof) are made available by embedding a message into those variables using a logic $\mathrm{XOR}$ gate. This message space is used for the transaction amount for wallet reconstruction.
To ensure that the transaction amount of the output cannot be spent by only opening the (Elliptic Curve) Pedersen Commitment $vG + bH$, the switch commitment hash and embedded message are woven into the Bulletproof range proof calculation. The initial part is done by seeding the random number generator used to calculate $\tau_1 , \alpha$ with the output from a seed function $\mathrm S$ that uses as input a nonce $\eta$ (which may be equal to the original blinding factor $b$), the (Elliptic Curve) Pedersen Commitmentdef $P$ and the switch commitment hash
$$\mathrm S (\eta \mspace{3mu} , \mspace{3mu} P \mspace{3mu} , \mspace{3mu} \mathrm{H_{B2}}(bJ \mspace{3mu} , \mspace{3mu} r) ) = \eta \mspace{3mu} \Vert \mspace{3mu} \mathrm{H_{S256}} (P \mspace{3mu} \Vert \mspace{3mu} \mathrm{H_{B2}}(bJ \mspace{3mu} , \mspace{3mu} r) ) \tag{2}$$
where $\mathrm{H_{S256}}$ is the SHA256 hash function. The Bulletproof range proof is then calculated with an adapted pair $\tilde{\alpha} , \tilde{\tau_1}$, using the original $\tau_1 , \alpha$ and two
32-byte words $m_{w1}$ and $m_{w2}$ that make up the 64-byte embedded message as follows:
$$\tilde{\alpha} = \mathrm {XOR} ( \alpha \mspace{3mu} , \mspace{3mu} m_{w1}) \mspace{12mu} \mathrm{and} \mspace{12mu} \tilde{\tau_1} = \mathrm {XOR} ( \tau_1 \mspace{3mu} , \mspace{3mu} m_{w2} ) \tag{3}$$
To retrieve the embedded message, the process is simply inverted. Note that the owner of an output needs to keep record of the blinding factor $b$, the nonce $\eta$ if not equal to the blinding factor $b$, as well as the wallet-seed derived random value $r$ to be able to claim such an output.
#### Improved Implementation
The latter Grin implementation ([56], [57]) uses Bulletproof range proof rewinding so that wallets can recognize their own transaction outputs. This negated the requirement to remember the wallet-seed derived random value $r$, nonce $\eta$ for the seed function $\mathrm S$ and use of the adapted pair $\tilde{\alpha} , \tilde{\tau_1}$ in the Bulletproof range proof calculation.
In this implementation, it is not necessary to remember a hash of the switch commitment as part of the transaction output set and for it to be passed around during a transaction. The switch commitment looks exactly like the original (Elliptic Curve) Pedersen Commitment $vG + bH$, but in this instance the blinding factor $b$ is tweaked to be
$$b = b^\prime + \mathrm{H_{B2}} ( vG + b^\prime H \mspace{3mu} , \mspace{3mu} b^\prime J ) \tag{4}$$
with $b^\prime$ being the user generated blinding factor. The (Elliptic Curve) Pedersen Commitment then becomes
$$vG + b^\prime H + \mathrm{H_{B2}} ( vG + b^\prime H \mspace{3mu} , \mspace{3mu} b^\prime J ) H \tag{5}$$
After activation of the switch commitment in the age of quantum adversaries, users can reveal $( vG + b^\prime H \mspace{3mu} , \mspace{3mu} b^\prime J )$, and verifiers can check if it is computed correctly and use it as if it were the ElGamal Commitmentdef $( vG + b H \mspace{3mu} , \mspace{3mu} b J )$.
#### GitHub Extracts
The following extracts of discussions depict the initial and improved implementations of the switch commitment and retrieving transactions amounts from Bulletproofs for wallet reconstruction.
Bulletproofs #273 [35]
{yeastplume} "The only thing I think we're missing here from being able to use this implementation is the ability to store an amount within the range proof (for wallet reconstruction). From conversations with @apoelstra earlier, I believe it's possible to store 64 bytes worth of 'message' (not nearly as much as the current range proofs)."
{apoelstra} "Ok, I can get you 64 bytes without much trouble (xoring them into* tau_1 and alpha which are easy to extract from tau_x and mu if you know the original seed used to produce the randomness). I think it's possible to get another 32 bytes into t but that's way more involved since t is a big inner-product*."
Message hiding in Bulletproofs #721 [21]
"Breaking out from #273, we need the wind a message into a bulletproof similarly to how it could be done in 'Rangeproof Classic'. This is an absolute requirement as we need to embed an output's SwitchCommitHash (which is otherwise not committed to) and embed an output amount for wallet reconstruction. We should be able to embed up to 64 bytes of message without too much difficulty, and another 32 with more difficulty (see original issue). 64 should be enough for the time being."
Switch Commits/Bulletproofs - Status #734 [34]
"The prove function takes a value, a secret key (blinding factor in our case), a nonce, optional extra_data and a generator and produces a 674 byte proof. I've also modified it to optionally take a message (more about this in a bit). It creates the Pedersen commitment it works upon internally with these values."
"The verify function takes a proof, a Pedersen commitment and optional extra_data and returns true if proof demonstrates that the value within the Pedersen commitment is in the range [0..2^64] (and the extra_data is correct)."
"Additionally, I've added an unwind function which takes a proof, a Pedersen commitment, optional extra_data and a 32 bit nonce (which needs to be the same as the original nonce used in order to return the same message) and returns the hidden message."
"If you have the correct Pedersen commitment and proof and extra_data, and attempt to unwind a message out using the wrong nonce, the attempt won't fail, you'll get out gibberish or just wildly incorrect values as you parse back the bytes."
"The SwitchCommitHash is currently a field of an output, and while it is stored in the Txo set and passed around during a transaction, it is not currently included in the output's hash. It is passed in as the extra_data field above, meaning that anyone validating the range proof also needs to have the correct switch commit in order to validate the range proof."
Removed all switch commitment usages, including restore #841 [55]
{ignopeverell} "After some discussion with @antiochp, @yeastplume and @tromp, we decided switch commitments weren't worth the cost of maintaining them and their drawbacks. Removing them."
{ignopeverell} "For reference, switch commitments were found to:
• add a lot of complexity and assumptions
• take additional space for little benefit right now
• allow the inclusion of arbitrary data, potentially for the worst
• provide little to no advantage in case of quantamageddon (as range proofs are still a weakness)"
{apoelstra} "After chatting with @yeastplume on IRC, I realize that we can actually use rangeproof rewinding for wallets to recognize their own outputs, which even avoids the "gap" problem of just scanning for pre-generated keys. With that in mind, it's true that the benefit of switch commitments for MW are not spectacular."
Switch commitment discussion #998 [56]
{antiochp} "Sounds like there is a "zero cost" way of getting switch commitments in as part of the commitment itself, so we would not need to store and maintain a separate "switch commitment" on each output. I saw that switch commitments have been removed for various reasons."
"Let me suggest a variant (idea suggested by Pieter Wuille initially): The switch commitment is (vG + bH), where b = b' + hash(vG + b'H,b'J). (So this "tweaks" the commitment, in a pay-to-contract / taproot style). Before the switch, this is just used like a normal Pedersen Commitment vG + bH. After the switch, users can reveal (vG + b'H, b'J), and verifiers check if it's computed correctly and use as if it were the ElGamal commitment (vG + bH, bJ)."
{@ignopeverell} modified the milestones: Beta / testnet3, Mainnet on 11 Jul.
{@ignopeverell} added the must-have label on 24 Aug.
## Conclusions, Observations and Recommendations
• Bulletproofs are not Bulletproofs are not Bulletproofs. This is evident by comparing the functionality, security and performance of all the current different Bulletproof implementations as well as the evolving nature of Bulletproofs.
• The security audit instigated by the Monero project on their Bulletproofs implementation as well as the resulting findings and corrective actions prove that every implementation of Bulletproofs has potential risk. This risk is due to the nature of confidential transactions; transacted values and token owners are not public.
• The growing number of open source Bulletproof implementations should strengthen the development of a new confidential blockchain protocol such as Tari.
• In the pure implementation of Bulletproof range proofs, a discrete-log attacker (e.g. a bad actor employing a quantum computer) would be able to exploit Bulletproofs to silently inflate any currency that used them. Bulletproofs are perfectly hidingdef (i.e. confidential), but only computationally bindingdef (i.e. not quantum resistant). Unconditional soundness is lost due to the data compression being employed ([1], [5], [6] and [10]).
• Bulletproofs are not only about range proofs. All the different Bulletproof use cases have a potential implementation in a new confidential blockchain protocol such as Tari; in the base layer as well as in the probable second layer.
## References
[1] B. Bünz, J. Bootle, D. Boneh, A. Poelstra, P. Wuille and G. Maxwell, "Bulletproofs: Short Proofs for Confidential Transactions and More", Blockchain Protocol Analysis and Security Engineering 2018 [online]. Available: http://web.stanford.edu/~buenz/pubs/bulletproofs.pdf. Date accessed: 2018‑09‑18.
[2] A. Poelstra, "Bulletproofs" (Transcript), Bitcoin Milan Meetup 2018‑02‑02 [online]. Available: https://diyhpl.us/wiki/transcripts/2018-02-02-andrew-poelstra-Bulletproofs. Date accessed: 2018‑09‑10.
[3] A. Poelstra, "Bulletproofs" (Slides), Bitcoin Milan Meetup 2018‑02‑02 [online]. Available: https://drive.google.com/file/d/18OTVGX7COgvnZ7T0ke-ajhMWwOHOWfKV/view. Date accessed: 2018‑09‑10.
[4] B. Feng, "Decoding zk-SNARKs" [online]. Available: https://medium.com/wolverineblockchain/decoding-zk-snarks-85e73886a040. Date accessed: 2018‑09‑17.
[5] B. Bünz, J. Bootle, D. Boneh, A. Poelstra, P. Wuille and G. Maxwell, "Bulletproofs: Short Proofs for Confidential Transactions and More" (Slides) [online]. Available: https://cyber.stanford.edu/sites/default/files/bpase18.pptx. Date accessed: 2018‑09‑18.
[6] B. Bünz, J. Bootle, D. Boneh, A. Poelstra, P. Wuille and G. Maxwell, "Bulletproofs: Short Proofs for Confidential Transactions and More (Transcripts)" [online]. Available: http://diyhpl.us/wiki/transcripts/blockchain-protocol-analysis-security-engineering/2018/Bulletproofs. Date accessed: 2018‑09‑18.
[7] "Merkle Root and Merkle Proofs" [online]. Available: https://bitcoin.stackexchange.com/questions/69018/Merkle-root-and-Merkle-proofs. Date accessed: 2018‑10‑10.
[8] "Bulletproofs Audit: Fundraising" [online]. Available: https://forum.getmonero.org/22/completed-tasks/90007/Bulletproofs-audit-fundraising. Date accessed: 2018‑10‑23.
[9] "The QuarksLab and Kudelski Security Audits of Monero Bulletproofs are Complete" [online]. Available: https://ostif.org/the-quarkslab-and-kudelski-security-audits-of-monero-Bulletproofs-are-complete. Date accessed: 2018‑10‑23.
[10] A. Poelstra, "Bulletproofs Presentation at Feb 2 Milan Meetup, Reddit" [online]. Available: https://www.reddit.com/r/Bitcoin/comments/7w72pq/Bulletproofs_presentation_at_feb_2_milan_meetup. Date accessed: 2018‑09‑10.
[11] "The OSTIF and QuarksLab Audit of Monero Bulletproofs is Complete – Critical Bug Patched [online]". Available: https://ostif.org/the-ostif-and-quarkslab-audit-of-monero-Bulletproofs-is-complete-critical-bug-patched. Date accessed: 2018-10-23.
[12] J. Bootle, A. Cerulli1, P. Chaidos, J. Groth and C. Petit, "Efficient Zero-knowledge Arguments for Arithmetic Circuits in the Discrete Log Setting", Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 327-357. Springer, 2016 [online]. Available: https://eprint.iacr.org/2016/263.pdf. Date accessed: 2018‑09‑21.
[13] J. Groth, "Linear Algebra with Sub-linear Zero-knowledge Arguments" [online]. Available: https://link.springer.com/content/pdf/10.1007%2F978-3-642-03356-8_12.pdf. Date accessed: 2018‑09‑21.
[14] T. Perrin, "The XEdDSA and VXEdDSA Signature Schemes", 2016-10-20 [online]. Available: https://signal.org/docs/specifications/xeddsa and https://signal.org/docs/specifications/xeddsa/xeddsa.pdf. Date accessed: 2018‑10‑23.
[15] A. Poelstra, A. Back, M. Friedenbach, G. Maxwell and P. Wuille, "Confidential Assets", Blockstream [online]. Available: https://blockstream.com/bitcoin17-final41.pdf. Date accessed: 2018‑09‑25.
[16] Wikipedia: "Zero-knowledge Proof" [online]. Available: https://en.wikipedia.org/wiki/Zero-knowledge_proof. Date accessed: 2018‑09‑18.
[17] Wikipedia: "Discrete Logarithm" [online]. Available: https://en.wikipedia.org/wiki/Discrete_logarithm. Date accessed: 2018‑09‑20.
[18] A. Fiat and A. Shamir, "How to Prove Yourself: Practical Solutions to Identification and Signature Problems". CRYPTO 1986: pp. 186‑194 [online]. Available: https://link.springer.com/content/pdf/10.1007%2F3-540-47721-7_12.pdf. Date accessed: 2018‑09‑20.
[19] D. Bernhard, O. Pereira and B. Warinschi, "How not to Prove Yourself: Pitfalls of the Fiat-Shamir Heuristic and Applications to Helios" [online]. Available: https://link.springer.com/content/pdf/10.1007%2F978-3-642-34961-4_38.pdf. Date accessed: 2018‑09‑20.
[20] "Mimblewimble Explained" [online]. Available: https://www.weusecoins.com/mimble-wimble-andrew-poelstra/. Date accessed: 2018‑09‑10.
[21] GitHub: "Message Hiding in Bulletproofs #721" [online]. Available: https://github.com/mimblewimble/grin/issues/721. Date accessed: 2018‑09‑10.
[22] Pedersen-commitment: "An Implementation of Pedersen Commitment Schemes" [online]. Available: https://hackage.haskell.org/package/pedersen-commitment. Date accessed: 2018-09-25.
[23] "Zero Knowledge Proof Standardization - An Open Industry/Academic Initiative" [online]. Available: https://zkproof.org/documents.html. Date accessed: 2018‑09‑26.
[24] "SEC 2: Recommended Elliptic Curve Domain Parameters, Standards for Efficient Cryptography", 20 September 2000 [online]. Available: http://safecurves.cr.yp.to/www.secg.org/SEC2-Ver-1.0.pdf. Date accessed: 2018‑09‑26.
[25] GitHub: "ElementsProject/secp256k1-zkp, Experimental Fork of libsecp256k1 with Support for Pedersen Commitments and Range Proofs" [online]. Available: https://github.com/ElementsProject/secp256k1-zkp. Date accessed: 2018‑09‑18.
[26] GitHub: "apoelstra/secp256k1-mw, Fork of libsecp-zkp d78f12b to Add Support for Mimblewimble Primitives" [online]. Available: https://github.com/apoelstra/secp256k1-mw/tree/Bulletproofs. Date accessed: 2018‑09‑18.
[27] GitHub: "bbuenz/BulletProofLib, Library for Generating Non-interactive Zero Knowledge Proofs without Trusted Setup (Bulletproofs)" [online]. Available: https://github.com/bbuenz/BulletProofLib. Date accessed: 2018‑09‑18.
[28] GitHub: "dalek-cryptography/Bulletproofs, A Pure-Rust Implementation of Bulletproofs using Ristretto" [online]. Available: https://github.com/dalek-cryptography/Bulletproofs. Date accessed: 2018-09-18.
[29] GitHub: "adjoint-io/Bulletproofs, Bulletproofs are Short Non-interactive Zero-knowledge Proofs that Require no Trusted Setup" [online]. Available: https://github.com/adjoint-io/Bulletproofs. Date accessed: 2018‑09‑10.
[30] GitHub: "mimblewimble/secp256k1-zkp, Fork of secp256k1-zkp for the Grin/MimbleWimble project" [online]. Available: https://github.com/mimblewimble/secp256k1-zkp. Date accessed: 2018-09-18.
[31] "The Ristretto Group" [online]. Available: https://ristretto.group/ristretto.html. Date accessed: 2018‑10‑23.
[32] "SafeCurves: Choosing Safe Curves for Elliptic-curve Cryptography" [online]. Available: http://safecurves.cr.yp.to/. Date accessed: 2018‑10‑23.
[33] R. Canetti, B. Riva and G. N. Rothblum, "Two 1-Round Protocols for Delegation of Computation" [online]. Available: https://eprint.iacr.org/2011/518.pdf. Date accessed: 2018‑10‑11.
[34] GitHub: "mimblewimble/grin, Switch Commits / Bulletproofs - Status #734" [online]. Available: https://github.com/mimblewimble/grin/issues/734. Date accessed: 2018-09-10.
[35] GitHub: "mimblewimble/grin, Bulletproofs #273" [online]. Available: https://github.com/mimblewimble/grin/issues/273. Date accessed: 2018‑09‑10.
[36] Wikipedia: "Commitment Scheme" [online]. Available: https://en.wikipedia.org/wiki/Commitment_scheme. Date accessed: 2018‑09‑26.
[37] Cryptography Wikia: "Commitment Scheme" [online]. Available: http://cryptography.wikia.com/wiki/Commitment_scheme. Date accessed: 2018‑09‑26.
[38] D. J. Bernstein, "Curve25519: New Diffie-Hellman Speed Records" [online]. Available: https://cr.yp.to/ecdh/curve25519-20060209.pdf. Date accessed: 2018‑09‑26.
[39] H. Hisil, K. Koon-Ho Wong, G. Carter and E. Dawson, "Twisted Edwards Curves Revisited", Information Security Institute, Queensland University of Technology [online]. Available: https://iacr.org/archive/asiacrypt2008/53500329/53500329.pdf. Date accessed: 2018‑09‑26.
[40] A. Sadeghi and M. Steiner, "Assumptions Related to Discrete Logarithms: Why Subtleties Make a Real Difference" [online]. Available: http://www.semper.org/sirene/publ/SaSt_01.dh-et-al.long.pdf. Date accessed: 2018-09-24.
[41] Crypto Wiki: "Cryptographic Nonce" [online]. Available: http://cryptography.wikia.com/wiki/Cryptographic_nonce. Date accessed: 2018‑10‑08.
[42] Wikipedia: "Cryptographic Nonce" [online]. Available: https://en.wikipedia.org/wiki/Cryptographic_nonce. Date accessed: 2018-10-08.
[43] T. Ruffing and G. Malavolta, " Switch Commitments: A Safety Switch for Confidential Transactions", Saarland University [online]. Available: https://people.mmci.uni-saarland.de/~truffing/papers/switch-commitments.pdf. Date accessed: 2018‑10‑08.
[44] "BLAKE2 — Fast Secure Hashing" [online]. Available: https://blake2.net. Date accessed: 2018‑10‑08.
[45] GitHub: "mimblewimble/rust-secp256k1-zkp" [online]. Available: https://github.com/mimblewimble/rust-secp256k1-zkp. Date accessed: 2018‑11‑16.
[46] GitHub: "monero-project/monero [online]". Available: https://github.com/monero-project/monero/tree/master/src/ringct. Date accessed: 2018‑11‑16.
[47] Wikipedia: "Arithmetic Circuit Complexity [online]". Available: https://en.wikipedia.org/wiki/Arithmetic_circuit_complexity. Date accessed: 2018‑11‑08.
[48] G. Maxwell, A. Poelstra1, Y. Seurin and P. Wuille, "Simple Schnorr Multi-signatures with Applications to Bitcoin", 20 May 2018 [online]. Available: https://eprint.iacr.org/2018/068.pdf. Date accessed: 2018‑07‑24.
[49] GitHub: "b-g-goodell/research-lab" [online]. Available: https://github.com/b-g-goodell/research-lab/tree/master/source-code/StringCT-java. Date accessed: 2018‑11‑16.
[50] Wikipedia: "One-way Function" [online]. Available: https://en.wikipedia.org/wiki/One-way_function. Date accessed: 2018‑11‑27.
[51] P. Sharma, A. K. Gupta and S. Sharma, "Intensified ElGamal Cryptosystem (IEC)", International Journal of Advances in Engineering & Technology, January 2012 [online]. Available: http://www.e-ijaet.org/media/58I6-IJAET0612695.pdf. Date accessed: 2018‑10‑09.
[52] Y. Tsiounis and M Yung, "On the Security of ElGamal Based Encryption" [online]. Available: https://drive.google.com/file/d/16XGAByoXse5NQl57v_GldJwzmvaQlS94/view. Date accessed: 2018‑10‑09.
[53] Wikipedia: "Decisional Diffie–Hellman Assumption" [online]. Available: https://en.wikipedia.org/wiki/Decisional_Diffie%E2%80%93Hellman_assumption. Date accessed: 2018‑10‑09.
[54] GitHub: "mimblewimble/grin, Bulletproof messages #730" [online]. Available: https://github.com/mimblewimble/grin/pull/730. Date accessed: 2018‑11‑29.
[55] GitHub: "mimblewimble/grin, Removed all switch commitment usages, including restore #841" [online]. Available: https://github.com/mimblewimble/grin/pull/841. Date accessed: 2018‑11‑29.
[56] GitHub: "mimblewimble/grin, switch commitment discussion #998" [online]. Available: https://github.com/mimblewimble/grin/issues/998. Date accessed: 2018‑11‑29.
[57] GitHub: "mimblewimble/grin, [DNM] Switch commitments #2007" [online]. Available: https://github.com/mimblewimble/grin/pull/2007. Date accessed: 2018‑11‑29.
[58] G. G. Dagher, B. Bünz, J. Bonneauy, J. Clark and D. Boneh1, "Provisions: Privacy-preserving Proofs of Solvency for Bitcoin Exchanges", October 2015 [online]. Available: https://eprint.iacr.org/2015/1008.pdf. Date accessed: 2018‑11‑29.
[59] A. Poelstra, "Bulletproofs: Faster Rangeproofs and Much More", February 2018 [online]. Available: https://blockstream.com/2018/02/21/bulletproofs-faster-rangeproofs-and-much-more/. Date accessed: 2018‑11‑30.
[60] B. Franca, "Homomorphic Mini-blockchain Scheme", April 2015 [online]. Available: http://cryptonite.info/files/HMBC.pdf. Date accessed: 2018‑11‑22.
[61] C. Franck and J. Großschädl, "Efficient Implementation of Pedersen Commitments Using Twisted Edwards Curves", University of Luxembourg [online]. Available: http://orbilu.uni.lu/bitstream/10993/33705/1/MSPN2017.pdf. Date accessed: 2018‑11‑22.
[62] A. Gibson, "An Investigation into Confidential Transactions", July 2018 [online]. Available: https://github.com/AdamISZ/ConfidentialTransactionsDoc/blob/master/essayonCT.pdf. Date accessed: 2018‑11‑22.
[63] J. Bootle, "How to do Zero-knowledge from Discrete-Logs in under 7kB", October 2016 [online]. Available: https://www.benthamsgaze.org/2016/10/25/how-to-do-zero-knowledge-from-discrete-logs-in-under-7kb. Date accessed: 2019‑01‑18.
## Appendices
### Appendix A: Definition of Terms
Definitions of terms presented here are high level and general in nature. Full mathematical definitions are available in the cited references.
• Arithmetic Circuits: An arithmetic circuit $C$ over a field $F$ and variables $(x_1, ..., x_n)$ is a directed acyclic graph whose vertices are called gates. Arithmetic circuits can alternatively be described as a list of addition and multiplication gates with a collection of linear consistency equations relating the inputs and outputs of the gates. The size of an arithmetic circuit is the number of gates in it, with the depth being the length of the longest directed path. Upper bounding the complexity of a polynomial $f$ is to find any arithmetic circuit that can calculate $f$, whereas lower bounding is to find the smallest arithmetic circuit that can calculate $f$. An example of a simple arithmetic circuit with size six and depth two that calculates a polynomial is shown below ([29], [47]).
• Argument of Knowledge System: Proof systems with computational soundness like Bulletproofs are sometimes called argument systems. The terms proof and argument of knowledge have exactly the same meaning and can be used interchangeably [29].
• Commitment Scheme: A commitment scheme in a Zero-knowledge Proofdef is a cryptographic primitive that allows a prover to commit to only a single chosen value/statement from a finite set without the ability to change it later (binding property) while keeping it hidden from a verifier (hiding property). Both binding and hiding properties are then further classified in increasing levels of security to be computational, statistical or perfect. No commitment scheme can at the same time be perfectly binding and perfectly hiding ([36], [37]).
• Discrete Logarithm/Discrete Logarithm Problem (DLP): In the mathematics of real numbers, the logarithm $\log_b^a$ is a number $x$ such that $b^x=a$, for given numbers $a$ and $b$. Analogously, in any group $G$, powers $b^k$ can be defined for all integers $k$, and the discrete logarithm $\log_ba$ is an integer $k$ such that $b^k=a$. Algorithms in public-key cryptography base their security on the assumption that the discrete logarithm problem over carefully chosen cyclic finite groups and cyclic subgroups of elliptic curves over finite fields has no efficient solution ([17], [40]).
• Elliptic Curve Pedersen Commitment: An efficient implementation of the Pedersen Commitment ([15], [22]) will use secure Elliptic Curve Cryptography (ECC), which is based on the algebraic structure of elliptic curves over finite (prime) fields. Elliptic curve points are used as basic mathematical objects, instead of numbers. Note that traditionally in elliptic curve arithmetic lower case letters are used for ordinary numbers (integers) and upper case letters for curve points ([60], [61], [62]).
• The generalized Elliptic Curve Pedersen Commitment definition follows (refer to Appendix B: Notation Used):
• Let $\mathbb F_p$ be the group of elliptic curve points, where $p$ is a large prime.
• Let $G \in \mathbb F_p$ be a random generator point (base point) and let $H \in \mathbb F_p$ be specially chosen so that the value $x_H$ to satisfy $H = x_H G$ cannot be found except if the Elliptic Curve DLP (ECDLP) is solved.
• Let $r$ (the blinding factor) be a random value and element of $\mathbb Z_p$.
• The commitment to value $x \in \mathbb Z_p$ is then determined by calculating $C(x,r) = rH + xG$, which is called the Elliptic Curve Pedersen Commitment.
• Elliptic curve point addition is analogous to multiplication in the originally defined Pedersen Commitment. Thus $g^x$, the number $g$ multiplied by itself $m$ times, is analogous to $xG$, the elliptic curve point $G$ added to itself $x$ times. In this context $xG$ is also a point in $\mathbb F_p$.
• In the Elliptic Curve context $C(x,r) = rH + xG$ is then analogous to $C(x,r) = h^r g^x$.
• The number $H$ is what is known as a Nothing Up My Sleeve (NUMS) number. With secp256k1, the value of $H$ is the SHA256 hash of a simple encoding of the pre-specified generator point $G$.
• Similar to Pedersen Commitments, the Elliptic Curve Pedersen Commitments are also additionally homomorphic, such that for messages $x$, $x_0$ and $x_1$, blinding factors $r$, $r_0$ and $r_1$ and scalar $k$ the following relation holds: $C(x_0,r_0) + C(x_1,r_1) = C(x_0+x_1,r_0+r_1)$ and $C(k \cdot x, k \cdot r) = k \cdot C(x, r)$.
• In secure implementations of ECC, it is as hard to guess $x$ from $xG$ as it is to guess $x$ from $g^x$. This is called the Elliptic Curve DLP (ECDLP).
• Practical implementations usually consist of three algorithms: Setup() to set up the commitment parameters; Commit() to commit to the message using the commitment parameters; and Open() to open and verify the commitment.
• ElGamal Commitment/Encryption: An ElGamal commitment is a Pedersen Commitment ([15], [22]) with an additional commitment $g^r$ to the randomness used. The ElGamal encryption scheme is based on the Decisional Diffe-Hellman (DDH) assumption and the difficulty of the DLP for finite fields. The DDH assumption states that it is infeasible for a Probabilistic Polynomial-time (PPT) adversary to solve the DDH problem. Note: The ElGamal encryption scheme should not be confused with the ElGamal signature scheme ([1], [51], [52], [53]).
• Fiat‑Shamir Heuristic/Transformation: The Fiat‑Shamir heuristic is a technique in cryptography to convert an interactive public-coin protocol (Sigma protocol) between a prover and a verifier into a one-message (non-interactive) protocol using a cryptographic hash function ([18], [19]).
• The prover will use a Prove() algorithm to calculate a commitment $A$ with a statement $Y$ that is shared with the verifier and a secret witness value $w$ as inputs. The commitment $A$ is then hashed to obtain the challenge $c$, which is further processed with the Prove() algorithm to calculate the response $f$. The single message sent to the verifier then contains the challenge $c$ and response $f$.
• The verifier is then able to compute the commitment $A$ from the shared statement $Y$, challenge $c$ and response $f$. The verifier will then use a Verify() algorithm to verify the combination of shared statement $Y$, commitment $A$, challenge $c$ and response $f$.
• A weak Fiat‑Shamir transformation can be turned into a strong Fiat‑Shamir transformation if the hashing function is applied to the commitment $A$ and shared statement $Y$ to obtain the challenge $c$ as opposed to only the commitment $A $.
• Nonce: In security engineering, nonce is an abbreviation of number used once. In cryptography, a nonce is an arbitrary number that can be used just once. It is often a random or pseudo-random number issued in an authentication protocol to ensure that old communications cannot be reused in replay attacks ([41], [42]).
• Zero-knowledge Proof/Protocol: In cryptography, a zero-knowledge proof/protocol is a method by which one party (the prover) can convince another party (the verifier) that a statement $Y$ is true, without conveying any information apart from the fact that the prover knows the value of $Y$. The proof system must be complete, sound and zero-knowledge ([16], [23]):
• Complete - if the statement is true and both prover and verifier follow the protocol, the verifier will accept.
• Sound - if the statement is false, and the verifier follows the protocol, the verifier will not be convinced.
• Zero-knowledge - if the statement is true and the prover follows the protocol, the verifier will not learn any confidential information from the interaction with the prover, apart from the fact that the statement is true.
### Appendix B: Notation Used
The general notation of mathematical expressions when specifically referenced is given here, based on [1].
• Let $p$ and $q$ be large prime numbers.
• Let $\mathbb G$ and $\mathbb Q$ denote cyclic groups of prime order $p$ and $q$ respectively.
• let $\mathbb Z_p$ and $\mathbb Z_q$ denote the ring of integers $modulo \mspace{4mu} p$ and $modulo \mspace{4mu} q$ respectively.
• Let generators of $\mathbb G$ be denoted by $g, h, v, u \in \mathbb G$. In other words, there exists a number $g \in \mathbb G$ such that $\mathbb G = \lbrace 1 \mspace{3mu} , \mspace{3mu} g \mspace{3mu} , \mspace{3mu} g^2 \mspace{3mu} , \mspace{3mu} g^3 \mspace{3mu} , \mspace{3mu} ... \mspace{3mu} , \mspace{3mu} g^{p-1} \rbrace \equiv \mathbb Z_p$. Note that not every element of $\mathbb Z_p$ is a generator of $\mathbb G$.
• Let $\mathbb Z_p^*$ denote $\mathbb Z_p \setminus \lbrace 0 \rbrace$ and $\mathbb Z_q^*$ denote $\mathbb Z_q \setminus \lbrace 0 \rbrace$, that is all invertible elements of $\mathbb Z_p$ and $\mathbb Z_q$ respectively. This excludes the element $0$ which is not invertible. | 13,236 | 52,547 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2021-25 | longest | en | 0.867765 |
http://www.mathynomial.com/problem/1291 | 1,529,355,048,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267861163.5/warc/CC-MAIN-20180618203134-20180618223134-00564.warc.gz | 460,449,662 | 3,376 | # Problem #1291
1291 Kate rode her bicycle for 30 minutes at a speed of 16 mph, then walked for 90 minutes at a speed of 4 mph. What was her overall average speed in miles per hour? $\mathrm{(A)}\ 7\qquad \mathrm{(B)}\ 9\qquad \mathrm{(C)}\ 10\qquad \mathrm{(D)}\ 12\qquad \mathrm{(E)}\ 14$ This problem is copyrighted by the American Mathematics Competitions.
Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved.
• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
• Exponents should be entered in the form 10^10.
• If the problem is multiple choice, enter the appropriate (capital) letter.
• Enter points with parentheses, like so: (4,5)
• Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i). | 303 | 1,050 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2018-26 | latest | en | 0.855336 |
www.dotandanchor.com | 1,721,666,792,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517890.5/warc/CC-MAIN-20240722160043-20240722190043-00614.warc.gz | 640,105,558 | 71,469 | # DOT AND ANCHOR
## FAMILY SESSION
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec…
## SHOOTS
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec…
### How To Calculate Stormwater Drainage?
If we want to manage rainfall runoff properly, which means preventing flooding and mitigating environmental damage, we need to calculate stormwater drainage. Estimating drainage areas, peak flow rates, and rainfall intensity are all part of this procedure. Runoff coefficients are determined using surface types and slopes.
For safe water disposal and regulatory compliance, accurate calculations are necessary for the design of effective drainage systems such as detention basins, gutters, and storm drains. Anyone working in infrastructure or environmental management, such as engineers, urban planners, or real estate developers, must be familiar with these procedures.
## How To Calculate Stormwater Drainage?
Calculating stormwater drainage involves determining the amount of rainwater that needs to be managed or redirected away from an area to prevent flooding or damage. Here are the basic steps to calculate stormwater drainage:
### Determine the Rainfall Intensity
Find the rainfall intensity for your area, usually provided in rainfall intensity-duration-frequency (IDF) curves. This data gives you the rainfall rate in inches per hour or millimetres per hour for different storm durations and frequencies (like 10-year, 25-year storms, etc.).
### Calculate Runoff Coefficient
Determine the runoff coefficient, which depends on the surface type (like concrete, grass, etc.) and the slope of the surface. This coefficient represents the fraction of rainfall that becomes runoff rather than infiltrating into the ground.
### Calculate Drainage Area
Measure or estimate the total area from which stormwater runoff will occur. This area is usually the roof, paved surfaces, or any area that contributes to runoff.
### Calculate the Peak Flow Rate
Multiply the rainfall intensity by the drainage area and the runoff coefficient to get the peak flow rate of stormwater runoff. This gives you the maximum amount of water that needs to be managed at any given time during a storm event.
### Design Drainage Systems
Based on the calculated peak flow rate, design appropriate drainage systems such as gutters, downspouts, storm drains, detention basins, or other stormwater management practices to safely convey or store the runoff.
### Consider Local Regulations
Ensure compliance with local regulations and standards for stormwater management, which may dictate specific design criteria and permissible discharge rates.
If you provide specific details about your project or area (such as location, size of the drainage area, and type of surface), I can help you with more precise calculations or information.
## How Deep Should A Soakwell Be?
The depth of a soak well, also known as an infiltration pit or dry well, depends on several factors such as soil type, local regulations, and the volume of stormwater runoff it needs to handle. Here are some general guidelines:
### Depth Considerations
Soakwells are typically designed to be at least 1.2 to 1.5 meters (4 to 5 feet) deep. This depth helps ensure adequate storage capacity for stormwater runoff and allows for effective infiltration into the surrounding soil.
### Soil Percolation Rate
The soil’s ability to absorb water (percolation rate) influences the design depth. If the soil has a high percolation rate, a deeper soak well may be necessary to accommodate faster drainage.
### Volume of Runoff
Calculate the volume of stormwater runoff from the contributing area to determine the appropriate size and depth of the soakwell. Larger volumes may require deeper soakwells to handle peak flow rates effectively.
### Local Regulations
Check local building codes and regulations, as they often specify minimum depth requirements for soakwells based on factors like soil conditions and groundwater levels.
### Professional Design
For precise calculations and design, especially for larger projects or where regulatory compliance is critical, consulting with a civil engineer or stormwater management specialist is recommended.
If you have specific details about your project or location, I can provide more tailored advice on the depth and design considerations for soakwells.
## How To Install A Polypropylene Soakwell?
Installing a polypropylene soak well involves several key steps to ensure effective stormwater management. Here’s a general guide to the installation process:
### Materials And Tools Needed
• Polypropylene soak well kit (includes soak well modules)
• Geotextile fabric
• Gravel or aggregate
• PVC pipes (for inlet and outlet)
• Tape measure
• Shovel or excavator
• Spirit level
• Backfill material (sand or soil)
### Installation Steps
#### Site Preparation
• Choose a suitable location for the soakwell(s) based on local regulations and site conditions. Ensure it is away from structures and utilities.
• Mark and excavate the area to the required depth, typically 1.2 to 1.5 meters (4 to 5 feet) deep, depending on soil type and design specifications.
#### Prepare the Base
• Level the bottom of the excavation using a spirit level to ensure a stable base for the soakwell modules.
• Lay a geotextile fabric at the base and along the sides of the excavation to prevent soil from entering and clogging the soakwell.
#### Assemble the Soakwell Modules
• Assemble the polypropylene soakwell modules according to the manufacturer’s instructions. Typically, these modules interlock or fit together like puzzle pieces to form a larger storage unit.
#### Install Inlet and Outlet Pipes
• Position PVC pipes for inlet (from downspouts or surface drainage) and outlet (to discharge excess water). Ensure they are securely connected to the soakwell modules and properly sealed to prevent leaks.
#### Place and Backfill
• Lower the assembled soakwell modules into the excavated area. Ensure they are placed level and snugly fit together.
• Backfill around the modules with gravel or aggregate to provide additional support and aid in drainage.
#### Complete Installation
• Backfill the remaining space around the soakwell modules with sand or soil, compacting gently as you go to avoid shifting.
• Ensure the inlet and outlet pipes are positioned correctly and securely capped until connected to the drainage system.
