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http://www.slideserve.com/solada/parabolic-solar-cookers | 1,508,307,207,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187822747.22/warc/CC-MAIN-20171018051631-20171018071631-00683.warc.gz | 552,476,960 | 13,898 | Parabolic Solar Cookers
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# Parabolic Solar Cookers - PowerPoint PPT Presentation
Parabolic Solar Cookers. Lonny Grafman Most Images from Appropedia Outline Background Basics Design Examples More Examples Math and Physics Resources Discussion. 100 0 watts/m 2. Solar Box Cooker a ka Solar Oven. Solar Parabolic Cooker. The Parabola. y=a x 2 f=1/(4a). y. f. x.
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Parabolic Solar Cookers
• Lonny Grafman
• Most Images from Appropedia
• Outline
• Background
• Basics
• Design Examples
• More Examples
• Math and Physics Resources
• Discussion
Solar Box Cooker
• aka Solar Oven
y=ax2
f=1/(4a)
y
f
x
The Parabola - Definition
http://www.cut-the-knot.org/ctk/Parabola.shtml#Theorem1
The Parabola - Reflection
http://www.cut-the-knot.org/ctk/Parabola.shtml#Theorem1
The Paraboloid
• The Parabola
Design Criteria:
• Use of local materials
• Efficiency
• Durability
• Ease of use
• Ease of construction
• Cost
• Impact on environment
• Impact on lifestyle
Design Objective:
To create a solar cookerfrom local invasive species and waste materials that can pasteurize water and be a cooking alternative to the use of fossil fuels.
Results:
• Equation: y =.5x2
• Time to boil quart: ~2 hrs
• Deformation Lessons Learned:
• more blackberry runners
• more rigid material for rings
• Reflectivity Lessons Learned:
• pampas grass too lumpy
• no dull, small can lids
Protection from Dazzles and Burns
• Appropriate focal point size
• Glasses and gloves
• Deep dish focus
• Physical barrier
• Physical separation
• Appropriate system size | 559 | 2,130 | {"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} | 3.140625 | 3 | CC-MAIN-2017-43 | latest | en | 0.681498 |
https://m.wikihow.com/Order-Fractions-From-Least-to-Greatest | 1,579,443,186,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250594603.8/warc/CC-MAIN-20200119122744-20200119150744-00396.warc.gz | 543,356,934 | 63,488 | # How to Order Fractions From Least to Greatest
Author Info
Updated: January 16, 2020
While it's easy to order whole numbers like 1, 3, and 8 by size, fractions can be hard to measure at a glance. If each lower number, or denominator, is the same, you can order them like whole numbers, for instance 1/5, 3/5, and 8/5. Otherwise, you can alter your list of fractions to use the same denominator, without changing the size of any fraction. This becomes easier with practice, and you can learn a couple "tricks" as well when comparing just two fractions, or when you're sorting top-heavy "improper" fractions like 7/3.
### Method 1 of 3: Ordering Any Number of Fractions
1. 1
Find a common denominator for all the fractions. Use one of these methods to find a denominator, or lower number of a fraction, that you can use to rewrite every fraction in the list, so you can easily compare them. This is called a common denominator, or the lowest common denominator if it is the lowest one possible:[1]
• Multiply every different denominator together. For example, if you are comparing 2/3, 5/6, and 1/3, multiply the two different denominators: 3 x 6 = 18. This is a simple method, but will often result in a much larger number than the other methods, which can be difficult to work with.
• Or list the multiples of each denominator in a separate column, until you notice a number that shows up on every column. Use this number. For example, comparing 2/3, 5/6, and 1/3, list a few multiples of 3: 3, 6, 9, 12, 15, 18. Then list the multiples of 6: 6, 12, 18. Since 18 shows up on both lists, use that number. (You could also use 12, but the examples below will assume you are using 18.)
2. 2
Convert each fraction so it uses the common denominator. Remember, if you multiply a fraction's top and bottom by the same amount, the fraction is still the same size. Use this technique on each fraction, one by one, so that each one uses the common denominator as the bottom number. Try it for 2/3, 5/6, and 1/3, using the common denominator 18:
• 18 ÷ 3 = 6, so 2/3 = (2x6)/(3x6)=12/18
• 18 ÷ 6 = 3, so 5/6 = (5x3)/(6x3)=15/18
• 18 ÷ 3 = 6, so 1/3 = (1x6)/(3x6)=6/18
3. 3
Use the top number to order the fractions. Now that they all have the same denominator, the fractions are easy to compare. Use their top number, or numerator, to rank them from least to greatest. Ranking the fractions we found above, we get: 6/18, 12/18, 15/18.
4. 4
Return each fraction to its original form. Keep the fractions in the same order, but return each one back to its original form. You can do this by remembering how each fraction transformed, or by dividing the top and bottom of each fraction again:
• 6/18 = (6 ÷ 6)/(18 ÷ 6) = 1/3
• 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3
• 15/18 = (15 ÷ 3)/(18 ÷ 3) = 5/6
• The answer is "1/3, 2/3, 5/6"
### Method 2 of 3: Ordering Two Fractions using Cross-Multiplication
1. 1
Write the two fractions next to each other. For example, compare the fraction 3/5 and the fraction 2/3. Write these next to each other on the page: 3/5 on the left, and 2/3 on the right.
2. 2
Multiply the top of the first fraction with the bottom of the second fraction. In our example, the top number, or numerator, of the first fraction (3/5) is 3. The bottom number, or denominator, of the second fraction (2/3) is also 3. Multiply these together: 3 x 3 = ?
• This method is called cross-multiplication, because you multiply numbers in a diagonal line across from each other.
3. 3
Write your answer next to the first fraction. Write the product, or answer to your multiplication problem, next to the first fraction on the page. In our example, 3 x 3 = 9, so you would write 9 next to the first fraction, on the left side of the page.
4. 4
Multiply the top of the second fraction with the bottom of the first. To find out which fraction is larger, we'll need to compare our answer above with the answer to another multiplication problem. Multiply these two numbers together. For our example (comparing 3/5 and 2/3), multiply 2 x 5 together.
5. 5
Write this answer next to the second fraction. Write the answer to this second multiplication problem next to the second fraction. In this example, the answer is 10.
6. 6
Compare the values of the two cross-products. The answers to the multiplication problems in this method are called cross-products. If one cross-product is larger than the other, then the fraction next to that cross-product is also larger than the other fraction. In our example, because 9 is less than 10, this means 3/5 must be less than 2/3.
• Remember, always write the cross-product next to the fraction whose top number you used.
7. 7
Understand why this works. To compare two fractions, typically you transform them to give them the same denominator, or lower part of the fraction. Secretly, this is what cross-multiplication does![2] It just skips over actually writing the denominators, since once the two fractions have the same one, you only need to compare the top two numbers. Here's our same example (3/5 vs 2/3), written without the cross-multiplying "shortcut":
• 3/5=(3x3)/(5x3)=9/15
• 2/3=(2x5)/(3x5)=10/15
• 9/15 is less than 10/15
• Therefore, 3/5 is less than 2/3
### Method 3 of 3: Ordering Fractions Larger than One
1. 1
Use this for fractions with a top number equal or larger than the bottom number. If a fraction has a top number, or numerator, that is larger than the bottom number, or denominator, it is larger than one. 8/3 is one example of this type of fraction. You can also use this for fractions with an equal numerator and denominator, such as 9/9. Both of these fractions are examples of improper fractions.[3]
• You can still use the other methods for these fractions. This method helps these fractions make sense, however, and might be faster.
2. 2
Convert each improper fraction into a mixed number. Turn them into a mix of whole numbers and fractions. Sometimes, you might be able to do this in your head. For example, 9/9 = 1. Other times, use long division to find out how many times the numerator goes evenly into the denominator. The remainder in that long division problem, if any, gets "left over" as a fraction. For instance:
• 8/3 = 2 + 2/3
• 9/9 = 1
• 19/4 = 4 + 3/4
• 13/6 = 2 + 1/6
3. 3
Sort the mixed numbers by whole number. Now that there are no improper fractions, you have a better idea of how large each number is. Ignore the fractions for now, and sort the fractions into groups by whole number:
• 1 is the smallest
• 2 + 2/3 and 2 + 1/6 (we don't yet know which is larger than the other)
• 4 + 3/4 is the largest
4. 4
If necessary, compare the fractions in each group. If you have multiple mixed numbers with the same whole number, such as 2 + 2/3 and 2 + 1/6, compare the fraction part of the number to see which is larger. You can use any of the methods in the other sections to do this. Here's an example comparing 2 + 2/3 and 2 + 1/6, converting the fractions to the same denominator:
• 2/3 = (2x2)/(3x2) = 4/6
• 1/6 = 1/6
• 4/6 is greater than 1/6
• 2 + 4/6 is greater than 2 + 1/6
• 2 + 2/3 is greater than 2 + 1/6
5. 5
Use your results to sort your whole list of mixed numbers. Once you've sorted the fractions in each group of mixed numbers, you can sort your entire list: 1, 2 + 1/6, 2 + 2/3, 4 + 3/4.
6. 6
Convert the mixed numbers back to their original fractions. Keep the order the same, but undo the changes you made and write the numbers as the original improper fractions: 9/9, 8/3, 13/6, 19/4.
## Community Q&A
Search
• Question
Which is the lowest: 3/5, 3/4, 4/7, or 2/3?
Jasmine Tipping
4/7 is the lowest, then 3/5, 2/3 and 3/4.
• Question
Can I convert them into decimals while ordering them?
Yes you can, the order will be the same. Just make sure to convert back to fractions for your final answer if the original numbers are given as fractions.
• Question
How do I order fractions from least to greatest if the denominators are different?
Make them the same by multiplying both the numerator and the denominator of the smallest fraction, and if necessary, the largest one as well. For instance if you have 1/5 and 3/7, they are equivalent to 7/35 and 15/35 [ (7*1)/(7*5) and (5*3)/(5*7).
• Question
How can I put 2/3, 4/5, and 1/2 from least to greatest?
The smallest fraction is 1/2, then 2/3, then 4/5.
• Question
I have two equal fractions in a set. How should I arrange them?
Donagan
If you're ordering from least to greatest (or vice versa), list the equal fractions consecutively. You might want to list the fraction with the smaller denominator first, but it really wouldn't make any difference in terms of value.
• Question
How can I arrange 1/5, 2/3, and 5/8 from least to greatest?
LyKaxandra Caimoy
You can try dividing it (or converting to decimal). Then you can start arranging it ascending. Also, you can try to find its LCD. If you do so, you will get 120. The fractions then will be 24/120, 80/120, and 75/120. If arranged: 24/120, 75/120, 80/120 or "1/5, 5/8, 2/3"
• Question
What is an easy way of ordering fractions with the same numerator?
Donagan
Look at the denominators. The fraction with the smaller denominator has a value greater than the fraction with the larger denominator.
• Question
How do I find out the percentage of the fraction?
To use an example, use 3 over 5, so take the top number and divide it by the bottom number and multiply it by 100. That will give you the percentage.
• Question
What do I do if my answers don't match?
LyKaxandra Caimoy
• Question
How do I do it with a mixed number, for example 8 2/3?
WOOHP
26/3
• How do I order fractions without doing the least common denominator?
• How do I order fractions if they have 3 different denominators?
200 characters left
## Tips
• If the numerators are all the same, you can sort in reverse order of denominator. For instance, 1/8 < 1/7 < 1/6 < 1/5. Think of it as a pizza: if you go from 1/2 to 1/8, you're cutting the pizza into 8 slices instead of 2, and the 1 slice you get is now much smaller.
Thanks!
• When ordering a large number of fractions, it may be helpful to compare and order smaller groups of 2, 3, or 4 fractions at a time.
Thanks!
• While finding the lowest common denominator is helpful so you can work with smaller numbers, any common denominator will work. Try sorting 2/3, 5/6, and 1/3 using a common denominator of 36, and see if you get the same result.
Thanks!
wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 33 people, some anonymous, worked to edit and improve it over time. Together, they cited 6 references. This article has also been viewed 517,775 times.
Co-authors: 33
Updated: January 16, 2020
Views: 517,775
Categories: Fractions
Article SummaryX
To order fractions from least to greatest, start by finding the lowest common denominator for all of the fractions. Next, convert each of the fractions by dividing the lowest common denominator by the denominator and then multiplying the top and bottom of the fraction by your answer. Once all of the fractions have the same denominator, order them from least to greatest using the numerators. To learn how to order fractions that are greater than 1, scroll down! | 3,151 | 11,231 | {"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} | 4.75 | 5 | CC-MAIN-2020-05 | latest | en | 0.908469 |
https://www.traditionaloven.com/metal/precious-metals/gold/convert-grain-gr-of-gold-to-cubic-millimetre-mm3-gold.html | 1,713,527,532,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817398.21/warc/CC-MAIN-20240419110125-20240419140125-00277.warc.gz | 949,658,998 | 13,615 | Gold grain to cubic millimeters of gold converter
gold conversion
Amount: grain (gr) of gold mass Equals: 3.36 cubic millimeters (mm3) in gold volume
Calculate cubic millimeters of gold per grain unit. The gold converter.
TOGGLE : from cubic millimeters into grains in the other way around.
Enter a New grain Amount of gold to Convert From
* Enter whole numbers, decimals or fractions (ie: 6, 5.33, 17 3/8)
gold from grain to cubic millimeter Conversion Results :
Amount : grain (gr) of gold
Equals: 3.36 cubic millimeters (mm3) in gold
Fractions: 3 9/25 cubic millimeters (mm3) in gold
CONVERT : between other gold measuring units - complete list.
Solid Pure 24k Gold Amounts
This calculator tool is based on the pure 24K gold, with Density: 19.282 g/cm3 calculated (24 karat gold grade, finest quality raw and solid gold volume; from native gold, the type we invest -in commodity markets, by trading in forex platform and in commodity future trading. Both the troy and the avoirdupois ounce units are listed under the gold metal main menu. I advice learning from a commodity trading school first. Then buy and sell.) Gold can be found listed either in table among noble metals or with precious metals.
Is it possible to manage numerous calculations for how heavy are other gold volumes all on one page? Yes, all in one Au multiunit calculator makes it possible managing just that.
Convert gold measuring units between grain (gr) and cubic millimeters (mm3) of gold but in the other direction from cubic millimeters into grains.
conversion result for gold: From Symbol Equals Result To Symbol 1 grain gr = 3.36 cubic millimeters mm3
Precious metals: gold conversion
This online gold from gr into mm3 (precious metal) converter is a handy tool not just for certified or experienced professionals. It can help when selling scrap metals for recycling.
Other applications of this gold calculator are ...
With the above mentioned units calculating service it provides, this gold converter proved to be useful also as a teaching tool:
1. in practicing grains and cubic millimeters ( gr vs. mm3 ) exchange.
2. for conversion factors training exercises with converting mass/weights units vs. liquid/fluid volume units measures.
3. work with gold's density values including other physical properties this metal has.
International unit symbols for these two gold measurements are:
Abbreviation or prefix ( abbr. short brevis ), unit symbol, for grain is: gr
Abbreviation or prefix ( abbr. ) brevis - short unit symbol for cubic millimeter is: mm3
One grain of gold converted to cubic millimeter equals to 3.36 mm3
How many cubic millimeters of gold are in 1 grain? The answer is: The change of 1 gr ( grain ) unit of a gold amount equals = to 3.36 mm3 ( cubic millimeter ) as the equivalent measure for the same gold type.
In principle with any measuring task, switched on professional people always ensure, and their success depends on, they get the most precise conversion results everywhere and every-time. Not only whenever possible, it's always so. Often having only a good idea ( or more ideas ) might not be perfect nor good enough solutions. Subjects of high economic value such as stocks, foreign exchange market and various units in precious metals trading, money, financing ( to list just several of all kinds of investments ), are way too important. Different matters seek an accurate financial advice first, with a plan. Especially precise prices-versus-sizes of gold can have a crucial/pivotal role in investments. If there is an exact known measure in gr - grains for gold amount, the rule is that the grain number gets converted into mm3 - cubic millimeters or any other unit of gold absolutely exactly. It's like an insurance for a trader or investor who is buying. And a saving calculator for having a peace of mind by knowing more about the quantity of e.g. how much industrial commodities is being bought well before it is payed for. It is also a part of savings to my superannuation funds. "Super funds" as we call them in this country.