#### Surface Finishing
• Once installed and backfilled, cover the area with topsoil and restore landscaping or surface materials as needed.
#### Testing and Maintenance
• After installation, test the soakwell system by directing water into the inlet pipe to ensure proper drainage and functionality.
• Regularly inspect and maintain the soakwell to prevent blockages and ensure efficient water management.
If you are worried about installation or if you are working on a larger project, you might want to consider speaking with a licensed plumber or a specialist who specializes in stormwater management. In addition to ensuring compliance with local legislation and best practices, they can provide assistance that is relevant to your specific location.
## Conclusion
The management of stormwater on residential and commercial premises can be accomplished practically by installing a polypropylene soakwell. Through the promotion of groundwater recharge and the reduction of demand on municipal drainage systems, a well-installed soakwell brings about an improvement in environmental sustainability.
This is in addition to the functional benefits that it offers, such as the prevention of erosion and flooding. During the procedure, it is necessary to take into account the characteristics of the site, correctly assemble the soakwell modules, and make certain that the intake and outlet pipe connections result in an acceptable drainage capacity.
Property owners can successfully limit the effects of heavy rain events by keeping to local restrictions and following these measures. In addition, they can make a constructive contribution to the efforts underway in their community to save water.
To further ensure that the system continues to function at its optimal level throughout time, routine maintenance and inspections should be performed periodically. This will provide property owners with peace of mind as well as long-term advantages for the environment.
### Is Perth Fun For Kids?
The vibrant capital of Western Australia, Perth, is an ideal vacation spot for families in search of excitement and adventure. Perth has a lot to offer in the way of fun things to do for kids, including gorgeous beaches, large parks, interactive museums, and exciting attractions.
Perth is a fantastic destination for families with kids of all ages, whether they enjoy outdoor adventures, learning about fascinating science, or petting animals. Come with us as we explore Perth and find out what the top family-friendly things to do are.
## Is Perth Fun For Kids?
Perth is known for being a family-friendly city with a variety of activities and attractions that are great for kids. Here are some highlights:
• Kings Park and Botanic Garden: One of the largest inner-city parks in the world, offering playgrounds, walking trails, and picnic areas.
• Perth Zoo: A popular destination with a wide range of animals and interactive exhibits.
• AQWA (The Aquarium of Western Australia): Kids can explore marine life from the coastlines of Western Australia.
• Scitech: An interactive science museum with exhibits and a planetarium.
• Adventure World: A theme park with water slides, roller coasters, and other rides.
• Cottesloe Beach: A beautiful beach that’s great for swimming, building sandcastles, and family picnics.
• Elizabeth Quay: Offers playgrounds, a water park, and boat rides.
• Perth Mint: An interesting place where kids can learn about gold mining and see gold being poured.
• Whiteman Park: Features playgrounds, a wildlife park, a tramway, and a motor museum.
• Bibra Lake Regional Playground: A huge playground with various equipment and a water play area.
These are just a few examples, and Perth offers even more in terms of parks, museums, and outdoor activities that cater to children and families.
## Is Perth A Good City For Kids?
Yes, Perth is a great city for kids. Here’s why:
• Abundant Outdoor Spaces: Perth boasts numerous parks and playgrounds, such as Kings Park and Botanic Garden, which offer plenty of space for kids to run, play, and explore.
• Beautiful Beaches: The city’s coastline features family-friendly beaches like Cottesloe Beach, perfect for swimming, sandcastle building, and picnics.
• Educational Attractions: Perth has many educational and interactive attractions, including the Perth Zoo, AQWA (The Aquarium of Western Australia), and Scitech, where kids can learn while having fun.
• Safe and Clean Environment: Perth is known for its clean, safe streets and well-maintained public spaces, making it a comfortable place for families to live and visit.
• Excellent Schools and Facilities: The city offers a range of high-quality schools and recreational facilities that cater to children’s educational and extracurricular needs.
• Community Events and Programs: Perth hosts various family-friendly events and programs throughout the year, such as festivals, markets, and holiday celebrations, ensuring there’s always something fun to do.
• Diverse Activities: From adventure parks like Adventure World to wildlife experiences at Whiteman Park, Perth provides diverse activities that cater to different interests and age groups.
Perth’s combination of natural beauty, safety, educational opportunities, and fun activities makes it an excellent city for kids.
## Where To Bring Kids In Perth?
Perth offers a wide range of places to bring kids for fun and educational experiences. Here are some top spots:
### Outdoor Activities
• Kings Park and Botanic Garden: This massive park features playgrounds, walking trails, picnic areas, and stunning views of the city.
• Cottesloe Beach: A beautiful, family-friendly beach perfect for swimming, building sandcastles, and picnicking.
• Whiteman Park: Offers playgrounds, a wildlife park, a tramway, and picnic areas.
• Bibra Lake Regional Playground: A huge playground with various equipment and a water play area.
• Elizabeth Quay: Features playgrounds, a water park, and boat rides.
### Animal and Nature Experiences
• Perth Zoo: Home to a wide range of animals, with interactive exhibits and educational programs.
• AQWA (The Aquarium of Western Australia): Kids can explore marine life from the coastlines of Western Australia.
• Caversham Wildlife Park: Offers close encounters with Australian animals like kangaroos, koalas, and wombats.
• Rottnest Island: A short ferry ride away, it’s great for bike rides, snorkelling, and spotting quokkas.
• Cultural and Community Events
• Fremantle Markets: Offers a vibrant atmosphere with various stalls, live music, and street performers.
• Perth Cultural Centre: Includes the Art Gallery of Western Australia and the WA Museum Boola Bardip, both offering family-friendly exhibits and programs.
These destinations ensure that kids of all ages can find something enjoyable and enriching to do in Perth.
## Why Do International Students Choose Perth?
International students choose Perth for a variety of compelling reasons:
#### High-Quality Education
• Reputable Institutions: Perth is home to several renowned universities such as the University of Western Australia (UWA), Curtin University, Murdoch University, and Edith Cowan University.
• Diverse Programs: These institutions offer a wide range of courses and programs, from undergraduate to postgraduate studies, catering to various academic interests and career aspirations.
#### Lifestyle and Environment
• Beautiful Climate: Perth enjoys a Mediterranean climate with plenty of sunshine, making it an attractive place to live and study.
• Stunning Natural Beauty: The city is known for its beautiful beaches, parks, and outdoor spaces, providing a high quality of life and numerous recreational opportunities.
#### Cultural Diversity and Support
• Multicultural Community: Perth is a multicultural city with a diverse population, making it easier for international students to integrate and feel at home.
• Support Services: Universities and local organizations offer extensive support services for international students, including orientation programs, language support, and social activities.
#### Safety and Stability
• Safe Environment: Perth is considered one of the safest cities in Australia, with low crime rates and a stable political environment.
• High Standard of Living: The city offers a high standard of living with modern infrastructure, healthcare, and public services.
#### Work Opportunities
• Work While Studying: International students in Perth can work part-time while studying, helping them gain valuable work experience and support themselves financially.
• Post-Study Work Rights: Australia offers post-study work visas, allowing graduates to stay and work in the country after completing their studies.
#### Affordability
• Cost of Living: While Perth is a major city, the cost of living can be more affordable compared to other Australian cities like Sydney and Melbourne.
• Scholarships and Financial Aid: Various scholarships and financial aid options are available for international students to help offset tuition and living expenses.
#### Quality of Life
• Healthy Lifestyle: With its emphasis on outdoor activities, sports, and healthy living, Perth promotes a balanced and healthy lifestyle.
• Cultural and Recreational Activities: The city offers a vibrant arts and culture scene, numerous festivals, and recreational activities that cater to a wide range of interests.
These factors combine to make Perth an attractive destination for international students seeking a high-quality education and a rewarding life experience.
## Conclusion
Perth is well-known among international students for its excellent education system, exciting nightlife, and welcoming community. Because of the welcoming ethnic society, mild year-round temperatures, and excellent educational institutions that provide a wide range of programs, students have no trouble adjusting to college life.
The city is even more attractive because of its low cost of living, plenty of job prospects, and relative safety. Perth offers international students a tempting destination for academic and personal growth, thanks to its strong emphasis on quality of life and recreational activities. The city provides an enriching and well-rounded experience.
Looking for more information? Visit this guide “free school holiday activities perth 2022”.
### What Is The Work Of Electrician Maintenance?
In a wide range of settings, from homes to businesses to factories, the safe and effective operation of electrical systems is dependent on electricians who focus on maintenance. Electrical systems rely on these trained experts to examine, diagnose, repair, and maintain them so that they continue to function at peak efficiency and without interruption.
Technical knowledge, strict attention to safety protocols, and preventative measures against electrical breakdowns are all part of their job description. To emphasize the significance of electricians in today’s infrastructure, this article delves into the many duties and critical activities that make up their maintenance labour.
## What Is The Work Of Electrician Maintenance?
The work of an electrician specializing in maintenance involves a range of tasks aimed at ensuring the safe and efficient operation of electrical systems and equipment. Here are the primary responsibilities and duties of an electrician in maintenance:
### Inspection and Diagnosis
• Regularly inspect electrical systems, wiring, and equipment.
• Identify and diagnose electrical problems using tools like voltmeters, ammeters, and oscilloscopes.
### Repair and Replacement
• Repair or replace faulty electrical components such as wiring, circuit breakers, outlets, switches, and fixtures.
• Ensure that all electrical repairs comply with safety standards and codes.
### Preventive Maintenance
• Perform routine preventive maintenance to ensure the longevity and reliability of electrical systems.
• Test and maintain electrical systems to prevent breakdowns and failures.
• Install new electrical systems, equipment, and components in existing buildings and structures.
• Upgrade outdated or inefficient electrical systems to meet current safety and performance standards.
### Safety Compliance
• Ensure that all electrical work is performed in compliance with local, state, and national electrical codes and regulations.
• Implement safety measures and protocols to protect themselves and others from electrical hazards.
### Troubleshooting
• Use diagnostic tools and techniques to troubleshoot complex electrical issues.
• Develop solutions to electrical problems and implement necessary repairs or adjustments.
### Documentation and Reporting
• Maintain detailed records of maintenance work, including inspections, repairs, and upgrades.
• Report any major issues or safety concerns to supervisors or relevant authorities.
### Emergency Response
• Respond to emergency electrical issues, such as power outages or hazardous conditions, and perform necessary repairs to restore service.
### Collaboration
• Work with other maintenance personnel, engineers, and contractors to coordinate electrical work and ensure efficient operation of systems.
### Training and Development
• Attend training sessions and obtain necessary certifications to enhance skills and knowledge.
Electrician maintenance work is critical in various settings, including residential, commercial, and industrial environments, to ensure that electrical systems are safe, reliable, and efficient.
## What Is The Most Common Electrical Service?
The most common electrical service provided by electricians typically involves residential electrical work. This includes a wide range of services aimed at maintaining, repairing, and upgrading the electrical systems within homes. Some of the most common residential electrical services include:
### Wiring and Rewiring
• Installation of new wiring in new homes or rewiring in older homes to replace outdated or unsafe wiring.
### Lighting Installation and Repair
• Installing, repairing, or upgrading indoor and outdoor lighting fixtures, including ceiling lights, chandeliers, and landscape lighting.
• Upgrading electrical panels to accommodate increased power demands or replacing outdated panels for improved safety and efficiency.
### Outlet and Switch Installation
• Installing new electrical outlets and switches, including GFCI (Ground Fault Circuit Interrupter) outlets in kitchens and bathrooms.
### Troubleshooting and Repairs
• Diagnosing and repairing electrical issues such as power outages, faulty wiring, and
• malfunctioning outlets or switches.
### Ceiling Fan Installation
• Installing or replacing ceiling fans to improve air circulation and comfort within homes.
### Home Automation and Smart Home Integration
• Installing and configuring smart home systems, including smart lighting, thermostats, and security systems.
### Electrical Safety Inspections
• Conducting comprehensive electrical inspections to ensure the safety and compliance of home electrical systems with local codes and regulations.
### Surge Protection
• Installing whole-house surge protectors to safeguard electrical devices and appliances from power surges.
### Generator Installation
• Installing backup generators to provide an alternative power source during outages.
These common services help homeowners maintain a safe, functional, and efficient electrical system, addressing both routine maintenance and urgent repairs.
## Is Electrician A Profession?
Yes, electrician is indeed a profession. Electricians are skilled tradespeople who specialize in installing, maintaining, and repairing electrical systems in various settings, including residential, commercial, and industrial environments. The profession requires a combination of technical knowledge, practical skills, and adherence to safety standards and regulations.
Key aspects of the electrician profession include:
### Education and Training
• Electricians typically undergo formal education and training, which may include technical school programs, apprenticeships, and on-the-job training.
• Apprenticeships usually combine classroom instruction with hands-on experience under the supervision of experienced electricians.
### Certification and Licensing
• Electricians often need to obtain certifications and licenses to practice legally, which involve passing exams that test their knowledge and skills.
• Licensing requirements vary by region and often include continuing education to stay updated on code changes and new technologies.
### Specializations
• Electricians can specialize in various areas, such as residential, commercial, industrial, or maintenance electrical work.
• Some may focus on specific systems, like HVAC (heating, ventilation, and air conditioning), renewable energy (solar or wind power), or home automation.
### Skills and Knowledge
• Electricians must have a solid understanding of electrical theory, wiring practices, safety codes, and the use of various tools and equipment.
• Problem-solving skills, attention to detail, and the ability to work in diverse environments are crucial.
### Work Environment
• Electricians work in a range of environments, from construction sites and factories to homes and offices.
• They may work independently or as part of a team, often collaborating with other tradespeople and contractors.
### Safety and Regulations
• Ensuring safety is a paramount concern in the profession, as electricians work with high-voltage systems and equipment that pose significant hazards if not handled properly.
• Compliance with national and local electrical codes and standards is mandatory to ensure safe and effective electrical installations.
The electrician profession is essential in modern society, playing a critical role in the installation, maintenance, and repair of the electrical systems that power our homes, businesses, and industries.
## Conclusion
Electricians play an essential role in today’s society, using their extensive knowledge and expertise to maintain the reliability and effectiveness of our electrical systems. Electrical work can be complex in a variety of settings, including homes, businesses, and factories, but electricians are prepared for the challenge thanks to their extensive training, certification, and education.
To keep our technology infrastructure running and our daily life powered, their knowledge of electrical system installation, maintenance, and repair is essential. Expert electricians are in high demand because of the critical role they play in maintaining electrical service reliability, compliance, and safety.
Electricians need technical knowledge, but they also need to be able to solve complex problems, pay close attention to detail, and prioritize safety. Because of these traits, they can properly and efficiently diagnose and fix complicated electrical problems.
Electrical code rules and technological developments are always evolving, therefore electricians must engage in ongoing education and training to keep up. Their ability to adjust to new difficulties and developments in the sector is guaranteed by their commitment to lifelong learning.
The need for effective communication and teamwork in the electrical industry is underscored by the fact that electricians frequently operate in tandem with other contractors, engineers, and craftsmen.
Electricians, whether on new building sites, in the field of routine maintenance, or in the event of an emergency, rely on their ability to work in close conjunction with others to ensure the safe and timely completion of all jobs. Working together as a team improves the overall quality of the job and guarantees compliance with all applicable safety laws.
Looking for a trusted electrician? Book your appointment today with andre electirician!
### What Do You Call Someone Who Plays The Flute?
When you hear the term “flautist,” what comes to mind? Perhaps a musician, gracefully holding a silver flute, coaxing beautiful, melodious sounds from the instrument with an effortless precision. Or maybe a member of an orchestra, contributing to a symphonic tapestry with ethereal notes that can both soar above and blend seamlessly with other instruments.
The word “flautist” is just one of the terms used to describe someone who plays the flute. This article delves into the intricacies of what it means to be a flautist, the history and evolution of the flute, and the various contexts in which flute players shine.
## Defining the Flutist: Terminology and Variations
The English language offers a few different terms for someone who plays the flute. “Flutist” and “flautist” are the most common, and the choice between them can depend on regional preferences or individual tastes. “Flutist” is more commonly used in American English, while “flautist” is favoured in British English. Both terms are correct and interchangeable, though some argue “flautist” has a more classical and refined connotation, derived from the Italian “flautista.”
Interestingly, the term “flautist” came into use in English only in the 19th century, influenced by Italian musicians and the Romantic era’s love for Italianate forms. “Flutist,” on the other hand, has roots going back to the Renaissance, reflecting a longer historical continuity in the English language.
Regardless of the term used, a flautist or flautist is a musician who plays the flute. This role can encompass a wide variety of contexts, from solo performances and orchestral participation to jazz ensembles and folk bands. The skill set required to excel as a flautist is diverse, involving technical proficiency, artistic expression, and a deep understanding of musical theory and history.
## The Flute: An Instrument with a Rich History
The flute is one of the oldest musical instruments in human history, with origins tracing back thousands of years. Early flutes, made from bones and reeds, have been discovered in archaeological sites around the world, indicating their widespread use in ancient cultures.
The modern concert flute, as recognized today, evolved significantly during the Baroque period (1600-1750). This era saw the standardization of the flute’s design, with key mechanisms being introduced to improve playability and range. Theobald Boehm, a 19th-century German inventor and flautist, made significant advancements to the flute’s design, creating the Boehm system which remains the basis for modern flutes.
Flutes are categorized into various types, including the concert flute (or C flute), piccolo, alto flute, and bass flute. Each type has its unique sound and role within different musical settings. For instance, the piccolo, with its high pitch, is often used for bright, piercing notes that cut through an orchestral texture, while the alto flute, with its mellow and rich tone, is favoured for its warm, lower register.
## The Path to Becoming a Flutist
Becoming a proficient flautist involves years of dedicated practice and study. Many flautists begin their musical journey at a young age, often starting with basic music education and progressing through more advanced studies. Here’s a look at the typical path of a flautist:
### Early Education:
Many flautists start learning music in elementary or middle school, often through school bands or private lessons. Early education focuses on basic techniques, such as breath control, finger placement, and reading music.
### Intermediate Development:
As students progress, they tackle more complex pieces and techniques. Participation in school bands, youth orchestras, and regional competitions helps build performance experience.
Aspiring professional flautists often pursue formal education in music schools or conservatories. Here, they receive specialized training in flute performance, music theory, and history. Advanced students also learn about different genres and styles, from classical to contemporary.
### Professional Career:
After completing their education, flautists may pursue various career paths. Some join orchestras or chamber groups, while others become solo performers or session musicians. Teaching is another common avenue, with many flautists sharing their expertise through private lessons or academic positions.
## The Flutist in Various Musical Contexts
Flutists have a versatile role in the music world, contributing to a wide range of genres and settings. Here are some key contexts in which flautists excel:
### Classical Music:
The flute is a staple of the classical orchestra, with an extensive repertoire of concertos, sonatas, and orchestral parts. Famous composers like Mozart, Bach, and Vivaldi have written significant works for the flute, showcasing its expressive capabilities. In orchestras, flautists often play both solo passages and ensemble parts, requiring a balance of individual artistry and collaborative skill.
### Jazz:
Jazz flautists bring a different set of skills to the table, including improvisation and a deep sense of rhythm. The flute’s agility and wide range make it a popular choice for jazz solos and ensemble playing. Notable jazz flautists like Herbie Mann and Hubert Laws have expanded the instrument’s role in the genre, incorporating it into a wide range of styles from bebop to Latin jazz.
### Folk and World Music:
The flute has deep roots in folk traditions around the world. From the Irish tin whistle to the Indian bansuri, flutes come in various forms and play a central role in many cultural musical expressions. Folk flautists often focus on traditional techniques and repertoires, bringing the rich heritage of their cultures to contemporary audiences.
### Contemporary and Experimental Music:
Many modern flautists push the boundaries of the instrument, exploring new techniques and sounds. Extended techniques such as multiphonics, flutter-tonguing, and beatboxing on the flute are common in contemporary classical and experimental music. These innovations expand the sonic possibilities of the flute, allowing flautists to create unique and avant-garde performances.
## Notable Flutists Throughout History
The history of the flute is marked by numerous influential players who have left an indelible mark on the music world. Here are a few notable flautists whose contributions have been particularly significant:
• Jean-Pierre Rampal: Often considered the greatest flautist of the 20th century, Rampal brought the flute into the spotlight as a solo instrument. His virtuosity and expressive playing set new standards for flautists worldwide.
• James Galway: An Irish flautist known for his brilliant technique and warm tone, Galway has enjoyed a long and celebrated career as a soloist. He has recorded extensively and collaborated with many leading orchestras and musicians.
• Marcel Moyse: A French flautist and pedagogue, Moyse’s teachings and writings have influenced generations of flautists. His exercises and etudes are standard practice material for students around the world.
• Herbie Mann: A pioneer of jazz flute, Mann’s work in the 1960s and 70s helped establish the flute as a legitimate jazz instrument. His blending of jazz with Latin and world music elements created a distinctive and influential style.
• Ian Anderson: As the frontman of the rock band Jethro Tull, Anderson brought the flute into the rock genre. His dynamic playing and charismatic stage presence made him one of the most recognizable flautists in popular music.
## The Flutist’s Role in Education and Outreach
Beyond performance, many flautists contribute to music education and outreach. Teaching the next generation of musicians is a vital aspect of a flautist’s career, whether through private lessons, workshops, or academic positions. Flautists often mentor young players, guiding them through technical challenges and helping them develop their musical voices.
Outreach programs also play a significant role in a flautist’s professional life. Many musicians participate in initiatives that bring music to underserved communities, schools, and hospitals. These programs can inspire a love of music in young people and provide therapeutic benefits to those in need. Flautists involved in outreach work help to make music accessible and meaningful to a broader audience.
## Challenges and Rewards of Being a Flutist
The life of a flautist, like any musician, comes with its unique set of challenges and rewards. The physical demands of playing the flute require maintaining good health and technique to avoid injuries. The competitive nature of the music industry means that flautists must continually strive for excellence and innovation.
However, the rewards are equally significant. The ability to create beautiful music and share it with others is a profound and fulfilling experience. The connections made through music, whether with audiences, fellow musicians, or students, are deeply meaningful. The sense of accomplishment from mastering a challenging piece or delivering a memorable performance is unparalleled.
## Conclusion
In conclusion, a flautist is much more than just someone who plays the flute. They are artists, educators, innovators, and ambassadors of music. The journey of a flautist is one of continuous learning, creativity, and passion. Whether performing a classical concerto, improvising a jazz solo, or teaching a young student, flautists bring a unique and valuable voice to the world of music. Their contributions enrich our cultural landscape, and their artistry inspires us all. So, the next time you hear the enchanting sounds of a flute, take a moment to appreciate the skill and dedication of the flautist behind the music.
### What Is Overhead Garage Storage?
Overhead garage storage is a clever and efficient way for homeowners to make the most of their garage space. The idea is to make use of the space up there in the garage for stowing away tools, seasonal decorations, and other large, seldom-used objects.
Overhead garage storage allows you to make better use of the space by removing clutter from the floor and walls through the installation of shelves, racks, or platforms that are hanging from the ceiling. In this article, we’ll take a look at the several kinds of overhead garage storage, how they work, some things to think about while installing them, and some pointers to help you get the most out of them.
## What Is Overhead Garage Storage?
When talking about garages, “overhead storage” is making use of the space up above to store stuff. Shelves, racks, or platforms fixed on the wall or suspended from the ceiling are common components of this sort of storage. Its clever design makes the most of the garage’s vertical space, providing ample storage for tools, camping gear, sports equipment, seasonal decorations, and other large, seldom-used goods.
Overhead garage storage is a great way to make the most of your garage’s storage capacity without sacrificing organization and floor space. A better storage solution that helps eliminate clutter and improves accessibility to regularly used items stored elsewhere in the garage is to lift items off the ground and utilize the overhead space. This allows homeowners to build a more effective storage system.
Shelving units suspended from the ceiling are one type of overhead garage storage system. More complex options include pulley systems or motorized platforms that lower for easier access. Considerations including garage ceiling height, item weight and size, and aesthetic and accessibility preferences all play a role in making a system selection.
When it comes to household storage needs, overhead garage storage is a practical solution that maximizes capacity, improves organization, and creates a more usable space.
## Is Overhead Garage Storage Safe?
Overhead garage storage can be safe when installed and used properly. Here are some key considerations to ensure safety:
• Weight Capacity: Ensure that the overhead storage system you install is rated to support the weight of the items you plan to store. Exceeding weight limits can compromise the integrity of the storage system and pose a safety risk.
• Installation: Follow the manufacturer’s instructions or guidelines provided by professionals for installation. Use appropriate hardware and ensure that the installation is secure and stable.
• Clearance: Maintain adequate clearance between the stored items and the garage door mechanism, car roofs, or any other structures to prevent interference or accidents.
• Accessibility: Ensure that stored items are securely placed and easily accessible. Use sturdy containers or bins to store smaller items to prevent them from falling.
• Regular Inspection: Periodically inspect the overhead storage system for any signs of wear, damage, or loosening hardware. Address any issues promptly to maintain safety.
• Professional Installation: For complex systems or if you are unsure about installation, consider hiring a professional to ensure it is done correctly and safely.
By following these guidelines and using common sense, overhead garage storage can provide a safe and efficient way to maximize storage space in your garage.
## How Do You Store Above A Garage?
Storing items above a garage typically involves utilizing the overhead space effectively. Here are several methods and considerations for storing items above a garage:
• Overhead Storage Racks: Install overhead storage racks or shelves that are mounted to the ceiling joists or rafters of the garage. These racks can be made of metal or wood and are designed to safely support heavy items. They provide a platform for storing bins, boxes, or other items that are not frequently accessed.
• Pulley Systems: Consider using a pulley system or motorized platform that allows you to lift and lower items from the ceiling. This is particularly useful for storing large or heavy items such as bicycles, kayaks, or storage bins that you want to access occasionally without having to lift them manually.
• Ceiling-mounted Shelving: Install shelves directly onto the ceiling or high on the walls of the garage. This method is ideal for storing lightweight items or smaller boxes that can be easily accessed with a step ladder.
• Hooks and Hangers: Use hooks, brackets, or hangers mounted to the ceiling or walls to store items such as ladders, garden tools, or sports equipment. Make sure to choose sturdy hooks that are appropriate for the weight and size of the items you plan to hang.
• Clear Plastic Bins: Store items in clear plastic bins or containers to keep them organized and protected from dust and moisture. Label the bins for easy identification of contents.
• Safety Considerations: Ensure that all overhead storage systems are installed securely and can support the weight of the items stored. Check regularly for any signs of wear or damage to maintain safety.
• Accessibility: Arrange items so that frequently used items are easily accessible, either by positioning them near the garage entrance or using a pulley system for convenient retrieval.
• Maximize Space: Utilize the entire overhead space efficiently by planning storage layouts that make the best use of the available ceiling area without overcrowding.
By employing these methods and considerations, you can effectively utilize the space above a garage for storage, keeping your belongings organized and maximizing the available storage capacity in your home.
## Is Overhead Garage Storage Worth It?
Whether overhead garage storage is worth it depends on your specific needs, space constraints, and how you plan to use your garage. Here are some factors to consider if garage overhead storage is worth it:
• Maximizing Space: Overhead storage can significantly increase your garage’s storage capacity by utilizing otherwise unused vertical space. This is especially beneficial if you have a small garage or limited floor space.
• Organization: It helps to keep your garage organized by storing items that are not frequently used up and out of the way. This can reduce clutter on the floor and make it easier to find and access items when needed.
• Safety and Accessibility: Properly installed overhead storage systems can provide a safe and accessible way to store bulky or seasonal items such as sporting equipment, holiday decorations, or tools. It can also prevent items from cluttering walkways or becoming damaged on the garage floor.
• Cost and Installation: The cost of overhead garage storage systems can vary depending on the type and complexity of the system you choose. Simple shelving or racks may be more affordable and easier to install yourself, while more complex systems like motorized platforms may require professional installation and be more expensive.
• Maintenance: Consider the maintenance required for the overhead storage system. Regular inspections and upkeep may be necessary to ensure safety and longevity.
If you need additional storage space in your garage and are looking to improve organization and accessibility, overhead garage storage can be a worthwhile investment. It allows you to make the most of your garage’s vertical space and create a more functional and efficient storage solution. Assess your specific needs and budget to determine if overhead garage storage is the right choice for you.
## Conclusion
One easy and effective technique to make the most of your garage’s storage space is to install overhead storage. Make better use of the space above your head to avoid wasting precious floor space and maintain a neat garage. Prioritizing safety by ensuring correct installation and weight capacity is essential whether choosing overhead storage racks, pulley systems, ceiling-mounted shelves, or hooks and hangers.
To keep your overhead storage system in good working order and safe condition for as long as possible, it is important to inspect and maintain it regularly. As a whole, overhead garage storage is a multipurpose way to keep your garage organized and useful, perfect for stowing away unused or seldom-used goods.
### How Much Does A Branding Agency Cost?
In today’s competitive market, establishing a strong brand identity is crucial for businesses of all sizes. A well-crafted brand not only distinguishes a company from its competitors but also fosters customer loyalty and drives long-term success. To achieve this, many businesses turn to branding agencies for their expertise in creating compelling brand identities.
However, one of the most common questions businesses ask is: How much does a branding agency cost? This article will delve into the factors that influence the cost of hiring a branding agency and provide a comprehensive overview of the various pricing structures and what businesses can expect to pay.
## What is a Branding Agency?
A branding agency is a firm that specializes in creating, developing, and managing brands. Their services typically include brand strategy, brand identity design, brand messaging, market research, and more. Branding agencies help businesses articulate their values, mission, and vision in a way that resonates with their target audience.
The ultimate goal is to create a consistent and memorable brand experience across all customer touchpoints.
## Factors Influencing Branding Agency Costs
### Scope of Work:
The extent of services required plays a significant role in determining the cost. A full rebranding, which includes a new logo, website redesign, marketing materials, and a brand strategy, will be more expensive than a partial rebranding or brand refresh.
### Agency Size and Reputation:
The size and reputation of the agency also impact costs. Well-established agencies with a strong portfolio and high-profile clients generally charge more than smaller or less experienced agencies.
### Industry and Niche:
Some industries, like luxury goods or technology, may require specialized knowledge and experience, which can affect pricing. Agencies that focus on specific niches might charge a premium for their specialized expertise.
### Geographical Location:
The location of the agency can influence costs. Agencies in major metropolitan areas or regions with a high cost of living typically charge more than those in smaller cities or regions with lower living costs.
### Project Timeline:
The timeframe for completing the project can also affect pricing. Expedited timelines may require additional resources and thus incur higher costs.
### Deliverables:
The type and number of deliverables required (e.g., logo, website, social media assets, packaging design) will influence the overall cost. More complex deliverables or a higher quantity will increase the price.
## Common Pricing Structures
Branding agencies use various pricing structures, and understanding these can help businesses budget more effectively. The most common pricing models include:
• Hourly Rates: Some agencies charge by the hour, with rates varying widely based on the agency’s experience and location. Hourly rates can range from \$100 to \$300 or more.
• Project-Based Pricing: Many agencies prefer a project-based approach, providing a fixed price for a defined scope of work. Project costs can range from \$5,000 to \$100,000 or more, depending on the complexity and scale of the project.
• Retainer Fees: For ongoing branding needs, some businesses opt for a retainer arrangement, paying a set monthly fee for a predetermined number of hours or services. Retainer fees can range from \$2,000 to \$20,000 per month or more.
• Value-Based Pricing: In some cases, agencies may use value-based pricing, which takes into account the potential return on investment (ROI) for the client. This approach is less common but can be beneficial for high-impact projects.
## Cost Breakdown by Agency Type
To provide a more detailed understanding, let’s break down the costs associated with different types of branding agencies:
• Freelance Branding Specialists: Freelancers can be a cost-effective option for small businesses or startups with limited budgets. Rates for freelancers typically range from \$50 to \$150 per hour, and total project costs can vary from \$1,000 to \$10,000.
• Boutique Branding Agencies: These smaller, specialized agencies offer personalized services and often work closely with clients. Costs for boutique agencies can range from \$10,000 to \$50,000 for a full branding project.
• Mid-Sized Agencies: These agencies provide a balance between personalized service and a wide range of expertise. Costs for mid-sized agencies typically range from \$50,000 to \$150,000.
• Large Agencies: Large, well-established agencies with a global presence and extensive resources charge the highest fees. Costs can start at \$150,000 and go up to \$1 million or more, depending on the project’s scope and complexity.
## What Do Branding Agency Fees Cover?
Understanding what you get for your investment is crucial. Here’s a breakdown of common services and deliverables included in branding agency fees:
• Brand Strategy: This includes market research, competitor analysis, target audience identification, and developing a brand positioning statement.
• Brand Identity Design: Creation of visual elements such as logos, colour palettes, typography, and style guides that define the brand’s look and feel.
• Brand Messaging: Developing a consistent voice and messaging framework that communicates the brand’s values, mission, and vision.
• Website Design and Development: Creating a user-friendly, visually appealing website that aligns with the brand’s identity.
• Marketing Collateral: Design of marketing materials such as business cards, brochures, social media assets, and packaging.
• Brand Guidelines: A comprehensive document that outlines how the brand should be presented across all mediums, ensuring consistency.
Beyond the initial fees charged by a branding agency, businesses should be aware of additional costs that might arise:
• Implementation Costs: Once the branding strategy and assets are created, there may be costs associated with implementing these changes across all platforms and materials.
• Ongoing Marketing: Maintaining and promoting the brand through marketing campaigns, social media, and other channels will incur additional expenses.
• Revisions and Updates: As businesses grow and evolve, they may need to update their brand identity, which could result in additional costs.
• Licensing and Legal Fees: Protecting the brand through trademarks and other legal means can add to the overall cost.
## How to Choose the Right Branding Agency
Selecting the right branding agency is crucial to ensure a successful partnership and a strong return on investment. Here are some tips for making an informed decision:
Clearly outline what you want to achieve with your branding project. This will help you communicate your needs to potential agencies and evaluate their proposals effectively.
### Review Portfolios:
Examine the portfolios of prospective agencies to assess their style, creativity, and experience in your industry.
### Check References and Reviews:
Speak with past clients and read reviews to gauge the agency’s reliability, professionalism, and ability to deliver results.
### Assess Communication and Fit:
Ensure the agency’s communication style and values align with your business. A good fit is essential for a smooth and productive collaboration.
### Understand Their Process:
Inquire about the agency’s process for developing a brand strategy and delivering projects. A well-defined process indicates professionalism and thoroughness.
### Compare Proposals:
Request detailed proposals from multiple agencies and compare their approaches, deliverables, timelines, and costs.
Wasn’t able to find one? Click on branding agency sydney
## Conclusion
The cost of hiring a branding agency can vary widely based on numerous factors, including the scope of work, agency size, industry, location, and deliverables required. By understanding these factors and the common pricing structures, businesses can make informed decisions and choose the right agency that fits their budget and needs.
Investing in professional branding is a significant but worthwhile expense that can yield substantial returns through increased brand recognition, customer loyalty, and business growth.
Ultimately, the value of a well-executed branding strategy goes beyond its price tag, positioning your business for long-term success in a competitive market. Whether you opt for a freelance specialist or a large, full-service agency, the key is to choose a partner who understands your vision and can bring your brand to life in a way that resonates with your target audience.
### Are Rec Solar Panels Good?
Choosing the right solar panels is an important first step in capturing solar energy. When compared to other solutions, REC solar panels are the most efficient and dependable. This article explores the many reasons why REC solar panels are so popular with both commercial and residential clients.
We look at what makes REC panels a great renewable energy investment, from their unique technology to their dedication to sustainability. Stay tuned to find out what all the fuss is about with REC solar panels, whether you’re already a solar power fanatic or just thinking about making the change.
## Are Rec Solar Panels Good?
The solar industry generally agrees that REC solar panels are the best. Renowned for making long-lasting and efficient solar panels, REC (Renewable Energy Corporation) has been in the business for quite some time. Recessed light-emitting diode (REC) panels are multi-purpose and have received a lot of attention for their ability to function in extremes of temperature and light.
The utilisation of cutting-edge technology and premium materials in the production of REC solar panels is a major contributor to their outstanding quality. Passivated Emitter Rear Cell (PERC) technology is one of the revolutionary characteristics commonly seen in REC panels. It increases efficiency by absorbing more sunlight and turning it into electricity.
The production methods and product certifications of REC also demonstrate their dedication to sustainability and environmental responsibility. An increasing number of REC panels have received environmental performance certifications from third-party groups that verify their use of sustainable manufacturing techniques.
let’s expand on the reasons why REC solar panels are considered a good choice, including examples that demonstrate their quality and performance.
• High Efficiency: REC solar panels are known for their high-efficiency rates. The company employs innovative technologies like Heterojunction Cell Technology (HJT) and Passivated Emitter Rear Contact (PERC), which increase the amount of energy each panel can generate from sunlight. This means REC panels can generate more electricity from the same amount of sunlight compared to some other brands.
• Durability and Longevity: REC panels are designed to withstand various environmental conditions, including extreme weather, high winds, and heavy snow loads. Their robust construction ensures they can last for decades. Many REC panels come with a 25-year linear power output warranty and a 10-year product warranty, demonstrating the company’s confidence in their product’s durability.
• Low Degradation Rates: Over time, solar panels lose their ability to generate electricity as efficiently as when they were new. REC panels are designed with lower degradation rates, meaning they maintain a higher percentage of their original efficiency throughout their lifespan. This can translate into more consistent energy production and a better return on investment.
• Positive Customer Reviews: REC panels generally receive positive feedback from customers and installers for their performance and ease of installation. This reputation among industry professionals and end-users adds to their credibility.
• Sustainability and Environmental Responsibility: REC is committed to sustainable practices in manufacturing. The company uses environmentally friendly processes, such as reducing energy and water consumption during production. Additionally, many REC products are certified by organizations like ISO for their environmental impact.
• Innovation and Research: REC invests in research and development to continually improve its products. This commitment to innovation ensures that REC panels remain competitive and meet the evolving needs of the solar market.