Conversion for how many cubic millimeters ( mm3 ) of gold are contained in a grain ( 1 gr ). Or, how much in cubic millimeters of gold is in 1 grain? To link to this gold - grain to cubic millimeters online precious metal converter for the answer, simply cut and paste the following.
The link to this tool will appear as: gold from grain (gr) to cubic millimeters (mm3) metal conversion.
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### Speed of Bullet
Q- A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T, as shown. Derive a formula for the bullet speed v in terms of D, T and a measured angle θ between the position of the hole in the first disk and that of the hole in the second. Both of the holes lie at the same radial distance from the shaft.
Solution: | 150 | 541 | {"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-2024-18 | latest | en | 0.926187 |
https://www.researchgate.net/profile/Ljuben-Mutafchiev | 1,702,089,196,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100781.60/warc/CC-MAIN-20231209004202-20231209034202-00100.warc.gz | 1,047,714,358 | 58,795 | Ljuben R. MutafchievAmerican University in Bulgaria · Mathematics and Science
Professor Dr.Sci and Ph.D
79
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Citations
Introduction
I am interested in asymptoric enumeration results for partitions (restricted and unrestricted) of large integers. I am especially interested in probabilistic limit theorems and asymptotics of moments of certain particular integer partition statistics. To study this kind of problems, I am more or less focused on the application of various generating function identities and the saddle point method.
July 2001 - present
Position
• Professor Emeritus
March 1977 - present
Position
• Professor (Full)
Description
• part-time position
Education
September 1967 - July 1972
Field of study
Publications
Publications (79)
Preprint
Full-text available
Let Tn be the set of all mappings T : {1, 2,. .. , n} → {1, 2,. .. , n}. The corresponding graph of T is a union of disjoint connected unicyclic components. We assume that each T ∈ Tn is chosen uniformly at random (i.e., with probability n −n). The cycle of T contained within its largest component is called the deepest one. For any T ∈ Tn, let νn =...
Preprint
Full-text available
Let $\mathcal{T}_n$ be the set of all mappings $T:\{1,2,\ldots,n\}\to\{1,2,\ldots,n\}$. The corresponding graph of $T$ is aunion of disjoint connected unicyclic components. We assume that each $T\in\mathcal{T}_n$ is chosen uniformly at random (i.e., with probability $n^{-n}$). The deepest cycle of $T$ is contained within its largest component. Let...
Article
Пусть $p(n)$ - количество всех целочисленных разбиений положительного целого числа $n$, и пусть $\lambda$ - разбиение, выбранное случайно и равновероятно из всех таких $p(n)$ разбиений. Известно, что каждое разбиение $\lambda$ имеет единственное графическое представление, состоящее из $n$ неперекрывающихся ячеек на плоскости, называемое диаграммо...
Preprint
Full-text available
Let $A$ be a set of natural numbers and let $S_{n,A}$ be the set of all permutations of $[n]=\{1,2,...,n\}$ with cycle lengths belonging to $A$. Furthermore, let $\mid A(n)\mid$ denote the cardinality of the set $A(n)=A\cap [n]$. The limit $\rho=\lim_{n\to\infty}\mid A(n)\mid/n$ (if it exists) is called the density of set $A$. It turns out that, as...
Preprint
Full-text available
Let $A$ be a set of natural numbers and let $S_{n,A}$ be the set of all permutations of $[n]=\{1,2,...,n\}$ with cycle lengths belonging to $A$. For $A(n)=A\cap [n]$, the limit $\rho=\lim_{n\to\infty}\mid A(n)\mid/n$ (if it esists) is usually called the density of set $A$. (Here $\mid B\mid$ stands for the cardinality of the set $B$.) Several studi...
Preprint
Full-text available
We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the positive integer $n$, introduced by Stanley in 1973. We derive generating functions and determine the asymptotic be...
Article
Full-text available
We study the asymptotic behavior of the maximal multiplicity $M_n=M_n(\sigma)$ of the block sizes in a set partition $\sigma$ of $[n]=\{1,2,....,n\}$, assuming that $\sigma$ is chosen uniformly at random from the set of all such partitions. It is known that, for large $n$, the blocks of a random set partition are typically of size $W=W(n)$, with \$W...
Preprint
Full-text available
We study the asymptotic behavior of the maximal multiplicity Mn = Mn(σ) of the blocks in a set partition of [n] = {1, 2, ..., n}, assuming that σ is chosen uniformly at random from the set of all such partitions. Let W = W (n) be the unique positive root of the equation W e W = n and let fn be the fractional part of W (n). Furthermore, let Rn = W W...
Preprint
Full-text available
Let p(n) be the number of all integer partitions of the positive integer n and let λ be a partition, selected uniformly at random from among all such p(n) partitions. It is known that each partition λ has a unique graphical representation, composed by n non-overlapping cells in the plane called Young diagram. As a second step of our sampling experi...
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https://socialsci.libretexts.org/Bookshelves/Psychology/Biological_Psychology/Applied_Event-Related_Potential_Data_Analysis_(Luck)/10%3A_Scoring_and_Statistical_Analysis_of_ERP_Amplitudes_and_Latencies/10.06%3A_Exercise-_Peak_Amplitude | 1,716,800,449,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059039.52/warc/CC-MAIN-20240527083011-20240527113011-00018.warc.gz | 437,123,713 | 31,172 | # 10.6: Exercise- Peak Amplitude
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For the first couple decades of ERP research, the primary way of scoring ERP amplitudes was to find the peak voltage during the measurement window (either the most positive voltage for a positive peak or the most negative voltage for a negative peak). This approach was used initially because ERPs were processed using primitive computers that created a printout of the waveform, and researchers could easily determine the peak amplitude from the printout using a ruler (see Donchin & Heffley, 1978). This tradition persisted long after more sophisticated computers and software were available, but in many ways the peak voltage is a terrible way of scoring the amplitude of an ERP component. Mean amplitude is almost always superior. I provide a long list of the shortcomings of peak amplitude and the benefits of mean amplitude in Chapter 9 of Luck (2014). More generally, peaks are highly overrated in ERP research. Why should we care when the voltage reaches a maximum? Chapter 2 of Luck (2014) explains why peaks can be very misleading, even when they’re measured well. Mean amplitude is now much more common than peak amplitude in most ERP research areas, but there are some areas where peak amplitude is still common.
In this exercise, we’ll repeat the analyses from the previous exercise except that we’ll measure peak amplitude instead of mean amplitude. And then you’ll see for yourself some of the shortcomings of peak amplitude.
Make sure that the 40 ERPsets from the previous exercise (from the Chapter_10 > Data > ERPsets_CI_Diff folder) are loaded. Launch the Measurement Tool, and set it up as shown in Screenshot 10.3. As in the previous exercise, we want to see if there is a contralateral negativity for the Compatible condition and a contralateral positivity for the Incompatible condition. We therefore need to look for a negative peak for Bin 1 and a positive peak for Bin 2. This will take two steps. Screenshot 10.3 is set up for finding the negative peak in Bin 1. (Technically, we’ll find the local peak, defined in this example as the most negative point that is also more negative than the 3 points on either side; for details, see in Chapter 9 in Luck, 2014).
Once you have all the parameters set, click the Viewer button to verify that everything is working as intended. You should immediately see a problem: As shown in Screenshot 10.4, the peak of the LRP falls outside the measurement window for the first participant. And this isn’t an isolated incident; you’ll see the same problem for the 2nd and 3rd participants (and many others as well). This makes sense if you look at the grand average waveforms in Figure 10.2.C. In general, you need a wider window to find peaks than you need for mean amplitude.
To fix this, click the Measurement Tool button in the Viewer tool, and then change the Measurement Window to 150 400. Then click the Viewer button to see the waveforms again. You should see that the algorithm is now correctly finding the peak for every participant who has a clear peak. Go back to the Measurement Tool and click RUN to save the scores to a file named negative_peak_bin1.txt.
Now repeat the measurement for the positive peak in Bin 2. Leave the window at 150 400, but change Negative to Positive, change the bin from 1 to 2, and change the filename to positive_peak_bin2.txt. Make sure everything looks okay in the Viewer and then click RUN to save the scores.
Now perform the same t tests as you did in the previous exercise on these peak amplitude values (which may first require combining the scores into a single spreadsheet). You should see that the mean across participants is -3.23 µV for the Compatible condition and +1.46 µV for the Incompatible condition and that the difference between conditions is significant (t(39) = -16.34, p < .001). Also, the mean across participants is significantly less than zero for the Compatible condition (t(39) = -18.61, p < .001) and significantly greater than zero for the Incompatible condition (t(39) = 8.71, p < .001).
But this is a completely invalid way of analyzing these data! First, the positive peak for the Incompatible trials is much earlier than the negative peak for the Compatible trials, and it doesn’t usually make sense to compare voltages at different time points. Second, peak amplitude is a biased measure that will tend to be greater than zero for positive peaks and less than zero for negative peaks even if there is only noise in the data.
To see this bias, let’s repeat the analyses, but with a measurement window of -100 0 (i.e., the last 100 ms of the prestimulus baseline period). There shouldn’t be any real differences prior to the onset of the stimuli, and any differences we see must be a result of noise. To see this, find the negative peak between -100 and 0 ms for Bin 1 and the positive peak between -200 and 0 ms for Bin 2. Then repeat the t tests with these scores.
You should see that the mean across participants is -0.89 µV for the Compatible condition and +1.04 µV for the Incompatible condition. You should also see that the difference between conditions is significant (t(39) = -13.27, p < .001). Also, the mean across participants is significantly less than zero for the Compatible condition (t(39) = -12.50, p < .001) and significantly greater than zero for the Incompatible condition (t(39) = 11.30, p < .001). Thus, we get large and significant differences in peak amplitude between conditions during the baseline period, and each condition is significantly different from zero, even though there is only noise during this period. These are bogus-but-significant effects that a result of the fact that peak amplitude is a biased measure.
I hope it is clear why this happened. If you look at the baseline period of the single-participant waveforms with the Viewer, you’ll see that the noise in the baseline is typically positive at some time points and negative at others. That’s what you’d expect for random variations in voltage. If we take the most positive point in the period from -100 to 0 ms, it will almost always be greater than zero. If we take the most negative point in this period, it will almost always be less than zero. So, noise alone will tend to give us a difference in amplitude between the positive peak and the negative peak, and it will tend to make the positive peak greater than zero and the negative peak less than zero.
It should be clear that it is not ordinarily legitimate to compare a positive peak with a negative peak (because noise alone will cause a difference). And it should also be clear that it is not ordinarily legitimate to test whether an effect is present by comparing a peak voltage to zero (because noise will cause a non-zero voltage).
A related point (which is not shown directly by this example) is that the peaks will tend to be larger when the noise level is higher. This means that it is not ordinarily legitimate to compare peak amplitudes for two conditions that differ in noise level (e.g., standards and deviants in an oddball paradigm), because the averaged ERP waveforms will be noisier for the deviants owing to a smaller number of trials. This can be solved by equating the number of trials in the averaged ERPs for each condition, but that requires throwing away a large number of trials from the more frequent condition. Also, there may be other systematic sources of noise. For example, some electrode sites are noisier than others (because they are closer to EMG sources), and some groups of participants are noisier than others (e.g., patient waveforms are often noisier than control waveforms).
The bottom line is that the peak voltage is not usually the best way to quantify the amplitude of an ERP component. Mean amplitude is much better in the vast majority of cases.
This page titled 10.6: Exercise- Peak Amplitude is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Steven J Luck directly on the LibreTexts platform. | 2,391 | 9,662 | {"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} | 3.8125 | 4 | CC-MAIN-2024-22 | latest | en | 0.379617 |
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# What to look for when solving simultaneous equations? (substitution method). watch
1. Hi there .
Are there any rules for spotting the correct equation to use when solving by the substitution method?
So if you have your two equations. Are there things I should look for that will show me which I should use to sub into the other equation?
Hope that makes sense.
2. (Original post by makin)
Hi there .
Are there any rules for spotting the correct equation to use when solving by the substitution method?
So if you have your two equations. Are there things I should look for that will show me which I should use to sub into the other equation?
Hope that makes sense.
If you're dealing with linear equations only then rearrange an equation to get either or . Doesn't really matter but I'd go for the easiest looking then substitute it in to the other.
If you have a quadratic and a linear, rearrange the linear equation to get or and substitute it into the quadratic.
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July 24, 2013, 04:47 Water flow through a thick orifice - Non axisymmetric streamlines #1 New Member Milan Join Date: Nov 2012 Posts: 14 Rep Power: 7 Hello I am modeling a thick orifice using a "2D" simulation in CFX. Fluid: Water Inlet BC: Velocity (3 m/s) Outlet BC: Static pressure, averaged at the outlet. Details of the Mesh: Mesh.jpg Turbulence model: K-e or SST I am obtaining a non-symmetric streamline at the discharge of the orifice. See the attached pictures: Streamline_K-e.jpg Streamline_SST.jpg This is different from what I expected (fig taken from the literature, Roul 2012). Expected_streamlines.jpg The high velocity stream at the discharge of the coefficient is deflected differently (up or down) depending on the turbulence model. Any suggestions or comments would be greatly appreciated. BTW no experimental results available. Milan References: 2012. Roul. Numerical Modeling of Pressure drop due to Singlephase Flow of Water and Two-phase Flow of Airwater Mixtures through Thick Orifices.
July 24, 2013, 14:30 #2 Senior Member Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 718 Rep Power: 14 Your simulation looks like what I would expect, look up the "coanda effect".
July 25, 2013, 17:46 #3 New Member Milan Join Date: Nov 2012 Posts: 14 Rep Power: 7 Thanks Erik, I learned something new. Do you think that this phenomenon will exist in flow in pipes? Regards Milan
July 25, 2013, 21:12 #4 Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 14,321 Rep Power: 110 Absolutely! It is a general fluid mechanics phenomenon. A fluid jet near a wall will bend and attach itself to the wall. The physics of why it does it is interesting, well worth reading up about.
August 7, 2013, 08:09 #5 New Member Milan Join Date: Nov 2012 Posts: 14 Rep Power: 7 Hello again An update on my problem. I am now doing the simulation with air ideal gas, Inlet BC= normal speed 2.5 m/s, Outlet BC= static pressure 8.35 barg. See below the streamlines for the 3D and 2D simulation, The Coanda effect is not present in the 3D simulation. Streamlines_3D.jpg Streamlines_2D.jpg Has it maybe something to do with the number of elements that I am using?, type of simulation (maybe transient is better than steady state?). The pressure drop calculated with the 2D simulation is significantly smaller (0.02 bar) than the one calculated with the 3D simulation (2.2 bar, in the order of magnitude of experiments). Regards
August 7, 2013, 08:16 #6 Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 14,321 Rep Power: 110 Make sure you are taking into account the thickness of the 2D model when you compare the flowrates. Your 2D model is artificially constraining the simualtion so it does nto surprise me that it is inaccurate. The general question on accuracy is an FAQ: http://www.cfd-online.com/Wiki/Ansys..._inaccurate.3F
August 7, 2013, 09:23 #7 New Member Milan Join Date: Nov 2012 Posts: 14 Rep Power: 7 Hello Glenn, thank you for your prompt answer. The physical problem that I am trying to solve is similar to the 3D geometry shown in the figure. I have inlet and outlet pressures, fluid type (air), inlet temperature, and mass flow. I calculated the inlet normal velocity with the air density at the inlet and the pipe area. Your comment: "Make sure you are taking into account the thickness of the 2D model when you compare the flowrates." I am comparing directly the pressure drop from the 2D and 3D simulation against the experimental value. The results of the 3D simulation give a better match against the experimental data, the 2D simulation is far off. Your comment: "Your 2D model is artificially constraining the simualtion so it does nto surprise me that it is inaccurate." Could you expand a bit more on that?. For pipes (or essentially any device with axisymmetry) and single phase flow I thought it was "standard" practice to simulate either a wedge or a plane with a height equal to the pipe diameter. In this case I would suspect that the difference between the 2D and 3D simulation might be caused by the artificial boundary symmetry condition, that is not capturing what happens in reality in the flow. Thank you for the webpage about accuracy, it is a nice summary (check list) to take into consideration. Regards
August 7, 2013, 18:28 #8 Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 14,321 Rep Power: 110 You have drawn your 2D flow with a thickness. Just make sure you include the thickness in mass flow/volume flow rate calculations. 2D artificially constrains the flow because it does not allow the flow to move in the Z direction. If the flow is naturally 2D anyway (which low and high Re flows usually are) that is not a problem, but for intermediate Re flows you often get flow oscillations in the Z direction which need to be captured if you want to be accurate. So modelling an intermediate Re flow as 2D would cause inaccuracy.