• Wide Range of Products: REC offers a variety of solar panel models suitable for different applications and budgets. This allows customers to choose the right panel for their specific requirements, whether they are installing solar for a residential home, commercial building, or larger solar project.
REC solar panels are a strong choice for those seeking reliable, efficient, and sustainable solar solutions. With advanced technology, robust warranties, and a focus on environmental responsibility, REC continues to be a leading player in the solar industry.
## Who Recycles Solar Panels In Australia?
In Australia, solar panel recycling is an emerging sector due to the increasing deployment of solar energy systems and the corresponding need for end-of-life management of solar panels.
Although recycling facilities for solar panels are not as widespread as traditional recycling, several companies and programs are dedicated to recycling solar panels in Australia. Here are some notable entities and programs involved in rec solar panels australia:
• Reclaim PV Recycling: Reclaim PV Recycling is one of the prominent companies in Australia dedicated to solar panel recycling. With locations in Adelaide and Melbourne, they specialize in recycling silicon-based solar panels, extracting valuable materials like glass, silicon, silver, and copper. Reclaim PV Recycling has a nationwide reach, collecting panels from across Australia to process them in their facilities.
• Veolia: Veolia, a global leader in waste management and resource recovery, operates in Australia and has established a solar panel recycling initiative. They work on dismantling panels to recover valuable components and materials, aiming to create a circular economy for solar panels.
• PV Industries: PV Industries is another company in Australia focusing on solar panel recycling. They aim to process panels in a way that maximizes material recovery and minimizes environmental impact.
• National Waste Policy: While not an entity itself, Australia’s National Waste Policy includes goals to address e-waste, including solar panels. Governmental initiatives and regulations are evolving to promote responsible recycling and waste management of electronic products like solar panels.
• State-Based Initiatives: Some states in Australia have introduced specific programs or regulations to encourage solar panel recycling. For instance, New South Wales and Victoria have frameworks for managing electronic waste, which includes solar panels.
As solar panel recycling in Australia continues to develop, it’s advisable to check with local waste management authorities or solar installers for guidance on recycling options in your area. Some solar installers and manufacturers offer take-back or recycling programs for solar panels at the end of their life cycle, ensuring a responsible approach to solar energy’s environmental impact.
## What Is The Lifespan Of Solar Panels In Australia?
The lifespan of solar panels in Australia typically ranges from 25 to 30 years, though they can continue to produce electricity beyond that time with reduced efficiency. Several factors contribute to the lifespan and longevity of solar panels, and Australia’s unique climate and environmental conditions play a significant role in determining how long solar panels last.
Here are some key points regarding the lifespan of solar panels in Australia:
• Manufacturer’s Warranty: Most solar panel manufacturers offer a warranty that indicates the expected panel lifespan. Typically, this includes a 25-year linear power output warranty and a 10-year product warranty. The power output warranty guarantees that the panels will maintain a certain percentage of their original efficiency over time, usually around 80-90% after 25 years.
• Degradation Rate: Solar panels experience a gradual loss of efficiency over time, known as degradation. The average degradation rate for quality solar panels is about 0.5% per year. This means that after 25 years, a solar panel might operate at approximately 85% of its original capacity.
• Environmental Factors: Australia’s diverse climates—from tropical in the north to temperate and desert regions—can affect the lifespan of solar panels. High temperatures, strong UV radiation, coastal salt air, and extreme weather conditions can accelerate degradation. However, quality solar panels are designed to withstand these elements, with features like UV-resistant coatings, corrosion-resistant frames, and robust construction.
• Maintenance and Care: Proper maintenance can extend the lifespan of solar panels. This includes regular cleaning, checking for damage, and ensuring that the mounting system is secure. In areas with heavy dust or bird droppings, regular cleaning may be more important.
• Inverter Lifespan: While not part of the solar panels themselves, the inverter is a critical component in a solar energy system. Inverters generally have a shorter lifespan, ranging from 10 to 15 years, and may require replacement during the lifetime of the solar panels.
• Extended Use Beyond Warranty: Although the typical warranty period is 25 years, many solar panels continue to produce electricity beyond that time. Panels installed in the 1990s and early 2000s are still operational today, indicating that quality panels can last longer with reduced efficiency.
While 25-30 years is the typical lifespan for solar panels in Australia, proper maintenance, careful installation, and choosing high-quality panels can result in a longer useful life. When considering solar panels, it’s important to account for long-term performance and maintenance needs to ensure a sustainable and efficient energy solution.
## Conclusion
The usual lifetime of solar panels in Australia is 25 to 30 years, though they can survive even longer with less efficiency. The solar panels’ quality, the installation site’s environmental conditions, and the care and maintenance they receive are the primary variables determining their longevity.
Solar panel manufacturers usually back their products with guarantees that they will work for a long period, but you should be aware that deterioration is inevitable. The optimal performance of panels throughout their lifespan can be achieved with proper care, which includes frequent cleaning and inspections.
The wide range of climates and environmental factors in Australia make it all the more important to select solar panels of the highest quality that can endure extreme heat, sunlight, and coastal environments. It is helpful to have reasonable expectations for the long-term maintenance of a solar energy system when you know that certain components, like inverters, could need to be replaced at some point.
Installing solar panels is an investment with big payoffs in the form of decreased energy bills and less pollution in the long run. Your solar energy system can continue to offer sustainable electricity for many years to come if you use long-lasting, energy-efficient panels and do routine maintenance as directed.
### How Do You Play Flute For Beginners?
The flute, with its enchanting melodies and ethereal tones, has captivated hearts for centuries. Whether you’re drawn to its serene sound or intrigued by its graceful design, learning to play the flute can be a rewarding journey filled with discovery and musical expression.
In this beginner’s guide, we’ll explore the fundamentals of playing the flute, from assembling the instrument to mastering basic techniques and nurturing a lifelong passion for music.
## Getting Started: Assembling Your Flute
Before you can begin playing, it’s essential to familiarize yourself with the parts of the flute and learn how to assemble them properly. Here’s a step-by-step guide to help you get started:
• Headjoint: This is the top section of the flute, where the mouthpiece is located. Before attaching it to the body of the flute, ensure that the embouchure hole (the small opening where you blow air) is clean and free from any obstructions.
• Body: The body of the flute consists of the main tubing and key mechanisms. Align the head joint with the body, making sure that the embouchure hole and the keys are in line.
• Footjoint: The footjoint is the bottom section of the flute, which contains additional keys and helps to extend the range of the instrument. Attach it to the body, ensuring a snug fit.
• Align the keys: Once all sections are assembled, check to ensure that the keys are aligned and move freely without any obstructions.
Now that your flute is assembled, it’s time to explore the basic techniques of playing.
## Mastering the Basics: Embouchure and Breath Control
The foundation of flute playing lies in developing a proper embouchure and mastering breath control. Here’s how to get started:
• Embouchure: The embouchure refers to the position and shape of your lips and mouth when playing the flute. To create a stable embouchure, place the flute’s lip plate against your lower lip, covering approximately one-third to one-half of the embouchure hole. Your upper lip should be relaxed and slightly rolled downward, forming a cushion for the airstream.
• Breath control: Controlling your breath is crucial for producing a clear and resonant tone on the flute. Practice taking deep breaths from your diaphragm, allowing your abdomen to expand as you inhale and contract as you exhale. Aim for a steady and consistent airflow when playing, avoiding excessive tension or force.
• Experiment with tone: As you begin to play, experiment with different air speeds and pressure to produce varying tones. Start with a gentle stream of air and gradually increase the pressure until you achieve a full, resonant sound. Remember to maintain a relaxed and open throat position to facilitate smooth airflow.
## Basic Fingerings and Technique
Once you’ve mastered the embouchure and breath control, it’s time to explore basic fingerings and techniques on the flute. Mastering basic fingerings and techniques is essential for any beginner flute player. These foundational skills lay the groundwork for playing melodies, scales, and eventually more complex pieces of music.
1. Hand position:
• Hold the flute horizontally with both hands, placing your left hand closer to the head joint and your right hand closer to the foot joint.
• Your left thumb should rest underneath the flute’s body, supporting its weight, while your right thumb operates the thumb key on the back of the flute.
• Keep your fingers relaxed and curved, hovering over the keys without pressing down unnecessarily.
1. Fingerings:
Each key on the flute corresponds to a specific note. Start by learning the fingerings for the fundamental notes of the flute’s range, including C, D, E, F, G, A, and B. Practice playing these notes slowly and evenly, focusing on producing a clear and consistent tone.
Here’s a basic fingering chart for these notes:
• C: ●●●|●○○|○○○
• D: ●●●|●●○|○○○
• E: ●●●|○○○|○○○
• F: ●●○|○○○|○○○
• G: ●●○|●○○|○○○
• A: ●●○|●●●|○○○
• B: ●●○|●●○|○○○
To play a note, press down the corresponding keys indicated by “●” while keeping all other keys closed (indicated by “○”).
1. Articulation:
Articulation refers to the way you begin and end each note. Experiment with different tonguing techniques, such as single tonguing (using the tip of your tongue to articulate each note) and double tonguing (alternating between the syllables “ta” and “ka” to articulate rapid passages). Practice articulating notes cleanly and precisely, aiming for smooth transitions between each note.
1. Scale Practice:
• Practice playing major and minor scales to develop fluency and dexterity in your fingers.
• Start with simple scales such as C major and A minor, then gradually expand to more challenging keys and scales.
• Focus on playing scales evenly and smoothly, paying attention to intonation and tone quality.
1. Dynamic Control:
• Experiment with different dynamics (loudness and softness) to add expression and musicality to your playing.
• Practice crescendos (gradually getting louder) and decrescendos (gradually getting softer) to develop control over your sound.
1. Listening and Imitation:
• Listen to recordings of flute music by accomplished flautists to study their tone, technique, and musical interpretation.
• Try to imitate the sound and style of professional players, paying attention to details such as articulation, phrasing, and dynamics.
• Incorporate what you learn from listening into your practice and performance.
## Developing a Practice Routine and Seeking Guidance
Like any skill, mastering the flute requires dedication, patience, and consistent practice. Here are some tips for developing an effective practice routine:
• Set realistic goals: Break down your practice sessions into manageable chunks and set specific goals for what you want to achieve. Whether it’s mastering a new piece of music or improving your technique, having clear objectives will help keep you focused and motivated.
• Practice regularly: Aim to practice the flute for at least 20-30 minutes each day, focusing on developing your tone, technique, and musicality. Consistency is key to progress, so try to establish a regular practice routine that fits into your schedule.
• Seek guidance: Consider taking lessons with a qualified flute teacher who can provide personalized instruction and feedback. A teacher can help you develop proper technique, expand your repertoire, and overcome any challenges you may encounter along the way.
## Exploring the World of Flute Music
As you continue your journey with the flute, don’t hesitate to explore the rich and diverse world of flute music. From classical repertoire to jazz, folk, and contemporary styles, there’s a vast array of music waiting to be discovered. Listen to recordings, attend concerts, and experiment with different genres and styles to expand your musical horizons.
## Conclusion
Learning to play the flute is a fulfilling and enriching experience that offers countless opportunities for creativity, self-expression, and personal growth. By mastering the fundamentals of embouchure, breath control, fingerings, and technique, you’ll unlock the full potential of this beautiful instrument and embark on a melodic journey that will inspire and delight you for years to come.
So pick up your flute, take a deep breath, and let the music begin! Check some lessons here in flute teacher Melbourne
### What Is The Most Commonly Used Freight Transportation?
The flow of goods is the lifeblood of the interconnected web of global trade, supporting economies and spurring growth. Freight transportation is the backbone of this complex dance of commerce, the conduits that allow goods to travel great distances to reach their final destinations. There are many different ways to transport freight, but one is the most common and effective all around.
This article delves into the realm of freight transportation to identify the most widely utilized approach, examining its subtleties, difficulties, and crucial function in moulding the contemporary economy. Discover the mysteries of the foundation of world trade as we take you on a voyage through towering container ships navigating enormous oceans and the incessant hum of trucks navigating highways.
## What Is The Most Commonly Used Freight Transportation?
The most popular freight transportation option varies based on several variables, including the location, kind of goods being transported, distance, cost issues, and the accessibility of infrastructure. On the other hand, container shipping, or maritime shipping, is the most widely utilized method of freight transportation worldwide.
Container shipping is the practice of moving cargo in uniform containers that are simple to move between various vehicles, including trucks, trains, and ships. Large amounts of goods can be transported over long distances with great efficiency and cost-effectiveness using this method, which is why international trade prefers it.
Here are some more examples of commonly used freight transportation methods:
• Trucking (Road Freight): Trucking is a vital component of freight transportation, particularly for short to medium-distance deliveries and for reaching areas not easily accessible by other modes of transportation. Trucks transport a wide range of goods, including consumer products, perishable goods, construction materials, and industrial equipment.
• Rail Freight: Rail transportation is efficient for long-distance freight movement, especially for bulky and heavy goods such as coal, minerals, and agricultural products. Rail freight networks are well-developed in many regions, offering cost-effective and environmentally friendly transportation solutions.
• Air Freight: While relatively expensive compared to other modes, air freight is invaluable for transporting high-value and time-sensitive goods, such as electronics, pharmaceuticals, and perishable goods. Air cargo services connect distant markets quickly and efficiently, making them essential for global supply chains.
• Pipeline Transportation: Pipelines are used extensively for transporting liquids and gasses, including crude oil, natural gas, and refined petroleum products. Pipeline transportation offers a safe, reliable, and cost-effective means of moving large volumes of commodities over long distances.
• Intermodal Transportation: Intermodal transportation involves the seamless integration of multiple modes of transportation, such as combining trucking, rail, and maritime shipping. Intermodal transportation offers flexibility, efficiency, and reduced costs by leveraging the strengths of each mode while overcoming their limitations.
• Inland Waterway Transportation: In regions with navigable rivers and canals, inland waterway transportation is utilized for moving bulk cargo such as grains, ores, and chemicals. Barges and towboats transport goods efficiently and economically along water routes, complementing other modes of transportation.
• Parcel Delivery Services: Parcel delivery services, including courier companies and postal services, specialize in transporting small packages and parcels. These services are widely used for shipping documents, small goods, and online purchases to individual consumers and businesses.
• Tanker Shipping: Tanker ships are specifically designed for transporting liquid cargoes such as crude oil, petroleum products, chemicals, and liquefied natural gas (LNG). Tanker shipping plays a crucial role in supplying energy resources and industrial chemicals globally.
• Refrigerated Transportation (Reefer): Refrigerated transportation involves the movement of temperature-sensitive goods, such as perishable foods (fruits, vegetables, meat, and dairy products) and pharmaceuticals. Reefer containers and specialized trucks maintain specific temperature conditions to preserve the quality and freshness of the cargo.
• Bulk Cargo Shipping: Bulk cargo shipping involves transporting unpackaged goods, such as grains, coal, ores, and minerals, in large quantities. Bulk carriers, specialized vessels designed to handle bulk commodities, transport these goods economically over long distances.
• Roll-on/Roll-off (Ro-Ro) Shipping: Ro-Ro vessels are designed to transport wheeled cargo, such as cars, trucks, trailers, and heavy machinery, that can be driven on and off the ship. Ro-Ro shipping is efficient for moving vehicles and heavy equipment between ports, facilitating international trade and logistics.
• LTL (Less-than-Truckload) and FTL (Full Truckload) Freight: Trucking companies offer both LTL and FTL services to accommodate varying shipment sizes. LTL carriers consolidate multiple smaller shipments from different customers into a single truckload, while FTL carriers transport larger shipments occupying the entire truck.
• Drayage: Drayage refers to the short-distance transportation of goods, typically between ports, terminals, and nearby distribution centres. Drayage services play a crucial role in the efficient movement of containers and other cargo within the logistics network.
These examples show the variety of freight transportation options available, each meeting a particular purpose and facilitating the seamless operation of international supply chains.
## What Are Examples Of Freight Transport?
Various ways and means of transporting goods from one place to another are included in examples of freight transport. These are a few typical examples:
• Trucking: Transporting goods by trucks is one of the most common methods of freight transport, especially for shorter distances or where other modes of transport are inaccessible.
• Railway Freight: Rail transport is utilized for moving large quantities of goods over long distances. It’s particularly suitable for heavy and bulky items like minerals, coal, and industrial materials.
• Maritime Shipping: Shipping goods via ships across oceans, seas, and waterways is a fundamental aspect of global trade. Container ships, bulk carriers, and tankers are examples of vessels used for maritime shipping.
• Air Freight: Air transport is used for high-value, time-sensitive, and perishable goods, or when urgent delivery is required. Cargo planes transport goods to various destinations worldwide.
• Pipeline Transport: Pipelines are employed for transporting liquids (e.g., crude oil, natural gas) and sometimes solids (e.g., coal slurry) over long distances, especially in industries like energy and chemicals.
• Intermodal Transport: Intermodal transport involves using multiple modes of transportation (e.g., truck, train, ship) within a single journey. Containers can be transferred seamlessly between different transport modes, enhancing efficiency and reducing costs.
• Courier and Parcel Services: Courier companies and postal services specialize in delivering small packages and parcels to individual consumers and businesses, often utilizing trucks, aeroplanes, and local delivery networks.
• Refrigerated Transport: This type of transport is used for perishable goods such as fruits, vegetables, pharmaceuticals, and certain chemicals, maintaining specific temperature conditions throughout the journey to preserve product quality.
• Drayage: Drayage refers to short-distance transportation, often between ports, terminals, and nearby distribution centres. It involves moving containers and cargo over relatively short distances, typically using trucks or other specialized vehicles.
• Specialized Transport: Some goods require specialized transport methods, such as heavy haulage for oversized machinery, livestock transport for animals, and hazardous material transport for chemicals and other dangerous goods.
These samples show the wide variety of freight transport options that are available, each with a specific cargo type, distance, timeliness, and logistical need in mind.
## Conclusion
When it comes to moving goods effectively and efficiently over a range of distances and terrains, freight transport refers to a wide range of techniques and modes. The vast stretches of ocean that container ships patrol and the busy highways that trucks traverse are examples of the human ingenuity and innovation that underpin the logistics network supporting global trade.
As a flexible and accessible option for last-mile deliveries and shorter distances, trucks continue to be a mainstay of the freight transport industry. Accompanying the vast network of maritime shipping routes that link continents and promote international trade is rail transport, which offers a dependable and economical means of transporting bulk goods over long distances.
Speed and urgency are paramount in the world of air freight, where cargo aircraft transport expensive and urgent goods quickly and efficiently to locations all over the world. Despite being less obvious, pipeline transport is essential to the chemical and energy sectors because it can move liquids and gasses across long distances with little negative environmental impact.
By utilizing the advantages of each mode, intermodal transport effectively combines several forms of transportation, increasing both cost-effectiveness and efficiency. As this is going on, specific transportation techniques address the particular needs of products like perishable food and large machinery.
### What Is The Importance Of Pest Control?
In both home and business settings, pest management is an essential component in the process of preserving a safe and healthy environment. There are many different kinds of pests, ranging from rodents to insects, that can be harmful to human health, property, and ecology.
The prevention of the transmission of diseases, the protection of food supplies, and the maintenance of the structural integrity of buildings are all purposes that need the implementation of efficient pest management measures.
The significance of pest management measures is investigated in depth in this article, with a particular emphasis placed on the crucial role that these measures play in reducing risks and increasing overall well-being.
## Pest Control | What Is It?
Pest control refers to the practice of managing and regulating populations of pests, which are organisms that interfere with human activities, cause property damage, or pose risks to health and the environment. This discipline encompasses various methods and techniques aimed at preventing, controlling, or eradicating pests effectively while minimizing negative impacts on non-target organisms and ecosystems.
Pest control measures may include:
• Biological Control: Introducing natural predators, parasites, or pathogens to regulate pest populations.
• Chemical Control: Using pesticides or insecticides to kill or repel pests. This method requires careful application to minimize risks to human health and the environment.
• Mechanical Control: Employing physical barriers, traps, or deterrents to prevent pests from accessing vulnerable areas or resources.
• Cultural Control: Implementing practices such as crop rotation, sanitation, and habitat modification to discourage pest infestations.
• Integrated Pest Management (IPM): Combining multiple control methods in a holistic and sustainable approach to manage pests effectively while minimizing reliance on chemical pesticides.
Pest control is essential in various contexts, including agriculture, public health, forestry, urban environments, and food processing. By implementing appropriate pest management strategies, individuals, businesses, and governments can mitigate risks associated with pest infestations, protect natural resources, and promote human well-being and economic prosperity.
## What Is The Importance Of Pest Control?
Pest control plays a crucial role in safeguarding public health, protecting property, and preserving the environment. Here are several key reasons highlighting its importance, click here:
• Health Protection: Pests such as mosquitoes, rodents, and cockroaches can transmit various diseases to humans, including malaria, dengue fever, salmonellosis, and asthma. Effective pest control measures help prevent the spread of these illnesses, reducing the risk of epidemics and protecting the well-being of individuals and communities.
• Food Safety: Pests pose a significant threat to food supplies, contaminating stored grains, fruits, and vegetables. Infestations in food processing facilities and restaurants can lead to foodborne illnesses, resulting in serious health hazards for consumers. Implementing pest control strategies is essential for ensuring food safety and preventing economic losses in the agricultural and food industry sectors.
• Property Preservation: Pests like termites, carpenter ants, and rodents can cause extensive damage to buildings, furniture, and infrastructure. Structural infestations weaken the integrity of constructions, leading to costly repairs and compromises in safety. By managing pest populations effectively, property owners can safeguard their investments and maintain the longevity of structures.
• Ecosystem Balance: While pests can disrupt ecosystems by outcompeting native species or consuming crops, indiscriminate use of pesticides can also harm beneficial organisms and disrupt the natural balance. Integrated Pest Management (IPM) techniques focus on minimizing environmental impact while effectively controlling pests, promoting sustainable practices that preserve biodiversity and ecosystem health.
• Economic Benefits: Pest infestations result in substantial economic losses through damage to crops, livestock, and stored products, as well as expenses associated with pest management and healthcare. Investing in proactive pest control measures helps minimize these losses, enhance productivity in agricultural and commercial sectors, and support economic stability and growth.
• Public Comfort and Well-being: Pest infestations can significantly impact the quality of life, causing stress, discomfort, and anxiety for individuals living or working in affected areas. Implementing pest control measures improves living conditions, enhances workplace environments, and contributes to overall comfort and well-being.
Pest control is essential for protecting public health, preserving property, promoting environmental sustainability, and supporting economic prosperity. By implementing comprehensive pest management strategies, individuals, businesses, and communities can mitigate risks associated with pest infestations and foster healthier, safer, and more resilient environments.
## When Should I Call A Pest Control Service?
You should consider calling a pest control service under the following circumstances:
• Visible Signs of Pest Infestation: If you notice signs of pests such as droppings, gnaw marks, nests, or sightings of insects or rodents in your home or property, it’s advisable to contact a pest control service. Prompt action can prevent the infestation from worsening.
• Unexplained Damage: If you observe unexplained damage to your property, such as holes in walls, chewed wires, or structural damage, pests may be the culprit. Calling a pest control professional can help identify the source of the damage and implement appropriate control measures.
• Seasonal Pest Activity: Certain pests may become more active during specific seasons. For example, ants and mosquitoes may proliferate in warmer months, while rodents may seek shelter indoors during colder weather. Consider scheduling preventive pest control treatments before peak activity periods to avoid infestations.
• Health Concerns: Pests can pose health risks by spreading diseases, triggering allergic reactions, or contaminating food and water sources. If you or your family members experience unexplained illnesses or allergic symptoms that could be related to pests, it’s essential to address the issue promptly with professional pest control services.
• Property Transactions: If you’re buying or selling a property, a pest inspection is often part of the due diligence process. Engaging a pest control service to conduct a thorough inspection can identify any existing infestations or potential risks, helping to facilitate a smooth transaction and protect the value of the property.
• Repeated DIY Failures: If your attempts to control pests using do-it-yourself methods prove ineffective or if the infestation persists despite your efforts, it’s time to seek professional assistance. Pest control professionals have the expertise, experience, and specialized equipment to address even the most challenging pest problems effectively.
• Preventive Maintenance: Regular pest control inspections and treatments can help prevent infestations before they occur, saving you time, money, and hassle in the long run. Consider scheduling routine pest control services to proactively manage pest populations and maintain a pest-free environment.
Contacting a pest control service at the first sign of a pest problem or as a preventive measure can help protect your property, health, and peace of mind.
## Conclusion
The ability to recognise when it is necessary to contact a pest control service is critical to preserving a safe, healthy, and pest-free environment. To prevent pests from causing further damage, it is essential to take immediate action, regardless of whether you are dealing with a visible infestation, property damage that cannot be explained, or seasonal insect activity.
Protecting your home, ensuring your health, and ensuring that you have peace of mind are all things that can be accomplished by recognising the signs of pest infestations and receiving professional aid when it is required. Taking preventative actions against pests is another way to reduce the likelihood of future infestations and reduce the risks associated with them.
To summarise, investing in expert pest control services is an investment in both your health and the longevity of your house.
### What Is The Meaning Of Interior Fit Out?
The process of preparing interior areas for habitation is referred to as “interior fit-out”. This might include a variety of tasks, including painting and decorating as well as installing fixtures and equipment. The various facets of interior fit-out and how it might alter a place will be discussed in this article.
We’ll also examine a few instances of prosperous fit-out projects and the advantages they can offer to both individuals and companies. Knowing the fundamentals of interior fit-out will help you accomplish your objectives, whether you’re a homeowner wishing to modernize your living space or a business owner trying to make your clients feel welcome.
## What Is The Meaning Of Interior Fit Out?
A building’s or space’s interior being prepared for its intended use is referred to as interior fit-out, sometimes known as interior fit-out or interior finishing. To improve the space’s use, appeal, and comfort, fixtures, fittings, and other components must be installed. Many different types of interior fit-out activities may be done, have a peek here:
• Partitioning: Creating separate areas within a space using walls, screens, or other barriers.
• Flooring: Installing flooring materials such as tiles, carpet, or hardwood.
• Ceilings: Installing ceiling tiles, panels, or other materials to cover the overhead space.
• Lighting: Installing lighting fixtures and systems to provide adequate illumination.
• HVAC: Installing heating, ventilation, and air conditioning systems to regulate temperature and air
quality.
• Electrical: Installing electrical wiring, outlets, switches, and other components.
• Plumbing: Installing plumbing fixtures such as sinks, toilets, and faucets.
• Cabinetry and Millwork: Installing custom-built cabinets, shelves, and other storage solutions.
• Painting and Wall Coverings: Applying paint, wallpaper, or other wall coverings to enhance the aesthetics of the space.
• Furniture: Selecting and installing furniture that complements the design and function of the space.
To guarantee that the completed area satisfies the client’s needs and standards, the interior fit-out is usually completed by specialist contractors or interior designers who collaborate closely with architects, engineers, and other experts. Creating an aesthetically pleasing space, cozy, and useful while also improving the occupants’ overall experience is the aim of interior fit-out.
## Why Is Interior Fit Out Important?
Interior fit-out is important for several reasons:
• Functionality: Interior fit-out ensures that the space is designed and configured in a way that supports its intended use. This includes installing fixtures, fittings, and equipment that facilitate the activities that will take place in the space, such as workstations in an office or kitchen appliances in a restaurant.
• Aesthetics: A well-designed interior can enhance the overall appearance of a space and create a positive impression on visitors or customers. This can be achieved through the use of materials, colours, and finishes that complement the design theme and branding of the business.
• Comfort: Interior fit-out can improve the comfort of a space by providing features such as adequate lighting, temperature control, and soundproofing. This can contribute to the well-being and productivity of the occupants.
• Safety: Interior fit-out includes the installation of safety features such as fire alarms, emergency exits, and accessibility features for people with disabilities. These measures help to ensure the safety and well-being of the occupants.
• Compliance: Interior fit-out must comply with building codes, regulations, and standards to ensure that the space is safe and suitable for its intended use. This includes requirements for structural integrity, fire safety, accessibility, and environmental sustainability.
• Brand Image: For businesses, interior fit-out can play a crucial role in shaping the brand image and identity. A well-designed interior that reflects the values and personality of the brand can help to create a memorable and distinctive experience for customers.
All things considered, interior fit-out is significant because it contributes to the creation of environments that are secure, pleasant, visually beautiful, and legally compliant. Whether in an institutional, commercial, or residential setting, this enhances the space’s overall efficacy and success.
## What Is An Interior Fit-Up?
The act of preparing the interior of a building or area for its intended use is known as “interior fit-up,” which is frequently used interchangeably with “interior fit-out” or “interior finishing.” This could include a variety of tasks, like putting in fixtures, fittings, and other components that enhance the room’s comfort, usability, and beauty.
The process of interior fit-up might involve a variety of jobs, such as installing furniture, painting and wall coverings, flooring, ceilings, lighting, HVAC, electrical, and plumbing. To improve the entire experience of the occupants, an interior fit-up aims to produce a space that is aesthetically pleasing, comfortable, and useful.
• Acoustic Treatments: Installing materials or features to improve sound quality and reduce noise levels, such as acoustic panels or soundproofing.
• Signage and Wayfinding: Installing signs and directional elements to help people navigate the space, such as room numbers, directional arrows, or informational signs.
• Security Systems: Installing security features such as surveillance cameras, access control systems, or alarm systems to ensure the safety and security of the occupants.
• Technology Integration: Installing technology infrastructure such as data cabling, networking equipment, or audiovisual systems to support the use of technology in space.
• Sustainability Features: Incorporating sustainable design elements such as energy-efficient lighting, low-flow plumbing fixtures, or recycled materials to reduce the environmental impact of the space.
• Customization: Creating custom-built elements such as built-in seating, display cases, or reception desks to meet the specific needs and preferences of the client.
• Finishing Touches: Adding decorative elements such as artwork, plants, or accessories to enhance the aesthetics of the space and create a welcoming atmosphere.
• Maintenance and Cleaning: Establishing protocols for ongoing maintenance and cleaning to ensure that the space remains in good condition and meets health and safety standards.
The numerous tasks that might be included in an interior fit-up are numerous; these are just a few examples. The particular duties and specifications will change based on the kind of space, how it will be used, and the client’s preferences.
## Conclusion
A critical step in designing interior spaces that are safe, visually beautiful, and functional is interior fit-out, also known as fit-up. Installing fixtures and fittings as well as integrating technology and sustainable elements are just a few of the many tasks involved.
Whether the occupants are customers, employees, or residents, the objective is to create an atmosphere that suits their requirements and preferences. Businesses and individuals alike can create environments that improve comfort, productivity, and general well-being by properly planning and carrying out an interior fit-out.
Conclusively, interior fit-out is a complex procedure that encompasses an array of activities designed to convert an area into a safe, aesthetically beautiful, and practical setting. A space that fulfils the demands and preferences of its residents is created via the careful consideration of every interior fit-out detail, from flooring and partitioning to lighting and technological integration.
Enterprises and individuals alike can create environments that improve efficiency, comfort, and general well-being by meticulously organizing and carrying out an interior fit-out.
In conclusion, interior fit-out is an all-encompassing procedure that includes a variety of tasks to convert a space into a secure, aesthetically beautiful, and practical setting. Each component of interior fit-out—from the placement of fixtures and fittings to the integration of technology and environmentally friendly elements—plays a critical part in ensuring that the space is customized to the requirements and tastes of its users.
Businesses and individuals alike can create environments that improve comfort, productivity, and general well-being by properly planning and carrying out an interior fit-out.
### Why Did You Choose HR Course?
Considering the fast-paced nature of the modern business environment, the human capital of any successful organisation is the organization’s beating heart. The function of Human Resources (HR) has emerged as a cornerstone for sustainable growth and organisational success as businesses traverse the complexity of globalisation, technological advancements, and developing workplace dynamics.
This is because HR is responsible for ensuring that businesses can adapt to these changes.
When you decide to embark on a trip into the world of human resources, you are not just making a choice; you are committing to comprehend the complex relationship that exists between people, policy, and performance.
Whether it is a deep-seated knowledge of the critical role that human resources play in determining the future of work, a fascination with talent development, or a desire to maximise organisational efficiency, the decision to pursue a study in human resources is frequently rooted in a passion for promoting inclusive workplaces, love for talent development, or desire to maximise organisational efficiency.
In this article, we look into the several reasons why people choose to embark on the enriching path of studying human resources from the perspective of the HR profession. From the appeal of unlocking human potential to the exhilaration of managing organisational problems, the motivation of each individual provides a unique insight into the rich tapestry that is the human resources profession.
Join us as we explore the compelling storylines that led to the decision to embrace human resources (HR) as more than just a course of study, but rather as a road to making a real difference in the world of work.
## What Is A Human Resource Degree?
The goal of an academic programme that is focused on educating students with the knowledge, skills, and competencies essential to be successful in the field of Human Resource Management (HRM) is to graduate with a degree in Human Resource administration.
Individuals who get this degree are equipped with a broad understanding of a variety of human resource responsibilities inside organisations, such as recruitment, training, performance evaluation, remuneration, employee relations, and strategic planning
Students acquire knowledge about efficiently managing human capital, overcoming legal and ethical concerns in the workplace, and cultivating a positive organisational culture through coursework, practical exercises, and real-world applications. These are all skills that are essential for success in the workplace.
An education in human resources equips graduates with the skills necessary to pursue a wide range of employment prospects in HR departments, consultancy businesses, government agencies, and non-profit organisations. These are all places where they play critical roles in changing the dynamics of the workforce and contributing to the success of the organisation.
## Why Did You Choose HR Course?
Some common reasons why individuals might choose to pursue a course in Human Resources (HR):
• Passion for People: Many individuals are drawn to HR because they have a genuine interest in working with people, understanding their needs, and helping them succeed within an organization.
• Impact and Influence: HR professionals have the opportunity to make a tangible impact on the culture, policies, and practices of an organization, ultimately shaping the work environment for employees.
• Problem-Solving and Conflict Resolution: HR involves addressing a wide range of issues, from resolving conflicts between employees to designing strategies for organizational growth and development. For those who enjoy problem-solving and navigating complex situations, HR can be an attractive field.
• Strategic Leadership: HR is increasingly recognized as a strategic partner in business operations, contributing to decisions related to talent acquisition, retention, and development. For individuals interested in strategic thinking and leadership roles, HR offers a path to influence organizational direction.
• Diversity and Inclusion: With a growing emphasis on diversity, equity, and inclusion in the workplace, many individuals are drawn to HR as a means of championing these values and driving positive change within organizations.
• Continuous Learning and Development: HR is a field that is constantly evolving, with new trends, technologies, and best practices emerging regularly. For those who enjoy learning and adapting to change, HR offers a dynamic and fulfilling career path.
These are only a handful of the numerous reasons why a person could decide to major in human resources. The decision is typically shaped by a mix of factors, including one’s hobbies, career goals, and the desire to make a difference in the workplace.
## Why Study Human Resource Management In Australia?
Studying Human Resource Management (HRM) in Australia offers several benefits and advantages:
• High-Quality Education: Australian universities are renowned for their high standards of education and rigorous academic programs. Many universities in Australia offer accredited HRM courses that are recognized internationally, providing students with a solid foundation in HR principles and practices.
• Diverse and Inclusive Culture: Australia is known for its multicultural society, which creates a diverse and inclusive learning environment. Studying HRM in Australia allows students to interact with peers from different cultural backgrounds, fostering cross-cultural understanding and enhancing their ability to work in globalized environments.
• Strong Economy and Job Opportunities: Australia has a strong and stable economy, with a robust labour market. Studying HRM in Australia can provide students with access to internship and job opportunities in various industries, including finance, healthcare, education, and technology.
• Industry-Relevant Curriculum: Australian universities often collaborate with industry partners to develop HRM programs that are aligned with the needs of the job market. Students can gain practical skills and knowledge through industry placements, case studies, and real-world projects, preparing them for successful careers in HRM.
• Networking Opportunities: Studying HRM in Australia allows students to connect with professionals and experts in the field through networking events, guest lectures, and industry seminars. Building a strong professional network can be valuable for career advancement and job opportunities after graduation.
• Quality of Life: Australia is known for its high quality of life, beautiful landscapes, and vibrant cities. International students studying HRM in Australia can enjoy a safe and welcoming environment, with access to world-class amenities, healthcare, and recreational activities.
Prospective human resource management professionals would do well to consider Australia as a study abroad destination due to the abundance of opportunities it presents, including a diverse and inclusive culture, a robust economy, excellent educational institutions, and hands-on training in HRM.
## Conclusion
There are a plethora of appealing benefits that come along with enrolling in a Human Resource Management (HRM) course within the Australian educational system. Because of its well-known reputation for providing high-quality education, a culture that is diverse and welcoming, a healthy economy, and abundant work possibilities,
Australia has emerged as an ideal place for individuals who are interested in pursuing careers in human resources.
Students studying human resource management in Australia are provided with the information, skills, and connections essential to prosper in the dynamic field of human resources. This is accomplished through the implementation of industry-relevant curricula, the provision of hands-on learning experiences, and the provision of access to a thriving network of professionals.
Additionally, the energising quality of life, secure environment, and friendly atmosphere of Australian cities all contribute to a wonderful educational journey, providing international students with an experience that is immersing and satisfying.
Ultimately, studying human resource management in Australia not only helps individuals develop the skills necessary for successful careers in the global economy but also encourages personal and professional development in an atmosphere that is both encouraging and stimulating.
Throughout the world’s ongoing recognition of the indispensable part that human resources play in the success of organisations, Australia has emerged as a shining example of excellence, fostering the next generation of human resource leaders and innovators.
### Can I Do Project Management Course Online?
In the dynamic landscape of today’s professional world, mastering project management has become a key competency for career success. As organizations increasingly prioritize effective project execution, individuals are seeking flexible and accessible ways to acquire project management skills.
Fortunately, the digital age has ushered in a plethora of opportunities, with online project management courses emerging as a popular and convenient option.
This article explores the advantages and considerations of pursuing a project management course online, shedding light on the transformative potential of virtual learning platforms. From the flexibility to learn at your own pace to the diverse range of course offerings, online project management courses have revolutionized how aspiring project managers can acquire and hone their skills.