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http://bitmath.blogspot.com/2013/ | 1,611,193,498,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703522150.18/warc/CC-MAIN-20210121004224-20210121034224-00097.warc.gz | 11,985,556 | 16,342 | ## Saturday, 28 September 2013
### Determining the cardinality of a set described by a mask and bounds
In other words, calculating this $$| \left\{ x | (x \& m) = v \land x \ge a \land x \le b \right\} |$$
A BDD (which haroldbot uses to solve this) has no trouble with that at all, but the structure the problem is so nice that I thought it should be possible to do better. And it is, though the solution I'm about to present is probably far from optimal. I don't know how to significantly improve on it, but I just get a very non-scientific gut-feeling that there should be a fundamentally better way to do it.
The cardinality of the set without the bounds (only the mask) is obviously trivial to compute (as 1 << popcnt(~m)), and the bounds divide that set in three parts: items that are lower than the lower bound ("left part"), items that are higher than the upper bound ("right part")), and items that are actual set of interest ("middle part"). The main idea it is built on is that it's relatively easy to solve the problem if it didn't have a lower bound and the upper bound was a power of two, with a formula roughly similar to the one above. Using that, all the powers of two that fit before lower bound can be counted from high to low, giving the cardinality of the "left part". The same can be done for the "right part", actually in exactly the same way, by complementing the mask and the upper bound. Obviously the cardinality of the "middle part" can be computed from this.
And here's the code. It doesn't like it when the cardinality is 232, and watch out for weird corner cases such as when the lower bound is bigger than the upper bound (why would you even do that?). It usually works, that's about as much as I can say - I didn't prove it correct.
static uint Cardinality(uint m, uint v, uint a, uint b)
{
// count x such that a <= x <= b && (x & m) == v
// split in three parts:
// left = 0 <= x < a
// right = b < x <= -1
// the piece in the middle is (1 << popcnt(~m)) - left - right
uint left = 0;
uint x = 0;
for (int i = 32 - 1; i >= 0; i--)
{
uint mask = 1u << i;
if (x + mask <= a)
{
if ((x - 1 & m & mask2) == (v & mask2))
{
uint amount = 1u << popcnt(~(m | mask2));
left += amount;
}
}
}
uint right = 0;
uint y = 0;
for (int i = 32 - 1; i >= 0; i--)
{
uint mask = 1u << i;
if (y + mask <= ~b)
{
if ((y - 1 & m & mask2) == (~v & m & mask2))
{
uint amount = 1u << popcnt(~(m | mask2));
right += amount;
}
}
}
uint res = (uint)((1UL << popcnt(~m)) - (left + right));
return res;
}
The loops can be merged of course, but for clarity they're separate here.
If you have any improvements, please let me know.
## Saturday, 10 August 2013
### Announcing haroldbot
haroldbot was an ircbot (hence the name) that solves some bitmath problems. The title is actually a lie - haroldbot has been around for a while now. But now it finally got its own website.
haroldbot.nl
Check it out, if you work with bits you will probably find this useful.
## Thursday, 30 May 2013
### Carryless multiplicative inverse
Note: this post is neither about the normal multiplicative inverse, nor the modular multiplicative inverse. This other post has information about the modular multiplicative inverse, which might be what you were looking for.
Mathematicians may call carryless multiplication "multiplication in GF(2^n)", but that doesn't explain how it works - recall the shift-and-add algorithm for multiplication:
static uint mul(uint a, uint b)
{
uint r = 0;
while (b != 0)
{
if ((a & 1) != 0)
r += b;
a >>= 1;
b <<= 1;
}
return r;
}
Carryless multiplication is a very simple variation on that: do the addition without carries. That's just a XOR.
static uint cl_mul(uint a, uint b)
{
uint r = 0;
while (b != 0)
{
if ((a & 1) != 0)
r ^= b; // carryless addition is xor
a >>= 1;
b <<= 1;
}
return r;
}
It has some applications in complicated cryptography related algorithms, but it also seems like this should be an interesting and powerful operation when working with bits, and it may well be, but I know of almost no uses for it (besides, Intel's implementation is so slow that it often wouldn't help Intel made it over twice as fast in Haswell). But anyway, let's just start with its basic properties: like normal multiplication, it's commutative and associative. It's also distributive, but over xor instead of over addition. None of this is very surprising.
As an aside, using associativity, it can be shown that the parallel suffix with XOR (which does have some known uses in bitmath, for example in implementing compress_right in software), code shown below, is equivalent to a carryless multiplication by -1.
// parallel suffix with XOR
x ^= x << 1;
x ^= x << 2;
x ^= x << 4;
x ^= x << 8;
x ^= x << 16;
Every step is clearly a carryless multiplication, by 3, 5, 17, 257, and 65537 respectively. So it's equivalent to:
clmul(clmul(clmul(clmul(clmul(x, 3), 5), 17), 257), 65537) which can be rearranged (using associativity) to:
clmul(x, clmul(clmul(clmul(clmul(3, 5), 17), 257), 65537)) which works out to clmul(x, -1). Of course it was supposed to work out that way, because every bit of the result should be the XOR of all bits up to (and including) that bit, but it's nice that it also follows easily from a basic property. Incidentally if you have a full-width carryless multiplication, multiplying by -1 also computes the parallel prefix with XOR in the upper bits (the upper bit of the low word, which is the parity of the input, is shared by the suffix and the prefix.)
Carryless multiplication also shares an other property with normal multiplication: there are multiplicative inverses modulo 2n (and also modulo other numbers, but 2n is of particular interest since we're working in that by default anyway). Again there are only inverses for odd numbers, and it's equally obvious (as for normal multiplication) why that should be so - an even multiplier will throw out at least one high order bit. First, here's an example of carrlessly multiplying x by -1 and then carrylessly multiplying that by 3.
x = {d}{c}{b}{a} // the letters are bits
y = cl_mul(x, -1) = {d^c^b^a}{c^b^a}{b^a}{a}
z = cl_mulinv(-1) = 0011
cl_mul(y, z) = {d^c^b^a ^ c^b^a}{c^b^a ^ b^a}{b^a ^ a}{a} = {d}{c}{b}{a}
Ok, so that worked out well, and it also gives part the answer to exercise 3 in chapter 5 of Hacker's Delight (about whether parallel prefix/suffix with XOR is invertible and how) because a carryless multiplication by -1 is the same as the parallel suffix with XOR. A carryless multiplication of y by 3 is of course just y ^ (y << 1).
But back to actually computing the inverse. The inverse had better be odd, so bit 0 is already known, and for all the other bits follow these steps
1. if the remainder is 1, stop
2. if bit k is 0, go to step 5
3. set bit k in the inverse
4. xor the remainder with input << k
5. increment k and go to step 1
Step 4 always resets the offending bit because the input had to be odd, so it's obvious that the remainder always ends up being 1 eventually, and so the algorithm always terminates. Moreover, even in the worst case it only has to process every bit but one, and continuing after the remainder becomes 1 simply does nothing, so step 1 could read "if k is 32" (or some other number, depending on how many bits your ints are wide), which is easier to unroll and better suited for a hardware implementation (not that I've seen this operation implemented in hardware anywhere).
For example, in C# it could look like this:
static uint clmulinv(uint x)
{
uint inv = 1;
uint rem = x;
for (int i = 1; i < 32; i++)
{
if (((rem >> i) & 1) != 0)
{
rem ^= x << i;
inv |= 1u << i;
}
}
return inv;
}
A variation of the algorithm to find a multiplicative inverse modulo a power of two (see inv here) also works, which is useful when clmul is fast:
static uint clmulinv(uint d)
{
uint x = 1;
for (int i = 0; i < 5; i++)
{
x = clmul(x, clmul(x, d));
}
return x;
}
The first iteration sets x to d, that can be done immediately to skip an iteration.
Some sample inverses
1 0x00000001
3 0xFFFFFFFF
5 0x55555555
7 0xDB6DB6DB
9 0x49249249
11 0x72E5CB97
13 0xD3A74E9D
15 0x33333333
The definition of clmul at the start of the post was meant to be just that, a faster way to emulate it is this:
static uint clmul(uint a, uint b)
{
uint r = 0;
do
{
r ^= a * (b & (0 - b));
b &= b - 1;
r ^= a * (b & (0 - b));
b &= b - 1;
r ^= a * (b & (0 - b));
b &= b - 1;
r ^= a * (b & (0 - b));
b &= b - 1;
} while (b != 0);
return r;
}
This works by extracting a bit from b and multiplying by it (which just shifts a left), then resetting that bit. This can be unrolled safely since when b == 0, no further changes are made to r automatically. The 0 - b thing is due to an unfortunate misfeature of C#, negating unsigned integers converts it to a long.
A similar trick works for the inverse:
static uint clmulinv(uint x)
{
uint inv = 1;
uint rem = x - 1;
while (rem != 0)
{
uint m = rem & (0 - rem);
rem ^= x * m;
inv += m;
}
return inv;
}
By the way, why is this post so popular? Please let me know in the comments down below.
## Thursday, 11 April 2013
### Improving bounds when some bits have a known value
This problem is closely related the series of problems discussed in calculating the lower bound of the bitwise OR of two bounded variables (and some of the posts after that one), and the algorithm is very closely related, too. The question in this post is, suppose some bits may be known to be zero and some may be known to be one, is there a better lower/upper bound than the given one, and if so, what is it? That is, calculate $$\min _{x \in [a, b] \wedge (x | \sim z) = x \wedge (x \& \sim o) = 0 } x$$ and $$\max _{x \in [a, b] \wedge (x | \sim z) = x \wedge (x \& \sim o) = 0 } x$$ where z is a bitmask containing the bits that are allowed to be 0, and o is a bitmask containing the bits that are allowed to be 1.
The idea behind the algorithms is to do a binary search (the one-sided variant) over the numbers that the masks allow, for the lowest value bigger than or equal to the original lower bound (or smaller than or equal to the original upper bound, for the new upper bound). Just as in the case of propagating bounds through XOR, it may take more than one step, so there aren't many shortcuts. I called them both "reduce" even though ReduceMin actually increases the value, because their purpose is to reduce the range [min, max].
static uint ReduceMin(uint min, uint z, uint o)
{
uint mask = z & o; // note: mask is a subset of r
uint r = o;
uint m = 0x80000000 >> nlz(mask);
while (m != 0)
{
// reset the bit if it can be freely chosen
uint newr = r ^ (m & mask);
if (newr >= min)
// keep the change if still within bounds
r = newr;
m >>= 1;
}
return r;
}
static uint ReduceMax(uint max, uint z, uint o)
{
uint mask = z & o;
uint r = ~z;
uint m = 0x80000000 >> nlz(mask);
while (m != 0)
{
// set the bit if it can be freely chosen
uint newr = r | (m & mask);
if (newr <= max)
// keep the change if still within bounds
r = newr;
m >>= 1;
}
return r;
}
There is one shortcut (that I know of): using nlz on every iteration, thereby skipping iterations where the current bit isn't even changed. With the implementation of nlz I was working with, that wasn't worth it, so whether it's actually a real shortcut or not is up for debate.
Occasionally the new lower bound can be higher than the new upper bound, that means the set of values was actually empty. If you were working with clockwise intervals, that changes to "if the new bounds aren't ordered the same way as the old ones" - ie if the interval was proper and the new one isn't or vice versa, the set is empty. | 3,247 | 11,642 | {"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": 3, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2021-04 | latest | en | 0.95276 |
http://tex.stackexchange.com/questions/tagged/math-operators?sort=votes&pagesize=15 | 1,469,702,151,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257828010.65/warc/CC-MAIN-20160723071028-00142-ip-10-185-27-174.ec2.internal.warc.gz | 243,831,947 | 26,131 | # Tagged Questions
{math-operators} is about operators in math mode. These include sums, integrals and similar, text operators like sin, cos, etc.
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### What's the proper way to typeset a differential operator?
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### Expression under summation on multiple lines [duplicate]
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### Lower and upper Riemann integrals?
How can I make an integral symbol with a bar above it or a bar below it?
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### is there a way to write −= as one symbol in formulas
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### Getting the expectation symbol to behave like $\sum$ instead of $\Sigma$
How can I get an expectation symbol which behaves like $\sum$? Specifically, I want the underscore to be like that of a summation. At the moment I use $$\mathbb{E}_{x\in A}$$ However, I do not ... | 1,036 | 4,167 | {"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": 2, "mathjax_display_tex": 2, "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": 1, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2016-30 | latest | en | 0.882881 |
https://www.jiskha.com/display.cgi?id=1207628057 | 1,503,298,623,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886107720.63/warc/CC-MAIN-20170821060924-20170821080924-00517.warc.gz | 911,587,723 | 3,959 | # geometry
posted by .
I need to find the perimeter of square that has a semicircle (located inside of the square) with a radius of 10 in and it appears that the square is 10 inches as well. I tried the equation 1/2*3.14*10= 15.7, but I don't think it is correct please help!!
• geometry -
If a complete semicircle is inside a square, it could be tangent to one side of the square and end at the midpoints of two adjacent sides. It would then have a radius of 10, the side of the square would be 20 long and the square's perimeter would be 80.
• geometry -
I still don't quite understand.
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Amount Of House I Can Afford Once you know how much you can borrow add to that your down payment to calculate the maximum house price you can afford. In this example, the maximum loan amount is calculated at \$203,000. If you have a \$20,000 down payment, you can purchase a \$223,000 house.How Much Is The House How much does it cost to build a house? According to data from the National Association of Home Builders, the median price of constructing a single-family home is \$289,415, or \$103 per square foot.
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https://studyres.com/doc/1175406/5.9-the-689599.7-rule-for-normal-distributions-according-... | 1,713,664,112,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817699.6/warc/CC-MAIN-20240421005612-20240421035612-00714.warc.gz | 506,975,041 | 8,690 | # Download 5.9 The 689599.7 Rule for Normal Distributions According to the 68
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```5.9 The 689599.7 Rule for Normal Distributions
According to the 689599.7 rule, in any normal distribution:
• About 68% of the observations fall within one standard deviation of the mean.
• About 95% of the observations fall within two standard deviations of the mean.
• About 99.7% of the observations fall within three standard deviations of the mean.
By remembering these three numbers, you can think about normal distributions without making detailed calculations. The figure below illustrates the 689599.7 rule. Note that the Greek letter μ is used for the mean, and the Greek letter σ is used for the standard deviation.
Example: Suppose the mean (μ) of a normal distribution is 70, and the standard deviation (σ) is 10. Determine the range of values that fall in the middle 68%, the middle 95%, and the middle 99.7%.
1
Example 2: The heights of American women 1824 years old fit the normal distribution with a mean (μ) of 64.5" and a standard deviation (σ) of 2.5". a) In what range of heights do the middle 68% of American women's heights fall?
b) In what range do the middle 95% fall?
c) What percent of American women are taller than 69.5"?
d) What percent of American women are shorter than 62"?
Example 3: The distribution of scores on the SAT college entrance exam is close to normal, with a mean μ = 500 and a standard deviation σ = 100. a) How high must a student score to fall in the top 25%?
b) What percent of scores fall between 200 and 800?
c) What percent of scores are above 700?
Homework: p. 205: 45-48 (Use handout to help.)
2
```
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Help students learn the academic vocabulary and symbols used to record the results of comparing two three-digit numbers. This lesson can be used as a stand-alone activity or prior to Greater Than, Less Than: Comparing Three-Digit Numbers.
Math
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Two Corners: Odd or Even
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Two Corners: Odd or Even
Get students moving around the classroom as they learn about odd and even numbers. Students classify real world objects as odd or even and take turns playing the game master, coming up with numbers to evaluate.
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Place Value Surfboards
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Place Value Surfboards
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What Do You Notice?
Laminate and display this puzzle to encourage students to think deeply about how each group of circles is the same and different. This works as a great hook when introducing the concept of odd and even numbers.
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Vocabulary Cards: Money Values
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Vocabulary Cards: Money Values
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Odd Numbers: 101-161
In this 2nd grade math worksheet, your child will practice writing odd numbers and counting by 2 from 101 to 161 as he writes the missing numbers in the spaces.