Let’s delve into the world of online project management education and discover why it’s a viable and effective path for professional development.
## Can I Do Project Management Course Online?
The popularity of online project management courses has grown because they provide people with a convenient and affordable means of improving their project management abilities. Online project management courses offer a convenient and efficient learning experience for a variety of learners, including fresh graduates entering the field, working professionals wishing to upskill, and those considering a career shift.
The following are some main justifications for taking an online project management course:
• Flexibility: Online courses allow you to learn at your own pace, fitting your studies around your existing commitments. This flexibility is particularly beneficial for working professionals or individuals with busy schedules.
• Accessibility: With online courses, you can access learning materials from anywhere with an internet connection. This eliminates geographical constraints, making it possible for individuals around the world to enrol in courses offered by renowned institutions.
• Diverse Course Options: There is a wide variety of online project management courses available, catering to different skill levels and areas of specialization. Whether you’re a beginner or an experienced project manager seeking advanced training, you can find a course that suits your needs.
• Interactive Learning: Many online courses use engaging multimedia content, quizzes, and interactive exercises to enhance the learning experience. This interactive approach helps reinforce concepts and ensures a more dynamic learning process.
• Cost-Effective: Online courses often come at a lower cost compared to traditional in-person programs. Additionally, you can save on commuting and accommodation expenses, making online learning a more affordable option.
• Certification and Recognition: Several reputable institutions and organizations offer online project management courses that provide recognized certifications. These certifications can boost your resume and credibility in the job market.
It’s crucial to investigate and select a reliable platform or institution that fits with your learning objectives before registering for a course. Make sure the teachers have relevant industry expertise and that the course material is thorough. Read past student reviews and feedback as well to get an idea of how beneficial the course is.
All things considered, taking an online project management course is a useful and effective approach to getting important skills that are in high demand across a range of industries.
## Is It Worth Doing A Project Management Course?
The value of taking a project management course will vary depending on your sector, personal situation, and professional objectives. Here are a few things to think about while deciding if taking project management training is worthwhile:
• Career Advancement: If you are in a field where project management skills are crucial, such as IT, construction, healthcare, or finance, a project management course can significantly enhance your career prospects. Many employers value individuals who can effectively plan, execute, and complete projects on time and within budget.
• Skill Enhancement: Project management courses provide a structured and comprehensive understanding of project management methodologies, tools, and best practices. Acquiring these skills can make you more efficient and effective in managing projects, leading teams, and solving complex problems.
• Certification: Completing a recognized project management course often leads to a certification, such as PMP (Project Management Professional) or PRINCE2. These certifications are globally recognized and can enhance your credibility, making you stand out in the job market.
• Adaptability: Project management skills are transferable across various industries. Regardless of your current field, learning project management can equip you with versatile skills that are applicable in different professional settings.
• Increased Employability: As organizations increasingly prioritize project management, individuals with formal project management education are often preferred candidates for roles involving leadership, coordination, and strategic planning. Having a project management course on your resume can give you a competitive edge in the job market.
• Networking Opportunities: Project management courses often provide opportunities to connect with professionals in the field, both through the course itself and any associated professional organizations. Networking can open doors to potential job opportunities and collaborations.
• Personal Development: Beyond professional benefits, project management courses can contribute to your personal development. They enhance your organizational and time-management skills, boost your problem-solving abilities, and improve your ability to work effectively in a team.
It’s important to evaluate your unique demands and circumstances, though. Think about the course fee, the amount of time it will take, and whether the skills you will learn will help you achieve your career objectives. Additionally, consider the standing of the organisation providing the training and, if relevant, the certification’s industry recognition.
The cost of project management training typically pays for itself in the form of improved earning potential, career development, and overall job satisfaction. It is important to investigate and pick a course that fits both your goals and the requirements of the sector you have chosen.
## Conclusion
Enrolling in a course on project management can prove to be a very beneficial expenditure for your career advancement. Acquiring project management experience is highly advantageous due to the dynamic nature of today’s work environment and the ever-increasing demand for skilled project managers across numerous industries.
Taking a course in project management has several advantages beyond just learning new technical skills. You will gain the skills to effectively manage resources, lead teams, and complete complicated projects with the help of this course’s organized and thorough examination of project management approaches.
As long as companies keep an eye on how well projects are executed, there’s a good chance you can climb the corporate ladder. You can boost your credibility and access new prospects by completing a project management course and earning a recognized certification, like PRINCE2 or PMP.
Online project management courses are convenient since students may study at their own speed and yet meet all of their other obligations; this broadens the courses’ potential enrollment. Quality education is now more accessible than ever before because of the affordability of many online programs.
Your professional objectives, the needs of your industry, and your ambitions should all be considered when deciding whether or not to enrol in a project management course. Making a well-informed decision requires research into respectable schools, thinking about how applicable the course material is, and calculating the possible ROI.
If you want to be a successful professional in a field where good project management is essential, taking a well-designed course will give you the skills you need. The advantages of a project management course make it an attractive and valuable endeavor whether your goal is to improve your present position, move into a profession in project management, or prepare yourself for the future.
### How Do I Find Old Tax Returns In Australia?
Finding previous tax returns in Australia is a chore that is essential for both individuals and organisations, regardless of whether you require them for reasons of financial planning, record-keeping, or compliance. This article will walk you through the steps necessary to retrieve previous tax returns in Australia, and we will do so in full detail.
We will offer you a complete overview of the actions involved, beginning with an awareness of the necessary authorities and continuing with an exploration of online platforms and traditional methods when applicable. You can follow our guidance to guarantee that the process of retrieving your returns goes smoothly and efficiently, regardless of whether you have misplaced them or simply require duplicates.
Because we are aware of the need to keep accurate financial records, our goal is to equip you with the knowledge and tools necessary to easily retrieve your previous tax returns in Australia.
## How Do I Find Old Tax Returns In Australia?
In Australia, there are several avenues to pursue and authorities to familiarise oneself with To retrieve previous tax returns. Find your past tax returns with this step-by-step guide:
### Australian Taxation Office (ATO) Online Services
• The ATO provides online services that allow individuals to access their tax information, including previous tax returns.
• Navigate to the ATO section and look for the “Tax” or “Income” category.
• You may find an option to view and download your past tax returns or income statements.
• If you used a tax agent to prepare and submit your tax returns, they may have copies of your past returns.
• Reach out to your tax agent and request copies of the relevant returns. Ensure you provide sufficient information to verify your identity.
### Request from the ATO
• You can request a copy of your tax return directly from the ATO. This can be done by completing a form available on the ATO website.
• Visit the ATO website, search for the form for obtaining copies of tax returns, and follow the instructions provided.
### Using the myTax Portal
• Individuals who use the myTax online lodgment system can access their previously submitted returns through the myTax portal.
### Visit an ATO Office
• If online methods are not suitable, you can visit a local ATO office in person.
• Bring identification documents and request assistance from ATO staff to retrieve your old tax returns.
### Contact ATO Support
• Reach out to the ATO support helpline for assistance. They can guide you on the specific steps to access your past tax returns.
• If you have physical copies of your tax returns, check your personal records, filing cabinets, or storage for any copies you may have kept.
Be careful and check that the method you choose conforms with security and privacy regulations. Before handling sensitive financial information, make sure you are who you say you are. Seek the counsel of an accountant or tax expert who can point you in the right direction if you run into problems.
## How Much Does A Tax Return Cost In Canberra?
How much it will cost to get your Canberra tax return prepared depends on several things, including how complicated your financial position is, which service provider you choose, and whether you utilise online tax software or consult a tax specialist. Some broad principles of tax return canberra are as follows:
### Online Tax Software
• If you choose to use online tax software to prepare and lodge your tax return, there are various options available. Some software may offer free versions for simple returns, while others may charge a fee for more complex tax situations.
• Prices for premium versions of tax software typically range from \$20 to \$100 or more, depending on the features and support offered.
### Tax Professionals
• If you prefer to enlist the help of a tax professional, such as an accountant or tax agent, the cost can vary widely.
• For a straightforward individual tax return, you might find professionals charging anywhere from \$100 to \$300 or more.
• The cost tends to increase for more complex tax situations, such as those involving multiple income sources, investments, or business income.
### Boutique Tax Firms
• Boutique tax firms may have their fee structures, and costs can vary based on the firm’s reputation, expertise, and the level of service provided.
During the process of determining the cost, two significant things to take into consideration are the complexity of your tax return and your respective personal financial condition. Additionally, keep in mind that pricing may differ from one service provider to another; hence, it is prudent to compare prices by asking for quotes from a variety of software suppliers or specialists.
It is important to exercise caution when employing a tax expert unless you can verify that they are registered with the Taxpayer and Business Bureau (TPB) and, if they provide tax agent services, that they have a valid Tax Agent Number (TAN). A verification of their competency and validity as a provider of tax services and guidance is accomplished by doing so.
Last but not least, before you commit, you should make sure that you have a complete understanding of the price structure and research whether or not there are any hidden fees for specific services. Before you hire a tax preparation service, you should make sure that you have a complete understanding of the cost.
## Conclusion
To obtain prior tax returns in Canberra, Australia, one must carefully study a wide variety of possibilities, such as making use of the web services provided by the Australian Taxation Office or talking with tax professionals. Whether you should retain the services of a tax professional or make use of online tax software will be determined by the complexity of your current financial situation as well as your personal preferences.
When gaining access to sensitive financial information, it is very necessary to place a high priority on security and to make use of permitted methods to make sure that your identity is verified.
You must be aware of the costs and price structures involved, regardless of whether you are employing a professional or using a platform that is accessible over the Internet.
Everything will be understandable and effective in this manner. If you follow these steps and take into consideration your requirements, you will be able to retrieve your previous tax returns and maintain correct financial records by the legislation governing taxes in Australia.
The discovery of prior tax returns in Canberra necessitates the implementation of a bespoke plan that is founded on particular circumstances. People are allowed to choose the method that is most suitable for them from among the several options that are provided by the Australian Taxation Office (ATO) and tax professionals.
It is essential to be aware of the fees and to ensure that you comply with the tax laws before embarking on any trip, regardless of whether you opt for individualised assistance or the convenience of online platforms.
In the end, individuals may assist with the management of their finances and compliance with the legislation governing Australian taxes by being proactive and being aware of the resources that are accessible to them to efficiently get their previous tax returns.
### How Do You Clean A Wedding Dress With Dirt?
Cleaning a dirty wedding dress can be a tricky but necessary process if you want to save your special day’s memories in pristine condition. Whether you’re cleaning up after an outdoor wedding or just some random dirt, having the correct tools and methods at your disposal is crucial.
Here, we’ll show you how to bring back the dress’s original lustre by cleaning it in a way that won’t damage it. You can trust that we will give you the experienced guidance and detailed instructions you need to get your wedding dress looking as beautiful as the day you wore it. So, let’s get down to the dirty business of restoring your cherished gown to its former lustre by learning the art of cleaning a wedding dress with dirt.
## How Do You Clean A Wedding Dress With Dirt?
It takes special care and attention to detail to clean a dirty wedding dress and return it to its original condition. So, how to clean a wedding dress? Cleaning a dirty wedding dress entails the following procedures:
### Assess the Dirt:
Before you begin cleaning, take a close look at the dirt stains on your wedding dress. Identify the type of dirt and any additional stains like grass, mud, or food. Different types of dirt may require specific cleaning methods.
### Check the Label:
Carefully read the care label on your wedding dress. The label often provides essential information about fabric composition and cleaning instructions. Follow any recommendations provided by the manufacturer.
### Spot Test:
It’s crucial to test any cleaning solution on an inconspicuous area of the dress to ensure it won’t cause damage or discolouration. Use a small, hidden seam or hem for this purpose.
### Gather Supplies: You will need the following supplies:
• A soft, clean white cloth or sponge
• Mild liquid detergent (preferably one designed for delicate fabrics)
• A basin or tub
• Lukewarm water
• White vinegar (optional)
• Baking soda (optional)
• A soft-bristle toothbrush
• Distilled water for rinsing
• Clean, dry towels
• A garment bag or storage box
### Pre-Treat Stains:
For fresh dirt stains, start by gently shaking or brushing off loose dirt. Do not rub the stains, as this can embed the dirt further. If the dirt is dry, use a soft brush or a toothbrush to remove as much as possible.
### Soak the Dress:
Fill a basin or tub with lukewarm water and add a small amount of mild liquid detergent. Mix it well until it forms suds. Submerge the stained parts of the dress in the soapy water. Allow it to soak for 15-30 minutes. Avoid soaking delicate fabrics for too long, as it can weaken the fibres.
### Gently Agitate:
After soaking, gently agitate the dress in the soapy water with your hands. Use a soft cloth or sponge to lightly rub the stained areas. Be careful not to scrub aggressively, as this can damage the fabric.
### Rinse Thoroughly:
Drain the soapy water and refill the basin with clean, lukewarm distilled water. Rinse the dress until all the detergent is removed. You may add a splash of white vinegar to the rinse water to help remove any remaining soap residue. Rinse until the water runs clear.
### Remove Excess Water:
Gently press the water out of the dress by pressing it between clean, dry towels. Do not wring or twist the dress, as this can damage the fabric.
### Air Dry:
Hang the dress on a padded hanger or lay it flat on a clean, dry towel. Ensure it is not exposed to direct sunlight or heat, as this can cause fabric discolouration. Allow the dress to air dry completely.
### Final Touches:
Once the dress is dry, carefully inspect it for any remaining stains. If needed, you can spot-treat the stains with a mixture of water and a small amount of baking soda. Use the toothbrush to gently scrub the stained areas.
### Store Properly:
After cleaning, store your wedding dress in a clean, dry place, preferably in a breathable garment bag or a storage box designed for preserving wedding gowns. Avoid using plastic bags, as they can trap moisture and cause yellowing.
Seek expert cleaning services for your wedding dress if you are unclear on how to clean it or if it has elaborate detailing or is made of delicate fabrics. A professional cleaner who specialises in bridal gowns is your best bet for achieving optimal results while protecting your dress’s integrity.
## How Late Is Too Late To Clean A Wedding Dress?
There is no hard and fast rule about when it is “too late” to clean a wedding dress, but sooner rather than later is always preferable. However, it might be more difficult to remove stains and prevent long-term damage to a wedding dress the longer you wait to clean it. Here are some things to think about:
• Type of Stains: The type of stains on the dress plays a significant role in how quickly you should clean it. Fresh stains, such as dirt or food, are usually easier to remove than set-in stains, like red wine or makeup. The longer stains are left untreated, the more difficult they can be to eliminate.
• Fabric and Color: Some fabrics and colours are more forgiving than others when it comes to stains. Light-coloured dresses may show stains more prominently, while certain delicate fabrics can be more susceptible to damage if not cleaned promptly.
• Hidden Stains: Stains that are not immediately visible may go unnoticed for a while. It’s a good practice to inspect your wedding dress shortly after the event to identify any hidden stains that may become more challenging to remove over time.
• Preservation: If you plan to preserve your wedding dress as a keepsake, cleaning it before storing it is crucial. Stains left untreated for an extended period can set and become nearly impossible to remove later.
• Professional Cleaning: Professional wedding dress cleaners often recommend getting the dress cleaned within a few weeks to a few months after the wedding. Many offer post-wedding cleaning and preservation services specifically designed to address stains and prevent yellowing or fabric degradation.
Although there is no hard and fast rule on when to clean a wedding dress, it is recommended that any stains be removed and the dress is cleaned as soon as possible after the wedding. This aids in making stains less difficult to remove and prolongs the life of the dress. Consult a professional wedding dress cleaner for advice and assistance if you are unsure of the best strategy or concerned about specific stains.
## Conclusion
A wedding dress that has been stained with dirt is a task that needs to be tackled with care and attention to detail to be successful. Even though there isn’t a hard and fast rule about when cleaning needs to be done, it is generally recommended to take care of stains as soon as possible after your wedding. This will prevent the stains from settling and becoming more difficult to remove later on.
The proper cleaning processes must be followed, spot tests be performed, and the recommendations on the care label be adhered to to maintain the gown’s beauty and the fabric’s integrity. If you are unsure how to clean anything or are dealing with stains that are difficult to remove, you might consider hiring a professional cleaning service.
In the end, you can ensure that your wedding dress will be a treasured memento of your special day for many years to come by providing it with the timely and careful care that it requires.
5/5
Rating:
4/5
## PHOTOGRAPHY REVIEWS
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec. All their equipment and instruments are alive. A red flare silhouetted the jagged edge of a wing. It was going to be a lonely trip back. | 24,125 | 131,191 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2024-30 | longest | en | 0.849125 |
http://www.chegg.com/homework-help/definitions/price-elasticity-12 | 1,472,682,685,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982939756.54/warc/CC-MAIN-20160823200859-00115-ip-10-153-172-175.ec2.internal.warc.gz | 359,546,333 | 13,385 | # Price Elasticity
Price elasticity is a measure of the responsiveness of demand or supply of a good or service to changes in price. The price elasticity of demand measures the ratio of the proportionate change in quantity demanded to the proportionate change of the price . The price elasticity of supply is analogous. Demand for a good is said to be "price elastic" if the elasticity measure is greater than one in absolute value and "inelastic" if less than one. The cross-price elasticity of demand measures the proportionate change in the quantity demanded of one good to the proportionate price change of another good. A positive cross-price elasticity indicates that the goods are substitutes for one another; a negative cross price elasticity indicates the goods are complements.
See more Economics topics
## Need more help understanding price elasticity?
We've got you covered with our online study tools
### Q&A related to Price Elasticity
Experts answer in as little as 30 minutes
• Q:
In 2004, a Massachusetts woman won 5.6 million dollars in the lottery, which would have paid her an initial gross payment of \$283,770 and 19 more yearly payments of \$280,000. Instead she sued the lottery commission f...
A:
• Q:
Assume that you borrow \$15,000 for five years (annual payments) at a market rate of 5%. Assuming that inflation is 3.5%, what would the equivalent equal annual payment be in constant dollars?_________________________...
A:
• Q:
what it is important that a manager understand conflict?
A:
See more related Q&A
### Top Economics solution manuals
Get step-by-step solutions
Get help on Economics with Chegg Study | 345 | 1,646 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2016-36 | latest | en | 0.927791 |
https://us.metamath.org/ilegif/onordi.html | 1,680,000,938,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948858.7/warc/CC-MAIN-20230328104523-20230328134523-00657.warc.gz | 652,866,134 | 3,610 | Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > onordi Unicode version
Theorem onordi 4262
Description: An ordinal number is an ordinal class. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
on.1
Assertion
Ref Expression
onordi
Proof of Theorem onordi
StepHypRef Expression
1 on.1 . 2
2 eloni 4211 . 2
31, 2ax-mp 7 1
Colors of variables: wff set class Syntax hints: wcel 1439 word 4198 con0 4199 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-in 3006 df-ss 3013 df-uni 3660 df-tr 3943 df-iord 4202 df-on 4204 This theorem is referenced by: ontrci 4263 onsucssi 4336 onsucsssucexmid 4356 onirri 4372
Copyright terms: Public domain W3C validator | 552 | 1,183 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2023-14 | longest | en | 0.133372 |
https://www.got-it.ai/solutions/excel-chat/excel-tutorial/data-validation/excel-data-validation-using-sum-function | 1,601,140,086,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400244353.70/warc/CC-MAIN-20200926165308-20200926195308-00664.warc.gz | 800,459,618 | 19,519 | Get instant live expert help with Excel or Google Sheets
“My Excelchat expert helped me in less than 20 minutes, saving me what would have been 5 hours of work!”
#### Post your problem and you’ll get Expert help in seconds.
Your message must be at least 40 characters
Our professional Expert are available now. Your privacy is guaranteed.
# Excel DATA VALIDATION using SUM Function
Figure 1. Excel DATA VALIDATION using SUM Function.
If we decide to restrict users to only input numeric values whose totally or sum does not exceed a specific amount within a selected range of cells, then we can achieve this by using a custom Data Validation formula.
## Formula Syntax
`=SUM(\$C\$2:\$C\$9)<=50000`
The Data Validation in Excel, requires us to set a custom formula based on the SUM function. This formula is to specify the amount users are limited to.
## How to use the SUM Function Data Validation in Excel.
1.In our worksheet example below, we have a list of a breakdown of monthly budgetary expenses for an office.
Figure 2. Excel DATA VALIDATION using SUM Function.
Be sure to provide an empty cell for Excel to return the desired validation result.
1. Our purpose here is to limit users from entering a total monthly budgetary amount greater than or equal to \$50,000.
The custom Data Validation formula we will enter into cell C2 of our worksheet example, is as follows;
`=SUM(\$B\$2:\$B\$8)<=50000`
Figure 3. Excel DATA VALIDATION using SUM Function.
Our validation result was returned as FALSE meaning, the total of the amounts within the cell range B2:B8 is greater than our specified limit of \$50,000.
Figure 4. Final Result.
## Instant Connection to an Expert through our Excelchat Service:
Our live Excelchat Service is here for you. We have Excel Experts available 24/7 to answer any Excel questions you may have. Guaranteed connection within 30 seconds and a customized solution for you within 20 minutes.
### Did this post not answer your question? Get a solution from connecting with the expert.
Another blog reader asked this question today on Excelchat:
Related blogs
Solution examples
I am trying to have a tab change color when the Sum of a row = 0. I am using code on the tab but it appears to be confused because the value of the given cell is not 0 it is "=SUM(G4:G17)"
Solved by S. F. in 41 mins
I need a formula to pop at the upper left corner of a spreadsheet. If I enter the month "January," I want the column number sum of January =SUM(AB11:AB75) from another section on the same excel page to pop right below the "January" cell, and not display the formula expression, but see the \$100.
Solved by T. Q. in 40 mins
Can't add (SUM) in imported numbers from bank account
Solved by F. C. in 40 mins
I need a formula to combine D2 to D100 to add together a column of numbers, then take away the same amount on the same row when column E is filled. i.e. column D is a price of an item, so the formula must calculate the total, then when the item is sold an 'a' is marked next to the item in column E, the formula then must deduct this amount from the total
Solved by X. W. in 20 mins
I would like to have a diagram in a new sheet, where the horizontal axis is the days, as they are in column DX. Each day shall show the sum of all unique leads of that day, and I would like to be able to check via a box of checkboxes, which facilities are shown, the facilities are in column BC.
Solved by I. A. in 45 mins | 805 | 3,452 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2020-40 | longest | en | 0.869088 |
https://www.ajokeaday.com/jokes/latest?page=2360 | 1,675,909,316,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764501066.53/warc/CC-MAIN-20230209014102-20230209044102-00372.warc.gz | 650,700,350 | 19,138 | # Latest Jokes
A fourth-grade teacher was giving her pupils a lesson in logic.
"Here is the situation," she said. "A man is standing up in a boat in the middle of a river, fishing. He loses his balance, falls in, and begins splashing and yelling for help. His wife hears the commotion, knows he can't swim, and runs down to the bank. Why do you think she ran to the bank?"
A girl raised her hand and asked,
"To draw out all his savings?"
CATEGORY School Jokes
posted by "HENNE" |
Saw my old car yesterday. It is a Rolls Canarly.
It rolls down one hill and canarly make up the the other.
posted by "Brake4music" |
COLLEGE MATHEMATICS EXAM PAPER
INSTRUCTIONS: ATTEMPT ALL QUESTIONS. ALL QUESTIONS CARRY EQUAL MARKS.
You have dated a girl for 2 years, eventually she drops you for another guy. Calculate the percentage of time wasted.
(20 marks)
You bought a phone for your girlfriend and she gave it to another guy. Using trigonometric identities, derive a general formula for this type of love.
(20 marks)
(For Boys) You’re dating around 15 girls and every girl is demanding for a Samsung Galaxy and an iPhone 6s.
(a) Plot a graph of girls against prices of phones.
(15 marks)
(5 marks)
You are dating other peoples’ sisters yet you don’t want to see any guy with your sister. Calculate the Percentage Error in your thinking capacity.
(20 marks)
You are a civil servant, your wife is a petty trader, your combined household income is less than \$500. Your daughter who is awaiting result is using iPhone 6s and Samsung Galaxy both worth \$2,000. Calculate the Percentage of your Parental Negligence.
(20 marks)
(For girls) You’re a girl and you have dated 20 guys with hard labor, use the law of diminishing return to calculate the substance that will be left for your husband to enjoy.
(20 marks)
You can’t give your wife \$15 for a pot of soup, but you spend over \$100 in bars and restaurants. Calculate the radius of your ‘stupidity’, take p=3.142.
(20 marks)
GOOD LUCK!
CATEGORY College Jokes | 491 | 2,017 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2023-06 | latest | en | 0.950569 |
http://www.jiskha.com/members/profile/posts.cgi?name=Caitlin | 1,462,043,747,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860112231.78/warc/CC-MAIN-20160428161512-00159-ip-10-239-7-51.ec2.internal.warc.gz | 610,906,707 | 12,104 | Saturday
April 30, 2016
# Posts by Caitlin
Total # Posts: 277
Math
Find two mixed numbers so that the sum is 7 2/4 and the difference is 5
March 10, 2016
Math
A chain saw requires 7 hours of assembly and a wood chipper 3 hours. A maximum of 63 hours of assembly time is available. The profit of \$190 on a chain saw and \$220 on a chipper. How many of each should be assembled for maximum profit?
March 6, 2016
science
Water is useful for reducing friction between objects. However you also learned that (due to friction) moving water causes rough rocks to become smooth. How can this be?
November 3, 2015
Quantitative Math
A bacteria has a doubling period of 5 days. If there are 3250 bacteria present now, how many will there be in 40 days? I've found the growth rate to be 0.14869, but I can not find the amount of bacteria.
November 1, 2015
Chemistry
A line in the Balmer series of hydrogen has a wavelength of 486 nm. From what state did the electron originate? In what region of the electromagnetic spectrum is this line observed?
October 21, 2015
Calculus
Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of the circle measured in inches is modeled by the function r(s)=3 sqrt root s , where s is time in seconds. The area of the spill when seconds is s=5 seconds.
September 18, 2015
Pre-Calculus
A rectangular window is topped with a semicircle. The height of the rectangular part is 1 more than 3 times its width, w meters. Which function represents the total area, A, of the window in terms of the width?
September 10, 2015
I have that same problem too and the answer is 11 836/1000
August 31, 2015
Chemistry
A monoprotic acid of 0.065 M concentration has a pH of 2. 75. Is this a strong or weak acid?
April 23, 2015
Chemistry
You have to prepare a pH 3.50 buffer, and you have the following 0.10M solutions available HCOOH, CH3COOH, H3PO4,CHOONa, CH3COONa, and NaH2PO4. a) What solutions would you use? b) How many milliliters of each solution would you use to make approximately 1 liter of the buffer? ...
April 21, 2015
Math
The front wheel of the worlds largest bicycle has a diameter of 3.05 metres. How many times will this wheel revolve in 1 kilometre?
March 23, 2015
English
Did you ever get the answers for this test
March 13, 2015
Science
Zn + 2HCl - ZnCl2 + H2 Assuming the acid was in excess (so all of the zinc reacts), how many mols of hydrogen would you produce?
March 9, 2015
Introduction programing visual basic
break even analysis. suppose a certain product sells for a dollars per unit. then the revenue from selling x units of the product is ax dollars if the cost of producting each unit of the product is b dollars and the company has overhead cost of c dollars then the total cost of...
March 4, 2015
Introduction programing visual basic
break even analysis. suppose a certain product sells for a dollars per unit. then the revenue from selling x units of the product is ax dollars if the cost of producting each unit of the product is b dollars and the company has overhead cost of c dollars then the total cost of...
March 4, 2015
Chemistry
The tomato is dropped. What is the velocity, v, of the tomato when it hits the ground? Assume 94.7% of the work done in Part A is transferred to kinetic energy, E, by the time the tomato hits the ground.
December 7, 2014
Math
Simultaneous equations- The tickets for a sports club disco cost £2 for members and £3 for non-members. a)The total ticket money collected was £580. x tickets were sold to members and y tickets were sold to non-members. Use this information to write down an ...
November 1, 2014
Physics
A 66.0 kg base runner begins his slide into second base when moving at a speed of 4.4 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. (a) How much mechanical energy is lost due to friction...
October 25, 2014
math
Are negative numbers are integers? True or false
August 27, 2014
Art and Design/ History
How did the first world war play an important role in many aspects of Art Deco and designers, How did it change the role of women and men?
August 4, 2014
alegerba
In the expression 90+5z, the coefficient is
April 15, 2014
Neuroscience
What are the 3 nuclei in the midbrain?
February 11, 2014
Physics`
A field hockey player's arm and stick form a rigid segment. Assuming she hits the ball when the stick is vertical, which of the following would result in the greatest velocity of the end of her stick immediately before she hits the ball? a) She stands still and swings her ...
November 25, 2013
Physics
A golf club is swung with an average angular acceleration of 1.7 rad/s^2. If thee time from start of the swing until the club hits the ball is .7 s, what is the angular velocity of the club when it strikes the ball?
November 7, 2013
Physics
Calculate the force of gravitational attraction between two spheres of mass 10.1kg and 45.2 kg that are 38.5m apart.
November 7, 2013
Physics
Calculate the force of gravitational attraction between two spheres of mass 10.1kg and 45.2 kg that are 38.5m apart.
November 7, 2013
Physics
A sample of an unknown material appears to weigh 275 N in air and 160 N when immersed in alcohol of specific gravity 0.700. What is the volume of the material? What is the density of the material?
October 28, 2013
Physics
A 2.0 mm diameter copper ball is charged to +42 nC. What fraction of its electrons have been removed? The density of copper is 8,920 kg/m3
October 1, 2013
Physics
a)What frequency is received by a person watching an oncoming ambulance moving at 120 km/h and emitting a steady 700 Hz sound from its siren? The speed of sound on this day is 345 m/s. b)What frequency does she receive after the ambulance has passed?
September 3, 2013
math
The number of customers that visit a local small business is 37,800 and has been continuously declining at a rate of 1.7% each year. What is the approximate number of customers that visit the business in 12 years?
July 28, 2013
algebra
You are using 0.05 gallons per mile of a SUV gas tank that holds 16 gallons. Note: this equation has a negative slope (m). Use x-values: 0, 160, and 320. I think the problem should be y=.05x+16 Confused since the teacher says it has a negative slope.
May 13, 2013
Science
If A tank with a flat bottom is filled with water to a height of four meters. what is the pressure at any point at the bottom of the tank? my teacher wants me to ignore atmospheric pressure when calculating my answer A. 3.5 kPa B. 3,500 kPa C. 34.3 kPa D. 34,300 kPa
May 7, 2013
Physics
what formula did you use???
May 6, 2013
Hess's law
I need some help with this one please... A+B ----> 2 D H= -765.3 kj S= 344 j/k C ------> D H= 521 kj S= -171 j/k calculate G at 298 K for A+B ------> 2C I know I need to use the formula G= H-TS but I dont know how to get the numbers.
March 20, 2013
english
How do you diagram this sentence: Driving to the mall, Ann stopped on the way to visit her girlfriend.
February 18, 2013
Chemistry
The heat lost or gained by a system is related to its temperature change by a property called its heat capacity. The molar heat capacity of metals at or above room temperature equals 24.92 J K-1mol-1. The temperature of a block of copper metal (molar mass 63.55 g mol-1) fell ...
February 6, 2013
physics
F=ma m=mass of the car a= given acceleration so.. F=(1236.9)(2.73) Fcar=3376.737 N
February 5, 2013
dress making
im pretty sure im right on most the question, just wanna make sure before i submit!! help Mrs. Shotto was once one of your regular customers, but she hasn't asked to have any garments made in approximately one year. You note she has lost weight. She would like you to make ...
January 28, 2013
dress making
1. Which one of the following is the most complete and accurate definition of fiber? A. A stringy substance from plants B. The hair of an animal C. Man-made threads and yarns D. Basic raw material from which fabric is made 2. An example of a natural fiber is A. nylon. B. ...
January 25, 2013
chem really need help!
i think my equation is wrong. should it be C4H6O4Hg + Na2SO4 -----------> Na(C4H6O4)+ HgSO4 but then there are no coefficients
January 17, 2013
chem really need help!
33.82g/318.678= 0.106 mols Mercury ii acetate 9.718g/142.04= 0.0684 mols sodium sulfate
January 17, 2013
chem really need help!
C4H6O4Hg + Na2SO4 -----------> 2Na(C4H6O4)+ HgSO4
January 17, 2013
chem really need help!
If a solution containing 33.82 g of mercury(II) acetate is allowed to react completely with a solution containing 9.718 g of sodium sulfate, how many grams of solid precipitate will be formed? How many grams of the reactant in excess will remain after the reaction?
January 17, 2013
If a solution containing 33.82 g of mercury(II) acetate is allowed to react completely with a solution containing 9.718 g of sodium sulfate, how many grams of solid precipitate will be formed? How many grams of the reactant in excess will remain after the reaction?
January 17, 2013
If a solution containing 33.82 g of mercury(II) acetate is allowed to react completely with a solution containing 9.718 g of sodium sulfate, how many grams of solid precipitate will be formed? How many grams of the reactant in excess will remain after the reaction?
January 17, 2013
Chemistry
If a solution containing 33.82 g of mercury(II) acetate is allowed to react completely with a solution containing 9.718 g of sodium sulfate, how many grams of solid precipitate will be formed? How many grams of the reactant in excess will remain after the reaction?
January 17, 2013
basic chem
If a solution containing 33.82 g of mercury(II) acetate is allowed to react completely with a solution containing 9.718 g of sodium sulfate, how many grams of solid precipitate will be formed? How many grams of the reactant in excess will remain after the reaction?
January 17, 2013
a tri angle has a base of 5.2 and a hieght of 19cm
January 9, 2013
Darin
wouldn't it be 5%?
November 30, 2012
Math
there would be 5 on each team hope i helped (:
November 29, 2012
Chemistry
A sample of oxygen is collected in a 387 mL container over water at 15◦C, and the barom- eter reads 738 torr. What volume would the dry gas occupy at 781 torr and 15◦C? Water’s partial pressure at 15◦C is 12.8 torr. Answer in units of mL
November 20, 2012
Chemistry
A sample of hydrogen (2.02 g/mol) effuses through a porous container about 8.85 times faster than an unknown gas. Estimate the molar mass of the unknown gas. Answer in units of g/mol
November 20, 2012
Chemistry
A meteorological balloon had a radius of 1.1 m when released at sea level at 20◦C. It ex- panded to a radius of 5 m when it had risen to its maximum altitude, where the temperature was −20◦C. What was the pressure inside the balloon at that altitude? The ...
November 20, 2012
Chemistry
Use van der Waals’ equation to calculate the pressure exerted by 2.33 mol of ammo- nia at −3.7◦C in a 1.25 L container. The van der Waals’ constants for ammonia are a = 4.00 L2·atm/mol2 and b = 0.0400 L/mol. (The values for a and b have been ...
November 20, 2012
Chemistry
Oxygen can be produced in the laboratory by the reaction 2 KClO3(s) → 2 KCl(s) + 3 O2(g) . How much potassium chlorate is needed to produce 2.75 L of oxygen, collected over water at 37◦C and 94.9 kPa? The vapor pressure of water at 37◦C is 6.28 kPa. 1. 0.189 ...
November 20, 2012
science
According to the principle of superposition, in a stack of undisturbed sedimentary rocks, the oldest rocks are _____. Gaps in rock layers are called ____. Which of the following is not a type of unconformity?
November 16, 2012
physics
You are given angular velocity initial, angular acceleration, and time. use wf=wi+at wf=0+(0.630rad/s)*(3s)
November 4, 2012
Physics
The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 10 Earth years. a) What is the asteroid's orbital radius? b)What is the asteroid's orbital speed?
October 23, 2012
physics
A ball is thrown from a point 1.38 m above the ground. The initial velocity is 19.9 m/s at an angle of 33.8° above the horizontal. Find the maximum height of the ball above the ground. Calculate the speed of the ball at the highest point in the trajectory.
September 23, 2012
Physics
A person climbs from a Paris metro station to the street level by walking up a stalled escalator in 96.5 s. It takes 60.0 s to ride the same distance when standing on the escalator when it is operating normally. How long would it take for him to climb from the station to the ...
September 20, 2012
Physics
A particle's constant acceleration is north at 108 m/s2. At t = 0, its velocity vector is 61.7 m/s east. At what time will the magnitude of the velocity be 102 m/s?
September 20, 2012
grammar
Click on the box below to choose the correct sentence pattern for the sentence below. There is good reason to be thankful. OPTIONS: Question patternS-V-DOS-LV-PNS-VS-LV-PAS-V-IO-DOE-V-SS-V-DO-OC
August 22, 2012
grammar
What is the correct sentence pattern for...I hereby declare Tuesday Shakespeare Day. OPTIONS: Question patternS-V-DOS-LV-PNS-VS-LV-PAS-V-IO-DOE-V-SS-V-DO-OC
August 22, 2012
science
August 10, 2012
science
A soccer ball is kicked with an initial speed of 8.4 m/s in a direction 22.0° above the horizontal.Find the magnitude and direction of its velocity at the following times. (Take the +x axis to be parallel to the ground, in the direction that the ball is kicked.)0.250 s ...
August 10, 2012
physics
Two strings are adjusted to vibrate at exactly 224 Hz. Then the tension in one string is increased slightly. Afterward, three beats per second are heard when the strings vibrate at the same time. What is the new frequency of the string that was tightened? (in Hz)
August 7, 2012
Calc
The arc of the parabola y=x^2 from (1,1) to (2,4) is rotated about the y-axis. Find the area of the resulting surface.
June 6, 2012
calculus
The base of a solid consists of the region bounded by the parabola y=rootx, the line x=1 and the x-axis. Each cross section perpendicular to the base and the x-axis is a square. Find the volume of the solid.
June 6, 2012
Calc
Are you sure about the 4w (324/w^2)? Shouldn't it be 8w (324/w^2), since you are multiplying the four sides by the cost of \$2 per square foot?