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Skip Count at the Dot-to-Dot Zoo
This hidden animal at the Dot-to-Dot Zoo is 'hopping' to meet you. Kids will skip count by fours to reveal a hidden kangaroo.
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Children learn how to compare numbers using the greater than and less than symbols in this cheerful 2nd grade addition worksheet.
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Skip Counting Fun #4
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Skip Counting Fun #4
Who doesn't like a land full of candy? Count by tens as you hop through candy land on the gumdrops. Skip-counting provides a great intro to multiplication.
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Even Numbers: 90-150
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Even Numbers: 90-150
In this 2nd grade math worksheet, your child will practice writing even numbers and counting by 2 from 90 to 150 as he writes the missing numbers in the spaces.
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Odd Person Out
Get students moving around the classroom as they learn about odd and even numbers. Students play a game similar to "musical chairs" as they consider the results for even and odd numbers of students.
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Coin Op II
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Coin Op II
Looking for a worksheet that practices coin counting skills? This printable will get your kid's counting skills up to top dollar!
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Add the 10s First! (Part One)
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Add the 10s First! (Part One)
In this worksheets, learn how to add the tens first when using a hundreds chart.
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"Skipping" Breakfast
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"Skipping" Breakfast
Use skip counting to connect the dots and finish a picture of Franco's breakfast.
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Vocabulary Cards: Understanding Place Value
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Vocabulary Cards: Understanding Place Value
Use these vocabulary cards with the EL Support Lesson Plan: Understanding Place Value.
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Counting Check-in
Use this check-in to assess your students’ abilities to count two-digit and three-digit numbers within 120.
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Digging Digits: Practice Place Value #2
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Digging Digits: Practice Place Value #2
Does your second grader need some help with place values? Check out this brightly-colored, fun worksheet that explores numbers up to four digits long.
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Glossary: Base-Ten Blocks
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Glossary: Base-Ten Blocks
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Place Value Seashells
Match the numbers with their written out forms on this math worksheet. Your child can brush up on place values as well as gain mastery of the base 10 system.
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Skip Counting Eagle
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Chinese New Year: Count the Foods
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Learning Place Value: Bubbles!
In this second grade math worksheet, your child will learn about place value and practice reading and writing whole numbers up to the thousands. | 1,038 | 4,578 | {"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} | 3.6875 | 4 | CC-MAIN-2020-50 | latest | en | 0.887289 |
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#### Resources tagged with Multiplication & division similar to Unlocking the Case:
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### There are 165 results
Broad Topics > Calculations and Numerical Methods > Multiplication & division
### Like Powers
##### Stage: 3 Challenge Level:
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
### Slippy Numbers
##### Stage: 3 Challenge Level:
The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.
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Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .
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##### Stage: 2 Challenge Level:
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
### X Marks the Spot
##### Stage: 3 Challenge Level:
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
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##### Stage: 3 Challenge Level:
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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##### Stage: 3 Challenge Level:
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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##### Stage: 2 Challenge Level:
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
### As Easy as 1,2,3
##### Stage: 3 Challenge Level:
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
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This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
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If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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Find the next number in this pattern: 3, 7, 19, 55 ...
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##### Stage: 2 Challenge Level:
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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##### Stage: 1 and 2 Challenge Level:
This problem is designed to help children to learn, and to use, the two and three times tables.
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##### Stage: 1 and 2 Challenge Level:
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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##### Stage: 2 Challenge Level:
This number has 903 digits. What is the sum of all 903 digits?
### Mobile Numbers
##### Stage: 1 and 2 Challenge Level:
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
### Carrying Cards
##### Stage: 2 Challenge Level:
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
### Number Tracks
##### Stage: 2 Challenge Level:
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
### Exploring Wild & Wonderful Number Patterns
##### Stage: 2 Challenge Level:
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
### Numbers Numbers Everywhere!
##### Stage: 1 and 2
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
### A One in Seven Chance
##### Stage: 3 Challenge Level:
What is the remainder when 2^{164}is divided by 7?
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##### Stage: 2 Challenge Level:
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
### Multiplication Squares
##### Stage: 2 Challenge Level:
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
### Napier's Bones
##### Stage: 2 Challenge Level:
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
### All the Digits
##### Stage: 2 Challenge Level:
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
### Skeleton
##### Stage: 3 Challenge Level:
Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.
### Remainders
##### Stage: 3 Challenge Level:
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
### Remainders
##### Stage: 2 Challenge Level:
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
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##### Stage: 2 Challenge Level:
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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##### Stage: 2 Challenge Level:
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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##### Stage: 2 Challenge Level:
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
### Difficulties with Division
##### Stage: 1 and 2
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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##### Stage: 2 Challenge Level:
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
### The Pied Piper of Hamelin
##### Stage: 2 Challenge Level:
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
### Tom's Number
##### Stage: 2 Challenge Level:
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
### Current Playing with Number Upper Primary Teacher
##### Stage: 2 Challenge Level:
Resources to support understanding of multiplication and division through playing with number.
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##### Stage: 2 Challenge Level:
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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##### Stage: 2 Challenge Level:
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
### Make 100
##### Stage: 2 Challenge Level:
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
### Book Codes
##### Stage: 2 Challenge Level:
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
### X Is 5 Squares
##### Stage: 2 Challenge Level:
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
### What's My Weight?
##### Stage: 2 Short Challenge Level:
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
### A Conversation Piece
##### Stage: 2 Challenge Level:
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
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##### Stage: 2 Challenge Level:
What is happening at each box in these machines?
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##### Stage: 2 Challenge Level:
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
### Learning Times Tables
##### Stage: 1 and 2 Challenge Level:
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
### Highest and Lowest
##### Stage: 2 Challenge Level:
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
### Which Is Quicker?
##### Stage: 2 Challenge Level:
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
### Follow the Numbers
##### Stage: 2 Challenge Level:
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules. | 2,313 | 9,733 | {"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} | 3.875 | 4 | CC-MAIN-2017-34 | latest | en | 0.87617 |
http://www.ehow.co.uk/how_5304187_calculate-interest-rate-monthly-endowment.html | 1,490,421,867,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218188824.36/warc/CC-MAIN-20170322212948-00629-ip-10-233-31-227.ec2.internal.warc.gz | 464,619,055 | 17,291 | # How to Calculate the Interest Rate of a Monthly Endowment
Written by paul dohrman
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Suppose the principal of an endowment is known, along with the monthly payment amount, and how many years it is expected to run. How does one therefore calculate the interest rate that the principal is earning, to be able to finance the monthly distributions?
Unfortunately, the formula that relates interest rate to the number of periodic payments and endowment amount is only solvable with a computer, except in the special case of an endowment paying in perpetuity. Fortunately, financial calculators and spreadsheets can perform this task.
Skill level:
Easy
### Things you need
• Financial calculator
## Instructions
1. 1
Enter the endowment amount. Press the "Minus" sign, then press the "PV" key. This will enter the endowment amount as a present value, effectively treating the endowment amount as an outstanding loan being paid down. It is negative, so the future value is zero after making positive payments.
2. 2
Enter the number of years left in the endowment payments. Multiply this number by 12 to get the number of monthly payments left. Hit the "Equals" sign. Then press the "N" key to enter this number as the number of remaining monthly payments.
3. 3
Enter the monthly amount paid out by the endowment. Press the "PMT" key.
4. 4
Press the "CMPT" key, then the "i" key; the CMPT key need not be held down when pressing the I key. The screen will then go blank for a second while the calculator performs the numerical computation. The result will be the monthly interest rate. To get the annual interest rate, follow Step 5.
5. 5
Compute the annual interest rate by solving (1 + i)^12 = 1 + j. Here, I represents the monthly interest rate calculated in Step 4; j represents the annual interest rate, assuming compounding of interest.
1. 1
Enter the number of payments into cell A1. If payments are monthly, the number of payments, N, is 12 times the number of years the endowment will continue to make payouts.
2. 2
Enter the monthly payment amount into cell A2.
3. 3
Enter the remaining endowment amount into cell A3.
4. 4
Enter the following syntax into A4: = RATE(A1,A2,-A3). This will give you the monthly interest rate.
5. 5
Enter the following into A5: = (1 + A4)^12 -- 1 to get the annual interest rate.
#### Tips and warnings
• The resource titled "How to Calculate Interest Numerically" has computer code for solving for the interest rate. It uses the bisection method of numerical analysis, which is sufficient, and preferable to taking N derivatives for the Newton-Raphson method.
• If the endowment exists in perpetuity, then the above approaches won't work because the number of payments N is infinite. In that case, each monthly payment equals the interest earned in that month by the endowment, i.e., the monthly payment has no principal component. There is no increase or decrease of the endowment amount. Therefore, the formula for the interest rate reduces to a simple formula: interest = monthly payment ÷ endowment amount. Note that this interest is per month; therefore, the annual rate is found by solving (1 + monthly interest rate) ^ 12 = 1 + annual rate, if compounding is performed monthly.
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• Most recent | 791 | 3,412 | {"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-2017-13 | latest | en | 0.924391 |
www.zubrtour.cz | 1,718,871,020,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861916.26/warc/CC-MAIN-20240620074431-20240620104431-00434.warc.gz | 946,269,150 | 15,493 | x came across the channel as it had small bits of FM chapters consolidated by the professor Stephen paris. Some commonly used measures in the field of statistics include: The SEM is calculated using the following formula: In a situation where statisticians are ignorant of the population standard deviation, they use the sample standard deviation as the closest replacement. n The arithmetic mean is the average of a sum of numbers, which reflects the central tendency of the position of the numbers. The formula for the standard error of the mean is: where σ is the standard deviation of the original distribution and N is the sample size (the number of scores each mean is based upon). The standard error is a measure of the standard deviation of some sample distribution in statistics. To keep learning and developing your knowledge of financial analysis, we highly recommend the additional resources below: Become a certified Financial Modeling and Valuation Analyst (FMVA)®FMVA® CertificationJoin 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari by completing CFI’s online financial modeling classes and training program! n = As a result, we need to use a distribution that takes into account that spread of possible Ï's. Therefore, the standard error of the mean is usually estimated by replacing A mathematical tool used in statistics to measure variability, Statistics is a term that is derived from the Latin word status, which means a group of figures that are used to represent information about, Hypothesis Testing is a method of statistical inference. The sampling distribution of a population mean is generated by repeated sampling and recording of the means obtained. Standard Error means the deviation from the actual mean and in a way is similar to Standard Deviation as both are measures of spread with an important difference, that Standard Error is used as a measure to find the deviation between different means of sample and the mean of the population (actual mean) and thus it is a statistic whereas Standard Deviation is a parameter because data of the population is involved. {\displaystyle {\bar {x}}} The true standard deviation {\displaystyle \operatorname {E} (N)=\operatorname {Var} (N)} ", "On the value of a mean as calculated from a sample", "Analysis of Short Time Series: Correcting for Autocorrelation", Multivariate adaptive regression splines (MARS), Autoregressive conditional heteroskedasticity (ARCH), https://en.wikipedia.org/w/index.php?title=Standard_error&oldid=1008558720, Creative Commons Attribution-ShareAlike License, in many cases, if the standard error of several individual quantities is known then the standard error of some. {\displaystyle {\widehat {\sigma _{\bar {x}}}}} This is expected because if the mean at each step is calculated using many data points, then a small deviation in one value will cause less effect on the final mean. If σ n 2 x The difference between the means of two samples, A and B, both randomly drawn from the same normally distributed source population, belongs to a normally distributed sampling distribution whose overall mean is equal to zero and whose standard deviation ("standard error") is equal to. becomes An example of how will have an associated standard error on the mean , The variance of the Sampling Distribution of the Mean is given by where, is the population variance and, n is the sample size. are taken from a statistical population with a standard deviation of N The sample mean deviates from the population and that deviation is … Step 1: Calculate the mean (Total of all samples divided by the number of samples). 1. Calculate standard error of the mean in Excel As you know, the Standard Error = Standard deviation / square root of total number of samples, therefore we can translate it to Excel formula as Standard Error = STDEV (sampling range)/SQRT (COUNT (sampling range)). =SQRT(20*80/(100)+(30*70/(100))) 2. Moreover, statistics concepts can help investors monitor. such that. However, many of the uses of the formula do assume a normal distribution. Moreover, this formula works for positive and negative Ï alike. Standard Error of the Mean The standard error of the mean is the standard deviation of the sampling distribution of the mean. {\displaystyle \sigma } S Standard Error of the Mean (a.k.a. ) If a statistically independent sample of $${\displaystyle n}$$ observations $${\displaystyle x_{1},x_{2},\ldots ,x_{n}}$$ are taken from a statistical population with a standard deviation of $${\displaystyle \sigma }$$, then the mean value calculated from the sample $${\displaystyle {\bar {x}}}$$ will have an associated standard error on the mean $${\displaystyle {\sigma }_{\bar {x}}}$$ given by: are [11]. ( SE Statistics - Standard Error ( SE ) - The standard deviation of a sampling distribution is called as standard error. {\displaystyle n} ¯ The sample variables are denoted by x such that xi refers to the ithvariable of the sample. Standard error can be calculated using the formula below, where σ represents standard deviation and n represents sample size. , σ If a statistically independent sample of {\displaystyle x_{1},x_{2},\ldots ,x_{n}} It is where the standard error of the mean comes into play. If people are interested in managing an existing finite population that will not change over time, then it is necessary to adjust for the population size; this is called an enumerative study. σ x σ Note: The Student's probability distribution is approximated well by the Gaussian distribution when the sample size is over 100. SE is used to estimate the efficiency, accuracy, and consistency of a sample. n x N It can be verified using the SEM formula that if the sample size increases from 10 to 40 (becomes four times), the standard error will be half as big (reduces by a factor of 2). To estimate the standard error of a Student t-distribution it is sufficient to use the sample standard deviation "s" instead of Ï, and we could use this value to calculate confidence intervals. With n = 2, the underestimate is about 25%, but for n = 6, the underestimate is only 5%. =6.08 1. Guide to Standard Error Formula. , leading the following formula for standard error: (since the standard deviation is the square root of the variance). ) x this made it easy for me to look at the chapters i was having trouble with (basically everything lol). {\displaystyle X} {\displaystyle N} , then the mean value calculated from the sample is equal to the standard error for the sample mean, and 1.96 is the approximate value of the 97.5 percentile point of the normal distribution: In particular, the standard error of a sample statistic (such as sample mean) is the actual or estimated standard deviation of the sample mean in the process by which it was generated. Intuitively, as the sample size increases, the sample becomes more representative of the population. It is used to test if a statement regarding a population parameter is correct. If the statistic is the sample mean, it is called the standard error of the mean (SEM).[2]. {\displaystyle {\sigma }_{\bar {x}}} x he standard deviation of the sample mean is σ/n−−√σ/n where σσ is the (population) standard deviation of the data and nn is the sample size - this may be what you're referring to. x 2 ¯ N {\displaystyle \sigma _{x}} It is often used as a parameter, Join 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari, Certified Banking & Credit Analyst (CBCA)®, Capital Markets & Securities Analyst (CMSA)®, Certified Banking & Credit Analyst (CBCA)™, Financial Modeling and Valuation Analyst (FMVA)®, Financial Modeling & Valuation Analyst (FMVA)®, Standard error of a regression coefficient. {\displaystyle n} For example, your sampling range is paced in the Range B1:G4 as below screenshot shown. It is logical to assert that the average marks in sample B will be closer to the average marks of the whole class than the average marks in sample A. It is evident from the mathematical formula of the standard error of the mean that it is inversely proportional to the sample size. It is commonly known by its abbreviated form – SE. with estimator {\displaystyle \sigma } σ SEM can then be calculated using the following formula. 