June 5, 2012
Calc
A closed box with a square base is to be constructed so that its volume is 324 cubed feet. The material for the top and bottom cost is \$3 per square foot, and that for the sides \$2 per square foot. Find the dimensions of the box so that the cost will be minimum.
June 5, 2012
Math 10
A cylinder has a surface area of 250cm2. The height is twice as big as the radius. What is the height of the cylinder?
May 21, 2012
Finance
The Isberg Company just paid a dividend of \$0.75 per share, and that dividend is expected to grow at a constant rate of 5.50% per year in the future. The company's beta is 1.25, the market risk premium is 5.00%, and the risk-free rate is 4.00%. What is the company's ...
April 2, 2012
Finance
Scanlon Inc.'s CFO hired you as a consultant to help her estimate the cost of capital. You have been provided with the following data: rRF = 4.10%; RPM = 5.25%; and b = 1.15. Based on the CAPM approach, what is the cost of equity from retained earnings? Several years ago ...
April 2, 2012
College Algebra
The height of a box is 3cm less than the width. The length is 2cm less than the width. The volume is 50cm^3. what is the width of the box?
April 2, 2012
algebra
Which situation would most likely be represented by a negative correlation: hours of practice and your golf score, hours of practice and the number of baskets you make in basketball, or hours of practice and the cost of a computer? Hint: In golf, the lower the score, the better.
March 19, 2012
Chemistry
Sorry, its 0.150 M solution of ammonia at 25 degrees celsius
March 18, 2012
Chemistry
At 25 degrees Celsius, the base ionization constant for NH3 is 1.8 x ^-5. Determine the percentage ionization of a M solution of ammonia at 25 degree Celsius.
March 18, 2012
Chemistry
How much heat in kJ is lost when 100.0g of steam at 200 deg C is cooled down until it forms ice at -30.0 deg C?
March 6, 2012
Chemistry
Calculate the heat (in kJ) required to change 40.0g of ice at -30.0 deg C to steam at 150.0 deg C?
March 6, 2012
Intergrated Math
Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents. (b ^4)^ 2
December 29, 2011
General chemistry
How much energy is released by the combustion of 1.00 mol of octane, C8H18?
November 7, 2011
Chemistry
Calculate the average mass (in amu) of 1 methane molecule (to .01 amu)
November 1, 2011
Chemistry
How do you find the number of bond angles for an octahedral structure? I believe it's more than one answer
October 28, 2011
Chemistry
How do you figure out the number of bond angles for an octahedral? It's more than one answer?
October 28, 2011
Chemistry
Predict the formal bond angles about the central atom for the following molecules: TeBr4 Express your answers using three significant figures separated by a comma. What are the bond angles for an octahedral structure and how many?
October 28, 2011
Chemistry
Describe what a chemical bond is in terms of electron density between two atoms. What are the bond angles for an octahedral structure and how many? Predict the formal bond angles about the central atom for the following molecules: TeBr4 Express your answers using three ...
October 28, 2011
physics
A sample of an unknown material appears to weigh 285 N in air and 165 N when immersed in alcohol of specific gravity 0.700. (a) What is the volume of the material? Answer is in m3 (b) What is the density of the material? Answer is in kg/m3
October 27, 2011
physics
(a) Calculate the mass flow rate (in grams per second) of blood (ρ = 1.0 g/cm3) in an aorta with a cross-sectional area of 2.0 cm2 if the flow speed is 33 cm/s. Answer is in g/s (b) Assume that the aorta branches to form a large number of capillaries with a combined cross...
October 27, 2011
Chemistry
Rank the carbon-carbon bonds in order of decreasing bond length. Rank carbon-carbon bonds from highest bond length to lowest. To rank bonds as equivalent, overlap them. 1,2,3
October 11, 2011
Chemistry
The dipole moment (mu) of HBr (a polar covalent molecule) is 0.851 D (debye), and its percent ionic character is 12.6 %. Estimate the bond length of the H-Br bond in picometers.
October 7, 2011
Chemistry
The bond in O2 is shorter than the O-O bond in compounds that contain an O-O single bond. Explain this observation.
October 7, 2011
Chemistry
The Lewis structure of O2
October 7, 2011
Chemistry
Explain why it is necessary to form a double bond in the Lewis structure.
October 7, 2011
Chemistry
Which of the subshells in the electron configuration of Hf behave as core orbitals Check all that apply 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d
October 4, 2011
Chemistry
What do we call the part of the universe that is not part of the system
October 4, 2011
Chemistry
What is the kinetic energy of the emitted electrons when cesium is exposed to UV rays of frequency 1.7×10^{15} Hz?
September 27, 2011
Physics
A horizontal spring attached to a wall has a force constant of 780 N/m. A block of mass 1.70 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in the figure below. The initial goal of this problem is to find the velocity at the ...
September 27, 2011
Chemistry
In the recent Chem Activities, we have been learning about how Coulombic attractions and repulsions determine properties of atoms like ionization energy and atomic radius. We have made two assumptions not completely justified by the data we had up to this point: electrons are ...
September 26, 2011
1. Pages:
2. 1
3. 2
4. 3
5. Next>> | 5,555 | 20,023 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2016-18 | longest | en | 0.946391 |
http://forums.wolfram.com/mathgroup/archive/2010/Nov/msg00120.html | 1,721,750,284,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518058.23/warc/CC-MAIN-20240723133408-20240723163408-00043.warc.gz | 12,995,321 | 8,126 | Re: Numerical solution of the heat equation on a disk
• To: mathgroup at smc.vnet.net
• Subject: [mg113636] Re: Numerical solution of the heat equation on a disk
• From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
• Date: Fri, 5 Nov 2010 05:13:40 -0500 (EST)
```Hi, Francois,
I would simply regularize the equation, i.e instead
u_t = u_rr + (1/r) u_r
I would solve
u_t = u_rr + (1/(r+eps)) u_r
with a small eps. The choice of its value should be done depending upon the origin of your equation. This will
remove the problem. Try this, for instance:
NDSolve[{D[u[t, r], t] == D[u[t, r], r, r] + D[u[t, r], r]/(r + 0.01),
u[0, r] == 10*(Exp[-r^2/5] - Exp[-1/5]),
u[t, 1] == 0, (D[u[t, r], r] /. r -> 0) == 0}, u, {t, 0, 2}, {r, 0,
1}]
Plot3D[Evaluate[u[t, r] /. %], {t, 0, 2}, {r, 0, 1}, PlotRange -> All,
AxesLabel -> {"t", "r", "u"}]
Have fun, Alexei
Hello,
I would like to get a numerical simulation of the heat equation with Dirichlet boundary conditions on a disk. With the problem I have, the function does not depend on theta, so we get :
u_t = u_rr + (1/r) u_r
It introduces a singularity as goes to 0 and Mathematica can not solve the problem with NDSolve. Is there a way to go around this ?
Best regards,
Francois
PS : I know that I can do Bessel expansion, but it's not what I want to do here.
--
Alexei Boulbitch, Dr. habil.
Senior Scientist
Material Development
IEE S.A.
ZAE Weiergewan
11, rue Edmond Reuter
L-5326 CONTERN
Luxembourg
Tel: +352 2454 2566
Fax: +352 2454 3566
Mobile: +49 (0) 151 52 40 66 44
e-mail: alexei.boulbitch at iee.lu
www.iee.lu
--
This e-mail may contain trade secrets or privileged, undisclosed or
otherwise confidential information. If you are not the intended
recipient and have received this e-mail in error, you are hereby
notified that any review, copying or distribution of it is strictly
prohibited. Please inform us immediately and destroy the original | 635 | 1,919 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2024-30 | latest | en | 0.812511 |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/192/3/t/a/ | 1,606,627,015,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141196324.38/warc/CC-MAIN-20201129034021-20201129064021-00015.warc.gz | 744,921,444 | 54,709 | # Properties
Label 192.3.t.a Level $192$ Weight $3$ Character orbit 192.t Analytic conductor $5.232$ Analytic rank $0$ Dimension $256$ CM no Inner twists $2$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 192.t (of order $$16$$, degree $$8$$, minimal)
## Newform invariants
Self dual: no Analytic conductor: $$5.23162107572$$ Analytic rank: $$0$$ Dimension: $$256$$ Relative dimension: $$32$$ over $$\Q(\zeta_{16})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$
## $q$-expansion
The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.
$$\operatorname{Tr}(f)(q) =$$ $$256q + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$256q + 144q^{22} + 400q^{26} + 240q^{28} - 80q^{32} - 240q^{34} - 560q^{38} - 720q^{40} - 208q^{44} - 624q^{50} + 384q^{51} - 528q^{52} - 144q^{54} + 512q^{55} - 784q^{56} + 512q^{59} - 288q^{60} - 96q^{62} + 96q^{64} + 288q^{66} - 128q^{67} + 480q^{68} + 672q^{70} - 1024q^{71} + 1232q^{74} - 768q^{75} + 208q^{76} + 720q^{78} - 512q^{79} + 816q^{80} + 1040q^{82} + 560q^{88} + 96q^{94} + O(q^{100})$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
19.1 −1.99032 0.196561i 1.44015 0.962276i 3.92273 + 0.782437i −1.54570 7.77077i −3.05550 + 1.63216i −11.5402 + 4.78010i −7.65368 2.32835i 1.14805 2.77164i 1.54901 + 15.7701i
19.2 −1.97540 0.312752i −1.44015 + 0.962276i 3.80437 + 1.23562i −0.279220 1.40373i 3.14581 1.45047i −3.62990 + 1.50355i −7.12870 3.63066i 1.14805 2.77164i 0.112549 + 2.86026i
19.3 −1.92244 + 0.551559i −1.44015 + 0.962276i 3.39156 2.12068i 1.64535 + 8.27175i 2.23785 2.64425i 8.64107 3.57925i −5.35040 + 5.94754i 1.14805 2.77164i −7.72546 14.9945i
19.4 −1.84535 + 0.771151i 1.44015 0.962276i 2.81065 2.84609i −0.118194 0.594202i −1.91552 + 2.88631i 4.91350 2.03524i −2.99188 + 7.41948i 1.14805 2.77164i 0.676329 + 1.00537i
19.5 −1.77755 0.916684i 1.44015 0.962276i 2.31938 + 3.25891i 0.937462 + 4.71294i −3.44204 + 0.390335i 6.22692 2.57928i −1.13543 7.91901i 1.14805 2.77164i 2.65389 9.23685i
19.6 −1.75449 + 0.960092i −1.44015 + 0.962276i 2.15645 3.36894i −0.982422 4.93897i 1.60285 3.07097i 2.14513 0.888543i −0.548972 + 7.98114i 1.14805 2.77164i 6.46551 + 7.72214i
19.7 −1.70771 1.04102i −1.44015 + 0.962276i 1.83257 + 3.55552i 1.29633 + 6.51710i 3.46110 0.144072i −5.83647 + 2.41754i 0.571859 7.97953i 1.14805 2.77164i 4.57065 12.4788i
19.8 −1.36103 1.46546i 1.44015 0.962276i −0.295169 + 3.98909i 0.242100 + 1.21712i −3.37027 0.800794i −4.94543 + 2.04846i 6.24761 4.99674i 1.14805 2.77164i 1.45414 2.01133i
19.9 −1.27767 + 1.53868i −1.44015 + 0.962276i −0.735101 3.93187i 0.251501 + 1.26438i 0.359399 3.44541i −9.71768 + 4.02520i 6.98913 + 3.89256i 1.14805 2.77164i −2.26682 1.22849i
19.10 −1.27046 + 1.54465i 1.44015 0.962276i −0.771866 3.92482i 0.951985 + 4.78595i −0.343273 + 3.44705i −6.47911 + 2.68373i 7.04309 + 3.79407i 1.14805 2.77164i −8.60206 4.60988i
19.11 −1.26075 1.55258i −1.44015 + 0.962276i −0.821030 + 3.91483i −1.08391 5.44919i 3.30968 + 1.02276i −3.97032 + 1.64456i 7.11321 3.66090i 1.14805 2.77164i −7.09379 + 8.55292i
19.12 −1.08433 1.68055i 1.44015 0.962276i −1.64847 + 3.64452i −1.65925 8.34160i −3.17874 1.37681i 7.15690 2.96448i 7.91227 1.18154i 1.14805 2.77164i −12.2193 + 11.8335i
19.13 −0.760241 + 1.84987i −1.44015 + 0.962276i −2.84407 2.81270i −0.194779 0.979220i −0.685230 3.39565i 6.99962 2.89934i 7.36532 3.12284i 1.14805 2.77164i 1.95951 + 0.384127i
19.14 −0.441777 1.95060i −1.44015 + 0.962276i −3.60967 + 1.72346i 0.109322 + 0.549600i 2.51324 + 2.38404i 6.48355 2.68558i 4.95644 + 6.27962i 1.14805 2.77164i 1.02375 0.456044i
19.15 −0.399279 1.95974i 1.44015 0.962276i −3.68115 + 1.56497i 0.758038 + 3.81092i −2.46083 2.43810i −10.7874 + 4.46830i 4.53673 + 6.58924i 1.14805 2.77164i 7.16573 3.00718i
19.16 −0.358174 + 1.96767i 1.44015 0.962276i −3.74342 1.40954i −0.809137 4.06781i 1.37761 + 3.17839i −6.21464 + 2.57419i 4.11429 6.86095i 1.14805 2.77164i 8.29390 0.135127i
19.17 0.143105 + 1.99487i 1.44015 0.962276i −3.95904 + 0.570954i −0.196739 0.989075i 2.12571 + 2.73521i 12.0254 4.98107i −1.70554 7.81608i 1.14805 2.77164i 1.94492 0.534012i
19.18 0.195531 + 1.99042i −1.44015 + 0.962276i −3.92354 + 0.778375i 1.68587 + 8.47543i −2.19693 2.67834i −3.67509 + 1.52227i −2.31646 7.65728i 1.14805 2.77164i −16.5400 + 5.01279i
19.19 0.377294 1.96409i 1.44015 0.962276i −3.71530 1.48208i 1.80347 + 9.06666i −1.34664 3.19164i 9.72216 4.02705i −4.31270 + 6.73800i 1.14805 2.77164i 18.4882 0.121382i
19.20 0.679497 1.88103i −1.44015 + 0.962276i −3.07657 2.55631i 0.892221 + 4.48550i 0.831497 + 3.36283i −2.40197 + 0.994929i −6.89902 + 4.05012i 1.14805 2.77164i 9.04363 + 1.36958i
See next 80 embeddings (of 256 total)
$$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 187.32 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
64.j odd 16 1 inner
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 192.3.t.a 256
64.j odd 16 1 inner 192.3.t.a 256
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
192.3.t.a 256 1.a even 1 1 trivial
192.3.t.a 256 64.j odd 16 1 inner
## Hecke kernels
This newform subspace is the entire newspace $$S_{3}^{\mathrm{new}}(192, [\chi])$$.
## Hecke characteristic polynomials
There are no characteristic polynomials of Hecke operators in the database | 2,993 | 5,790 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2020-50 | latest | en | 0.424312 |
https://oeis.org/A235845 | 1,638,034,771,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358208.31/warc/CC-MAIN-20211127163427-20211127193427-00349.warc.gz | 500,443,783 | 3,617 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235845 Number of (n+1)X(3+1) 0..3 arrays with the upper median unequal to the lower median in every 2X2 subblock 1
16228, 1133608, 80556656, 5778908484, 415698469568, 29937676955084, 2156857770093828, 155414194184061336, 11199079002464581764, 807017035004418681844, 58154884407935003132880, 4190741598855907942838336 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS Column 3 of A235849 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 R. H. Hardin, Empirical recurrence of order 55 FORMULA Empirical recurrence of order 55 (see link above) EXAMPLE Some solutions for n=1 ..1..2..0..1....3..2..2..3....0..0..0..1....3..0..2..0....3..3..3..2 ..1..2..0..1....0..0..1..3....3..2..2..0....1..0..2..1....1..1..0..1 CROSSREFS Sequence in context: A031624 A035921 A278607 * A254163 A254170 A254452 Adjacent sequences: A235842 A235843 A235844 * A235846 A235847 A235848 KEYWORD nonn AUTHOR R. H. Hardin, Jan 16 2014 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified November 27 12:37 EST 2021. Contains 349394 sequences. (Running on oeis4.) | 494 | 1,478 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2021-49 | latest | en | 0.60319 |
http://www.doc.ic.ac.uk/~phjk/AdvancedCompArchitecture/Exercises/Ex4-SpMvMExploration/Ex4-SpMvMExploration.html | 1,511,400,951,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806715.73/warc/CC-MAIN-20171123012207-20171123032207-00558.warc.gz | 394,915,659 | 4,923 | # Exercise 4: Sparse matrix-vector multiply
### Background
A sparse matrix is one with a large proportion of zero elements. Many important algorithms involve multiplying a sparse matrix by a vector, . This key computational kernel'' is the focus of the main laboratory project for this course.
Applications include:
• Solving partial differential equations on unstructured (tetrahedronal) meshes - for example to simulate fluid flow
• Calculating the eigenvalues of the web's hyperlink connectivity graph, for example in order to compute Google's Pagerank''
• Solving a Markov process - derive the probability of a system being in a particular state, given a matrix of state transition probabilities.
Dense (that is not sparse) matrix-vector multiplication looks like this:
double A[A_rows][A_cols];
double x[A_rows], y[A_rows];
for ( i=0; i<A_rows; i++ ) {
sum = 0.0;
for ( k=1; k<=A_cols; k++ )
sum += A[i][k]*x[k];
y[i] = sum;
}
To make this sparse we need to choose a storage scheme. A popular choice is compressed row'':
struct MatrixElement {
long col;
double val;
};
/* no of non-zeroes in each row */
int SA_entries[A_rows];
/* array of pointers to list of non-zeroes in each row */
MatrixElement** SA = (struct MatrixElement**)malloc(sizeof(struct MatrixElement)*A_rows);
/* When SA_entries is known we can allocate just enough memory for data */
for(i=0; i<A_rows; i++) {
SA[i] = (struct MatrixElement*)malloc(sizeof(struct MatrixElement)*A_entries[i]);
}
The idea here is that for each row, we keep an array of the non-zero matrix elements, pointed to by SA[i]. For each element SA[i][j] we need its value, and its column number. So, if A[i][j] is the nth non-zero in row i, its value will be stored at SA[i][n].val, and SA[i][n].col will be j.
Now the matrix-vector multiply can be written as:
for(i=0; i<A_rows; i++) {
sum = 0;
for(j=0; j<SA_entries[i]; j++) {
sum += ((SA[i][j]).val)*x[(SA[i][j]).col];
}
y[i] = sum;
}
You can find the source code in
/homes/phjk/ToyPrograms/C/smv-V1
Copy this directory tree to your own directory:
cd
cp -r /homes/phjk/ToyPrograms/C/smv-V1 ./
Now run some setup scripts:
cd smv-V1
source SOURCEME.csh
./scripts/PutInputFilesOnLocalDisk.sh
./scripts/MakeMatrices.sh 1 2 3
This creates a directory /tmp/USERNAME/spmv/ and builds some sample matrices there. You should compile the application using the following commands:
cd solver/csteady/
make
Now you can run the program:
./csteady ../../inputs/courier1/ ../../inputs/courier1/STEADY
This reads input from the directory for problem size 1, and writes its output to a file called STEADY'' in the same directory. This is problem size 1 - very tiny. Problem size 3 is more substantial. 1
## What to do
Your job is to characterise the behaviour of the Jacobi program, and study how the performance varies with array size.
1. Choose a linux machine on the DoC network2 and measure the execution time of csteady on problem size 3.
Try to make sure no other processes are active as they will interfere with your results. How many times do you need to repeat your experiments to get a reliable result?
2. Use the cachegrind simulator to estimate csteady's cache performance:
cachegrind ./solver/csteady/csteady inputs/courier1/ inputs/courier1/STEADY
3. Plot a graph that shows how the rate of level-1 data cache misses changes with cache size using problem size 1. Start with:
cachegrind --L2=64,1,16 ./solver/csteady/csteady inputs/courier1/ inputs/courier1/STEADY}
This simulates a 1-way (ie direct-mapped) cache with 64, 16 byte lines. Now replace 64 with powers of two up to . See below for hints on how to automate this.
When you have finished, explore other cache parameters, such as block size and associativity. It would also be interesting to look at larger problem sizes - though this will take some time!
## What's it for?
The program solves a Markov chain derived from a probabilistic Petri model (see see Figure 1) of a simple communication protocol. The problem size corresponds to the protocol's window size'' - the number of messages which can be in sent before the transmitter blocks awaiting acknowledgement. Execute the following commands to see the final results:
cd inputs/courier1
./perf
The output shows the values for the following metrics of the protocol's performance:
psend:
Probability that the sender's application level is idle
precv:
Probability that the receiver's application level is idle
psess1:
Probability that the sender's session level is idle
psess2:
Probability that the receiver's session level is idle
ptransp1:
Probability that the sender's transport level is idle
ptransp2:
Probability that the receiver's transport level is idle
lambda:
data throughput rate of the protocol
## Tools and tips
### Running the experiments
Run cachegrind over a range of parameters you need to write a shell script. You might find the following Bash script useful:
#!/bin/bash -f
for ((x=64; x <= 1048576 ; x *= 2))
do
echo -n Size $x cachegrind --D1=$x,1,16 ./solver/csteady/csteady inputs/courier1/ inputs/courier1/STEADY \
2>&1 | grep D1 miss rate''
done
(The final line combines stdout and stderr and selects just the D1 miss rate from the simulation output). You can run this script by typing
./scripts/cg-loop.sh > results
This writes all the results to a file results''. It takes quite a while!
### Producing a table
You need to convert the results'' file to a neat table of problem size against performance. Try:
awk '{print $2,$6, $8,$10}' <results > table
This picks out the miss rate data columns. The output is sent to the file table''.
### Plotting a graph
Try using the gnuplot program. Type gnuplot''. Then, at its prompt type:
plot 'table' with linespoints
plot 'table' using 0:2 with linespoints, 'table' using 0:3 w lp, 'table' u 0:4 w lp
Paul Kelly, Imperial College London, 2004
#### Footnotes
... substantial.1
You can make much larger problem sizes using /scripts/MakeMatrices.sh 4 (264MBytes), or ./scripts/MakeMatrices.sh 5 (more than 800MBytes). Apparently in the Markov chain commnity this state explosion effect is called the largeness'' problem! However you may run into quota problems as the matrix is built in the solver directory then copied to /tmp/. To overcome this, install in /tmp or wait for the next release.
... network2
See https://www.doc.ic.ac.uk/csg/computers/. | 1,615 | 6,389 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2017-47 | latest | en | 0.720353 |
http://lotterywinnerstories.com/Lottery/most-common-lottery-numbers-drawn-together-lotto-47/ | 1,519,493,601,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891815918.89/warc/CC-MAIN-20180224172043-20180224192043-00384.warc.gz | 216,764,722 | 10,097 | ## Lotto Dominator Winning Software Lotto 47
Playing the Lotto 47 lottery can be very exciting especially if from time to time you are a winner. Winning can be accomplished quit often if the correct system is used. There are many so called experts in the market offering winning number secrets and scratch off ticket recommendations that promise to help you win. Most are not legit. However, there are a few systems on the market that has produced some promising results.
When you consider that that there are many different lottery systems available and lots of past winners you remain anonymous or don’t talk about their winning strategies how many more winners might there be who have used such systems?
Think about it: is it possible that a huge percentage of lottery winners are actually using mathematical or statistical formulas to help them win? If that is the case then anyone who is not using a system is merely feeding the prize fund and has an almost zero chance of winning.
## Would You Like to Win The Lotto 47 lottery?
Have you been searching for Pick 3 lottery workout systems that actually work? Are you tired of guessing and relying on luck? Well here's one system that you should try. It only involves simple mathematics and a bit of concentration. This system is one of the oldest. Although it doesn't guarantee a hundred percent, it has a high percentage hit. It is called the 123 workout. Here is how it works:
o You begin by using the preceding numbers drawn from the Pick 3 lottery. Just to provide a concrete example, let us use the numbers 468. We will call it the stack number.
o Important Rule of the 123 workout: Do not carry over when adding or subtracting the numbers. Here is an example: 5 + 9 = 4 (instead of 14)
o Monitor all the numbers that come out in the following days. You will realize that one out of the 22 combinations will be the next hit. Let's face it; it is better than having to choose from a million other combinations. Your chance of winning the next lottery is now greater having to choose from a smaller set.
Others have tried other Pick 3 lottery workout systems. Some of them are just too complicated. They would require the work of your personal computer, plus it costs much and takes time to download them. This system only requires a pen and a piece of paper. Try this method and see if the numbers really come out. What have you got to lose?
## Megamillions Lottery Odds - How to Increase Your Chances of Winning!
Lottery predictions is quite popular these days. People used to be skeptical with the predictions as they thought that the winning numbers are a matter of luck and fortunes. Not many people believe that lottery can be won by using some kind of a sophisticated science based predictions. It was not until the late 90s when lottery players began using lottery predictions to help them to win lottery or at least get closer to the winning numbers. When Gonzalo Garcia-Pelayo, a Spanish man who managed to study and analyze many games in two different countries, Spain and the US and win a lot of money by using different strategies. After him people started to believe that lottery results can be predicted.Lottery players start thinking about how to win the lotteries using predictions. They use many kinds of predictions: from mechanical predictions on mechanical lotteries to technological predictions using computer software. A lot of people use algorithm to analyze and predict lottery results.Analysis of GroupsThere are many kinds of group analysis that lottery predictors use to get into the winning numbers. Lottery players can group the months having the best winning numbers of a certain period or they can group the numbers winning in certain period of time.Analysis of Hot-Cold TrendThis algorithm analysis is one of the most favourite so far as it can record the frequency ranks and use the variations to predict the tendencies of hot and cold numbers in the next drawings.Analysis of Repetition PatternA lot of lottery players share the same opinion that repetition is quite important to predict the winning numbers as most of jackpots will appear again in the future.The analysis mentioned above represents only a part of the strategies that lottery players can use. There are still many other algorithm analysis that can be done by predictors to help them win.
Winning the Lotto 47 lottery is very rewarding. Give this system a spin and watch your winnings grow. | 889 | 4,462 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2018-09 | longest | en | 0.962507 |
http://sudhansu-codezone.blogspot.com/2016/08/find-k-closest-elements-to-given-value.html | 1,558,644,651,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232257396.96/warc/CC-MAIN-20190523204120-20190523230120-00281.warc.gz | 189,523,909 | 14,599 | ## Saturday, August 6, 2016
### Find k closest elements to a given value
Given a sorted array arr[] and a value X, find the k closest elements to X in arr[].
Examples:
Input: K = 4, X = 35
arr[] = {12, 16, 22, 30, 35, 39, 42, 45, 48, 50, 53, 55, 56}
Output: 30 39 42 45
Method:
1) Start from the first element and search for the crossover point (The point before which elements are smaller than or equal to X and after which elements are greater). We will use Binary search for this.This step takes O(logn) time.
2) Once we find the crossover point, we can compare elements on both sides of crossover point to print k closest elements. This step takes O(k) time.
Time: For k elements it takes O(Logn + k) time.
http://www.geeksforgeeks.org/find-k-closest-elements-given-value/ | 227 | 780 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2019-22 | latest | en | 0.779729 |
http://www.samyoung.co.nz/2020/07/test-technique.html | 1,643,086,685,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304760.30/warc/CC-MAIN-20220125035839-20220125065839-00529.warc.gz | 121,350,325 | 22,096 | ## Wednesday, 29 July 2020
### Test technique
Many students struggle with how to tackle examinations. In general with tests and examinations, I am not looking for an essay: I am simply wanting my students to demonstrate that they understand - own - the material that we have covered.
The advice I give my students is to divide the minutes available for the test by the marks (normally that ratio will come out at a little over two minutes per mark). We use the number our calculation gives us to budget our time against the marks for each question.
• For example, an 80 minute test of 40 marks would be very tight. We would need to budget 1.6 minutes per mark so we had a little over 15 minutes to review before the end of the test. For a ten mark question, we allow ourselves 16 minutes.
• On the other hand, a 120 minute test of 50 marks would allow us 2 minutes per mark with 20 minutes for review. For a ten mark question, we can safely allow 20 minutes.
We should work our mark to time ratio out at the beginning of the test, and note how much time we should spend per question, against the question (or question title), to remind us of how we are trackingHaving a little time left over to proof and double-check at the end can make a huge difference to our performance.
There is also technique in answering certain types of questions:
When tackling a short to medium answer question, I give the following advice for students sitting examinations in the Polytechnic sector, where learning needs to be applied. There are three aspects that we need to show the examiner: that we understand the theory by defining it, that we can demonstrate what it means to ourselves, and that we can apply it to a real situation or case.
To show that we know the theory, we need to be able to define the theory, and explain what it does. We need to be able to break the theory down into its key components. Then we need to explain how that theory sits with us, personally. We are likely to be asked how we may use it ourselves, or if we have used it, or if we have seen it used, or if - or how - we have seen it demonstrated in a case.
Definition. Demonstration. Application.
Multiple Choice Questions:
A good general strategy for multiple choice is to go through them as quickly as we can, and answer each question we know the answer to. My general rule of thumb is to spend one minute per unknown question, and leave each one that we don’t know the answer to after that minute is up. We then simply note down any questions we don’t know the answers to, which we can come back to later, in our proofing time.
Only when we have run out of questions do we go back to tackle the questions we didn't know how to answer.
I also have a strategy for when we run short of time, or are stuck:
Stuck: if we are stuck, define the theory we think we are being asked about, detail the components, then paraphrase what we think the examiner is asking us, and answer that question to the best of our ability, providing examples. Even if we are off track, other students too may have misread or not been able to interpret the question, and the examiner may give us marks for what we have answered.
Short of time: if we are running out of time, quickly define the theory we think we are being asked about, again, paraphrase what the examiner is asking us, then just list list where we were aiming to go with our answer in brief bullet points. It may not get us many marks, but some marks are better than none.
Another point that is worth noting is that open book exams can make us feel secure, because we can have as much information as we need. However, looking things up takes a lot of time. Knowing the information and studying ahead of time is much more useful, as retrieval from brain to keyboard is much faster if it isn't first diverted via several pdfs or textbooks.
Definition. Demonstration, Application. Good luck!
Sam | 850 | 3,911 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2022-05 | longest | en | 0.953471 |
https://git.ao2.it/flexagon-toolkit.git/commitdiff/33f6577dfdb6b5f075c913b0239c5fa20e21b7a5 | 1,679,946,406,000,000,000 | application/xhtml+xml | crawl-data/CC-MAIN-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00673.warc.gz | 350,269,566 | 3,065 | author Antonio Ospite Tue, 26 Jun 2018 13:42:26 +0000 (15:42 +0200) committer Antonio Ospite Wed, 27 Jun 2018 13:16:35 +0000 (15:16 +0200)
Move draw_rect_from_center from cairo_diagram.py to diagram.py as it
does not depend on any specific backend.
index 9aab30e..fd632d7 100755 (executable)
@@ -143,20 +143,6 @@ class CairoDiagram(Diagram):
cr.line_to(x2, y2)
self._stroke(stroke_color)
- def draw_rect_from_center(self, cx, cy, width, height, theta=0.0,
- stroke_color=None,
- fill_color=(1, 1, 1, 0.8)):
- # the position of the center of a rectangle at (0,0)
- mx = width / 2.0
- my = height / 2.0
-
- # calculate the position of the bottom-left corner after rotating the
- # rectangle around the center
- rx = cx - (mx * cos(theta) - my * sin(theta))
- ry = cy - (mx * sin(theta) + my * cos(theta))
-
- self.draw_rect(rx, ry, width, height, theta, stroke_color, fill_color)
-
def draw_rect(self, x, y, width, height, theta=0,
stroke_color=None,
fill_color=(1, 1, 1, 0.8)):
index eee9fc6..a949577 100755 (executable)
@@ -86,3 +86,22 @@ class Diagram(object):
apothem_angle = theta + pi / sides
return self.draw_star(cx, cy, sides, apothem, apothem_angle, stroke_color)
+
+ def draw_rect(self, x, y, width, height, theta=0,
+ stroke_color=None,
+ fill_color=(1, 1, 1, 0.8)):
+ raise NotImplementedError
+
+ def draw_rect_from_center(self, cx, cy, width, height, theta=0.0,
+ stroke_color=None,
+ fill_color=(1, 1, 1, 0.8)):
+ # the position of the center of a rectangle at (0,0)
+ mx = width / 2.0
+ my = height / 2.0
+
+ # calculate the position of the bottom-left corner after rotating the
+ # rectangle around the center
+ rx = cx - (mx * cos(theta) - my * sin(theta))
+ ry = cy - (mx * sin(theta) + my * cos(theta))
+
+ self.draw_rect(rx, ry, width, height, theta, stroke_color, fill_color) | 827 | 2,077 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2023-14 | latest | en | 0.075108 |
https://vacation-tahoe-rentals.com/math-solver-866 | 1,669,454,425,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446706285.92/warc/CC-MAIN-20221126080725-20221126110725-00618.warc.gz | 633,039,021 | 5,665 | # Tangent solver
Math can be a challenging subject for many students. But there is help available in the form of Tangent solver. Keep reading to learn more!
## The Best Tangent solver
A composition of functions solver is a tool that helps to determine the composition of two or more functions. In mathematics, function composition is the process of combining two or more functions to create a new function. The resulting function is typically a simpler or more efficient version of the original functions. Composition of functions is a powerful technique that can be used to solve complex problems. By breaking down a problem into smaller pieces, it can be easier to find a solution. A composition of functions solver can be used to help find the composition of two or more functions. This tool can be an essential part of solving complex mathematical problems.
There's no need to be intimidated by equations with e in them - they're not as difficult to solve as they may first appear. Here's a step-by-step guide to solving equations with e. First, identify the term with e in it and isolate it on one side of the equation. Then, take the natural logarithm of both sides of the equation. This will result in an equation that only has numbers on one side, and e on the other. Next, use basic algebra to solve for the variable. Finally, take the exponential of both sides to undo the natural logarithm and arrive at the solution. With a little practice, you'll be solving equations with e like a pro!
As any math student knows, calculus can be a difficult subject to grasp. The concepts are often complex and require a great deal of concentration to understand. Fortunately, there are now many calculus solvers available that can help to make the subject more manageable. These tools allow you to input an equation and see the steps involved in solving it. This can be a great way to learn how to solve problems on your own. In addition, calculus solvers with steps can also help you to check your work and ensure that you are getting the correct answer. With so many helpful features, it is no wonder that these tools are becoming increasingly popular among math students of all levels. | 437 | 2,191 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2022-49 | latest | en | 0.950687 |
https://universityhomeworkhelp.com/mathematical-introduction-and-vectors-homework/ | 1,721,384,194,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514900.59/warc/CC-MAIN-20240719074314-20240719104314-00149.warc.gz | 514,000,811 | 51,096 | Select Page
# Mathematical Introduction and Vectors Homework
Get help with your college and university homework from skilled subject experts.
Get the Desired Score with Mathematical Introduction and Vectors Homework Help
Growing up, most people knew students who were scared of the subject Mathematics. There were those who excelled in the subject and didn’t fear it at all. It seemed like they know it all. However, when in college most students who love math even struggle with their assignment. Hence, we decided to come up with an ideal Mathematical Introduction and Vectors homework help which would assist scholars to excel in this subject.
We are universityhomeworkhelp.com, and our primary aim is to aid students by providing them with everything they require for their assignment.
What is vector?
Vector refers to an object which has direction and magnitude both. Geometrically speaking, an individual can picture vectors as an intended line segment. The line’s length is the magnitude and an arrow points towards the direction.
However, this is a simple definition of vector. As one goes deep inside to understand operation on vectors and more, things get complicated. This is when pupils start making mistakes which makes their project of a low grade.
Moreover, this hinders their knowledge as well as their ability to score well in assignments and written exams. Thus, we help the students to understand this with our Mathematical Introduction and Vectors homework help.
Reason for online tutors’ increasing demand on this subject
If you surf the internet, you will see online mentors huge demand. This will keep on growing as more and more student’s need help from professionals. Have a look at it in detail!
• The number of students in the world who opt for physics and go through problems in vectors will keep rising. Hence, they will need online mentors who will give them the necessary amount of time to understand a topic and create a worthy assignment on it.
• Moreover, these experts are certified and highly experienced, making them the ultimate solution to all of scholars’ assignment issue. This is why people keep ordering our Mathematical Introduction and Vectors homework help.
• Online assistance offers 24×7 service. This means students have the freedom of receiving aid anytime they require and this is perfect to fit their busy everyday schedule. Also, this means at any moment they are stuck they can quickly clear their confusion and doubts.
What problems do students face while working with vectors?
1. Students can face many problems when working with vectors. One of the issues is that they make silly mistakes when they are doing addition, subtraction or scalar multiplication. One needs to have the correct and in-depth knowledge for not making an error when working with these. Most students don’t posses these.
2. Secondly, it is not possible for a single student to go through numerous books and also search different sites on the internet for information and solutions. Every project comes with a time constraint and thus without professional Mathematical Introduction and Vectors homework help there is nothing much one can do.
3. Moreover, only experts are the people who know how one should write a project such as where to express an opinion, where real-world examples would go, where to put up statistics, etc. Unless these are in order, scholars won’t get the marks they wish to receive.
Our online mentors take these things into account when they take up an assignment. Hence, these problems which students face are not an issue for them and efficiently clear these obstacles for our clients.
Why opt for universityhomeworkhelp.com?
We offer the best services in the writing business. We have professionals who are more than qualified to handle any issue which might rise when a student tries to do his or her project. Other perks of taking our assistance are:
1. Reasonable price for services we provide. This means no feeling the heat of massive expenditure every time you require aid for your assignment.
2. Our Mathematical Introduction and Vectors assignment help consist of impeccable materials which will impress any professor. This is your ticket to the astonishing grades that you have been working hard to achieve all year long.
• Online tutors with the highest knowledge and industry experienced work with us. This proves that there will be zero mistakes on the work you receive. Correct information plus error-free work equals positive impression on professors that means guaranteed remarkable grade for your assignment.