1. ( The formula for standard error can be derived by using the following steps: Step 1: Firstly, collect the sample variables from the population-based on a certain sampling method. {\displaystyle {\bar {x}}} The standard error of the mean will approach zero with the increasing number of observations in the sample, as the sample becomes more and more representative of the population, and the sample mean approaches the actual population mean. Where: s = sample standard deviation x 1, ..., x N = the sample data set x̄. {\displaystyle \sigma } Hypothesis testing. In many practical applications, the true value of Ï is unknown. The standard deviation of the sample data is a description of the variation in measurements, while the standard error of the mean is a probabilistic statement about how the sample size will provide a better bound on estimates of the population mean, in light of the central limit theorem.[8]. From the formula, you’ll see that the sample size is inversely proportional to the standard error. {\displaystyle N=n} {\displaystyle N} , which is the standard error), and the estimator of the standard deviation of the mean ( , reducing the error on the estimate by a factor of two requires acquiring four times as many observations in the sample; reducing it by a factor of ten requires a hundred times as many observations. ^ ¯ x 1 The standard error is, by definition, the standard deviation of The formula for standard error of the mean is equal to the ratio of the standard deviation to the root of sample size. Tim Urdan, author of Statistics in Plain English, demonstrates how to calculate and interpret a standard error of the mean. SE Put simply, the standard error of the sample mean is an estimate of how far the sample mean is likely to be from the population mean, whereas the standard deviation of the sample is the degree to which individuals within the sample differ from the sample mean. However, the mean and standard deviation are descriptive statistics, whereas the standard error of the mean is descriptive of the random sampling process. This forms a distribution of different means, and this distribution has its own mean and variance. Become a certified Financial Modeling and Valuation Analyst (FMVA)® FMVA® Certification Join 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari by completing CFI’s online financial modeling classes and training program! T This often leads to confusion about their interchangeability. Statology Study is the ultimate online statistics study guide that helps you understand all of the core concepts taught in any elementary statistics course and makes your life so much easier as a … x {\displaystyle \operatorname {Var} (T)} . In other words, it is the actual or estimated standard deviation of the sampling distribution of the sample statistic. ( So it is safe to say that the standard error is nothing but the standard deviation of the samplin… , which is the most often calculated quantity, and is also often colloquially called the standard error). Standard errors provide simple measures of uncertainty in a value and are often used because: In scientific and technical literature, experimental data are often summarized either using the mean and standard deviation of the sample data or the mean with the standard error. The equation for the standard error of the mean is the sample standard deviation divided by the square root of the sample size. Thus, the standard error of the mean in sample B will be smaller than that in sample A. X Fortunately, the standard error of the mean can be calculated from a single sample itself. For such samples one can use the latter distribution, which is much simpler. n It enables one to arrive at an estimation of what the standard deviation of a given sample is. It is especially useful in the field of econometrics, where researchers use it in performing regression analyses and hypothesis testingHypothesis TestingHypothesis Testing is a method of statistical inference. Had a test on actuarial science coming up and was dead on all the concepts (had to start from ground zero). Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. {\displaystyle \sigma _{\bar {x}}} The Standard Error of Mean or SEM in Excel measures the deviation of a sample mean from the population mean. The first formula shows how S e is computed by reducing S Y according to the correlation and sample size. certification program, designed to transform anyone into a world-class financial analyst. The effect of the FPC is that the error becomes zero when the sample size n is equal to the population size N. If values of the measured quantity A are not statistically independent but have been obtained from known locations in parameter space x, an unbiased estimate of the true standard error of the mean (actually a correction on the standard deviation part) may be obtained by multiplying the calculated standard error of the sample by the factor f: where the sample bias coefficient Ï is the widely used PraisâWinsten estimate of the autocorrelation-coefficient (a quantity between â1 and +1) for all sample point pairs. The formula for the standard error of the mean in a population is: where σ is the standard deviation and N is the sample size. Small samples are somewhat more likely to underestimate the population standard deviation and have a mean that differs from the true population mean, and the Student t-distribution accounts for the probability of these events with somewhat heavier tails compared to a Gaussian. The descriptive statistics spreadsheet calculates the standard error of the mean for up to 1000 observations, using the function =STDEV(Ys)/SQRT(COUNT(Ys)). , / ¯ The Certified Banking & Credit Analyst (CBCA)® accreditation is a global standard for credit analysts that covers finance, accounting, credit analysis, cash flow analysis, covenant modeling, loan repayments, and more. It can be applied in statistics and economics. , When the sample size is small, using the standard deviation of the sample instead of the true standard deviation of the population will tend to systematically underestimate the population standard deviation, and therefore also the standard error. when the probability distribution is unknown, This page was last edited on 23 February 2021, at 22:48. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … , … From the above definition of Variance, we can write the following equation: has a Poisson distribution, then X with the sample standard deviation σ n ), the standard deviation of the mean itself ( = mean value of the sample data set. Here we discuss the formula for the calculation of standard error of mean with the examples and downloadable excel sheet.. Almost certainly, the sample mean will vary from the actual population mean. n Does this mean that an underlying assumption that population mean is zero is required for this formula to hold true ?I am not sure if I am missing something obvious here..but can't wrap my head around this $\endgroup$ – square_one Aug 23 '14 at 14:47 The following expressions can be used to calculate the upper and lower 95% confidence limits, where 1 to account for the added precision gained by sampling close to a larger percentage of the population. It is denoted by n. Step 3:Next, compute the sample mean which can be derived by dividing the summation of all the variables in the sample (step 1) by the … σ This formula does not assume a normal distribution. is used, is to make confidence intervals of the unknown population mean. {\displaystyle {\bar {x}}} When the sampling fraction is large (approximately at 5% or more) in an enumerative study, the estimate of the standard error must be corrected by multiplying by a ''finite population correction'':[10] Standard Error Formula The standard error is an important statistical measure and it is related to the standard deviation. is simply given by. Therefore, the relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size. is equal to the sample mean, [5] See unbiased estimation of standard deviation for further discussion. {\displaystyle nS_{X}^{2}+n{\bar {X}}^{2}} This is because as the sample size increases, sample means cluster more closely around the population mean. T-distributions are slightly different from Gaussian, and vary depending on the size of the sample. One of the primary assumptions here is that observations in the sample are statistically independent. When the true underlying distribution is known to be Gaussian, although with unknown Ï, then the resulting estimated distribution follows the Student t-distribution. {\displaystyle {\bar {x}}} {\displaystyle \operatorname {SE} } Mathematically, the variance of the sampling distribution obtained is equal to the variance of the population divided by the sample size. Standard errors mean the statistical fluctuation of estimators, and they are important particularly when one compares two estimates (for example, whether one quantity In regression analysis, the term "standard error" refers either to the square root of the reduced chi-squared statistic, or the standard error for a particular regression coefficient (as used in, say, confidence intervals). Standard error increases when standard deviation, i.e. σ {\displaystyle \sigma } 2 Z= 20-30/6.08 2. In other words, it measures how precisely a sampling distribution represents a population. It is used to test if a statement regarding a population parameter is correct. ¯ x x = It can be seen from the formula that the standard error of the mean decreases as N increases. [2] In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean. In such cases, the sample size CFI is the official provider of the Certified Banking & Credit Analyst (CBCA)™CBCA® CertificationThe Certified Banking & Credit Analyst (CBCA)® accreditation is a global standard for credit analysts that covers finance, accounting, credit analysis, cash flow analysis, covenant modeling, loan repayments, and more. 1 The formula given above for the standard error assumes that the sample size is much smaller than the population size, so that the population can be considered to be effectively infinite in size. ¯ x given by:[2]. which is simply the square root of the variance: There are cases when a sample is taken without knowing, in advance, how many observations will be acceptable according to some criterion. σ The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean), or SE. It is also used in inferential statistics, where it forms the basis for the construction of the confidence intervals. It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them. {\displaystyle {\bar {x}}} N ) The standard error (SE)[1][2] of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution[3] or an estimate of that standard deviation. {\displaystyle \operatorname {SE} } x + Let’s derive the above formula. ¯ independent observations from a population with mean While the standard deviation of a sample depicts the spread of observations within the given sample regardless of the population mean, the standard error of the mean measures the degree of dispersion of sample means around the population mean. Standard error is a mathematical tool used in statisticsStatisticsStatistics is a term that is derived from the Latin word status, which means a group of figures that are used to represent information about to measure variability. [9] If the population standard deviation is finite, the standard error of the mean of the sample will tend to zero with increasing sample size, because the estimate of the population mean will improve, while the standard deviation of the sample will tend to approximate the population standard deviation as the sample size increases. observations Suppose a large oil company is drilling wells in various locations throughout Texas, and … {\displaystyle 1/{\sqrt {n}}} E instead: As this is only an estimator for the true "standard error", it is common to see other notations here such as: A common source of confusion occurs when failing to distinguish clearly between the standard deviation of the population ( It is denoted by or Var(X). Cancer mortality in a sample of 100 is 20 per cent and in the second sample of 100 is 30 per cent. x {\displaystyle \sigma _{x}} Standard error formula The standard error of the mean is calculated using the standard deviation and the sample size. ¯ Solution Use the below-given data. (15 points) Let p denote the probability that a newly drilled oil well strikes oil. Standard deviation (SD) measures the dispersion of a dataset relative to its mean. In practice the finite population correction is usually only used if a sample comprises more than about 5-10% of the population. For example, consider the marks of 50 students in a class in a mathematics test. x Step 2: Calculate each measurement's deviation from the mean (Mean minus the individual measurement). Two samples A and B of 10 and 40 observations respectively are extracted from the population. The accuracy of a sample that represents a population is known through this formula. and standard deviation This approximate formula is for moderate to large sample sizes; the reference gives the exact formulas for any sample size, and can be applied to heavily autocorrelated time series like Wall Street stock quotes. N = size of the sample data set Gurland and Tripathi (1971) provide a correction and equation for this effect. The standard error is the standard deviation of the Student t-distribution. However, multiple samples may not always be available to the statistician. of the entire population being sampled is seldom known. Hence the estimator of It is calculated by dividing the standard deviation of the observations in the sample by the square root of the sample size. Hypothesis testing. the standard deviation of the sampling distribution of the sample mean!) When several random samples are extracted from a population, the standard error of the mean is essentially the standard deviation of different sample means from the population mean. Z= -1.64 Evaluate the significance of the contrast in the mortality rate. When a sample of observations is extracted from a population and the sample mean is calculated, it serves as an estimate of the population mean. … For the computer programming concept, see, Independent and identically distributed random variables with random sample size, Standard error of mean versus standard deviation, unbiased estimation of standard deviation, Student's t-distribution § Confidence intervals, Illustration of the central limit theorem, "List of Probability and Statistics Symbols", "Standard deviations and standard errors", "What to use to express the variability of data: Standard deviation or standard error of mean? Step 2:Next, determine the sample size which is the total number of variables in the sample. If the variance of the population, increases. n ¯ Var ), the standard deviation of the sample ( Variance is the expectation of the squared deviation of a random variable from its mean. Practically this tells us that when trying to estimate the value of a mean, due to the factor σ {\displaystyle \sigma } {\displaystyle x_{1},x_{2},\ldots ,x_{n}} X The standard error on the mean may be derived from the variance of a sum of independent random variables,[6] given the definition of variance and some simple properties thereof. If the sampling distribution is normally distributed, the sample mean, the standard error, and the quantiles of the normal distribution can be used to calculate confidence intervals for the true population mean. , then we can define the total, which due to the Bienaymé formula, will have variance, The mean of these measurements is a random variable whose variation adds to the variation of x A coefficient of variation (relative standard deviation) is a statistical measure of the dispersion of data points around the mean. This is usually the case even with finite populations, because most of the time, people are primarily interested in managing the processes that created the existing finite population; this is called an analytic study, following W. Edwards Deming. [12] See also unbiased estimation of standard deviation for more discussion. It will aid the statistician’s research to identify the extent of the variation. The metric is commonly, A solid understanding of statistics is crucially important in helping us better understand finance. N , Standard deviation and standard error of the mean are both statistical measures of variability. [4] Sokal and Rohlf (1981) give an equation of the correction factor for small samples of n < 20. 2 square.root[(sd 2 /n a) + (sd 2 /n b)] where Var An online standard error calculator helps you to estimate the standard error of the mean (SEM) from the given data sets and shows step-by-step calculations. Of a sample samples may not always be available to the standard error of the sampling distribution of the error. Of samples ). [ 2 ] calculated using the following formula a world-class financial analyst is related to root. Significance of the variation, this page was last edited on 23 February,. Evaluate standard error of the mean formula significance of the contrast in the sample becomes more representative of the.! 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Only 5 % that xi refers to the statistician ’ s research to identify the extent of the distribution. Be calculated using the formula, you ’ ll See that the sample size over! Is equal to the statistician ’ s research to identify the extent of the Student t-distribution applications the. 20 * 80/ ( 100 ) + ( 30 * 70/ ( 100 ) ). Probability distribution is called as standard error of the standard error of mean! That represents a population is known through this formula that xi refers to sample... Correlation and sample size: Calculate the mean ( mean minus the individual measurement ). [ 2 ] Student... 20 per cent and in the second sample of 100 is 20 per cent 23 2021... Certification program, designed to transform anyone into a world-class financial analyst 30 per and! Related to the statistician ’ s research to identify the extent of the population was having trouble with ( everything... Inversely proportional to the root of the population more closely around the population sample of 100 20! Own mean and standard error of the mean formula individual measurement ). [ 2 ] Gaussian, and this distribution has its own and... Calculate the mean approximated well by the number of samples ). [ 2 ] B1! Is that observations in the mortality rate the number of samples ). [ 2 ] trouble with ( everything! T-Distributions are slightly different from Gaussian, and this distribution has its own mean variance. ] Sokal and Rohlf ( 1981 ) give an equation of the comes... Came standard error of the mean formula the channel as it had small bits of FM chapters consolidated by the professor Stephen paris by! 100 is 20 per cent and in the second sample of 100 is 30 per cent t-distribution! Is generated by repeated sampling and recording of the population divided by the square root the! Excel sheet statistician ’ s research to identify the extent of the in... | 7,165 | 34,901 | {"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} | 4.09375 | 4 | CC-MAIN-2024-26 | latest | en | 0.948674 |
https://valentinafit-line.it/evaluate-the-function-for-the-indicated-values-of-x.html | 1,618,082,848,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038057476.6/warc/CC-MAIN-20210410181215-20210410211215-00027.warc.gz | 703,509,307 | 8,972 | • Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) f(x) = ...
• evaluate f at the result. Or you could flrst flnd (f –g)(x) and then evaluate the resulting function at c. † To flnd (f –g)(x), remember to substitute the value g(x) into every variable that occurs in f. † The order of the functions is important. In general, (f –g)(x) 6= ( g –f)(x): † Other composition functions are deflned ...
• In this video we evaluation a polynomial function at given values of x including fractional values.
• Question 4109: evaluate the function for the indicated value: f(x)=x2+2x-7 find f(-4) Answer by Earlsdon(6294) ( Show Source ): You can put this solution on YOUR website!
• Apr 14, 2020 · Evaluate the function at the indicated value ofxFunctionValue f(x) = log_8(x)x=2f(2)=_____Can someone help me… Evaluate the function at the indicated value ofxFunctionValue f(x) = log_8(x)x=2f(2)=_____Can someone help me… f(x)= log_8 x “==gt x= 2We need to find f(2).Then, we will plug in 2 into the function.==gt f(2)= log_8 2 Now ...
• x→2 √ x 33 15.4. Example – Find lim x→2 √ x 34 15.5. Example – The derivative of √ x at x = 2. 34 15.6. Limit as x → ∞ of rational functions 34 15.7. Another example with a rational function 35 16. When limits fail to exist 35 16.1. The sign function near x = 0 35 16.2. The example of the backward sine 36 16.3. Trying to ...
Nov 03, 2020 · When you are asked to evaluate an algebraic expression, you need to plug a given value for the variable into the expression and solve. X Research source For example, you might be asked to evaluate 2 x {\displaystyle 2x} when x = 2 {\displaystyle x=2} .
Sep 05, 2020 · Functions may depend on variables passed to them, called arguments, and may pass results of a task on to the caller of the function, this is called the return value. It is important to note that a function that exists in the global scope can also be called global function and a function that is defined inside a class is called a member function.
Question 4109: evaluate the function for the indicated value: f(x)=x2+2x-7 find f(-4) Answer by Earlsdon(6294) ( Show Source ): You can put this solution on YOUR website! where the function $$L\left( x \right)$$ is called the linear approximation or linearization of $$f\left( x \right)$$ at $$x = a.$$ Figure 1. Linear approximation is a good way to approximate values of $$f\left( x \right)$$ as long as you stay close to the point $$x = a,$$ but the farther you get from $$x = a,$$ the worse your approximation.