1. Maintaining the deadline for projects are mandatory. We pride ourselves in saying that our team have never missed a deadline given by our clients. Even if it is a short period, we ensure that students get top-notch materials from our side so that they can submit their assignment on time. Hence, as days pass, more pupils are opting for our Mathematical Introduction and Vectors assignment help.
2. Your solution will depend on the topic you have and the problems faced by you. Hence, it will be without question a unique piece of work. Originality and fresh content are what makes people come to us for assistance. Moreover, we also guarantee 100% customer satisfaction.
How to order the work from universityhomeworkhelp.com?
Just follow the below points. These steps are easy. Take a look!
1. When you visit the website go to the page where you can submit a form.
2. You require filling all the details namely your name, address, email id, etc. along with details of the topic you want help with, submission date, etc.
3. Upon reviewing the order, we will send you the cost which you have to pay.
4. You need to make the payment before we start working on your project through secure paying methods.
5. Lastly, we will email you the copy of Mathematical Introduction and Vectors assignment help through email before the deadline given by you.
We strive to provide you with better solutions every time you approach us. We are successful in keeping all our clients satisfied with the high quality work they are paying us. So, no matter in which country you reside you can reach out to us through email. We will respond as soon as possible, and once you order the solution, we get to work and deliver it before your deadline.
Hence, get our Mathematical Introduction and Vectors assignment help today! | 1,230 | 6,407 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2024-30 | latest | en | 0.970206 |
https://www.physicsforums.com/threads/mechanical-energy-and-electricity.259357/ | 1,539,916,539,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583512268.20/warc/CC-MAIN-20181019020142-20181019041642-00038.warc.gz | 1,023,952,807 | 13,741 | # Mechanical Energy and Electricity
1. Sep 25, 2008
### lorenzotr
Hi, my question is rather simple.
Supose you can generate 10 000N, by any means, such as pedaling a bycicle.
What calculations should you make to know how much electricity would 10 000 N of force will generate.
-Assuming a generator efficiency of 100%, leaving friction aside, etc.
An example would be, how much electricity will i produce by pulling a string attached to the rotor of the generator, and the total force that will exert during 1 hour will be 10,000 N?
If you also please tell me how i can convert the result to kWh?
I have a very basic understanding of physics, and if you think i would not be able to understand your answer at this stage, may you please tell me what prior reading i should make before asking this question, or if you may give me a very detailed answer to my question.
By the way, this is an amazing forum, and all its participants are really making an effort to help others. Thank you to you all.
2. Sep 25, 2008
### Staff: Mentor
Welcome to PF.
Newtons are a force, not an energy (and there is no "total force" over time) and so there is no direct relationship between the two. However, given the mechanical advantage required to get a person to generate 10,000 N of force, I'd say they'd probably be able to generate zero energy.
Work (energy) is force times distance. Power is force times distance divided by time. That and mechanical advantage (divide or multiply by the ratio of the lever arms or gear ratios) are the only concepts you need here.
3. Sep 26, 2008
### lorenzotr
So let's take this for example:
I pull a box which weighs 10 Kg, attached to a pulley.
The pulley is at a height of 10 meters. And i pull the rope for 10 meters, so the box will be at a height of 10 meters. Then, lets assume that i do this process in a total of 1 hour. Then will that be right:
(10 Kg * 10 meters)/3600 seconds = 100/3600
Is that right so far? If yes, what will 100/3600 equal to? Newtons? How can i convert my answer to kWh? May you please give me an example of how you would have solved this? Thanks.
4. Sep 26, 2008
### Staff: Mentor
A kg is 9.8 N, so it is 10*9.8/3600=0.027 Joules/second (watts)
Kwh and watt-hours are energy, watts is power. .027 watts for 1 hour is .027 watt-hours or .000027 kWh.
5. Sep 26, 2008
### Staff: Mentor
An easier way to estimate this would be as follows:
A 155lb person on a stationary bicycle burns about http://www.nutristrategy.com/activitylist.htm" [Broken]. If you optimistically assume a 50% efficiency in the human converting food energy to mechanical energy and 50% efficiency converting the mechanical energy into electrical energy then you are generating 88 kcal/hr of electricity which is 102 watts.
Last edited by a moderator: May 3, 2017 | 718 | 2,808 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2018-43 | latest | en | 0.940262 |
https://blog.cambridgecoaching.com/topic/gmat | 1,623,573,172,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487607143.30/warc/CC-MAIN-20210613071347-20210613101347-00337.warc.gz | 148,299,690 | 13,435 | For anyone else like me who’s naturally a planner, you’ve probably found yourself particularly frustrated by all the wrenches thrown at you and your MBA decision processes during the pandemic. You may find yourself asking questions like:
Tags: GMAT
One of the basic tenets of my coaching philosophy is to teach a student to teach themselves. The vast majority of the learning process should take place solo. Learning the LSAT or the GMAT is more like learning a language than it is like learning a subject, and there is just no way—no matter how long you stick with it—that you’re going to learn that language in 90 minutes a week. My goal as a tutor is to shape the way that the student thinks, ideally bending it toward the way that the test-makers think.
Tags: study skills, LSAT, GMAT
## For many people, Critical Reasoning are among the toughest verbal questions on the GMAT.
The Critical Reasoning arguments on the GMAT can get pretty convoluted! We are presented with a series of statements and assumptions, followed by some conclusion. Then, we are asked to either strengthen the argument, weaken the argument, or consider any unstated assumptions that may underpin the argument. To break down an intricate argument and five equally complicated answer choices in two minutes is an understandably daunting task. How do we work quickly and efficiently without getting bogged down by details?
Tags: GMAT
We have all encountered factor trees at some point during grade school. When I first encountered them as a kid, the whole exercise seemed unnecessary and silly. I thought to myself, “Great. I can list all the prime factors of 48. But, to what end?” It was not until much later that I realized the utility of prime factorizations. On an exam like the GMAT, where we are expected to do some pretty big calculations without a calculator, finding a prime factorization can be clutch.
Tags: GMAT
## Focus on one aspect of the sentence to narrow down your options.
Face it. GMAT Sentence Corrections can be a little overwhelming! And, if you are like most people, you might approach a sentence correction by carefully reading through all five responses and picking the answer that “sounds best.” You may even answer many questions correctly using this approach. However, reading through all five answers can be time-consuming. One way to speed up this process is to focus on a single error and to immediately cross off all answer choices with this error. This is a great way to apply process of elimination on the GMAT Sentence Corrections. In this post, we will focus on one of these error types: subject-verb errors.
Tags: GMAT
For many people studying for the GMAT, Work/Rate/Time problems prove to be a particularly sore spot on the Quantitative Reasoning section. In this lesson, we will learn an efficient and effective way to tackle these problem types algebraically.
Tags: GMAT
As someone who’s spent over twenty years in school and is currently pursuing both MD and MPP degrees, I’ve taken my fair share of tests. For as long as I can remember, tests have been both milestones and gatekeepers. The first “high-stakes” tests I took were the SAT and ACT in preparation for college admissions. After many midterms and finals in college, I faced the MCAT for admission to medical school and the GRE for admission to public policy school. Since then, I have gone through three USMLE Step exams for my medical license and numerous finals during medical school. Along the way of taking all these tests, I settled on three strategies for success.
Tags: LSAT, ACT, GMAT, SAT, GRE, MCAT, PSAT
Questions that ask you to determine if a number is prime are ubiquitous on the GMAT. You can expect to come across at least a few on exam day, so knowing how to quickly determine a number’s “primeness” will be necessary if you’re looking to break the 700 ceiling.
Tags: GMAT
Trusting your ear can get you far, but knowing some key grammar rules gets you even farther! | 841 | 3,980 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2021-25 | latest | en | 0.954209 |
https://www.dataunitconverter.com/nibble-per-day-to-petabyte-per-minute | 1,701,603,690,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100499.43/warc/CC-MAIN-20231203094028-20231203124028-00282.warc.gz | 824,801,902 | 16,354 | # Nibble/Day to PB/Min → CONVERT Nibbles per Day to Petabytes per Minute
info 1 Nibble/Day is equal to 0.0000000000000000003472222222222222222222 PB/Min
Input Nibbles per Day (Nibble/Day) - and press Enter.
Nibble/Day
You are converting .
Sec
Min
Hr
Day
Sec
Min
Hr
Day
S = Second, M = Minute, H = Hour, D = Day
## Nibbles per Day (Nibble/Day) Versus Petabytes per Minute (PB/Min) - Comparison
Nibbles per Day and Petabytes per Minute are units of digital information used to measure storage capacity and data transfer rate.
Nibbles per Day is one of the very "basic" digital unit where as Petabytes per Minute is a "decimal" unit. One Nibble is equal to 4 bits. One Petabyte is equal to 1000^5 bytes. There are 2,000,000,000,000,000 Nibble in one Petabyte. Find more details on below table.
Nibbles per Day (Nibble/Day) Petabytes per Minute (PB/Min)
Nibbles per Day (Nibble/Day) is a unit of measurement for data transfer bandwidth. It measures the number of Nibbles that can be transferred in one Day. Petabytes per Minute (PB/Min) is a unit of measurement for data transfer bandwidth. It measures the number of Petabytes that can be transferred in one Minute.
## Nibbles per Day (Nibble/Day) to Petabytes per Minute (PB/Min) Conversion Formula and Steps
Nibble/Day to PB/Min Calculator Tool allows you to easily convert from Nibbles per Day (Nibble/Day) to Petabytes per Minute (PB/Min). This converter uses the below formula and steps to perform the conversion.
The formula of converting the Nibbles per Day (Nibble/Day) to Petabytes per Minute (PB/Min) is represented as follows :
diamond CONVERSION FORMULA PB/Min = Nibble/Day x 4 ÷ (8x10005) / ( 60 x 24 )
Source Data Unit Target Data Unit
Nibble
Equal to 4 bits
(Basic Unit)
Petabyte
Equal to 1000^5 bytes
(Decimal Unit)
Now let us apply the above formula and see how to manually convert Nibbles per Day (Nibble/Day) to Petabytes per Minute (PB/Min). We can further simplify the formula to ease the calculation.
FORMULA
Petabytes per Minute = Nibbles per Day x 4 ÷ (8x10005) / ( 60 x 24 )
STEP 1
Petabytes per Minute = Nibbles per Day x 4 ÷ (8x1000x1000x1000x1000x1000) / ( 60 x 24 )
STEP 2
Petabytes per Minute = Nibbles per Day x 4 ÷ 8000000000000000 / ( 60 x 24 )
STEP 3
Petabytes per Minute = Nibbles per Day x 0.0000000000000005 / ( 60 x 24 )
STEP 4
Petabytes per Minute = Nibbles per Day x 0.0000000000000005 / 1440
STEP 5
Petabytes per Minute = Nibbles per Day x 0.0000000000000000003472222222222222222222
Example : If we apply the above Formula and steps, conversion from 1 Nibbles per Day (Nibble/Day) to Petabytes per Minute (PB/Min) will be processed as below.
1. = 1 x 4 ÷ (8x10005) / ( 60 x 24 )
2. = 1 x 4 ÷ (8x1000x1000x1000x1000x1000) / ( 60 x 24 )
3. = 1 x 4 ÷ 8000000000000000 / ( 60 x 24 )
4. = 1 x 0.0000000000000005 / ( 60 x 24 )
5. = 1 x 0.0000000000000005 / 1440
6. = 1 x 0.0000000000000000003472222222222222222222
7. = 0.0000000000000000003472222222222222222222
8. i.e. 1 Nibble/Day is equal to 0.0000000000000000003472222222222222222222 PB/Min.
Note : Result rounded off to 40 decimal positions.
You can use above formula and steps to convert Nibbles per Day to Petabytes per Minute using any of the programming language such as Java, Python or Powershell.
### Unit Definitions
#### Nibble
A Nibble is a unit of digital information that consists of 4 bits. It is half of a byte and can represent a single hexadecimal digit. It is used in computer memory and data storage and sometimes used as a basic unit of data transfer in certain computer architectures.
arrow_downward
#### Petabyte
A Petabyte (PB) is a decimal unit of digital information that is equal to 1,000,000,000,000,000 bytes (or 8,000,000,000,000,000 bits) and commonly used to measure the storage capacity of enterprise storage arrays and data centers. It is also used to express data transfer speeds and in the context of data storage and memory, the binary-based unit of Pebibyte (PiB) is used instead.
## Excel Formula to convert from Nibbles per Day (Nibble/Day) to Petabytes per Minute (PB/Min)
Apply the formula as shown below to convert from 1 Nibbles per Day (Nibble/Day) to Petabytes per Minute (PB/Min).
A B C
1 Nibbles per Day (Nibble/Day) Petabytes per Minute (PB/Min)
2 1 =A2 * 0.0000000000000005 / ( 60 * 24 )
3
If you want to perform bulk conversion locally in your system, then download and make use of above Excel template.
## Python Code for Nibbles per Day (Nibble/Day) to Petabytes per Minute (PB/Min) Conversion
You can use below code to convert any value in Nibbles per Day (Nibble/Day) to Nibbles per Day (Nibble/Day) in Python.
nibblesperDay = int(input("Enter Nibbles per Day: "))
petabytesperMinute = nibblesperDay * 4 / (8*1000*1000*1000*1000*1000) / ( 60 * 24 )
print("{} Nibbles per Day = {} Petabytes per Minute".format(nibblesperDay,petabytesperMinute))
The first line of code will prompt the user to enter the Nibbles per Day (Nibble/Day) as an input. The value of Petabytes per Minute (PB/Min) is calculated on the next line, and the code in third line will display the result.
## Frequently Asked Questions - FAQs
#### How many Petabytes(PB) are there in a Nibble?expand_more
There are 0.0000000000000005 Petabytes in a Nibble.
#### What is the formula to convert Nibble to Petabyte(PB)?expand_more
Use the formula PB = Nibble x 4 / (8x10005) to convert Nibble to Petabyte.
#### How many Nibbles are there in a Petabyte(PB)?expand_more
There are 2000000000000000 Nibbles in a Petabyte.
#### What is the formula to convert Petabyte(PB) to Nibble?expand_more
Use the formula Nibble = PB x (8x10005) / 4 to convert Petabyte to Nibble.
#### Which is bigger, Petabyte(PB) or Nibble?expand_more
Petabyte is bigger than Nibble. One Petabyte contains 2000000000000000 Nibbles.
## Similar Conversions & Calculators
All below conversions basically referring to the same calculation. | 1,776 | 5,907 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2023-50 | latest | en | 0.752724 |
https://boards.straightdope.com/t/math-question/54872 | 1,600,518,909,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400191780.21/warc/CC-MAIN-20200919110805-20200919140805-00196.warc.gz | 318,441,757 | 5,589 | # Math Question!
Does anyone know why any number to the power of 0 equals 1? I had it figured out a long time ago, and it’s so that another operation could work, but I can’t remember!!
There might be other reasons which aren’t coming to me at the moment since it’s 8:00 on a Saturday morning, but the first thing that came to me was powers of ten.
10[sup]4[/sup] = a 1 followed by 4 zeroes
10[sup]3[/sup] = a 1 followed by 3 zeroes
10[sup]2[/sup] = a 1 followed by 2 zeroes
10[sup]1[/sup] = a 1 followed by 1 zeroes
Therefore,
10[sup]0[/sup] = a 1 followed by no zeroes
Somebody else (possibly me) will be along shortly to present a more detailed reason.
Caffeine - taking - effect… eyes openeing… muscles flexing… I am- AWAKE! (cape flapping in breeze)
Now then. Flipping through some of my moldy oldies proof books for mathematics, this is all I could come up with:
In order to be able to generalize the algebraic rule that: a[sup](b + c)[/sup] = a[sup]b[/sup] × a[sup]c[/sup], for example, even when b = 0, we have to set a[sup]0[/sup] = 1. Therefore, it is the convention that a[sup]0[/sup] = 1. This convention is needed in order to have consistency in this algebraic rule of operations.
An easy way to think of it is this:
3[sup]3[/sup] = 27
3[sup]2[/sup] = 9 or 3[sup]2[/sup] = 3[sup]3[/sup]/3
This of course, holds for all numbers, giving the following generalization:
a[sup]x[/sup] = a[sup]x+1[/sup]/a
*exception - when a = 0, weird stuff happens
So, 3[sup]0[/sup] = 3[sup]1[/sup]/3, or 3/3, or 1.
I think this qualifies as a proof, or at least a general property of powers, since by this, 3[sup]-1[/sup] = 3[sup]0[/sup]/3, or 1/3, which is quite correct.
Here’s a threadfrom last year in which this point is discussed:
What about negative and fractional exponents? I get negative exponents, but how are fractional exponents calculated?
of course, there is no such thing as multiplying 3 by itself -1 or 1.5 times, is there?
Wait, forgot. Fractional exponents have to do with square roots. Gee, it’s been so long since I’ve taken a math class. <takes out precalc book>
I’ve always thought this was an intuitive way of thinking of it:
What do you get if you add three to itself zero times? I would argue that it’s zero, since zero is the additive identity (the “nothing” of addition). So an “empty sum” is zero.
What do you get if multiply three by itself zero times? Again, I would argue that it’s one, since one is the multiplicative identity (the “nothing” of multiplication). So an “empty product” is one.
If you think of X[sup]n[/sup] as the product of n copies of X multiplied together, then X[sup]0[/sup] makes no sense. The definition of exponentation must be extended to allow exponents that are not positive integers. We want to extend the definition so that X[sup]n[/sup] still follows as many of the same rules as the product defintion. One rule is:
X[sup]m[/sup]/X[sup]n[/sup] = X[sup]m-n[/sup], for m>n
If we allow m = n we get,
X[sup]m[/sup]/X[sup]m[/sup] = X[sup]m-m[/sup]
1 = X[sup]0[/sup]
X[sup]0[/sup] must equal one so that the rules still apply. | 930 | 3,099 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2020-40 | latest | en | 0.888598 |
https://www.teacherspayteachers.com/Product/Addition-Word-Problems-1596309 | 1,529,309,855,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267860089.13/warc/CC-MAIN-20180618070542-20180618090542-00303.warc.gz | 917,930,407 | 18,312 | Subject
Resource Type
Common Core Standards
Product Rating
File Type
Compressed Zip File
37 MB|54 pages
Share
Product Description
Addition Word Problems - This 1st Grade Math Center bundle covers all the 1st grade Common Core Standards for word problems. All the different word problem situations are included with the unknowns in all positions. There are one step and multi-step problems. This bundle combines all of these sets I sell separately:
1st Grade Subtraction Word Problems Farm Theme
I have added this holiday bonus to this bundle:
Together these sets include all the different word problem types for the 1st Grade Common Core Standards!
The One Step Addition and Subtraction Problems include 24 worksheets aligned with the 1st grade CCSS 1.OA.A.1. All the different word problem situations are covered and there are unknowns in all positions. The questions are written at a 1st grade level using a farm animal theme. The students show their work using ten frames, drawing and using an equation. The students also write the answer showing that they understand the question. This packet comes with an answer key that also tells what type of situation each word problem is.
The Multi Step Addition Word Problems include twelve worksheets aligned with the 1st grade CCSS 1.OA.A.2. All the problems have three addends with sums of 20 or less. There are problems with the addend unknown or with the sum unknown. The students show their work using ten frames, drawing and using an equation. Because the answers are not always the sum, students also write the answer separately showing that they understand the question. This packet comes with an answer key that also tells what type of situation each word problem is.
Here are my other word problem worksheets you may be interested in:
One Step Addition Word Problem Worksheets Level 1, 2 & 3
One Step Subtraction Word Problem Worksheets Level 1, 2 & 3
One Step Addition & Subtraction Word Problem Worksheets Level 1, 2 & 3 Bundle
One Step Multiplication Word Problem Worksheets Level 1
One Step Multiplication Word Problem Worksheets Level 2
One Step Division Word Problem Worksheets Level 1
One Step Division Word Problem Worksheets Level 2
One Step Multiplication & Division Word Problem Worksheets Level 1 & 2 Bundle
Here are my word problems for journals you may be interested in:
Addition and Subtraction Word Problems for Math Journals
Multiplication and Division Word Problems for Math Journals
Word Problems for Math Journals - Multiplication, Division, Addition & Subtraction Bundle
If you’re an individual educator or a school representative purchasing a Non-Transferable License, your license is Non-Transferable. This means only you or the educator this license was purchased for may use it, and the license cannot be reused by another teacher.
If you represent a school purchasing a Transferable License, your license is transferable. This means only one educator may use the resource at a time, and if you experience personnel changes year over year or during the year, you may transfer the license to another educator in your school.
Learning Engineer
Total Pages
54 pages
Included
Teaching Duration
N/A
Report this Resource
\$8.00 | 669 | 3,225 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2018-26 | latest | en | 0.91748 |
https://www.homeworkminutes.com/question/view/198117/DeVry-ECET210-Lab-6-Frequency-Response-of-Low | 1,526,922,245,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864461.53/warc/CC-MAIN-20180521161639-20180521181639-00629.warc.gz | 756,091,786 | 9,492 | Question
Offered Price \$35.00
# DeVry ECET210 Lab 6 Frequency Response of Low...........
Question # 00198117
Subject: Engineering
Due on: 06/15/2016
Posted On: 02/16/2016 07:50 AM
Rating:
4.1/5
Posted By
Questions:
4852
Tutorials:
4854
Feedback Score:
Question
Laboratory Procedures
DeVry University
College of Engineering and Information Sciences
OBJECTIVES
To analyze a RC Low Pass Filter using simulation and circuit measurement.
To analyze a RC High Pass Filter using simulation and circuit measurement.
To analyze a LC Band Pass Filter using simulation and circuit measurement.
II. PARTS LIST
Equipment:
IBM PC or Compatible
Function Generator
Dual Channel Oscilloscope
Parts:
1 - 50 ? Resistor 1 - 470 nF, 50 V Capacitor
1 - 330 ? Resistor 4 - 47 µF, 35 V Capacitor
4 - 4.7 mH Inductor 2 - 100 µF, 25 V Capacitor
1 - 470 mH, Inductor
Software:
MultiSim 11
III. PROCEDURE
Simulation of RC Low Pass Filter |
Enter the circuit shown in Figure 1 in MultiSim.
Figure 1 - Low Pass Filter
Set the function generator voltage, VIn = 1 VP.
Simulate the circuit shown for various frequencies indicated in Table 1 below. Record the output voltage, VOut, for each frequency and calculate the gain using the formula: 20 log(VOut P-P / VIn P-P).
Frequency, Hz VOut P-P GaindB Frequency, Hz VOut P-P GaindB
100 2000
200 4000
400 8000
800 10000
1000
Table 1 – Low Pass Filter Frequency Response Simulation Data
Low
Determine the voltage “Gain/Loss” in dB for the frequency response plot. Plot the simulation data of on the semi-log graph sheet below. The frequency must be on the X axis and the GaindB on the Y–axis.
What is the 3 dB cutoff frequency from the plot?
fC =___________________
Calculate the 3 dB Cutoff frequency using the formula: fC = 1/(2 ? R C)
fC =___________________
Does the simulated measurement agree with the theoretical calculation?
Yes ______ No ______
B. Simulation of RC High Pass Filter
Enter the circuit shown in Figure 2 in MultiSim.
Figure 2 - High Pass Filter
Set the function generator voltage, VIn = 1 VP
Simulate the circuit shown for various frequencies indicated in Table 2 and record the output voltage and gain.
Frequency, Hz VOut P-P GaindB Frequency, Hz VOut P-P GaindB
100 2000
200 4000
400 8000
800 10000
1000
Table 2 - Low Pass Filter Frequency Response Simulation Data
Determine the voltage “Gain/Loss” in dB for the frequency response plot. Plot the simulation data of on the semi-log graph sheet below.
What is the 3 dB cutoff frequency from the plot?
fC =___________________
Calculate the 3 dB Cutoff frequency using the formula: fC = 1/(2 ? R C)
fC =___________________
Does the simulated measurement agree with the theoretical calculation?
Yes ______ No ______
C. Simulation of LC Band Pass Filter
Enter the circuit shown in Figure 3 in MultiSim.
Figure 3 - LC Band Pass Filter
Setup the function generator voltage, VIn = 1 VP.
Simulate the circuit shown for various frequencies indicated in Table 3 and record the output voltage and gain.
Frequency, Hz VOut P-P GaindB Frequency, Hz VOut P-P GaindB
200 340
250 344
280 348
290 355
300 352
320 356
324 360
330
Table 3 – Band Pass Filter Frequency Response Simulation Data
Determine the voltage “Gain/Loss” in dB for the frequency response plot. Plot the simulation data of on the semi-log graph sheet below.
What are the 3 dB cutoff frequencies from the plot?
Upper fC =_____________ Low fC =_____________
The LC band pass filter is PI- Section filter which has been designed using the website:
http://www.raltron.com/cust/tools/band_pass_filters.asp
The filter has been designed to operate at a center frequency, fo of 340 Hz and a 3dB Bandwidth of 10% of fo.
Log in to the above website; feed the data of center frequency and the bandwidth desired. Verify if the design values chosen for the lab experiment are close enough.
What are the calculated 3 dB cutoff frequencies?
Upper fC =_____________ Low fC =_____________
Do the simulated measurements agree with the theoretical calculations?
Yes ______ No ______
Increase or decrease the center frequency by 5 and recalculate the element values. Note and record the new design parameters. What can you comment on the new design values when compared with the original values?
The filter can be reconfigured to a T–type using the transformation shown below:
Some useful formulas for the Constant K type band pass filter design:
fC = Filter Center Design frequency
R0 = Filter Design Impedance
f1 and f2 => 3 dB cutoff frequencies, Lower & Upper..
Also, f1 x f2 = fC2
Bandwidth = f2 – f1
L_1= R_0/(? (f_2- f_1))
L_2= (R_0 (f_2- f_1))/(4? f_C^2 )
C_1= ( (f_2- f_1))/(4? ?R_0 f?_C^2 )
C_2= 1/(? R_0 (f_2- f_1))
Source for the above formulas: “HANDBOOK OF LINE COMMUNICATIONS”, A Royal Signals Pub., 1947.
Using the suggested transformation, change the original PI type filter to T-type and simulate to verify if it works as the original. Include the new filter topology below here.
Did the filter work as the original? YES NO
D. Breadboard Construction of the three Filters
Build the three filters simulated above on a breadboard, one at a time
Use a Function Generator to excite the filters and check for the pass band and the cut off frequencies.
Submit a photograph of each of your working circuits (online) or have your instructor sign-off each circuit (onsite).
Tutorials for this Question
Available for
\$35.00
#### DeVry ECET210 Lab 6 Frequency Response of Low...........
Tutorial # 00192998
Posted On: 02/16/2016 07:51 AM
Posted By:
jia_andy
Questions:
4852
Tutorials:
4854
Feedback Score:
Tutorial Preview …6…
Attachments
solution-file.zip (652.26 KB)
Preview not available.
* - Additional Paypal / Transaction Handling Fee (3.9% of Tutorial price + \$0.30) applicable | 1,501 | 5,782 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2018-22 | longest | en | 0.675286 |
regulafalsi.fandom.com | 1,579,380,708,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250593937.27/warc/CC-MAIN-20200118193018-20200118221018-00082.warc.gz | 634,527,000 | 74,861 | 4 Pages
## Regula FalsiEdit
In numerical analysis, the false position method or regula falsi method is a root-finding algorithm that combines features from the bisection method and the secant method.
A method of calculating an unknown quantity by first making an estimate and then using this and the properties of the unknown to obtain it. Also known as rule of false position.
## The MethodEdit
The Regula–Falsi Method is a numerical method for estimating the roots of a polynomial f(x). A value x replaces the midpoint in the Bisection Method and serves as the new approximation of a root off(x). The objective is to make convergence faster. Assume that f(x) is continuous.
Algorithm for the Regula–Falsi Method: Given a continuous function f(x)
1. Find points a and b such that a < b and f(a) * f(b) < 0.
2. Take the interval [a, b] and determine the next value of x1.
3. If f(x1) = 0 then x1 is an exact root, else if f(x1) * f(b) < 0 then let a = x1, else if f(a) * f(x1) < 0 then let b = x1.
4. Repeat steps 2 & 3 until f(xi) = 0 or |f(xi)| £DOA, where DOA stands for degree of accuracy.
Observe that :
EC / BC
=
E / AB
[ x – a ] / [ b – a ]
=
[ f(x) – f(a) ] / [ f(b) – f(a) ]
x – a
=
[ b – a ] [ 0 – f(a) ] / [ f(b) – f(a) ]
x
=
a + [ b – a ] [ – f(a) ] / [ f(b) – f(a) ]
x
=
a – [ b – a ] f(a) / [ f(b) – f(a) ]
Note that the line segment drawn from f(a) to f(b) is called the interpolation line.
Graphically, if the root is in [ a, xi ], then the next interpolation line is drawn between ( a, f(a) ) and ( xi, f(xi) ); otherwise, if the root is in [ xi, b ], then the next interpolation line is drawn between ( xi, f(xi) )and (b, f(b)).
Community content is available under CC-BY-SA unless otherwise noted. | 527 | 1,742 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2020-05 | latest | en | 0.867819 |
http://math.stackexchange.com/questions/91906/how-do-you-find-small-coefficients-that-satisfy-a-particular-modular-equation | 1,469,266,650,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257821671.5/warc/CC-MAIN-20160723071021-00294-ip-10-185-27-174.ec2.internal.warc.gz | 160,726,146 | 17,025 | # How do you find small coefficients that satisfy a particular modular equation
Let's say $p=16301$. How do I best find sets of small values for $a$, $b$ and $c$ for an equation like
$$a p^3+b p^2+c p=11263 \mod\ 2^{16}.$$
I can use the lindep command in PARI/GP which uses PSLQ to find solutions for
$$a p^3+b p^2+c p+d 11263+e 2^{16}=0,$$
but this doesn't work very well because I want to force the coefficient $d$ to be $-1$ and I don't care about how big $e$ gets. The PARI/GP command qflll takes a matrix so there's probably more knobs to tweak and it performs similar magic but I don't know how to structure the problem to give the results I want. For example $a=6$, $b=5$ and $c=4$ is the answer I'm looking for.
For the real application of this maths, the problem would be larger in every way so a simple search is not suitable.
-
If there is method for finding small solutions for integer (not modular) equations, then how far will you get by reducing the powers $p^j$ modulo $2^{16}$, say to an interval $(-2^{15},2^{15}]$, and then "guessing" the value of $e$. After reducing the powers of $p$, if $a,b,c$ are small, then $e$ has to be small as well... This approach may not scale well, when you increase the number of terms, though. – Jyrki Lahtonen Dec 16 '11 at 9:54
Yes, this is what I do and I get useful results for about 17 terms with numbers around 2^128. Every solution for which d is not +1 or -1 has to be thrown away though and this is what kills the efficiency. – Richard Dec 16 '11 at 16:41 | 443 | 1,522 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2016-30 | latest | en | 0.912094 |
http://www.slideserve.com/anila/answering-multiple-choice-questions | 1,490,772,912,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218190234.0/warc/CC-MAIN-20170322212950-00041-ip-10-233-31-227.ec2.internal.warc.gz | 685,702,593 | 16,467 | This presentation is the property of its rightful owner.
1 / 4
# Answering Multiple Choice Questions PowerPoint PPT Presentation
Answering Multiple Choice Questions. Know your test – For AP Statistics No penalties for wrong answers ( Answer every one ) Bubble BEST ANSWER in the context of the question No answer choice may be precisely correct or More than one choice may be correct
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
#### Presentation Transcript
• Know your test – For AP Statistics
• BubbleBEST ANSWER in the context of the question
• No answer choice may be precisely correct or
• More than one choice may be correct
• Often the stem has extraneous information
• Often data is given, but there may also be a summary metric which precludes the need for calculations
• NoHighlighting BUT YOU CAN WRITE ON THE TEST
• Weakly erased answers or stray marks often result in wrong scanned scores – and no one will know that!
• One or two questions may make a huge difference in your normalized score! (It is based on relative performance) - EVERY ONE QUESTION COUNTS BIG TIME
### Multiple Choice Questions #2
• Cover answer choices (called distracters!):
• Read (skim if long) the stem of the question
• Do not start calculations until you understand the question
• Underline the precise question (usually at the end of the stem)
• Think about the intent of the question (what content is the author trying to find out if you know)
• Reread the stem thinking of the precise question and intent
• Determine the most likely answer(s)
### Multiple Choice Questions #3
• Look at each answer choice & mark off those that are clearly impossible choices
• Watch out for answers that are part of your solution calculations/considerations but do not answer the precise question
• If you are sure of an answer – circle it and move on --- DO NOT BUBBLE ANY ANSWERS AT THIS TIME
• If Not sure, leave possible choices unmarked (you should designate the answer that seems most likely). Mark this question (On the test) and return to it later
### Multiple Choice Questions #4
• Often as you do a test you will get an idea on an earlier problem
• DO NOT SPEND TOO MUCH TIME ON ONE QUESTION – figure your pace and more on! – for the AP Exam there are 90 minutes for 40 questions
• So MOVE ON if a question is not answered in 2 minutes
• Most kids finish the MC test in one hour so you should have plenty of time to go back.
• BUBBLE in the last 10 minutes (WATCH YOUR TIME) . Do not bubble early to minimize erasers | 663 | 2,944 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2017-13 | longest | en | 0.867613 |
https://slideplayer.com/slide/8815395/ | 1,713,616,312,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817650.14/warc/CC-MAIN-20240420122043-20240420152043-00140.warc.gz | 473,185,159 | 21,119 | # Adding a Sequence of numbers (Pairing Method)
## Presentation on theme: "Adding a Sequence of numbers (Pairing Method)"— Presentation transcript:
Adding a Sequence of numbers (Pairing Method)
1. Find the sum of …… Problem Solving Strategy :- Step 1 – Divide the last number by 2 50 ÷ 2 = 25{ to get the numbers of pairs } Step 2 – Add 1 to the last number ( 50 ) = 51 { The sum of each pair is 51 } Step 3 – Multiply the results from steps 1 and 2 : 25 x 51 = 1275
Adding a Sequence of numbers (Pairing Method)
Now you try : - 2. Find the sum of …… What if the sequence of numbers that does not end with even numbers? Now you try : - 3. Find the sum of …… Now you try : - 4. Find the sum of ……
Adding a Sequence of numbers (Triangle Method)
1. Find the sum of …… Problem Solving Strategy :- Step 1 – Multiply the last number (50) by the next higher number (51) and divide the product by 2. 50 x 51 ÷ 2 = 1275 Now you try : - 2. Find the sum of ……
Adding a Sequence of numbers (Average Method)
What if the sequence of consecutive number does not start with 1? 1. Find the sum of …… Problem Solving Strategy :- Step 1 – Subtract the first number from the last number and add 1 (50 – 11) + 1 = 40{ to get the numbers of Terms } Step 2 – Add the first number to the last number and divide the result by 2. ( ) ÷ 2 = 30.5 { The average is 30.5 } Step 3 – Multiply the results from steps 1 and 2 : 40 x 30.5 = 1220 Now you try : - 2. Find the sum of ……
Adding a Sequence of numbers (Average Method)
Now you try : - 3. Find the sum of …… Now you try : - 4. Find the sum of ……
Adding a Sequence of odd numbers
1. Find the sum of …… Problem Solving Strategy :- Step 1 – Add 1 to the last number and divide the last number by 2 (1 + 51)÷ 2 = 26{ to get both the Average and the numbers of Terms } Step 2 – Square the results from step 1. 26 x 26 = 676 Now you try : - 2. Find the sum of ……
Adding a Sequence of odd numbers
What if the sequence of consecutive number does not start with 1? 1. Find the sum of …… Problem Solving Strategy :- Step 1 – Subtract the first number from the last number, divide it by 2 and add 1 (33 – 7) ÷ = 14{ to get the numbers of Terms } Step 2 – Add the first number to the last number and divide the result by 2. (7 +33) ÷ 2 = 20 { The average is 20 } Step 3 – Multiply the results from steps 1 and 2 : 14 x 20 = 280 Now you try : - 2. Find the sum of ……
Adding a Sequence of even numbers
1. Find the sum of …… Problem Solving Strategy :- Step 1 – Divide the last number by 2 50 ÷ 2 = 25{ to get the numbers of Terms } Step 2 – Add 2 to the last number and divide the sum by 2. (50 + 2) ÷ 2 = 26 {to get the average} Step 3 – Multiply the results from steps 1 and 2 25 x 26 = 650 Now you try : - 2. Find the sum of ……
Adding a Sequence of even numbers
What if the sequence of consecutive number does not start with 2? 1. Find the sum of …… Problem Solving Strategy :- Step 1 – Subtract the first number from the last number, divide it by 2 and add 1 (34 – 8) ÷ = 14{ to get the numbers of Terms } Step 2 – Add the first number to the last number and divide the result by 2. (8 +34) ÷ 2 = 21 { The average is 20 } Step 3 – Multiply the results from steps 1 and 2 : 14 x 21 = 294 Now you try : - 2. Find the sum of …… | 991 | 3,249 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.8125 | 5 | CC-MAIN-2024-18 | latest | en | 0.769221 |
https://www.teachoo.com/8755/2772/Smallest-number-divided-to-get-perfect-square/category/Smallest-number-divided-to-get-perfect-square/ | 1,726,333,400,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651580.73/warc/CC-MAIN-20240914161327-20240914191327-00616.warc.gz | 946,608,987 | 21,705 | Smallest number divided to get perfect square
Chapter 5 Class 8 Squares and Square Roots
Concept wise
Let’s do this by examples
#### Finds the smallest number divided to 32 to get a perfect square.
Since 2 does not occur in pairs,
we divide by 2 to make it a pair
So, our number becomes
32 × 1/2 = 2 × 2 × 2 × 2 × 2 × 1/2
Now, it becomes a perfect square.
So, we divide 32 by 2 to make it a perfect square
#### Finds the smallest number divided to 90 to get a perfect square.
Here,
2 & 5 do not occur in pairs
So, we divide by 2 and 5 to make pairs
So, our number becomes
90 × 1/2 × 1/ 5 = 2 × 3 × 3 × 5 × 1/2 × 1/5
Now, it becomes a perfect square.
So, we divide 90 by 2 × 5
i.e. 10 to make it a perfect square
#### Finds the smallest number divided to 120 to get a perfect square.
Here,
2, 3 & 5 do not occur in pairs
So, we divide by 2, 3 and 5 to make pairs
So, our number becomes
Now, it becomes a perfect square.
So, we divide 120 by 2 × 3 × 5
i.e. 30 to make it a perfect square | 329 | 1,013 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2024-38 | latest | en | 0.901455 |
https://codegolf.stackexchange.com/questions/194462/mirror-mirror-on-the-wall-whos-the-fairest-of-them-all | 1,618,263,893,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038069267.22/warc/CC-MAIN-20210412210312-20210413000312-00137.warc.gz | 290,011,921 | 44,863 | # Mirror, Mirror, on the wall. Who's the fairest of them all?
Well, you know it's Snow White, and the evil Queen is at it again. Will Snow White be saved? Will she fall asleep once again? Will the Prince find her?
# Challenge:
Given an arbitrary number (>= 2) of possibly duplicated hexadecimal color values (ranging from #000000 to #FFFFFF) and paired strings, calculate the following:
• If #FF0800 (Candy apple red) appears in the input, return "Return to Sleeping Death"
• If #000000 appears in the input, return "Saved by Grumpy"
• If #A98AC7 or #111111 appears in the input, return "Saved by Happy"
• If #21E88E or #222222 appears in the input, return "Saved by Sleepy"
• If #32DCD5 or #333333 appears in the input, return "Saved by Bashful"
• If #43D11C or #444444 appears in the input, return "Saved by Sneezy"
• If #54C563 or #555555 appears in the input, return "Saved by Dopey"
• If #65B9AA or #666666 appears in the input, return "Saved by Doc"
• If #76ADF1 or #777777 appears in the input, return "Saved by the Seven Dwarfs"
• If #FFFAFA (Snow) appears in the input, return "Saved by Love's first kiss"
• If an F variant appears in the input, return "Press F to pay respects to Snow White"
• An F variant is any number that contains at least one F in its hexadecimal form, and is otherwise all 0s (e.g. #0FF0F0, #FFFFFF, #00000F, #F00F00)
• If multiple of the preceding occur, return the "fairest" answer. The "fairest" answer is calculated as follows:
• For all N occurrences of special color values, choose the (N-1)/2-th (truncating division) occurrence. The associated special output is the "fairest" answer.
"Appears in the input" here refers to only the hexadecimal color values, and not to the paired strings.
• If none of the preceding occur, return the "fairest" answer. The "fairest" answer is calculated as follows:
• Take the hexadecimal color value at the end of input values, write it down, and exclude that single color-string pair from consideration as the "fairest" answer
• Show its binary form to the mirror, computing a reflection of only the last 24 (#FFFFFF is the mask) bits.
• Choose the hexadecimal color with least Hamming distance from the reflection. If there are multiple (N) such colors, choose the middle ((N-1)/2-th, truncating division) instance of the color. The "fairest" answer is the associated string for the color.
# Inputs:
A sequence of hexadecimal color values and String values separated by a space. The input may also be read as two separate sequences of hexadecimal color values and String values, or a single sequence of 2-tuples (either (hexValue, stringValue) or (stringValue, hexValue) is permissible, as long as the ordering is consistent across all 2-tuples). Input order matters - for each index, the corresponding element in the supply of color values is "associated" with the corresponding element in the supply of String values, and duplicates can affect the "fairest" answer. The effect is something like Function(List(HexColorValue),List(AssociatedStrings)) -> "fairest" answer. Hexadecimal color values may be represented as either (your choice of) a String "#"+6 digits, or 6 digits alone, as long as the representation is consistent across all color values.
Here's an example input:
76ADF1 Return to Sleeping Death
2FE84E Return whence ye came!
Here's another example input:
2FE84E Return to Sender
4FFAFC Return of the Obra Dinn
2FE84E Return of the Jedi
Here's the third example input:
2FE84E Return to Sender
4FFAFC Return of the Obra Dinn
7217F8 Return of the King
Here's the final sample input:
F4A52F Eating hearts and livers
F4A52F Eating apples
F4A52F Eating porridge
F4A52F Eating candy houses
F4A52F A Modest Proposal
# Outputs:
The "fairest" answer as computed by the specified logic. For example, on the first sample input, the "fairest" answer would be Saved by the Seven Dwarfs, due to the special hex color 76ADF1 appearing within the input.
In the second sample, there are no special inputs. First, we take "2FE84E Return of the Jedi", which has value #2FE84E. In binary, this is:
001011111110100001001110
We take the reflection from the mirror, getting:
011100100001011111110100
We compare it against 2FE84E (001011111110100001001110) and 4FFAFC (010011111111101011111100), which have Hamming distances of 18 and 12 from the reflection, respectively. Since #4FFAFC has the uniquely lowest Hamming distance from the reflection, the "fairest" answer is Return of the Obra Dinn.
In the third sample input, there are no special inputs. First, we take "7217F8 Return of the King", which has value #7217F8. In binary, this is:
011100100001011111111000
We take the reflection from the mirror, getting:
000111111110100001001110
We compare it against 2FE84E (001011111110100001001110) and 4FFAFC (010011111111101011111100), which have Hamming distances of 2 and 8 from the reflection, respectively. All 3 instances of hexadecimal color value #2FE84E have minimum Hamming distance from the reflection, so we take the (3-1)/2=1th instance (0-indexed) of #2FE84E. Therefore, the "fairest" answer is Return to the house immediately, young lady!.
In the last sample input, there are no special inputs. First, we take "F4A52F A Modest Proposal", which has value #F4A52F. In binary, this is:
1111010011001100101111
We take the reflection from the mirror, getting:
1111010011001100101111
We compare it against F4A52F (1111010011001100101111), which has Hamming distance 0 from the reflection. All instances of hexadecimal color value #F4A52F have minimum Hamming distance from the reflection. There are FOUR instances of #F4A52F, because we always exclude the last hexadecimal color instance from evaluation. Therefore, we take the (4-1)/2=1th instance (0-indexed) of #F4A52F, and the "fairest" answer is Eating apples. If you don't exclude the last value from consideration, you actually get the (5-1)/2=2th instance of #F4A52F (Eating porridge), which is wrong.
# Rules:
• No standard loopholes
• Input/output taken via standard input/output methods.
• The output must be exactly equal to the "fairest" answer
# Scoring:
This is code golf, so shortest program wins.
• I'll be honest, 3 downvotes without any explanation whatsoever is a real downer. I left this in the sandbox for two weeks so that people could give feedback and spent hours clarifying the examples. If you didn't do your job of giving feedback, how am I supposed to improve my question? – Avi Oct 18 '19 at 21:00
• I was not aware that it was my personal "job" to go through every single sandbox post in existence, but okay. There's a chat; I usually go to it to get feedback, because with no positive or negative feedback, it's really a toss-up how main reception will go, and I'm slightly more experienced so I can usually gauge how my challenges will go, but even then, I still go to chat for final feedback before posting. – hyper-neutrino Oct 18 '19 at 22:13
• I didn't downvote, but my eyes glaze over looking at this challenge and I can't motivate myself to read it. It's not just that it's long, but that by the time I'm hit with a bunch of specifics, I don't really know what the overall idea is or why this would be interesting to golf. And my initial impression is that I wouldn't enjoy coding or golfing it because I'd need to implement a long, rigid algorithm with finicky details that requires encoding a big lookup table. – xnor Oct 18 '19 at 22:29
• Shouldn't #A98AC7 be #01B207 so that it's consistent with the other patterns? Or did you change it on purpose? – Arnauld Oct 18 '19 at 22:48
• @Arnauld In decimal, #A98AC7 is 11111111 – Avi Oct 18 '19 at 23:41
# C# (Visual C# Interactive Compiler), 557 bytes
a=>b=>{var k=a.Select(l=>l==0xFF0800?"Return to Sleeping Death":\$"{l:X}".All(x=>x>69|x<49)?"Press F to pay respects to Snow White":"Saved by "+"Grumpy,Happy,Sleepy,Bashful,Sneezy,Dopey,Doc,the Seven Dwarfs,Love's first kiss, ".Split(',')[l==0xFFFAFA?8:l==11111111?0:l%1118481<1?l/1118481:l%1111111<1?l/1111111:9]);int j=a.Last(),i=0,e=24;for(;e-->0;i|=j%2,j>>=1)i*=2;var m=k.Where(o=>o[9]!=9);var t=a.SkipLast(1).Select(o=>Convert.ToString(o^i,2).Sum(y=>y-48)).ToList();return(m.Any()?m:m=b.SkipLast(1).Where((x,y)=>t.Min()==t[y])).ToList()[~-m.Count()/2];}
Try it online!
• Suggest j/=2)i+=i+j%2; instead of i|=j%2,j>>=1)i*=2; – ceilingcat Aug 17 '20 at 4:24
# JavaScript (Node.js), 433 bytes
Takes input as a list of tuples [color, string].
a=>(h=a=>a[a.length-1>>1])(a.flatMap(([c])=>(s=c-0xFFFAFA?"Grumpy/Happy/Sleepy/Bashful/Sneezy/Dopey/Doc/the Seven Dwarfs".split/[(d=c-11111111?c/1118481:1)%1?c/1111111:d]:"Love's first kiss")?"Saved by "+s:c-0xFF0800?(g=n=>n?n%16%15||g(n>>4):0)(C=c)?[]:"Press F to pay respects to Snow White":"Return to Sleeping Death"))||h(a.map(m=([c,s])=>[(d=g(c,i=24))>m?d:m=d,s],a.pop(g=n=>i--&&(n^C>>i)%2+g(n/2))).flatMap(([d,s])=>d-m?[]:s))
Try it online!
• Very impressive - I especially liked the computation for correct hex indices :) – Avi Oct 19 '19 at 3:14 | 2,574 | 9,022 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2021-17 | latest | en | 0.856308 |
https://www.tensorflow.org/api_docs/python/tf/keras/metrics/MeanAbsoluteError | 1,620,393,818,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988793.99/warc/CC-MAIN-20210507120655-20210507150655-00045.warc.gz | 1,063,327,820 | 61,638 | Save the date! Google I/O returns May 18-20
# tf.keras.metrics.MeanAbsoluteError
Computes the mean absolute error between the labels and predictions.
Inherits From: `Mean`, `Metric`, `Layer`, `Module`
### Used in the notebooks
Used in the guide Used in the tutorials
`name` (Optional) string name of the metric instance.
`dtype` (Optional) data type of the metric result.
#### Standalone usage:
````m = tf.keras.metrics.MeanAbsoluteError()`
`m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]])`
`m.result().numpy()`
`0.25`
```
````m.reset_states()`
`m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]],`
` sample_weight=[1, 0])`
`m.result().numpy()`
`0.5`
```
Usage with `compile()` API:
``````model.compile(
optimizer='sgd',
loss='mse',
metrics=[tf.keras.metrics.MeanAbsoluteError()])
``````
## Methods
### `reset_states`
View source
Resets all of the metric state variables.
This function is called between epochs/steps, when a metric is evaluated during training.
### `result`
View source
Computes and returns the metric value tensor.
Result computation is an idempotent operation that simply calculates the metric value using the state variables.
### `update_state`
View source
Accumulates metric statistics.
`y_true` and `y_pred` should have the same shape.
Args
`y_true` Ground truth values. shape = `[batch_size, d0, .. dN]`.
`y_pred` The predicted values. shape = `[batch_size, d0, .. dN]`.
`sample_weight` Optional `sample_weight` acts as a coefficient for the metric. If a scalar is provided, then the metric is simply scaled by the given value. If `sample_weight` is a tensor of size `[batch_size]`, then the metric for each sample of the batch is rescaled by the corresponding element in the `sample_weight` vector. If the shape of `sample_weight` is `[batch_size, d0, .. dN-1]` (or can be broadcasted to this shape), then each metric element of `y_pred` is scaled by the corresponding value of `sample_weight`. (Note on `dN-1`: all metric functions reduce by 1 dimension, usually the last axis (-1)).
Returns
Update op.
[{ "type": "thumb-down", "id": "missingTheInformationINeed", "label":"Missing the information I need" },{ "type": "thumb-down", "id": "tooComplicatedTooManySteps", "label":"Too complicated / too many steps" },{ "type": "thumb-down", "id": "outOfDate", "label":"Out of date" },{ "type": "thumb-down", "id": "samplesCodeIssue", "label":"Samples / code issue" },{ "type": "thumb-down", "id": "otherDown", "label":"Other" }]
[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }] | 749 | 2,705 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2021-21 | longest | en | 0.64815 |
https://www.testpreparationz.com/find-factorial-number-in-java/ | 1,726,208,074,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651507.67/warc/CC-MAIN-20240913034233-20240913064233-00285.warc.gz | 945,749,200 | 48,257 | # find factorial number in java
## Java Program to Find the Factorial of a Number
Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720.
Below questions may asked by interviewer
Q) So, basically what is factorial?
Ans: A factorial is a function that multiplies number by every number. For example 4!= 4*3*2*1=24. The function is used, among other things, to find the number of ways “n” objects can be arranged.
Q) How to calculate?
For example :
Consider :
• 2! = 2 x 1 = 2
The possibility of 2! is two ways like {2,1}, { 1,2 }.
Same as like :
4! = 4 x 3 x 2 x 1 = 24.
• 24 = the arrangement of 4! is {1,2,3,4}, {2,1,3,4}, {2,3,1,4}, {2,3,4,1}, {1,3,2,4}, etc.
Same as like 5! , 10! , N!.
The following program has been written in 5 different ways, using while loop, for loop, do while loop, using method.
Now, let’s get into the programming part.
1. Java Program To Calculate Factorial using standard values with outputs
Method 1
```/*
* Author: Zameer Ali
* */
class Factoral {
public static void main(String arg[]) {
int n = 5, fact = 1;
for (int i = 1; i <= n; i++) {
fact = fact * i;
}
System.out.println("factoral=" + fact);
}
}
```
Output:
factorial =120
2. Find Factorial Using For Loop getting user input
Method 2
```/*
* Author: Zameer Ali
* */
import java.util.Scanner;
class Factorial {
public static void main(String arg[])
{
long n, fact = 1;
Scanner sc = new Scanner(System.in);
System.out.println("enter number");
n = sc.nextLong();
for (int i = 1; i <= n; i++) {
fact = fact * i;
}
System.out.println("fact=" + fact);
}
}
```
Output:
enter number
7=5040
3. Find Factorial using Function
Method 3
```/*
* Author: Zameer Ali
* */
import java.util.Scanner;
class Factorl {
public static void main(String args[])
{
long n, fact = 0;
n = Long.parseLong(args[0]);
fact = factCal(n);
System.out.println("fact=" + fact);
}
static long factCal(long x) {
long fact = 1;
for (int i = 1; i <= x; i++) {
fact = fact * i;
}
return fact;
}
}
```
Output:
C:\Users\ZameerAli\Desktop\E>javac.java
C:\Users\ZameerAli\Desktop\E>java Factorl 10
factorl=3628800
4. Find Factorial Using Recursion
Recursion: A Recursion is a function call itself – you can check out more information about what is recursion in java here?
Method 4
```/*
* Author: Zameer Ali
* */
import java.util.Scanner;
class Factorl {
public static void main(String arg[]) {
long n;
Scanner sc = new Scanner(System.in);
System.out.println("enter number");
n = sc.nextLong();
long f = Factorl.fact(n);
System.out.println("factorial=" + f);
}
static long fact(long n) {
if (n <= 0)
return 1;
return Factorl.fact(n - 1) * n;
}
}
```
Output:
enter number
30
Factorl=8764578968847253504
5. Find Factorial Using while loop and do while loop
Method 5
```/*
* Author: Zameer Ali
* */
import java.util.Scanner;
class Factrl {
public static void main(String arg[])
{
long n, fact = 1;
Scanner sc = new Scanner(System.in);
System.out.println("enter number");
n = sc.nextLong();
int i = 1;
while (i <= n) {
fact = fact * i;
i++;
}
System.out.println("fact=" + fact);
}
}
```
Output:
enter number
10
fact=3628800
Do while loop example
Method 6
```/*
* Author: Zameer Ali
* */
import java.util.Scanner;
class Fact1 {
public static void main(String arg[])
{
long n, fact = 1;
Scanner sc = new Scanner(System.in);
System.out.println("enter number");
n = sc.nextLong();
int i = 1;
do {
fact = fact * i;
i++;
}
while (i <= n);
System.out.println("fact=" + fact);
}
}
```
Output:
output:
enter number
7
fact=5040 | 1,090 | 3,649 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2024-38 | latest | en | 0.660596 |
https://www.pmbypm.com/tag/project-network-diagram/ | 1,712,923,787,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296815919.75/warc/CC-MAIN-20240412101354-20240412131354-00404.warc.gz | 837,673,056 | 30,335 | ## Critical Path Analysis Example – 2 Ways to Calculate Critical Path
Critical Path Analysis Example – Using 0 and 1 Method I got introduced to Critical Path Analysis in the year 1997. I am a software engineer by education. I learned most of the project management concepts while managing software projects – Critical Path Analysis was one such concept. I learned about Critical Path while using…
## What is a Gantt Chart?
What is a Gantt Chart? Is Gantt Chart same as a Scheduling Bar Chart? What is a Time Scaled Logic Diagram? Is it same as Gantt chart? What is a Time Scaled Network Diagram? How is it different from Gantt Chart? Project Schedule can be represented in many ways. In one of my previous articles,…
Lead and Lag Demystified There are many terms that perturb project management professionals. Lead and Lag are two such terms. I interact with many professionals on a regular basis. I often find that many of them are not fully aware of meaning of these terms. Even though they know the correct definitions of these terms,…
## How to Use Leads and Lags in Project Schedule?
Leads and Lags – Definitions, Explanations & Examples Leads and Lags are essential for making a good project schedule. They are the basic building blocks of scheduling. Many scheduling experts don’t use them. Instead, they often apply (incorrect) alternatives. In my opinion, Leads and Lags are easy to use and implement. They should always be…
## Start to Finish [SF] Relationship (Dependency) With Examples
Start To Finish is a logical relationship (or dependency) in which a successor activity cannot finish until its predecessor activity has started. Start to Finish (SF) is one of the four activity relationships of project management. These are used while preparing project schedule. The other three relationships are: Finish to Start (FS) Start to Start…
## Finish to Finish [FF] Relationship (Dependency) With Examples
Finish To Finish is a logical relationship (or dependency) in which a successor activity cannot finish until its predecessor activity has finished. Finish to Finish (FF) is one of the four activity relationships of project management. These are used while preparing project schedule. The other three relationships are: Finish to Start (FS) relationship Start to…
## Start to Start [SS] Relationship (Dependency) With Examples
Start To Start is a logical relationship (or dependency) in which a successor activity cannot start until its predecessor activity has started. Start to Start (SS) is one of the four activity relationships of project management. These are used while preparing project schedule. The other three relationships are: FS Relationship FF Relationship SF Relationship Let…
## Finish to Start [FS] Relationship (Dependency) With Examples
Finish To Start is a logical relationship (or dependency) in which a successor activity cannot start until its predecessor activity has finished. Finish to Start (FS) is one of the four activity relationships of project management. These are used while preparing project schedule. The other three relationships are: Start-to-Start (SS) dependency Finish-to-Finish (FF) dependency Start-to-Finish…
## How To Use Project Schedule Network Diagram? [Example]
A project schedule network diagram is used for pictorial representation of logical relationships among the project activities. They are drawn to depict project dependencies or relationships between two activities and/or milestones. They are also called logical network diagrams. There are three ways to draw a project network diagram. These are: Precedence Diagramming Method (PDM): This…
## 4 Sure-Fire Steps to Solve PDM PMP Questions – Precedence Diagramming Method Example
In this post, I have solved a small question on Precedence Diagramming Method (PDM) that is used to draw project management network diagrams. There are a number of PDM Questions in the PMP Exam. I have taken a small network diagram example to showcase how PDM PMP questions can be solved using sequence of 4… | 807 | 4,030 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2024-18 | longest | en | 0.944432 |
https://efteruddannelse.kurser.ku.dk/course/2018-2019/NFYA05060U | 1,544,705,140,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376824822.41/warc/CC-MAIN-20181213123823-20181213145323-00100.warc.gz | 591,179,296 | 13,339 | Optics
Course content
The course gives a detailed understanding of optical phenomena in nature and in modern optical sciences. In addition, the course gives a good basis for optics course on msc level (kandidatuddannelsen), such as quantum optics, and quantum photonics.
Education
B.Sc. Physics
MSc Programme in Physics w. minor subject
Learning outcome
With this course we aim at preparing the participant such that she/he can:
• find wave solutions to Maxwell equations in homogene isotropic media, and to demonstrate the difference between longitudinale and transversal wave motion,
• write up simple models for insulators and metals optical properties, and to apply these in connection with refraction and reflection,
• understand geometrical optics as an approximation of wave optics and apply geometrical optics and ray tracing to optical components such as lenses, prisms, fibers etc,
• understand polarization of light field and ways to prepare various polarized states of light, such as linearly and circularly polarized light, birefrigent crystals, find the optical axis, describe its nature, give details on polarization states of light upon reflections from metals and insulators,
• understand interference and multilayer interference and their applications, using the matrix method and more simple approaches,
• apply Huygens- Fresnel principle to various diffraction phenomena, and understand the basis for diffraction theory generally,
• Understand the principles of the laser apply and describe Einsteins stimulates and spontaneous emission processes and their relevance for the laser.
• Classify and apply modern optical components such as aspheric and spherical lenses, wave plates, optical crystals, etc.
• have good experimental knowledge on how to measure and characterize optical components such as lenses, prisms, polarization states, diffraction from small holes, interference of light in various setups.
Knowledge
The optics course deals with classical optics and target both geometrical optics and wave optics. We will look at metals and insulators optical properties and give detailed descriptions based on the classical theory of conductivity of electrons in various materials.
Wave optics is based on solutions to the Maxwell equations and various approximate solution methods are discussed, such as the Huygens- Fresnel principle.
We discuss important applications in modern optics, such as PBS units, AOMs, wave plates, optical cavities, scattering of light.
Thoughout the course we discuss optical phenomena in nature such as, color, rainbow, sun dogs, hallows, green flash, atmospheric refraction, etc.
Elctromagnetic waves. Spreading of Light. Geomatrical Optics. Polarisation. Interference. Diffraction. The Laser. Applications in modern optics.
Competences
This course gives the student a competent background needed for following other, more advanced, optics courses.
The course consists of 4-6 hours lecture per week where demonstration experiments are included, 3 hours laboratory exercises where the student will play with optical phenomena related to the lectures. Finally there is 3 hours of problem session where the student will solve problems guided by a teacher. The problems also relate to the laboratory exercises and will provide an important basis for understanding the laboratory sessions.
See Absalon for final course material. The following is an example of expected course literature.
We use lecture notes, important historical articles any student should be familiar with and as a supplement Eugene Hecht, ”Optics”, fourth edition (Addison-Wesley 2002).
At least one course of electromagnetism and one of quantum mechanics.
ECTS
7,5 ECTS
Type of assessment
Oral examination, 25 min
No preparation time
Aid
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
More internal examiners
Criteria for exam assessment
See learning outcome
Single subject courses (day)
• Category
• Hours
• Lectures
• 28
• Theory exercises
• 28
• Exam
• 0,5
• Preparation
• 149,5
• English
• 206,0 | 827 | 4,081 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2018-51 | longest | en | 0.880941 |
https://www.jiskha.com/display.cgi?id=1347926385 | 1,498,666,690,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128323711.85/warc/CC-MAIN-20170628153051-20170628173051-00063.warc.gz | 928,558,823 | 3,855 | Math
posted by .
Jared and 5 friends wanted to make mac and cheese for lunch. they decided to use 3 boxes and each box needs 1` 2/3 cups of milk. the milk carton has 4 cups of milk left in it. do they have enough milk to make their lunch? Prove answer
I put
Yes because if 1 box needs 1 2/3 cups of milk than that means boxes need 3 2/3 cups of milk and there is 4 cups.
• Math -
How did you multiply 1 2/3 by 3 and get 3 2/3?
Try again.
Answer This Question
First Name School Subject Your Answer
Related Questions
More Related Questions
Post a New Question | 161 | 568 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2017-26 | longest | en | 0.96987 |
http://www.askiitians.com/forums/Analytical-Geometry/24/8237/please-answer-sir.htm | 1,477,448,729,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720475.79/warc/CC-MAIN-20161020183840-00316-ip-10-171-6-4.ec2.internal.warc.gz | 318,773,287 | 31,491 | Click to Chat
0120-4616500
CART 0
• 0
MY CART (5)
Use Coupon: CART20 and get 20% off on all online Study Material
ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R
There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list
Get extra R 350 off
USE CODE: SSPD25
``` The symmetric form of the equation of the line of intersection of the planes x+y-z = 1 and 2x-3y+z=2 is
```
6 years ago
Share
``` Dear deepika
planes x+y-z = 1 and 2x-3y+z=2
let the direction ratio of the line are a,b,c
so a+b-c =0 and 2a-3b+c =0
so from these two equation
a/2 = b/3 =c/5
now we have to find out the point of intersection of these two planes.
let x=0
so y-z =1 and -3y + z =2
so y=-3/2
z = -5/2
so equation of line become
(x-0)/2 = (y +3/2)/3 = (z+5/2)/5
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin
```
6 years ago
# Other Related Questions on Analytical Geometry
Show that the semi latus rectum of the parabola y^2=4ax is the harmonic mean between the segments of any focal chord.
let the coordinates of end points for the focal chord drawn of the parabola be: P(at1^2,2at) and Q (at2^2, 2at2) respectively. SP = a+ at1^2 = > a (1+ t1^2) SQ = a(1 + t2^2) Now write SQ in ...
Vikas TU 2 months ago
1)If (1,a) , (3,9a) , (4,b) , (6,18) are collinear then (a,b/a)= A.(6,13) B.(6/7,13) C.(6/7,13/7) D.(21,13) 2)If A,B,C are collnear points A=(3,4) , B=(7,7) and AC = 10 then C = A.(5,2)...
Hii 1) find out their slopes and equate for all the pair of points . You will get the answer 2) Just equate the value of slope m = (y2-y1)/(x2-x1). You will get the answer
Sourabh Singh 2 months ago
Show that (-1, 4, -3) is the circumcentre of triangle formed by the points (3, 2, -5) (-3, 8, -5) (-3, 2, 1)
LET THE THREE POINTS OF THE TRIANGLE AS A,B,C. LET ‘S(x,y,z)’ BE THE CIRCUM CENTRE OF THE TRIANGLE. TAKE AS=BS OR AS=CS AND SOLFOR x,y,z. TRY IT YOUR SELF AND POST IF U HAVE ANY FURTHER...
find all pairs of positive integers a,b such that a^b-b^a=3
Since RHS is odd, we must have either a is even and b is odd or vice versa. Case I: a is even, b is odd Also if , we must haveclearly, b>a. Hence and hence . (In fact looking modulo 3, a is ...
2017 years ago
Why we consider speed as a scalar quantity, as while describing speed we know that an object is moving with a particular speed in some direction? It cannot happen that an object moving with ...
Scalar physical quantities are following physics laws and having magnitude ONLY.. Speed is just the rate of conversion of distance travelled, not associated with any concept of direction.....
Saurabh Kumar one year ago
hi Scalar physical quantities are following physics laws and having magnitude ONLY.. Speed is just the rate of conversion of distance travelled, not associated with any concept of...
Ankit Jaiswal 9 months ago
googlelo photoes remove cheyandi.please what is the way to remove photo from iitians.
first google lo photos ela pettalo chepandi kalavathi garu tharvatha ela remove cheyalo memu chepthamu thondharge chepandi
bunnypriya 6 months ago
this question is only for who works in iit. if you know give answer.thank you for your reply bunnypriya garu.
kalavathi 6 months ago
View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: R 15,000
• View Details
Get extra R 3,750 off
USE CODE: SSPD25
Get extra R 350 off
USE CODE: SSPD25
More Questions On Analytical Geometry | 1,167 | 3,773 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2016-44 | longest | en | 0.831241 |
https://kmmiles.com/70880-km-in-miles | 1,660,253,616,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571502.25/warc/CC-MAIN-20220811194507-20220811224507-00795.warc.gz | 337,584,193 | 6,679 | kmmiles.com
# 70880 km in miles
## Result
70880 km equals 44016.48 miles
You can also convert 70880 miles to km.
## Conversion formula
Multiply the amount of km by the conversion factor to get the result in miles:
70880 km × 0.621 = 44016.48 mi
## How to convert 70880 km to miles?
The conversion factor from km to miles is 0.621, which means that 1 km is equal to 0.621 miles:
1 km = 0.621 mi
To convert 70880 km into miles we have to multiply 70880 by the conversion factor in order to get the amount from km to miles. We can also form a proportion to calculate the result:
1 km → 0.621 mi
70880 km → L(mi)
Solve the above proportion to obtain the length L in miles:
L(mi) = 70880 km × 0.621 mi
L(mi) = 44016.48 mi
The final result is:
70880 km → 44016.48 mi
We conclude that 70880 km is equivalent to 44016.48 miles:
70880 km = 44016.48 miles
## Result approximation
For practical purposes we can round our final result to an approximate numerical value. In this case seventy thousand eight hundred eighty km is approximately forty-four thousand sixteen point four eight miles:
70880 km ≅ 44016.48 miles
## Conversion table
For quick reference purposes, below is the kilometers to miles conversion table:
kilometers (km) miles (mi)
70881 km 44017.101 miles
70882 km 44017.722 miles
70883 km 44018.343 miles
70884 km 44018.964 miles
70885 km 44019.585 miles
70886 km 44020.206 miles
70887 km 44020.827 miles
70888 km 44021.448 miles
70889 km 44022.069 miles
70890 km 44022.69 miles
## Units definitions
The units involved in this conversion are kilometers and miles. This is how they are defined:
### Kilometers
The kilometer (symbol: km) is a unit of length in the metric system, equal to 1000m (also written as 1E+3m). It is commonly used officially for expressing distances between geographical places on land in most of the world.
### Miles
A mile is a most popular measurement unit of length, equal to most commonly 5,280 feet (1,760 yards, or about 1,609 meters). The mile of 5,280 feet is called land mile or the statute mile to distinguish it from the nautical mile (1,852 meters, about 6,076.1 feet). Use of the mile as a unit of measurement is now largely confined to the United Kingdom, the United States, and Canada. | 622 | 2,262 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2022-33 | latest | en | 0.813434 |
http://rasch.org/rmt/rmt83g.htm | 1,490,632,233,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218189490.1/warc/CC-MAIN-20170322212949-00238-ip-10-233-31-227.ec2.internal.warc.gz | 297,800,506 | 7,112 | ## PROX with missing data, or known item or person measures
The Normal Approximation Estimation Algorithm (PROX) is a computationally simpler Rasch estimation algorithm invented by Leslie Cohen in 1972 for responses by persons to dichotomous items with no missing data. It has been extended to many-facet polytomous data sets with missing data. The essential specification is that each element (e.g., person, item, task) encounters a symmetrically distributed sample of challenges (e.g., person facing items+tasks+judges). The distributions of challenges faced by the elements may have different means and variances.
Dichotomous Data
Iterative PROX: the theory
For convenience, consider the two-facet case of persons of ability {Bn} facing items of difficulty {Di}. Then, according to the Rasch model, for each dichotomous encounter there is the logistic relationship
(1)
Sum for each item i across all Ni persons it encounters,
(2)
where Si is the raw score of successes on item i, and Ψ is the standard logistic function.
When the {Bn} are symmetrically distributed, summing across them can be approximated by integrating across Ni normal distributions of {B} with mean μi and standard deviation σi for item i:
(3)
where Φ is the normal cumulative distribution function.
An equivalence between logistic Ψ and normal cumulative probability distributions Φ (Camilli 1994) is
(4)
producing,
(5)
But, in general, for the cumulative normal distribution function,
(6)
Then, since 1.702² = 2.9,
(7)
Substituting the logistic for the normal ogive,
(8)
and rearranging, produces an estimation equation for Di, the logit difficulty of item i,
(9)
where μi is the mean and σi the standard deviation of the logit abilities of the persons encountering item i.
The comparable estimation equation for person n with logit ability, Bn, is
(10)
where Rn is the raw score achieved by person n on Nn items, and μn and σn summarize the distribution of logit item difficulties encountered by person n.
The model standard errors of PROX measures follow:
(11)
Iterative PROX: in practice
1. Start with all person and item difficulties set to 0, so that μi=0, σi=0, mu;n=0, σn=0
2. Compute the item difficulties:
(9)
If the data are complete, then μi (the mean of the person estimates) and σi (the S.D. of the person estimates) are the same for every item.
3. Subtract the mean item difficulty from all the item difficulties in order to maintain the sum of the item difficulties at 0: ΣDi=0
4. Compute the person abilities:
(10)
If the data are complete, then μn (the mean of the item estimates) and σn (the S.D. of the item estimates) are the same for every person.
5. Repeat 2., 3. and 4. until the bigggest change in any item difficulty or person ability is less than .01 logits.
6. The item difficulties and the person abilities are the Rasch PROX estimates with standard errors:
(11)
For more than two facets, the {μi} and {σi} summarize the distribution of the combined measures of the other facets, as encountered by item i, and similarly for the persons, tasks, judges, etc.
## PROX for Complete Data
If data are complete, then μi and σi can be treated as constant across items, and μn and σn constant across persons. This, with further simplifications, permits the non-iterative estimation equations derived by Cohen (1979):
L = count of items
N = count of persons
Si is the raw score of successes on item i
Sn is the raw score of successes by person n
SDL = sample S.D. of item raw scores
SDN = sample S.D. of person raw scores
Item difficulties:
XL = item difficulty expansion factor = √ [(1+SDN/2.89)/(1-SDLSDN/8.35)]
Provisional difficulty of item i = - XL*ln[(Si)/(N-Si)]
Difficulty of item i = Provisional difficulty of item i - Average provisional difficulty of all items
with S.E. of item i = XL*√[N /(Si*(N-Si))]
Person abilities:
XN = person ability expansion factor = √ [(1+SDL/2.89)/(1-SDLSDN/8.35)]
Ability of person n = 0 + XN*ln[(Sn)/(L-Sn)]
with S.E. of person n = XN*√[L /(Sn*(L-Sn))]
PROX estimation equations for polytomous data will be derived in the next RMT.
John Michael Linacre
Camilli, G. 1994. Origin of the scaling constant d=1.7 in item response theory. Journal of Educational and Behavioral Statistics. 19(3) p.293-5.
Cohen, L. 1979. Approximate expressions for parameter estimates in the Rasch model. British Journal of Mathematical and Statistical Psychology 32(1) 113-120.
PROX with missing data, or known item or person measures. Linacre JM. … Rasch Measurement Transactions, 1994, 8:3 p.378
Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez
Forum Rasch Measurement Forum to discuss any Rasch-related topic
Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement
Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.
Coming Rasch-related Events
March 31, 2017, Fri. Conference: 11th UK Rasch Day, Warwick, UK, www.rasch.org.uk
April 2-3, 2017, Sun.-Mon. Conference: Validity Evidence for Measurement in Mathematics Education (V-M2Ed), San Antonio, TX, Information
April 26-30, 2017, Wed.-Sun. NCME, San Antonio, TX, www.ncme.org - April 29: Ben Wright book
April 27 - May 1, 2017, Thur.-Mon. AERA, San Antonio, TX, www.aera.net
May 26 - June 23, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 30 - July 29, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
July 31 - Aug. 3, 2017, Mon.-Thurs. Joint IMEKO TC1-TC7-TC13 Symposium 2017: Measurement Science challenges in Natural and Social Sciences, Rio de Janeiro, Brazil, imeko-tc7-rio.org.br
Aug. 7-9, 2017, Mon-Wed. In-person workshop and research coloquium: Effect size of family and school indexes in writing competence using TERCE data (C. Pardo, A. Atorressi, Winsteps), Bariloche Argentina. Carlos Pardo, Universidad Catòlica de Colombia
Aug. 7-9, 2017, Mon-Wed. PROMS 2017: Pacific Rim Objective Measurement Symposium, Sabah, Borneo, Malaysia, proms.promsociety.org/2017/
Aug. 10, 2017, Thurs. In-person Winsteps Training Workshop (M. Linacre, Winsteps), Sydney, Australia. www.winsteps.com/sydneyws.htm
Aug. 11 - Sept. 8, 2017, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 18-21, 2017, Fri.-Mon. IACAT 2017: International Association for Computerized Adaptive Testing, Niigata, Japan, iacat.org
Sept. 15-16, 2017, Fri.-Sat. IOMC 2017: International Outcome Measurement Conference, Chicago, jampress.org/iomc2017.htm
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com | 2,387 | 9,005 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2017-13 | longest | en | 0.878643 |
http://www.beaconlearningcenter.com/Lessons/Lesson.asp?ID=765 | 1,611,070,683,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703519395.23/warc/CC-MAIN-20210119135001-20210119165001-00410.warc.gz | 124,115,071 | 2,395 | ## Munchy Multiplication
### Mary Ann TaylorBay District Schools
#### Description
Students will learn the concept of multiplication by putting goldfish crackers into groups, adding them up, and writing multiplication sentences to show what they have done.
#### Objectives
The student understands and explains the effects of addition, subtraction, and multiplication on whole numbers, decimals, and fractions, including mixed numbers, and the effects of division on whole numbers, including the inverse relationship of multiplication and division.
The student selects the appropriate operation to solve specific problems involving addition, subtraction, and multiplication of whole numbers, decimals, and fractions, and division of whole numbers.