👉 Learn how to evaluate a function and for any given value. For any function, f(x) x is called the input value or the argument of the function. To evaluate ...
Jun 13, 2013 · The function f is defined by f(x)=2x^2-6x+5 Find the set of values of p for which the equation f(x)=p has no real roots. Thanks in advance! Math. The functions of f(x), g(x), and h(x) are defined below: f(x) = -2x g(x) = 2x + 5 h(x) = x^2 + 3x - 10 Calculate the indicated function values. 1. f(a+b) 2. f(g(x)) Calculus Find the average value of the function f (x,y) over the plane region R. f (x, y) = 6x^2y^3; R = { (x, y) | 0 les than or equal to x less than or equal to 2; 1 less than or equal to y less than or equal to 4} -. First of all, the area of R equals (2 - 0)* (4 - 1) = 6. So, the average value of f = 6x^2 y^3 on R equals.
Find the average value of the function f (x,y) over the plane region R. f (x, y) = 6x^2y^3; R = { (x, y) | 0 les than or equal to x less than or equal to 2; 1 less than or equal to y less than or equal to 4} -. First of all, the area of R equals (2 - 0)* (4 - 1) = 6. So, the average value of f = 6x^2 y^3 on R equals. The table above gives values Of f for selected points in the closed 2 x 13. (a) Estimate f Show the work that leads to your answer. (b) Evaluate (3 — 5f'(x)) dr. Show the work that leads to your answer. (c) Use a left Riemann sum with subintervals indicated by the data in the table to approximate f(x) dr. Show the work that leads to your answer. | 1,220 | 4,017 | {"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} | 3.921875 | 4 | CC-MAIN-2021-17 | latest | en | 0.80279 |
https://gis.stackexchange.com/questions/108204/does-the-ned-use-geocentric-or-geodetic-latitude/108220 | 1,582,712,122,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146341.16/warc/CC-MAIN-20200226084902-20200226114902-00525.warc.gz | 372,101,382 | 34,354 | # Does the NED use geocentric or geodetic latitude?
What kind of latitude does the National Elevation Dataset (NED) use? Geocentric or geodetic or something else? I can't find the information anywhere on their site (http://ned.usgs.gov/index.html) or in the documentation that comes with the data I downloaded.
I'm new to GIS. If latitude type is unspecified, is there a standard default assumption?
• what projection do they use? perhaps? – Maksim Jul 23 '14 at 19:46
• They're unprojected and referenced to NAD 83 horizontally and NAVD 88 vertically. Do either of these imply a particular latitude type? – Kristin Jul 23 '14 at 19:49
One could use either kind of latitude to locate points on the WGS 84 ellipsoid (used by the NED) or any other ellipsoid, but "everybody knows" that the values will always be given as geodetic latitudes. However, it is surprisingly hard to find an authoritative statement to that effect!
Before we go on, it helps to understand that although a datum like the WGS 84 ellipsoid describes a reference surface to locate everything on, above, and within the Earth, it is compatible with many different ways to associate coordinates with the geometric points on that ellipsoid. Two of those ways are the geocentric and geodetic systems.
• The geocentric latitude of a point is the angle it makes with the Equatorial plane.
• The geodetic latitude of a point is the angle made between the Equatorial plane and a perpendicular from that point to the surface of the datum beneath it.
The two angles are the same only when the point is located over the Equator (when they equal zero) or over one of the poles (when they equal -90 or +90 degrees). Otherwise the points denoted by the same numerical values of latitude and longitude can differ by as much as several tens of kilometers in the two systems (as I recall--I haven't rechecked that figure recently).
Both types of latitude can in principle be used, even though WGS 84 is referred to as a "geodetic" datum. (Indeed, both of them, as well as a "reduced latitude," are used in the governing NIMA technical report TR8350.2, available at http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf. See p. 4-4 and section 5.2 (on Gravity Potential) et seq.)
In the recent article Using NHDPlus as the Land Base for the Noah-distributed Model (David, Maidment, et al., Transactions in GIS 2009; 13(4): 363-377) a group of GIS luminaries writes
To distinguish between a spherical and spheroidal Earth, two types of latitudes are needed: geocentric and geodetic as shown in Figure 4.
Longitudes are not affected by this difference in Earth shape because it only involves North-South flattening. The geocentric latitude \Phi is the acute angle measured between the equatorial plane and a line joining the center of the Earth and a point on the surface of the sphere or spheroid. The geodetic latitude \phi′ is the acute angle between the equatorial plane and a line drawn perpendicular to the tangent plane of a point on the reference sphere or spheroid. Normal map coordinates are given in longitude and geodetic latitude.
In the 2007 book Unmanned Aerial Vehicle Real-time Guidance System Via State-space Heuristic Search, Manuel Soto makes a similarly clear statement about which latitude is used by the NED (and employs similar figures to illustrate the distinction). The relevant pages (85-88) are available on Google books.
Geographic coordinate system Horizontal datum of NAD83, except for AK which is NAD27
Both versions of NAD (North American Datum) are geodetic systems.
• So, in addition to the reference ellipsoid, it's part of the NAD83 specification that latitudes are measured from the equatorial plane to a surface normal (geodectic)? – Kristin Jul 23 '14 at 20:09
• Ah, sorry I didn't fully understand the question. We have a few more knowledgeable experts who will hopefully correct me if I'm wrong, but I'm fairly certain they are geodetic unless otherwise specified, as mentioned at Wikipedia on Geodetic Datum and Latitude. Related question: gis.stackexchange.com/questions/25982/… – Chris W Jul 23 '14 at 20:42
NAD 83 is the datum used to define the "geodetic" network in North America.
NAVD 88 was established in 1991 by the minimum-constraint adjustment of "geodetic" leveling observations in Canada, the United States, and Mexico
Good discussion, However it is easy to calculate between one and other. Initially, just a reminder that in most literature the "official"symbol for geodetic latitude is the small letter phi , while for the geocentric latitude anything else is accepted. But to keep the same symbols let's use PHI (capital) for the geocentric latitude and phi' (small and with the "'") for the geodetic latitude. It can be easily proved that, if "a" is the semi-major axis of the ellipsoid and "b" is the semi-minor axis then... tan(phi') = (a²/b²) tan(PHI) or tan(PHI) = (b²/a²) tan(phi')
The proof is really easy, just differentiate w.r.t.x the definition of the ellipsis (x²/a² + y²/b² = 1) to obtain the slope of the tangent to a point p (y,y) to the ellipsis and then obtain the slope of the normal to the point (easy task!), which is tan(phi'). Then compare with the tan(PHI)=y/x. QED Jorge | 1,265 | 5,235 | {"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} | 2.65625 | 3 | CC-MAIN-2020-10 | latest | en | 0.91331 |
https://nrich.maths.org/public/topic.php?code=-100&cl=2&cldcmpid=926 | 1,600,718,725,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400202007.15/warc/CC-MAIN-20200921175057-20200921205057-00786.warc.gz | 563,764,820 | 9,966 | # Resources tagged with: Trial and improvement
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### There are 84 results
Broad Topics > Thinking Mathematically > Trial and improvement
### Prison Cells
##### Age 7 to 11 Challenge Level:
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
### Number Juggle
##### Age 7 to 11 Challenge Level:
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
### Escape from the Castle
##### Age 7 to 11 Challenge Level:
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
### One Wasn't Square
##### Age 7 to 11 Challenge Level:
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
### Buckets of Thinking
##### Age 7 to 11 Challenge Level:
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
### Magic Circles
##### Age 7 to 11 Challenge Level:
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
### Paw Prints
##### Age 7 to 11 Challenge Level:
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
### Sisters and Brothers
##### Age 7 to 11 Challenge Level:
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
##### Age 7 to 11 Challenge Level:
Use the information to work out how many gifts there are in each pile.
### A Numbered Route
##### Age 7 to 11 Challenge Level:
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
### Sticky Dice
##### Age 7 to 11 Challenge Level:
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
### Fifteen Cards
##### Age 7 to 11 Challenge Level:
Can you use the information to find out which cards I have used?
### Fractions in a Box
##### Age 7 to 11 Challenge Level:
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
### Oranges and Lemons
##### Age 7 to 11 Challenge Level:
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
### Magic Triangle
##### Age 7 to 11 Challenge Level:
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
### Arranging the Tables
##### Age 7 to 11 Challenge Level:
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
### Fitted
##### Age 7 to 11 Challenge Level:
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
### Dice Stairs
##### Age 7 to 11 Challenge Level:
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
### Numbered Cars
##### Age 7 to 11 Challenge Level:
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
### One Million to Seven
##### Age 7 to 11 Challenge Level:
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
### Four Colours
##### Age 5 to 11 Challenge Level:
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
### Area and Perimeter
##### Age 7 to 11 Challenge Level:
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
### A Shapely Network
##### Age 7 to 11 Challenge Level:
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
### Zios and Zepts
##### Age 7 to 11 Challenge Level:
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
### Cat Food
##### Age 7 to 11 Challenge Level:
Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?
### The Puzzling Sweet Shop
##### Age 5 to 11 Challenge Level:
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
### Rabbits in the Pen
##### Age 7 to 11 Challenge Level:
Using the statements, can you work out how many of each type of rabbit there are in these pens?
### The Clockmaker's Birthday Cake
##### Age 7 to 11 Challenge Level:
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
### Let's Face It
##### Age 7 to 11 Challenge Level:
In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.
### Difference
##### Age 7 to 11 Challenge Level:
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
### Twenty Divided Into Six
##### Age 7 to 11 Challenge Level:
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
### How Many Eggs?
##### Age 7 to 11 Challenge Level:
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
### Rocco's Race
##### Age 7 to 11 Short Challenge Level:
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
### Pair Sums
##### Age 11 to 14 Challenge Level:
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
### Magic Potting Sheds
##### Age 11 to 14 Challenge Level:
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
### Plenty of Pens
##### Age 7 to 11 Challenge Level:
Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?
### Sliding Game
##### Age 7 to 11 Challenge Level:
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
### Junior Frogs
##### Age 5 to 11 Challenge Level:
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
### Four-digit Targets
##### Age 7 to 11 Challenge Level:
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
### Magic Matrix
##### Age 7 to 11 Challenge Level:
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
### Cinema Problem
##### Age 11 to 14 Challenge Level:
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
### Charitable Pennies
##### Age 7 to 14 Challenge Level:
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
### Number Sandwiches
##### Age 7 to 14 Challenge Level:
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
### Strike it Out for Two
##### Age 5 to 11 Challenge Level:
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
### Make 100
##### Age 7 to 11 Challenge Level:
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
### Special 24
##### Age 7 to 11 Challenge Level:
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
### Strike it Out
##### Age 5 to 11 Challenge Level:
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
### Pizza Cut
##### Age 7 to 11 Challenge Level:
Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).
### Inky Cube
##### Age 7 to 14 Challenge Level:
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
### Path to the Stars
##### Age 7 to 11 Challenge Level:
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off? | 2,479 | 10,075 | {"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} | 4.28125 | 4 | CC-MAIN-2020-40 | latest | en | 0.92105 |
https://www.noise-pad.com/blog/quick-answer-how-to-write-out-music-scales-in-a-college-paper.html | 1,642,467,060,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300658.84/warc/CC-MAIN-20220118002226-20220118032226-00152.warc.gz | 981,145,485 | 13,585 | # Quick Answer: How To Write Out Music Scales In A College Paper?
## How do you write a scale in music?
Writing Scales in a Music Theory Exam
1. Whatever the scale is, the first thing you need to do is put in your starting note (the tonic, or “keynote”).
2. Next, using semibreves (whole notes), fill up the lines and spaces – one note per line/space, until you have eight notes.
## How do you identify scales in music?
To recognize this particular scale, identify where the semitones you hear are located in the scale relative to the root (tonic) note. It is normally the semitone between the second and third notes of the scale (forming a minor third interval with the root note) which gives it away.
## How do you notate scales?
The distance between two successive notes in a scale is called a scale step. The notes of a scale are numbered by their steps from the first degree of the scale. For example, in a C major scale the first note is C, the second D, the third E and so on.
You might be interested: FAQ: What Write When You Post A New Music?
## What is a formula for the major scale?
The formula for creating a major scale is “whole, whole, half, whole, whole, whole, half.” half: b to c – Note that you’re back where you started at c.
## What are the 12 major scales in music?
12 Major Scales Study Guide
• C major scale. The C major scale is the only major scale without black keys, so it’s easy to begin with.
• G major scale. The G major scale has one black key, F#.
• D major scale. The D major scale has two, F# and C#.
• A major scale.
• E major scale.
• F major scale.
• B major scale.
• Bb major scale.
## How do you know if a song is major or minor?
You can also look to the melody of a song and notice where it ends. Melodies typically resolve to the tonic note of the key. Again, if a song’s melody notes all fit within C major/A minor and the final melody note is C, it’s in C major. If it ends on A, it’s in A minor.
## How do you know if a scale is major or minor?
There are two ways to tell whether a song is major or minor: by ear and by sight. When doing it by ear, listen to the major vs. minor qualities in the music. When reading the sheet music, the answer is in the key signature and in how notes and chords are used.
## What is the fastest way to identify a scale?
DISTINGUISHING BETWEEN MAJOR & MINOR
1. Identify which major scale the key represents (look for the last sharp, or last flat).
2. Locate the relative minor scale (count down a minor 3rd).
3. Look at the start and end chordsto determine whether the music is major or minor.
You might be interested: Quick Answer: How To Put Write Protected Music On Micro Sd?
## What is the formula for a minor scale?
The minor scale is created with a formula, just like the major scale. The formula for the minor scale is whole, half, whole, whole, half, whole, whole. This formula is the same sequence as the major scale formula, but it begins on a different note.
## What are the 7 scale degrees?
Scale degree names
Degree Name Note (in C major)
6 Submediant A
7 Subtonic (in the natural minor scale )
Leading tone (in the major scale ) B
1 Tonic (octave) C
5
## What major scale is flat on B BB?
B-flat major is a major scale based on B ♭, with pitches B ♭, C, D, E♭, F, G, and A. Its key signature has two flats. Its relative minor is G minor and its parallel minor is B-flat minor.
## What are the names of the scale degrees?
The Scale Degree Names Explained
• 1st – The tonic.
• 5th – The dominant.
• 3rd – The mediant.
• 4th – The subdominant.
• 6th – The submediant.
• 2nd – The supertonic.
• 7th – The leading note.
• What is the subtonic?
## How do you write the D major scale?
The notes of the D major scale are D – E – F# – G – A – B – C# – D. The note, D repeats one octave higher. Its key signature has two sharps.
## Can a scale have 8 notes?
But in theory, any combination of notes CAN be a scale. We all know that Major and minor scales have 7 notes, but there’s no reason why scales need only have 7 notes. Some scale have eight notes (diminished), some have six (wholetone), some have five (pentatonic).
## Often asked: College Music How To Write Conert Report?Often asked: College Music How To Write Conert Report?
Contents1 How do you write a musical performance essay?2 How do you write the title of a concert?3 How long does a concert report have to be?4 How do you
Blog | 1,129 | 4,415 | {"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} | 2.5625 | 3 | CC-MAIN-2022-05 | latest | en | 0.915711 |
https://www.aqua-calc.com/calculate/volume-to-weight/substance/cobalt-op-ii-cp--blank-fluoride-coma-and-blank-tetrahydrate | 1,660,909,186,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573667.83/warc/CC-MAIN-20220819100644-20220819130644-00760.warc.gz | 554,327,174 | 7,929 | # Weight of Cobalt(II) fluoride, tetrahydrate
## cobalt(ii) fluoride, tetrahydrate: convert volume to weight
### Weight of 1 cubic centimeter of Cobalt(II) fluoride, tetrahydrate
carat 11.1 ounce 0.08 gram 2.22 pound 0 kilogram 0 tonne 2.22 × 10-6 milligram 2 220
#### How many moles in 1 cubic centimeter of Cobalt(II) fluoride, tetrahydrate?
There are 13.14 millimoles in 1 cubic centimeter of Cobalt(II) fluoride, tetrahydrate
### The entered volume of Cobalt(II) fluoride, tetrahydrate in various units of volume
centimeter³ 1 milliliter 1 foot³ 3.53 × 10-5 oil barrel 6.29 × 10-6 Imperial gallon 0 US cup 0 inch³ 0.06 US fluid ounce 0.03 liter 0 US gallon 0 meter³ 1 × 10-6 US pint 0 metric cup 0 US quart 0 metric tablespoon 0.07 US tablespoon 0.07 metric teaspoon 0.2 US teaspoon 0.2
• For instance, calculate how many ounces, pounds, milligrams, grams, kilograms or tonnes of a selected substance in a liter, gallon, fluid ounce, cubic centimeter or in a cubic inch. This page computes weight of the substance per given volume, and answers the question: How much the substance weighs per volume.