#### Materials
-Chalkboard
-Chalk
-Large construction paper goldfish
–Tape or magnets
–Enough goldfish crackers for each student to have 24
–Blue construction paper
–Notebook paper
-Pencils
#### Preparations
1. Make 24 large goldfish out of yellow construction paper.
2. Buy enough goldfish crackers for each student to have 24.
3. Have tape or small magnets at the chalkboard.
4. Have enough blue construction paper, notebook paper, and pencils readily available.
#### Procedures
1. Using tape or magnets put 4 groups of 2 goldfish on the chalkboard. Draw a circle around each pair of goldfish.
2. Ask how many goldfish are on the chalkboard altogether. Call on a volunteer to give the answer. Ask the volunteer how he/she came up with the answer 8. (Adding)
3. Write 2 + 2 + 2 + 2 =8 on the chalkboard. Tell the students there is a quicker to “add” the goldfish. It is called multiplication. Write multiplication is a quick way to add equal groups, on the chalkboard. Say 4 groups of 2 equals 8 goldfish. Write 4 x 2 = 8. Continue to do this with different amounts of groups of 2 until you’ve covered all the multiplication sentences for 2’s.
4. Give each student a piece of blue construction paper, notebook paper, and a pencil. Have students draw 12 fairly large circles on their blue construction paper.
5. Pass out 24 goldfish crackers to each child.
6. Tell the students to listen carefully to the directions. If they do, when the lesson is over, they can eat their goldfish crackers.
7. Go to the chalkboard and repeat step one. Have students copy this with their goldfish crackers on their blue construction paper.
8. Ask a volunteer what multiplication sentence you could write for this.
9. Have all the students write 4 x 2 = 8 on their papers. Continue to do this in random order until all the multiplication sentences for 2’s have been covered.
10. Have the students put their notebook paper with the multiplication sentences in their backpacks to take home to practice.
11. Pass out new pieces of notebook paper.
12. Write 5 multiplication sentences using 2’s without the answers on the chalkboard. Have the students copy them off the board onto their papers.
13. Tell the students to complete each multiplication sentence with its answer on their paper. Also, they are to write 5 different complete multiplication sentences using 2’s on their paper. They may use their goldfish crackers if needed.
14. Take up papers and check answers. 15. Let students eat their goldfish crackers!
#### Assessments
Students who correctly answer 80% of the multiplication sentences on the chalkboard and correctly make up 80% of their own multiplication sentences will have shown mastery of this skill.
#### Extensions
You could do the same lesson teaching multiplication sentences for 3’s, 4’s, 5’s, etc… | 773 | 3,578 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2021-04 | latest | en | 0.89994 |
https://mirmgate.com.au/v-calculator/vector-add-calculator.html | 1,716,857,397,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059055.94/warc/CC-MAIN-20240528000211-20240528030211-00013.warc.gz | 348,341,860 | 5,765 | Searching for Vector Add Calculator? At mirmgate.com.au we have compiled links to many different calculators, including Vector Add Calculator you need. Check out the links below.
### Vector Add, Subtract Calculator - Symbolab
Free vector add, subtract calculator - solve vector operations step-by-step
### Vector Calculator - Symbolab
https://www.symbolab.com/solver/vector-calculator
The common types of vectors are cartesian vectors, column vectors, row vectors, unit vectors, and position vectors. How do you add two vectors? To add two vectors, add the …
Welcome to Omni's vector addition calculator, where we'll learn all about adding vectors in 2D or 3D. Our tool allows us to give the …
### Vector Calculator - Math is Fun
https://www.mathsisfun.com/algebra/vector-calculator.html
Vector Calculator Enter values into Magnitude and Angle ... or X and Y. It will do conversions and sum up the vectors. Learn about Vectors and Dot Products. Vectors …
### Online calculator: Vector Addition Calculator - PLANETCALC
https://planetcalc.com/8066/
Vector Addition Calculator This online calculator performs vector addition and displays vectors and vector sum graphically. Below you can find the vector addition calculator. …
### Vector Calculator - with all steps - MathPortal
https://www.mathportal.org/calculators/matrices-calculators/vector-calculator.php
This calculator performs all vector operations in two and three dimensional space. You can add, subtract, find length, find vector projections, find dot and cross product of two …
Vector A = (1, 4) Vector B = (6, 8) Solution: Using the vector addition formula: Vector A + Vector B = (1, 4) + (6, 8) Vector A + Vector B = (1+6, 4+8) Vector A + Vector B = (7, …
### Vector Addition - Vectors | Vector Components
Explore vectors in 1D or 2D, and discover how vectors add together. Specify vectors in Cartesian or polar coordinates, and see the magnitude, angle, and components of each vector. Experiment with vector equations and …
### Vector Space -- from Wolfram MathWorld
https://mathworld.wolfram.com/VectorSpace.html
A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where … | 502 | 2,253 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2024-22 | latest | en | 0.779153 |
http://www.mathisfunforum.com/viewtopic.php?pid=159564 | 1,394,561,948,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1394011240122/warc/CC-MAIN-20140305092040-00007-ip-10-183-142-35.ec2.internal.warc.gz | 437,774,800 | 12,339 | Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
## #1 2010-12-30 03:21:38
Au101
Power Member
Offline
### Vector Equations
Hi,
I'm not sure how to do a question which I have on vector equations - vectors have never been my strong point .
The points A and B have position vectors
And
Respectively. The points A and B are transformed by the linear transformation T to the points A' and B' respectively.
The transformation T is represented by the matrix T, where
.
a) Find the position vectors of A' and B'.
I was able to work out that:
.
And
.
b) Hence find a vector equation of the line A'B'.
Here is where I'm completely stuck . I haven't done any of the vector units which precede this one.
## #2 2010-12-30 03:43:13
bobbym
Administrator
Online
### Re: Vector Equations
Hi Au101;
Take a look here and see if this helps you.
http://www.revisesmart.co.uk/maths/core … -line.html
Here is an interesting vid that covers some basics of it.
http://www.youtube.com/watch?v=6keGU18t … re=related
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
## #3 2010-12-30 06:53:52
bob bundy
Moderator
Offline
### Re: Vector Equations
hi Au101,
Back so soon ?
Part (a) all correct!
Part (b)
A vector equation is similar to the cartesian equation y = mx + c
In y = mx + c you have an independant variable = x; a direction = m; a fixed point = c ( strictly 0,c ) and dependant variable = y
For vectors
lambda is the independant variable and is a scalar number; A'B' is the direction; OA' is the fixed point (you could use OB'); and r is the dependant variable.
So find A'B' and substitute in the general vector equation.
To get to any point on the line, first go from the origin to A'(OA') , and then take a variable trip along the vector A'B' (scalar.A'B')
To test if your equation works, find the lambda that makes r = OB, then find the lambda that finds the mid-point of A'B'
Bob
Uploaded Images
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #4 2010-12-30 07:01:06
Au101
Power Member
Offline
### Re: Vector Equations
Hmmm thanks Bobby, so could I then say:
Oh hi Bob Bundy, I didn't see your reply there, you replied just as I was, thanks a lot
Last edited by Au101 (2010-12-30 07:02:50)
## #5 2010-12-30 07:35:29
bob bundy
Moderator
Offline
### Re: Vector Equations
hi Au101,
Right answer! Well done.
You could still do these bits:
To test if your equation works, find the lambda that makes r = OB, then find the lambda that finds the mid-point of A'B'
Bob
Last edited by bob bundy (2010-12-30 07:36:38)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #6 2010-12-30 07:42:43
Au101
Power Member
Offline
### Re: Vector Equations
Certainly I shall, if only out of interest, I was especially interested in whether my layout was appropriate. Thanks, once again
## #7 2010-12-30 08:00:50
bobbym
Administrator
Online
### Re: Vector Equations
HIi Au101;
I am looking at some of the videos over there they are pretty good. What did you think of them?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
## #8 2010-12-30 08:23:49
Au101
Power Member
Offline
### Re: Vector Equations
Hi Bobbym, I agree, instructive and well laid out, good quality as well - sometimes they can be difficult to read - thanks
## #9 2010-12-30 08:31:18
bob bundy
Moderator
Offline
### Re: Vector Equations
hi Au101
Layout:
Your layout is fine.
Just as you can have y =mx + c OR mx = y - c OR c = y - mx .......
so you can have your vector equation in a variety of forms.
And you can go to a different point on the line
That's OB' followed by a 'different' lambda
Or even:
These are all the same line. Makes it hell to mark when every student may submit a correct, but different, equation.
For this reason you may also find your answer looks different from the book answer.
That's why it is worth trying to generate particular points on the line just to check it works.
If you get one answer and the book another, they are the same when they generate the same points.
Bob
Last edited by bob bundy (2010-12-30 08:32:40)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #10 2010-12-30 08:32:58
bobbym
Administrator
Online
### Re: Vector Equations
Sometimes it is a lot easier to learn by watching some videos rather than going through a book. They supplememnt each other well.
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
## #11 2010-12-30 23:18:49
bob bundy
Moderator
Offline
### Re: Vector Equations
Hi Au101 and bobbym
What follows is my first ever attempt at this.
This Shockwave version is 1.24M and the conversion has killed the resolution.
http://www.bundy.demon.co.uk/images/vectorline.swf
Try the avi version
http://www.bundy.demon.co.uk/images/vectorline.avi
It's now 2.8M and you'll need Windows Media Player.
Comments for improvements welcomed.
Bob
Last edited by bob bundy (2010-12-31 00:33:26)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #12 2010-12-31 00:04:19
bobbym
Administrator
Online
### Re: Vector Equations
Hi Bob;
Nice!
The program you used to make the movie? Some of them can monitor a portion of the screen, Snagit can I think. In other words they make a movie out of a selected area on the screen. What program are you using? Does it have that capability?
In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
## #13 2010-12-31 00:30:46
bob bundy
Moderator
Offline
### Re: Vector Equations
hi bobbym,
It's a free download called Camstudio and I've just discovered how to do exactly that. New version is now uploaded and it is only 2.8M.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #14 2010-12-31 01:29:07
Au101
Power Member
Offline
### Re: Vector Equations
That's very nice . I think I get what the equation means now, thanks!!! . I am, however, stumped by a new, but similar form of question, I have a worked example, but as I've alluded to this is the last chapter of a unit which is way ahead of anything I've done and I don't really understand some of the ideas, perhaps someone could explain what to do and why?
The transformation
Is represented by the matrix T, where
.
The plane
is transformed by T to the plane
.
The plane
Has Cartesian equation
Find a Cartesian equation of
.
Last edited by Au101 (2010-12-31 01:29:41)
## #15 2010-12-31 01:40:46
bob bundy
Moderator
Offline
### Re: Vector Equations
Hi Au101,
I've got the bug for videos now. I've just put a sine curve video link into Teaching Resources. If you get a chance, please have a look. That may be it for now, as these vids have used up all my allocated web space!
Now to your problem. You seem to have moved a long way in 24 hours!
Planes have the form ax + by + cz = 0 so that they have two degrees of freedom. If you think about the line, it had just one because you could only choose the value of lambda. Now with a plane you have two choices, say, x and y; then z is determined.
The vector
is perpendicular to the plane. (Do you need that explained because it is another post in itself).
edit: I think what I said here was wrong. See post 20 for correction.
Bob
Last edited by bob bundy (2010-12-31 05:16:20)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #16 2010-12-31 01:48:02
Au101
Power Member
Offline
### Re: Vector Equations
Hmmm such an explanation may indeed be helpful - the reason why I've moved so far in so short a time is that my textbook assumes knowledge of chapters I haven't yet covered. Also, I'm sorry to hear that you're out of bandwidth but I would be happy to have a look, I don't quite know where you mean by 'teaching resources' however?
## #17 2010-12-31 01:51:03
bob bundy
Moderator
Offline
### Re: Vector Equations
http://www.mathisfunforum.com/viewtopic.php?id=14858
B
explanation in prep Do you know what is meant by the dot product (also called the scalar product) ?
Last edited by bob bundy (2010-12-31 01:54:30)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #18 2010-12-31 01:57:05
Au101
Power Member
Offline
### Re: Vector Equations
Ah, thank you. I haven't covered dot product, but I have looked at it before and I'm fairly sure that I know what it does and how to use it.
## #19 2010-12-31 02:00:28
Au101
Power Member
Offline
### Re: Vector Equations
Ooooh that is, indeed, very nice, I must say, it is very clear and well-done. It is good to see it explained this way - of course I've come across it many times - but it was originally explained to me arguably less well.
## #20 2010-12-31 02:48:48
bob bundy
Moderator
Offline
### Re: Vector Equations
hi Au101,
Thanks for the comments.
I've finished playing about with these posts now. Either they are right or my brain will explode!
There's so much I'm going to split this post in two. First a look at the scalar product; the general equation for a plane; and then the particular case where the plane goes through the origin.
But I now don't think I was right to assume that the perpendicular vectors get transformed the same way so I'll put a proper method into the next post.
Three stages:
(i) The dot product.
If a and b are vectors then a.b is defined as |a|.|b|.cos θ = a1b1 + a2b2 + a3c3.
(θ is the angle between the vectors)
In particular if the vectors are perpendicular then a.b = 0
(ii) The general equation of a plane.
see picture below
To get the position vector of D, find how much you need to go in the 'a' direction and the 'b' direction to get from C to D, then do OC + CD.
.
Now suppose that vector 'n' is perpendicular to the plane. That means it is prependicular to every vector in the plane.
Then
But a.n = b.n = 0 as these vectors are perpendicular.
So r.n = c.n = some constant as c and n are fixed.
So if x,y and z are the components of r and n1, n2 and n3 are the components of n
x.n1 + y.n2 + z.n3 = constant.
This can be used to define the plane eg 3x + 4y - 6z = 27
(iii) Planes that go through (0,0)
Matrix multiplication can only be used for transformations that leave the origin invariant
ie. M . 0 = 0
So your transform must be one of these otherwise they couldn't set this question. And we can see that the origin is a point in the plane as x = y = z = 0 fits.
So the plane constant must be zero
So
is a possible vector for n, perpendicular to the plane. (Or any multiple of n)
Bob
Uploaded Images
Last edited by bob bundy (2010-12-31 06:20:17)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #21 2010-12-31 06:14:27
bob bundy
Moderator
Offline
### Re: Vector Equations
hi
post part two
steps: (i) find two vectors in the first plane (ii) transform them (iii) form an equation for the plane that contains these.
step (i)
By inspection these vectors will both lie in the plane
step (ii)
Transform these to get
step (iii)
so the equation is:
so
A x 6 =>
Then add C
also add B and C
E x 8 =>
add D
Bob
Last edited by bob bundy (2010-12-31 06:15:11)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #22 2010-12-31 07:10:11
Au101
Power Member
Offline
### Re: Vector Equations
Ooooh thanks very much for all of your hard work Bob, I think I've genuinely got it now, the only thing I don't think I quite follow, ironically, is the first step which, I assume, is the easier step, where did you get those vectors from?
## #23 2010-12-31 07:47:12
bob bundy
Moderator
Offline
### Re: Vector Equations
hi Au101,
The equation was
So I wanted two vectors (chosing x, y and z) that would fit that equation.
I just spotted x=y=z=1 as one possibility and then x = 1 y = 0 and z = -1 as another.
I was pleased to choose those because the numbers were easy to work with.
But any three numbers that fit the equation would do for a vector in the plane:
Let's have x = 39 and y = 22. Then z = 44 - 39 = 5.
That's what I meant before by two degrees of freedom.
Choose any two and that fixes the third.
So z = -3, y = 100 => x = 200 + 3 = 203. And so on.
But 1,1,1 and 1,0,-1 were easier to work with.
The only choice you cannot make is to have two vectors that are parallel, eg. x = y = z = 1 for one choice and x = y = z = 2 for the other. They are valid choices but you cannot solve the problem because you don't get enough independent equations to solve for mu and lambda.
Look back to my diagram for the plane. If vectors a and b are parallel you would not be able to get to all possible places for D.
The vectors have to be 'independent' (meaning one cannot be made by multiplying the other by a fixed amount). I expect you'll meet that idea again in this module.
Bob
Last edited by bob bundy (2010-12-31 07:54:27)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
## #24 2010-12-31 08:29:32
Au101
Power Member
Offline
### Re: Vector Equations
Ahhhhhhh I see, thanks!!!
## #25 2011-01-01 03:06:41
Au101
Power Member
Offline
### Re: Vector Equations
Last edited by Au101 (2011-01-01 03:13:20)
## Board footer
Powered by FluxBB | 3,939 | 14,200 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2014-10 | longest | en | 0.874405 |
https://docs.trifacta.com/display/r076/EXAMPLE+-+String+Comparison+Functions | 1,627,148,892,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046150307.84/warc/CC-MAIN-20210724160723-20210724190723-00510.warc.gz | 218,329,928 | 24,585 | ##### Page tree
Outdated release! Latest docs are Release 8.2: EXAMPLE - String Comparison Functions
The following example demonstrates functions that can be used to compare two sets of strings. These functions include the following:
• `STRINGGREATERTHAN` - Evaluates to `true` if the first string is greater than the second string. See STRINGGREATERTHAN Function
• `STRINGGREATERTHANEQUAL` - Evaluates to `true` if the first string is greater than or equal to the second string. See STRINGGREATERTHANEQUAL Function.
• `STRINGLESSTHAN` - Evaluates to `true` if the first string is less than the second string. See STRINGLESSTHAN Function.
• `STRINGLESSTHANEQUAL` - Evaluates to `true` if the first string is less than or equal to the second string. See STRINGLESSTHANEQUAL Function.
• `EXACT` - Evaluates to `true` if the first string is an exact match with the second string. See EXACT Function.
Source:
The following table contains some example strings to be compared.
rowIdstringAstringB
`1``a``a`
`2``a``A`
`3``a``b`
`4``a``1`
`5``a``;`
`6``;``1`
`7``a`` a`
`8``a``aa`
`9``abc``x`
Note that in row #6, `stringB` begins with a space character.
Transformation:
For each set of strings, the following functions are applied to generate a new column containing the results of the comparison.
Transformation Name `New formula` `Single row formula` `STRINGGREATERTHAN(stringA,stringB)` `'greaterThan'`
Transformation Name `New formula` `Single row formula` `STRINGGREATERTHANEQUAL(stringA,stringB) ` `'greaterThanEqual'`
Transformation Name `New formula` `Single row formula` `STRINGLESSTHAN(stringA,stringB)` `'lessThan'`
Transformation Name `New formula` `Single row formula` `STRINGLESSTHANEQUAL(stringA,stringB)` `'lessThanEqual'`
Transformation Name `New formula` `Single row formula` `EXACT(stringA,stringB)` `'exactEqual'`
Results:
In the following table, the `Notes` column has been added manually.
rowIdstringAstringBlessThanEquallessThangreaterThanEqualgreaterThanexactEqualNotes
`1``a``a``true``false``true``false``true`Evaluation of differences between `STRINGLESSTHAN` and `STRINGGREATERTHAN` and greater than versions.
`2``a``A``true``true``false``false``false`Comparisons are case-sensitive. Uppercase letters are greater than lowercase letters.
`3``a``b``true``true``false``false``false`
Letters later in the alphabet (b) are greater than earlier letters (a).
`4``a``1``false``false``true ``true ``false`
Letters (a) are greater than digits (1).
`5``a``;``false``false``true``true``false`Letters (a) are greater than non-alphanumerics (;).
`6``;``1``true``true``false``false``false`
Digits (1) are greater than non-alphanumerics (;). Therefore, the following characters are listed in order of evaluation:
`Aa1;`
`7``a`` a``false``false``true``true``false`Letters (and any non-breaking character) are greater than space values.
`8``a``aa``true``true``false``false``false`The second string is greater, since it contains one additional string at the end.
`9``abc``x``true``true``false``false``false`The second string is greater, since its first letter is greater than the first letter of the first string. | 872 | 3,134 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2021-31 | longest | en | 0.563673 |
catalog.harmonyed.com | 1,558,611,131,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232257243.19/warc/CC-MAIN-20190523103802-20190523125802-00537.warc.gz | 36,150,724 | 11,926 | Select Page
# K12: Math 8- Algebra
## Description
Students develop algebraic fluency by learning the skills needed to solve equations and perform manipulations with numbers, variables, equations, and inequalities. They also learn concepts central to the abstraction and generalization that algebra makes possible. Students learn to use number properties to simplify expressions or justify statements; describe sets with set notation and find the union and intersection of sets; simplify and evaluate expressions involving variables, fractions, exponents, and radicals; work with integers, rational numbers, and irrational numbers; and graph and solve equations, inequalities, and systems of equations. They learn to determine whether a relation is a function and how to describe its domain and range; use factoring, formulas, and other techniques to solve quadratic and other polynomial equations; formulate and evaluate valid mathematical arguments using various types of reasoning; and translate word problems into mathematical equations and then use the equations to solve the original problems. | 193 | 1,101 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2019-22 | latest | en | 0.909588 |
https://courses.lumenlearning.com/prealgebra/chapter/using-the-properties-of-triangles-to-solve-problems-2/ | 1,642,685,141,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301863.7/warc/CC-MAIN-20220120130236-20220120160236-00446.warc.gz | 238,732,113 | 12,724 | ## Using the Properties of Triangles to Solve Problems
### Learning Outcomes
• Find the area, base and height of a triangle
• Find the length of one side of a triangle given the perimeter and two other lengths
We now know how to find the area of a rectangle. We can use this fact to help us visualize the formula for the area of a triangle. In the rectangle below, we’ve labeled the length $b$ and the width $h$, so it’s area is $bh$.
The area of a rectangle is the base, $b$, times the height, $h$.
We can divide this rectangle into two congruent triangles (see the image below). Triangles that are congruent have identical side lengths and angles, and so their areas are equal. The area of each triangle is one-half the area of the rectangle, or $\frac{1}{2}bh$. This example helps us see why the formula for the area of a triangle is $A=\frac{1}{2}bh$.
A rectangle can be divided into two triangles of equal area. The area of each triangle is one-half the area of the rectangle.
The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.
To find the area of the triangle, you need to know its base and height. The base is the length of one side of the triangle, usually the side at the bottom. The height is the length of the line that connects the base to the opposite vertex, and makes a $\text{90}^ \circ$ angle with the base. The image below shows three triangles with the base and height of each marked.
The height $h$ of a triangle is the length of a line segment that connects the the base to the opposite vertex and makes a $\text{90}^ \circ$ angle with the base.
### Triangle Properties
For any triangle $\Delta ABC$, the sum of the measures of the angles is $\text{180}^ \circ$.
$m\angle{A}+m\angle{B}+m\angle{C}=180^\circ$
The perimeter of a triangle is the sum of the lengths of the sides.
$P=a+b+c$
The area of a triangle is one-half the base, $b$, times the height, $h$.
$A=\frac{1}{2}bh$
### example
Find the area of a triangle whose base is $11$ inches and whose height is $8$ inches.
Solution
Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. the area of the triangle Step 3. Name. Choose a variable to represent it. let A = area of the triangle Step 4.Translate. Write the appropriate formula. Substitute. Step 5. Solve the equation. $A=44$ square inches. Step 6. Check: $A=\frac{1}{2}bh$ $44\stackrel{?}{=}\frac{1}{2}(11)8$ $44=44\checkmark$ Step 7. Answer the question. The area is $44$ square inches.
### example
The perimeter of a triangular garden is $24$ feet. The lengths of two sides are $4$ feet and $9$ feet. How long is the third side?
### example
The area of a triangular church window is $90$ square meters. The base of the window is $15$ meters. What is the window’s height?
### Isosceles and Equilateral Triangles
Besides the right triangle, some other triangles have special names. A triangle with two sides of equal length is called an isosceles triangle. A triangle that has three sides of equal length is called an equilateral triangle. The image below shows both types of triangles.
In an isosceles triangle, two sides have the same length, and the third side is the base. In an equilateral triangle, all three sides have the same length.
### Isosceles and Equilateral Triangles
An isosceles triangle has two sides the same length.
An equilateral triangle has three sides of equal length.
### example
The perimeter of an equilateral triangle is $93$ inches. Find the length of each side.
### example
Arianna has $156$ inches of beading to use as trim around a scarf. The scarf will be an isosceles triangle with a base of
$60$ inches. How long can she make the two equal sides? | 966 | 3,773 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.96875 | 5 | CC-MAIN-2022-05 | latest | en | 0.87253 |
https://www.12000.org/my_notes/kamek/mma_12_maple_2019/KERNELsubsection828.htm | 1,721,832,861,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518304.14/warc/CC-MAIN-20240724140819-20240724170819-00510.warc.gz | 529,272,287 | 2,864 | #### 2.828 ODE No. 828
$y'(x)=\frac {(y(x)+1) (2 y(x)+1)}{x \left (2 x y(x)^4+x y(x)^3-2 y(x)-2\right )}$ Mathematica : cpu = 0.407943 (sec), leaf count = 56
$\text {Solve}\left [-\frac {1}{8} y(x)^2+\frac {3 y(x)}{8}-\frac {1}{2 x (2 y(x)+1)}-\frac {1}{2} \log (y(x)+1)+\frac {1}{16} \log (2 y(x)+1)=c_1,y(x)\right ]$ Maple : cpu = 0.217 (sec), leaf count = 54
$\left \{ y \left ( x \right ) ={\frac {1}{2}{{\rm e}^{{\it RootOf} \left ( x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{3}-8\,x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+16\,\ln \left ( 1/2\,{{\rm e}^{{\it \_Z}}}+1/2 \right ) x{{\rm e}^{{\it \_Z}}}+8\,{\it \_C1}\,x{{\rm e}^{{\it \_Z}}}-2\,{\it \_Z}\,x{{\rm e}^{{\it \_Z}}}+7\,{{\rm e}^{{\it \_Z}}}x+16 \right ) }}}-{\frac {1}{2}} \right \}$ | 398 | 759 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2024-30 | latest | en | 0.1787 |
https://www.edplace.com/worksheet_info/11+/keystage2/year5/topic/1170/6503/interior-angles-of-regular-polygons | 1,726,868,187,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725701423570.98/warc/CC-MAIN-20240920190822-20240920220822-00297.warc.gz | 679,539,363 | 12,292 | # Interior Angles of Regular Polygons
In this worksheet, students calculate the interior angle of regular polygons.
Key stage: KS 2
Curriculum topic: Maths and Numerical Reasoning
Curriculum subtopic: 2D Shapes: Circles, Angles and Bearings
Difficulty level:
#### Worksheet Overview
Regular polygons have interior angles which are all equal to each other.
To work out the sum of the interior angles of a polygon, we first work out the sum of its angles by splitting it into triangles.
We then divide this sum by the number of angles.
Example
Work out the interior angle of a regular hexagon.
The hexagon can be split into triangles.
There are 4 triangles inside the hexagon.
4 x 180º = 720º
The sum of the interior angles of a hexagon is 720º.
There are 6 equal angles inside the hexagon.
Each interior angle is 720º ÷ 6 = 120º
### What is EdPlace?
We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.
Get started | 283 | 1,247 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2024-38 | latest | en | 0.877051 |
https://scigraph.springernature.com/pub.10.1007/s12190-021-01594-x | 1,642,665,016,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301730.31/warc/CC-MAIN-20220120065949-20220120095949-00112.warc.gz | 585,445,203 | 16,715 | # Few-weight ZpZp[u]-additive codes from down-sets
Ontology type: schema:ScholarlyArticle
### Article Info
DATE
2021-09-08
AUTHORS ABSTRACT
In this paper, we study a special class of ZpZp[u]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_p{\mathbb {Z}}_p[u]$$\end{document}-additive code CL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_L$$\end{document} defined in terms of the down-set, where u2=u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u^2=u$$\end{document} and p is an odd prime. By a proper choice of the down-set, we determine the weight distribution of the additive code CL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_L$$\end{document}. In particular, we obtain several infinite families of minimal and optimal few-weight p-codes via the Gray map, and these codes can be applied to secret sharing schemes. More... »
PAGES
1-8
### References to SciGraph publications
• 2017-10-24. Few-weight codes from trace codes over a local ring in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
• 2019-08-14. One-weight and two-weight ℤ2ℤ2[u,v]-additive codes in CRYPTOGRAPHY AND COMMUNICATIONS
• 2017-11-24. Linear codes from simplicial complexes in DESIGNS, CODES AND CRYPTOGRAPHY
• 2017-10-28. New Classes of p-Ary Few Weight Codes in BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
### Identifiers
URI
http://scigraph.springernature.com/pub.10.1007/s12190-021-01594-x
DOI
http://dx.doi.org/10.1007/s12190-021-01594-x
DIMENSIONS
https://app.dimensions.ai/details/publication/pub.1140944115
Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net
JSON-LD is the canonical representation for SciGraph data.
TIP: You can open this SciGraph record using an external JSON-LD service:
[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Information and Computing Sciences",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, China",
"id": "http://www.grid.ac/institutes/grid.252245.6",
"name": [
"Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, China"
],
"type": "Organization"
},
"familyName": "Wang",
"givenName": "Shukai",
"id": "sg:person.016326742634.42",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016326742634.42"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, China",
"id": "http://www.grid.ac/institutes/grid.252245.6",
"name": [
"Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, China"
],
"type": "Organization"
},
"familyName": "Shi",
"givenName": "Minjia",
"id": "sg:person.012012432235.16",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012012432235.16"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/s12095-019-00391-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1120333610",
"https://doi.org/10.1007/s12095-019-00391-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s40840-017-0553-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1092416652",
"https://doi.org/10.1007/s40840-017-0553-1"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10623-017-0442-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1092948267",
"https://doi.org/10.1007/s10623-017-0442-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00200-017-0345-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1092340940",
"https://doi.org/10.1007/s00200-017-0345-8"
],
"type": "CreativeWork"
}
],
"datePublished": "2021-09-08",
"datePublishedReg": "2021-09-08",
"description": "In this paper, we study a special class of ZpZp[u]\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {Z}}_p{\\mathbb {Z}}_p[u]$$\\end{document}-additive code CL\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C_L$$\\end{document} defined in terms of the down-set, where u2=u\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$u^2=u$$\\end{document} and p is an odd prime. By a proper choice of the down-set, we determine the weight distribution of the additive code CL\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C_L$$\\end{document}. In particular, we obtain several infinite families of minimal and optimal few-weight p-codes via the Gray map, and these codes can be applied to secret sharing schemes.",
"genre": "article",
"id": "sg:pub.10.1007/s12190-021-01594-x",
"inLanguage": "en",
"isAccessibleForFree": false,
"isPartOf": [
{
"id": "sg:journal.1136398",
"issn": [
"1598-5865",
"1865-2085"
],
"name": "Journal of Applied Mathematics and Computing",
"publisher": "Springer Nature",
"type": "Periodical"
}
],
"keywords": [
"weight P",
"weight",
"family",
"choice",
"primes",
"class",
"terms",
"distribution",
"weight distribution",
"code",
"set",
"maps",
"U2",
"proper choice",
"secret sharing scheme",
"sharing scheme",
"paper",
"special class",
"odd prime",
"scheme",
"infinite family",
"Gray map"
],
"name": "Few-weight ZpZp[u]-additive codes from down-sets",
"pagination": "1-8",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1140944115"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s12190-021-01594-x"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s12190-021-01594-x",
"https://app.dimensions.ai/details/publication/pub.1140944115"
],
"sdDataset": "articles",
"sdDatePublished": "2022-01-01T19:02",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_889.jsonl",
"type": "ScholarlyArticle",
"url": "https://doi.org/10.1007/s12190-021-01594-x"
}
]
HOW TO GET THIS DATA PROGRAMMATICALLY:
JSON-LD is a popular format for linked data which is fully compatible with JSON.
curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s12190-021-01594-x'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s12190-021-01594-x'
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12190-021-01594-x'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12190-021-01594-x'
This table displays all metadata directly associated to this object as RDF triples.
98 TRIPLES 22 PREDICATES 50 URIs 38 LITERALS 4 BLANK NODES
Subject Predicate Object
2 anzsrc-for:08
3 schema:author N8ed11659955d43e6b218978c6e15fcce
4 schema:citation sg:pub.10.1007/s00200-017-0345-8
5 sg:pub.10.1007/s10623-017-0442-5
6 sg:pub.10.1007/s12095-019-00391-5
7 sg:pub.10.1007/s40840-017-0553-1
8 schema:datePublished 2021-09-08
9 schema:datePublishedReg 2021-09-08
10 schema:description In this paper, we study a special class of ZpZp[u]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_p{\mathbb {Z}}_p[u]$$\end{document}-additive code CL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_L$$\end{document} defined in terms of the down-set, where u2=u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u^2=u$$\end{document} and p is an odd prime. By a proper choice of the down-set, we determine the weight distribution of the additive code CL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_L$$\end{document}. In particular, we obtain several infinite families of minimal and optimal few-weight p-codes via the Gray map, and these codes can be applied to secret sharing schemes.
11 schema:genre article
12 schema:inLanguage en
13 schema:isAccessibleForFree false
14 schema:isPartOf sg:journal.1136398
15 schema:keywords Gray map
16 U2
18 choice
19 class
20 code
21 distribution
22 family
23 infinite family
24 maps
25 odd prime
26 paper
27 primes
28 proper choice
29 scheme
30 secret sharing scheme
31 set
32 sharing scheme
33 special class
34 terms
35 weight
36 weight P
37 weight distribution
38 schema:name Few-weight ZpZp[u]-additive codes from down-sets
39 schema:pagination 1-8
41 Nf99cc21e6fa3486397d2b99de2e68e37
42 schema:sameAs https://app.dimensions.ai/details/publication/pub.1140944115
43 https://doi.org/10.1007/s12190-021-01594-x
44 schema:sdDatePublished 2022-01-01T19:02
47 schema:url https://doi.org/10.1007/s12190-021-01594-x
49 sgo:sdDataset articles
50 rdf:type schema:ScholarlyArticle
51 N4770ef0b051d47acade63902ce964cab schema:name Springer Nature - SN SciGraph project
52 rdf:type schema:Organization
54 schema:value pub.1140944115
55 rdf:type schema:PropertyValue
56 N885eafc77c4641b4b0bc40f8551e4522 rdf:first sg:person.012012432235.16
57 rdf:rest rdf:nil
58 N8ed11659955d43e6b218978c6e15fcce rdf:first sg:person.016326742634.42
59 rdf:rest N885eafc77c4641b4b0bc40f8551e4522
60 Nf99cc21e6fa3486397d2b99de2e68e37 schema:name doi
61 schema:value 10.1007/s12190-021-01594-x
62 rdf:type schema:PropertyValue
63 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
64 schema:name Mathematical Sciences
65 rdf:type schema:DefinedTerm
66 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
67 schema:name Information and Computing Sciences
68 rdf:type schema:DefinedTerm
69 sg:journal.1136398 schema:issn 1598-5865
70 1865-2085
71 schema:name Journal of Applied Mathematics and Computing
72 schema:publisher Springer Nature
73 rdf:type schema:Periodical
74 sg:person.012012432235.16 schema:affiliation grid-institutes:grid.252245.6
75 schema:familyName Shi
76 schema:givenName Minjia
77 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012012432235.16
78 rdf:type schema:Person
79 sg:person.016326742634.42 schema:affiliation grid-institutes:grid.252245.6
80 schema:familyName Wang
81 schema:givenName Shukai
82 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016326742634.42
83 rdf:type schema:Person
84 sg:pub.10.1007/s00200-017-0345-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092340940
85 https://doi.org/10.1007/s00200-017-0345-8
86 rdf:type schema:CreativeWork
87 sg:pub.10.1007/s10623-017-0442-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092948267
88 https://doi.org/10.1007/s10623-017-0442-5
89 rdf:type schema:CreativeWork
90 sg:pub.10.1007/s12095-019-00391-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1120333610
91 https://doi.org/10.1007/s12095-019-00391-5
92 rdf:type schema:CreativeWork
93 sg:pub.10.1007/s40840-017-0553-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092416652
94 https://doi.org/10.1007/s40840-017-0553-1
95 rdf:type schema:CreativeWork
96 grid-institutes:grid.252245.6 schema:alternateName Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, China
97 schema:name Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, China
98 rdf:type schema:Organization | 4,693 | 14,588 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-05 | latest | en | 0.400769 |
https://community.dataiku.com/discussion/21048/diff-function-for-date-does-not-work | 1,721,553,551,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517663.24/warc/CC-MAIN-20240721091006-20240721121006-00234.warc.gz | 148,760,779 | 108,462 | Public
# Diff function for date does not work
Options
Registered Posts: 3 ✭✭✭
Hi, I'm usind the Diff function to calculate a difference between two dates and I want the formula to return me the difference in weeks.
This formula works well for almost all the cases but for the case when there is only 1 week between two dates (for example 2021/41 and 2021/42) the function returns me 0 instead of 1.
I don't know how to face this issue. Can you help me ? Maybe it's a problem of parameters ?
Thank's
• Dataiker, Registered Posts: 29 Dataiker
Options
Hi @llyly32
,
Thanks for these precisions, now I get it!
The 'diff" function returns only whole week count, namely 7 days. It does not count incomplete weeks with less than 7 days. To achieve your expected outcome, you should make sure that the days are at the start of the week. The "trunc" function, which rounds a date to the first day of the specified time unit, can help you compute what you want :
`diff(trunc('2021-10-25', "weeks"), trunc('2021-10-21',"weeks"), 'weeks')`
• Dataiker, Registered Posts: 29 Dataiker
edited July 17
Options
Hi @llyly32
,
Thanks for reporting this issue. What is your exact formula?
The following formula returns 1 for me :
```diff('2021-10-18','2021-10-11', 'weeks')
```
• Registered Posts: 3 ✭✭✭
edited July 17
Options
Hi @Marine
Yes it's this function. When I used it with these dates :
`diff('2021-10-25', '2021-10-21', 'weeks')`
These two dates are in two weeks differents (2021/43 and 2021/42) but the function returns 0 instead of 1.
I think the problem is because there is less than 7 days between 21/10 and 25/10 but I'm not sure.
Do you understand what I mean ?
• Registered Posts: 3 ✭✭✭
Options
@Marine thank you for your solution. It's work fine !
Help me… | 503 | 1,779 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2024-30 | longest | en | 0.900277 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.