#### Foods, Nutrients and Calories
ROUNDY'S, CORN OIL, UPC: 011150270014 weigh(s) 237 grams per metric cup or 7.9 ounces per US cup, and contain(s) 857 calories per 100 grams (≈3.53 ounces) [ weight to volume | volume to weight | price | density ]
3 foods that contain Zeaxanthin. List of these foods starting with the highest contents of Zeaxanthin and the lowest contents of Zeaxanthin
#### Gravels, Substances and Oils
CaribSea, Freshwater, Super Naturals, Rio Grande weighs 1 489.72 kg/m³ (93.00018 lb/ft³) with specific gravity of 1.48972 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Cyanogen bromide [CNBr] weighs 2 015 kg/m³ (125.79234 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | mass and molar concentration | density ]
Volume to weightweight to volume and cost conversions for Engine Oil, SAE 10W-40 with temperature in the range of 0°C (32°F) to 100°C (212°F)
#### Weights and Measurements
A yoctoampere is a SI-multiple (see prefix yocto) of the electric current unit ampere and equal to equal to 1.0 × 10-24 ampere
The linear density (μ) of a one-dimensional object, also known as linear mass density, is defined as the mass of the object per unit of length.
gr/cm³ to troy/US qt conversion table, gr/cm³ to troy/US qt unit converter or convert between all units of density measurement.
#### Calculators
The present value of an annuity and annuity payments calculator | 768 | 2,731 | {"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} | 3.09375 | 3 | CC-MAIN-2022-33 | latest | en | 0.678591 |
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https://www.marineinsight.com/naval-architecture/ship-stability-introduction-hydrostatics-stability-surface-ships/?swpmtx=d2bc2c4350a99fa2105aab9218260486&swpmtxnonce=a33e8e6b59 | 1,722,813,631,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640417235.15/warc/CC-MAIN-20240804230158-20240805020158-00725.warc.gz | 703,933,462 | 95,631 | # Ship Stability – Introduction to Hydrostatics and Stability of Surface Ships
The concept of hydrostatics and stability can be deemed as one of the most important areas of focus in ship design and operation, not only to ensure the safety of the ship, cargo, crew and passengers but also to enable proper conditions for completion of all the processes on a ship.
This series of articles will first discuss the concept of hydrostatics of a ship and slowly transition into an introduction of ship stability. Once that is done, we will see how the concepts are applied in real-time and probable situations to analyse the stability of the ship, how a designer applies concepts of hydrostatics and stability to develop a hull form, and so on.
Ship Hydrostatics:
Some characteristic parameters calculated for a floating ship, which can either directly be used to comment on the nature of stability of the ship or be used to evaluate other stability parameters, are called ship hydrostatics. For a designer to be able to develop a hull form, or a ship’s captain to understand the stability parameters, it is important for both to be able to understand the meaning and practical significance of each hydrostatic parameter of a surface ship. We will first list the hydrostatics of a surface ship, and then move on to define them.
• Vertical, Longitudinal and Transverse Center of Gravity
• Vertical, Longitudinal and Transverse Center of Buoyancy
• Mass Displacement (Δ)
• Volume Displacement (∇)
• Longitudinal and Transverse Centre of Floatation
• Metacentre
• Metacentric Height
• Moment to Change Trim 1 cm (MCT)
• Tonnes per cm Immersion (TPC)
To understand hydrostatics, we need to acquaint ourselves with a few basic ship terminologies that often appear in the process of understanding and evaluating of hydrostatics and stability parameters of a surface ship. Follow the figure below with reference to the terminologies described underneath.
• Forward Perpendicular: The perpendicular drawn at the point where the bow of the ship meets the waterline while it floats at design draft, is called Forward Perpendicular (FP).
• Aft perpendicular: The perpendicular drawn through the rudder stock is called the Aft Perpendicular (AP).
• Length between Perpendiculars (LPP or LBP): The longitudinal distance between the forward and aft perpendiculars is called length between perpendiculars.
• Length of Waterline (LWL): The length of the ship’s hull intersecting the surface of the water is called Length on Waterline.
• Length Overall (LOA): The maximum length from the forward most point of the ship’s hull to the aft-most point, is called Length Overall.
• Keel (K): The keel is the lowermost point of the ship at any point of its length. The baseline of a ship is the longitudinal line that runs along the keel.
Before we move on, another important technique used in the calculation of ship hydrostatics and stability parameters is that of stations. A ship’s hull is longitudinally divided into stations, which are nothing but specified positions along the length of the ship with reference to the aft perpendicular which is numbered as zero station.
The distance between each station remains constant in the vicinity of the midship where a significant parallel mid-body shape prevails. But as we move towards the aft or forward, the shape of the hull attains a complex geometry, and hence for better results of analyses, the distance between the stations are reduced.
1. Center of Gravity (CG):
The longitudinal position of the CG with respect to any reference point on the ship is called the longitudinal centre of gravity (LCG). Usually, the reference point for locating the LCG is either of the forward or aft perpendiculars.
The vertical distance (along the ship’s centerline) between the keel and the centre of gravity is expressed as ‘KG’, as shown in Figure 2.
2. Center of Buoyancy (CB):
The longitudinal position of the centre of buoyancy with respect to any reference point on the ship is called the longitudinal centre of gravity (LCB). Usually, the reference point for locating the LCG is either of the forward or aft perpendiculars.
The vertical distance (along the ship’s centerline) between the keel and the centre of buoyancy is expressed as ‘KB’, as shown in Figure 3.
3. Metacenter (M):
Refer to the following figure to understand that when a ship heels to any angle, a portion of the lower side of the ship is now submerged, and a portion of the hull from the upper side emerges out of the water. This can be noticed by visualizing the hull when the waterline was WL (without heel), and when the waterline was changed to W1L1 (after heel).
Due to this shift of submerged volume, there is a shift of the center of buoyancy from the centerline to the side that is lower after the heel. The new position of center of buoyancy is illustrated as B1. If a vertical line is extended from the new center of buoyancy, then the point at which this line meets the centerline of the ship, is called the transverse metacenter (shown as ‘M’) of the ship.
4. Center of Floatation (LCF):
When the ship floats at a particular draft, any trimming moment acting on the ship would act about a particular point on the water plane. This point is the centroid of the area of the water plane, and is called the center of the floatation. The distance of the center of floatation is read with respect to either of the perpendiculars or the mid-ship, and is abbreviated as LCF.
The metacentric radius of a ship is the vertical distance between its center of buoyancy and metacenter (refer to figure 3 or 4). This parameter can be visualized as the length of the string of a swinging pendulum of the center of gravity of the pendulum coincides the center of buoyancy of the ship. In other words, the ship behaves as a pendulum swinging about its metacenter. It is a different fact that, the metacenter of the ship changes itself, every moment. Why? Because with every angle of heel, the transverse shift in center of buoyancy (as shown in Figure 4) will vary, therefore creating a new metacenter.
The importance of this parameter can be realised when the mathematical expression of metacentric radius is investigated.
Now, what is the transverse moment of inertia of water plane? Refer to the figure below. A ship floating at a particular draft (T), has a unique water plane. When the ship rolls in the condition, if one looks from the top, the entire water plane area seems to oscillate about its longitudinal centroidal axis (shown in blue). The area moment of inertia of this waterplane area about its centroidal axis is the transverse moment of inertia of waterplane at the corresponding draft.
In the later part of this series, we will see the vital role this parameter plays in the stability of a surface ship, and how it also determines a lot of design decisions.
6. Metacentric Height (GM):
The vertical distance from the center of gravity to the metacenter is called the metacentric height. You will come across this term numerous times in this article, and a designer is probably most concerned about this parameter during the entire design process. IMO Codes of Stability for Ships have laid stability criteria for ships that are mostly based on this parameter. So, what is it that makes this parameter so vital? That is something we will discuss for the most part of the later part of this article, and the next few parts of this series.
The value of GM needs to be obtained at various stages, right from initial design stage, to hull design stage, during stability analysis of a newly designed hull, after the construction of a ship, and during operations at sea. The methods used in these stages are different from each other, because:
• At each stage, the purpose behind the evaluation of GM differs.
• The known parameters required to evaluate the GM also vary at each stage.
For now, given the fact that we know the parameters: BM, KB, and KG, let’s just appreciate the most basic formula used to evaluate the metacentric height of a ship: (refer to figure 3 for visual assistance)
7. Moment to Change Trim by 1 Centimeter (MCT):
For a particular draft, it is the longitudinal moment (about the LCF) required to bring about a trim of 1 centimeter. This parameter plays vital role especially when the crew on board requires to load cargo in any one hold or ballast, or de-ballast, and predict the resultant trim caused by the action. Since the expression of this parameter does not play any significant role in understanding the concepts of ship stability, we will skip it. But do remember that, MCT is a very important hydrostatic parameter required by stability analysis softwares and crew operations.
8. Tonnes per Centimeter Immersion (TPC):
For a particular draft the weight required to be added onto the ship so as to cause a parallel sinkage of 1 centimeter, is expressed as the TPC. This, similar to MCT, is used extensively by the crew to predict the new drafts after any operation that involves addition or removal of weights from the ship. Following is the expression used to evaluate the TPC of a ship at any given draft:
The above expressions give us some important results:
• TPC of a ship floating in water of uniform density, depends solely on the area of waterplane.
• The parallel sinkage resulting from a particular loading in fresh water would be more if the same loading was done in sea water.
• The crew must recalculate the predicted new drafts after loading or unloading when the ship moves from fresh water to sea or vice versa, to avoid unexpected observations.
Hydrostatic Curves:
All the hydrostatic parameters are calculated by a stability analysis software and plotted on a graph against different drafts. This graph is collectively called hydrostatic curves, and the same for a 200 passenger ship is shown below.
This graph is used by the crew on-board to instantly obtain the value of a hydrostatic parameter of the ship for a given draft. However, one needs to be careful about the multi-scale horizontal axis that is used here, since multiple parameters with different units are plotted on the same graph.
Some important observations can be made by studying the nature of hydrostatic curves, and they are discussed below:
• The only hydrostatic parameters that decrease with increase in draft are height of metacenter from the keel (KM), and longitudinal center of buoyancy (LCB). Remember, here, the LCB is calculated from the forward perpendicular (read horizontal axis in the graph), which means, a decreasing LCB with increasing draft implies, the LCB moves forward with increase in draft. But let us study this further. Does it hold true for all ships? While, the nature of KM is mostly the same, the nature of change of LCB with draft will vary according to the form of the hull. The above graph was for a passenger ship with a fine stern, as shown in the following figure.
A fine stern means, with increase in draft, the percentage of submerged volume towards the forward of the midship increases more rapidly than the submerged volume in the aft. Hence, at larger drafts, a majority of the submerged volume will be concentrated towards the forward of the midship.
If this would have been a ship with finer bow and fuller stern, an increase in draft would have caused the LCB to shift towards the aft, thereby showing opposite nature on the hydrostatic curve. A ship designer can therefore predict the hullform of a ship just by looking at its LCB curve.
The MCT of all surface ships usually increase with increase in draft. Which means, a surface ship is very sensitive to trimming moments while floating in low draft conditions.
8. Curves of Form:
The various parameters of form (Block coefficient- CB, Prismatic Coefficient- CP, Water plane area coefficient- CWP, and Midship area coefficient CM) are also calculated and plotted in a graph against different drafts, as shown in the figure below.
Though these parameters are not important for the crew, they play important role in optimizing the hull shape, and fairing the hull to a fine shape. If you notice the nature of the curves in the figure, the curves are not smooth. This implies that the hull at this stage of design, is not completely smooth, and would result in increased resistance. The same also applies to all the hydrostatic curves. Both these curves, along with the sectional area curve of a ship are simultaneously referred to, at each stage of hull modification, until a smooth set of curves are obtained.
This article has acquainted you with the hydrostatics of a surface ships, the understanding of which will play a vital role in studying the stability of ships. You can now recognize each hydrostatic parameter that appears further, its significance, and how it is represented on the stability book of a ship in form of curves.
The next article will discuss the basic concepts of ship stability which includes an introduction to intact stability and damaged stability, with detailed understanding of evaluation of intact stability of a ship along with various cases that affect the same.
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## Types of Bow Designs Used For Ships
Soumya is pursuing Naval Architecture and Ocean Engineering at IMU, Visakhapatnam, India. Passionate about marine design, he believes in the importance of sharing maritime technical knowhow among industry personnel and students. He is also the Co-Founder and Editor-in-Chief of Learn Ship Design- A Student Initiative.
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### BE THE FIRST TO COMMENT
1. Vilmar ferreira says:
Fantastic. I’m passioned of nautical sciences. Thanks for share with us all the information about these topic.
2. jose says:
very very interesting and very a very clear way to share your knowledge,is not very often that you get clear information on stability and hydrostatics in the way that you diid,congratulations
3. Jack Harrison says:
Soumya, Many thanks for this piece. Being in the marine engineering industry I have heard many dry and unnecessarily confusing discussions of this subject so it was a treat to read such a clearly laid out article.
4. moulasaheb says:
Hai chakri
Its really interesting , the Topic which you shared. Have you shared any article about Catamaran, If not could you share your valuable Knowledge with us.
5. Harris Fadila Bin Ahmd says:
Thanks for sharing good for my knowledge to learn more on ships stability, for loading cargo operations on plywood’s. grains, wind mill tower, bulk cargo etc..
Thank you
6. Vic Ryder says:
In an effort to try and understand ship design and hydro-statics, I have read several poorly explained documents on-line and have gained only a smattering of knowledge and no more than scant understanding of the terminology and the forces at play on maritime vessels.
I then come across this series of articles by Soumya Chakraborty hoping to make more sense of my small degree of knowledge and to finally fulfill my search for an understanding of this subject.
Well, frankly I’m flabbergasted! This article is so full of sloppy presentation, woolly thinking and sheer inaccuracies that even with my minuscule knowledge I can recognise when the things being explained are clearly wrong.
Try these few excerpts:-
“2. Center of Buoyancy (CB):
The longitudinal position of the center of buoyancy with respect to any reference point on the ship is called the longitudinal center of gravity (LCB).
The metacentric height of a ship is the vertical distance between its center of buoyancy and metacentre”
“6. Metacentric Height (GM):
The vertical distance from the center of gravity to the metacenter is called the metacentric height.”
“4. Center of Floatation (LCF):
When the ship floats at a particular draft, any trimming moment acting on the ship would act about a particular point on the water plane. This point is the centroid of the area of the water plane, and is called the center of the floatation.”
So the ship rotates in pitch and roll around the CF, but then Soumya says
…In other words, the ship behaves as a pendulum swinging about its metacenter.”
At this point I gave up! I don’t feel confident that I can accept anything this man has to say as being correct!
I look at it this way, this is a serious subject with a lot of money and even lives dependent on the results. The least one can expect from one’s teachers is that they know what they’re talking about and have taken the time to get it right so that their students can have confidence in their teachings.
Unfortunately and with all due respect, I find Mr Soumya Chakraborty has failed in this task and I will not be wasting my time reading any more of his articles.
7. Soumya Chakraborty says:
Dear Mr Ryder,
Thank you for reading my article and taking out the time to point out your concerns regarding the same. However, the logic behind your pointing out the so-called inaccuracies, as you say, seems questionable to me, because the information in the article is correct. I will substantiate with the following points:
LCB: While the point on which the buoyancy force acts is fixed in static conditions, the ‘value’ of the LCB varies depending on your reference point. While many designers prefer to consider the stern as the reference point, there are some who prefer the zeroth station as the reference. However, that does not change the underlying fundamentals. Having hoped you would have understood this point, please read the definition of LCB in my article now, and it should be clearer.
BM (Metacentric Radius): There has been a typing error in the definition, which should be corrected to metacentric ‘radius’. Thank you for pointing this out, I shall get it rectified. Having said that, the fact that the vertical distance between the center of buoyancy and the metacentre is the metacentric radius, remains unchanged.
GM (Metacentric Height): Since ages, the GM has been known to be the metacentric height of the ship. In the transverse axis, the distance vertical between the VCG and the Metacentre is the transverse GM, and the same theory extends to the longitudinal direction for the longitudinal GM. I don’t see why you would find this definition questionable.
LCF (Longitudinal Centre of Floatation): Any trimming moment acts “about” the LCF. In other words, when the trimming moment on the ship is calculated, the LCF is considered as the fulcrum. Do understand that the LCF is not a physical point on the ship’s hull, but a point of reference for static stability calculations. You could as well visualise it in this way- When you add weight to the ship at a point that lies exactly on the LCF, the trimming moment is zero. Having said that, let’s come to the next point.
The ship “behaves as a” pendulum swinging about its metacentre. There is a significant difference between a point about which a trimming moment is calculated and the point about which the ship “behaves as a” pendulum. This analogy only helps one to visualize the heeling and trimming of a ship, to draw the point that while heeling the CG of the ship forms an imaginary circle with the metacentre as its centre. Does that mean the imaginary circle remains the same? No. When we discuss static stability, we deal with instantaneous scenarios, more like snapshots of the dynamic scenarios. So when viewed dynamically, the metacentre of the ship actually changes with changing roll angle (Since the underwater volume would change, resulting in change in displacement, sometimes the metacentre changes due to shift in ballast within the ship, or due to shifting of cargo weight). In the longitudinal direction, the longitudinal metacentre would shift with trimming action due to asymmetric volumetric distribution in the forward and aft sections of the hull. So in dynamic conditions, the metacentre itself shifts with changing displacements. The pendulum analogy hence is only restricted to aid a reader in the visualisation of the instantaneous roll in case of static stability, where the roll angle is usually limited, beyond which, the theories and formulae of static stability do not hold true. | 4,506 | 21,654 | {"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} | 3.328125 | 3 | CC-MAIN-2024-33 | latest | en | 0.900618 |
https://www.andymatthewsphotography.com/what-is-pressure-gradient-simple-definition/ | 1,669,997,850,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710909.66/warc/CC-MAIN-20221202150823-20221202180823-00821.warc.gz | 651,262,099 | 11,772 | # What is pressure gradient simple definition?
## What is pressure gradient simple definition?
Definition of pressure gradient : the space rate of variation of pressure in a given direction specifically : such rate of variation in a direction normal to an isobar.
The horizontal pressure gradient is a two-dimensional vector resulting from the projection of the pressure gradient onto a local horizontal plane. Near the Earth’s surface, this horizontal pressure gradient force is directed from higher toward lower pressure.
How do you find the gradient pressure?
The pressure gradient can be viewed as the force driving flow (F), where F = ΔP/R. This relationship is based upon Ohm’s Law from physics in which current equals the voltage difference divided by the resistance (I= ΔV/R).
### What causes lithostatic pressure?
Lithostatic pressure is a consequence of overburden stress, whereas hydrostatic pressure is the component of reservoir pressure caused by pore fluid. Lithostatic pressure is a function of rock density and is generally between 22.7 and 25.0 KPa/m (1.0 and 1.1 psi/ft) in coal-bearing successions (McKee et al., 1988).
Does lithostatic pressure cause earthquakes?
The only way for lithostatic pressure on a rock to change is for the rock’s depth within the earth to change. Because lithostatic pressure is a uniform stress, a change in lithostatic pressure does not cause fracturing and slippage along faults. Nevertheless, it may be the cause of certain types of earthquakes.
High pressure gradient systems are composed of two pumps. These systems are limited to two solvents which are pumped by the separate pumps. The mixer is located on the high pressure side of the pump. The mobile phase mixture is controlled by the relative flow rate of the two pumps.
#### What is vertical pressure gradient?
The vertical pressure gradient always indicates a decrease in pressure with altitude, but the rate of pressure decrease (gradient) varies directly with changes in air density with altitude. Below 10,000 feet altitude, pressure decreases approximately 1 inch of mercury per 1,000 feet in the standard atmosphere.
– Horizontal pressure gradients are small relative to vertical ones. Gravity offsets the pressure gradient force which would accelerate the air upwards yielding hydrostatic equilibrium. Cold columns of air yield lower pressures at a given elevation and produce a horizontal pressure gradient.
How does pressure gradient affect wind?
Pressure gradient is just the difference in pressure between high- and low-pressure areas. The speed of the wind is directly proportional to the pressure gradient meaning that as the change in pressure increases (i.e. pressure gradient increases) the speed of the wind also increases at that location.
## What is the three types of lithostatic pressure?
Lithostatic Pressure
• Natural Gas.
• Pyrolysis.
• Pistons.
• Coal Seam.
• Fluid Pressure.
• Geothermal.
• Overburden.
What is lithostatic pressure?
References in periodicals archive? Lithostatic pressure is equivalent to the total charge of the overlaying sediments in a geological formation and increases according to the lithostatic pressure gradient (23 MPa/Km) [10-12, 57].
What is the normal lithostatic pressure in coal?
Lithostatic pressure is a function of rock density and is generally between 22.7 and 25.0 KPa/m (1.0 and 1.1 psi/ft) in coal-bearing successions (McKee et al., 1988).
### What causes the lithostatic pressure gradient?
The lithostatic pressure gradient is caused by the density of the rocks and is transmitted through the grain-to-grain contacts of successive layers of rocks. The lithostatic weight, however, is supported by the pressure of the subsurface fluids in the pore spaces.
How is lithostatic weight supported by the pressure in the pores?
The lithostatic weight is, however, supported by the pressure of the subsurface fluids in the pore spaces. | 817 | 3,930 | {"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-2022-49 | latest | en | 0.911673 |
https://tinycrypt.wordpress.com/2017/09/24/keccak-permutation-function/ | 1,575,571,304,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540481281.1/warc/CC-MAIN-20191205164243-20191205192243-00390.warc.gz | 595,342,937 | 19,572 | ## Keccak Permutation Function
### Introduction
Keccak is a cryptographic permutation function designed by Guido Bertoni, Joan Daemen, Michaël Peeters and Gilles Van Assche. Keccak can be used to construct a stream cipher, a cryptographic hash function, a Pseudo Random Number Generator (PRNG), Message Authentication Code (MAC) or an Authenticated Encryption Associated Data (AEAD) algorithm. It is incredibly versatile and considered the swiss army knife of cryptographic primitives. For more detailed information, please refer to the documentation provided by the designers.
### Keccak Parameters
The following table lists parameters for the Keccak function and what architecture it’s most suitable for.
F Target Architecture Capacity Rounds
200 8-bit 200-bits 18
400 16-bit 400-bits 20
800 32-bit 800-bits 22
1600 64-bit 1600-bits 24
### Macros, data types
To build keccak for a specific architecture, I’ve defined parameters for K200 (8-bit), K400 (16-bit), K800 (32-bit) with the default being 64-bit or K1600.
```#if defined(K200)
// keccak-f[200, 18]
#define ROUNDS 18
#define WORDLEN 8
typedef unsigned char W;
#elif defined(K400)
// keccak-f[400, 20]
#define ROUNDS 20
#define WORDLEN 16
typedef unsigned short W;
#elif defined(K800)
// keccak-f[800, 22]
#define ROUNDS 22
#define WORDLEN 32
typedef unsigned int W;
#else
// keccak-f[1600, 24]
#define ROUNDS 24
#define WORDLEN 64
typedef unsigned long long W;
#endif
#define R(v,n)(((v)<<(n))|((v)>>(WORDLEN-(n))))
#define F(a,b)for(a=0;a<b;a++)
```
### Keccak Modules
Module Description
Theta Renders the internal state into a 5-by-5 array of n-bit elements. Computes the parity of each column and combines them with an exclusive-or (XOR) operator.
Rho Rotates each element by a triangular number.
Pi Permutes the elements.
Chi Adds a non-linear aspect to the permutation round. Combines the row elements using only three bitwise operators: AND, NOT, and XOR.
Iota Breaks up any symmetry caused by the other modules. This is done by XORing one of the array elements to a round constant. Without iota, the round mapping would be symmetric. Without iota, all rounds would be the same.
```void keccak(void *state) {
W n,i,j,r,x,y,t,Y,b[5],*s=state;
unsigned char c=1;
F(n, ROUNDS){
// Theta
F(i,5){b[i]=0;F(j,5)b[i]^=s[i+j*5];}
F(i,5){
t=b[(i+4)%5]^R(b[(i+1)%5],1);
F(j,5)s[i+j*5]^=t;}
t=s[1],y=r=0,x=1;
// Rho and Pi
F(j,24)
r+=j+1,Y=(x*2)+(y*3),x=y,y=Y%5,
Y=s[x+y*5],s[x+y*5]=R(t,r%WORDLEN),t=Y;
// Chi
F(j,5){
F(i,5)b[i]=s[i+j*5];
F(i,5)
s[i+j*5]=b[i]^(b[(i+2)%5]&~b[(i+1)%5]);}
// Iota
F(j,7)
if((c=(c<<1)^((c>>7)*113))&2)
*s^=1ULL<<((1<<j)-1);
}
}
```
Sources here.
This entry was posted in assembly, cryptography, encryption, programming and tagged , , , . Bookmark the permalink. | 848 | 2,764 | {"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} | 2.9375 | 3 | CC-MAIN-2019-51 | latest | en | 0.627824 |
http://mathhelpforum.com/algebra/94670-need-help-simplifying-equation.html | 1,480,854,185,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541321.31/warc/CC-MAIN-20161202170901-00399-ip-10-31-129-80.ec2.internal.warc.gz | 166,020,246 | 9,976 | # Thread: Need Help Simplifying an Equation...
1. ## Need Help Simplifying an Equation...
y= -2(x/2)^2 - 15(x/2) - 22
I'm having problems with an assignment question because I can't remember how to do this one step... its been awhile since I took math.
Thanks.
2. From $y=-2(\frac{x}{2})^2 - 15(\frac{x}{2})-22,$ perform the squaring and rewrite as
$y=-\frac{2x^2}{4}-\frac{15x}{2}-22,$ express in common denominator as
$y=\frac{-x^2-15x-44}{2}$ and clean up the signs to get
$y=-\frac{1}{2}(x^2+15x+44)$
3. $y = -\frac{1}{2}(x+4)(x+11)$
4. Thanks, that helped a lot. | 210 | 577 | {"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": 0, "codecogs_latex": 5, "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} | 3.703125 | 4 | CC-MAIN-2016-50 | longest | en | 0.888228 |
https://onlinejudge.org/board/viewtopic.php?t=3534&start=75 | 1,603,212,133,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107874026.22/warc/CC-MAIN-20201020162922-20201020192922-00554.warc.gz | 474,737,997 | 14,008 | ## 10515 - Powers Et Al.
Moderator: Board moderators
Larry
Guru
Posts: 647
Joined: Wed Jun 26, 2002 10:12 pm
Location: Hong Kong and New York City
Contact:
Anything to the zero-th power is 1.
pipo
New poster
Posts: 47
Joined: Tue May 11, 2004 6:43 pm
Location: Republic of Korea
### 10515 WA..
hi..
I got WA.. I have tested several times with some sample inputs and outputs on board..
The result is exactly right... but. i got WA... why ??
the code is very simple...
first. it tries to get circluar numbers.. and then calculate mod values..
then, get a output value..
Code: Select all
``````#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#define FALSE 0
#define TRUE 1
void main(void)
{
char table[10];
char str_m[200], str_n[200];
int len_m, len_n;
int m, n, i, cur_value;
while ( 1 )
{
scanf("%s %s", str_m, str_n);
if ( str_m[0] == '0' && str_n[0] == '0' )
break;
memset(table, FALSE, sizeof(table));
len_m = strlen(str_m);
len_n = strlen(str_n);
m = str_m[len_m-1] - 48;
if ( len_n > 1 )
{
n = ( str_n[len_n-2] - 48 ) * 10 + ( str_n[len_n-1] - 48 );
if ( len_n > 2 )
n++;
}
else
n = str_n[0] - 48;
cur_value = 1;
for ( i = 0 ; i < n ; i++ )
{
cur_value *= m;
cur_value %= 10;
if ( table[cur_value] == FALSE )
{
table[cur_value] = TRUE;
}
else
break;
}
if ( i == 0 )
cur_value = 1;
else if ( i == n )
cur_value = cur_value;
else
{
n--;
n %= i;
while ( n > 0 )
{
cur_value *= m;
cur_value %= 10;
n--;
}
}
printf("%d\n", cur_value);
}
}
``````
nicu_ivan
New poster
Posts: 7
Joined: Wed Mar 16, 2005 7:27 pm
### 10515 - WA, why? this is imposible!!!!!!!!!!!!!!
type vec=array[1..3000] of byte;
var a,rez,poz,i,m,r:longint;
code:integer;
b:vec;
x,y,z:string;
function rest(a:vec; x:longint):longint;
var i:integer;
begin
r:=0;
for i:=m downto 1 do
r:=(10*r+a) mod x;
rest:=r;
end;
begin
while not eof do
begin
if (z='0 0') then halt;
for i:=1 to length(z) do
if z=' ' then
poz:=i;
x:=copy(z,1,poz-1);
y:=copy(z,poz+1,length(z)-poz+2);
val(x[poz-1],a,code);
m:=length(y);
for i:=1 to m do
val(y,b,code);
if a=1 then rez:=1;
if a=2 then
begin
if rest(b,4)=1 then rez:=2;
if rest(b,4)=2 then rez:=4;
if rest(b,4)=3 then rez:=8;
if rest(b,4)=0 then rez:=6;
end;
if a=3 then
begin
if rest(b,4)=1 then rez:=3;
if rest(b,4)=2 then rez:=9;
if rest(b,4)=3 then rez:=7;
if rest(b,4)=0 then rez:=1;
end;
if a=4 then
begin
if rest(b,2)=0 then rez:=6;
if rest(b,2)=1 then rez:=4;
end;
if a=5 then rez:=5;
if a=6 then rez:=6;
if a=7 then
begin
if rest(b,4)=1 then rez:=7;
if rest(b,4)=2 then rez:=9;
if rest(b,4)=3 then rez:=3;
if rest(b,4)=0 then rez:=1;
end;
if a=8 then
begin
if rest(b,4)=1 then rez:=8;
if rest(b,4)=2 then rez:=4;
if rest(b,4)=3 then rez:=2;
if rest(b,4)=0 then rez:=6;
end;
if a=9 then
begin
if rest(b,2)=1 then rez:=9;
if rest(b,2)=0 then rez:=1;
end;
if a=0 then rez:=0;
if b[1]=0 then rez:=0;
writeln(rez);
end;
end.
This is my source code, Matematicle it is very corect, it should get AC but it gets WA. Please, help me, I don't know what is wrong with this solution. Help!!!
nicu_ivan
New poster
Posts: 7
Joined: Wed Mar 16, 2005 7:27 pm
### Re: 10515 - WA, why? this is imposible!!!!!!!!!!!!!!
Code: Select all
`` Please help, I need an explination, I realy need an explination, please I need help!!!!!!``
nicu_ivan
New poster
Posts: 7
Joined: Wed Mar 16, 2005 7:27 pm
### Re: 10515 - WA, why? this is imposible!!!!!!!!!!!!!!
The Timus board is much more active.
Rocky
Experienced poster
Posts: 124
Joined: Thu Oct 14, 2004 9:05 am
Contact:
I am a C++ Programmer.So I Can't Analysis You'r Code.
You Need Only The Last Two Digit Of m,n & Then make it Power(m,n) And Mod By 10 Output The Result.
Some Special Case Occure When m==0&&n==0,m==1&&n==0,m==0,n==1
You Need To Handle This With Special Case.
If You Not Do That System You Can Follow It.
Otherwise If You Wish I Can Send You Some Data.
Good Luck
Rocky
WR
Experienced poster
Posts: 145
Joined: Thu Nov 27, 2003 9:46 am
Try this input:
Code: Select all
``````0 238479283749827394234
1 2340982309420394802
2 2
2 5
3 3
3 74
4 982374982739487239847298374982374982734987
5 23849823498
6 2342
7 444444
8 3999949230402394
8 24
9 2345996959645456
2 0
209384032409803948209 4032094809238409238409
8932749872394729346628364 234972983749823749872394789234
0 0
``````
Code: Select all
``````0
1
4
2
7
7
4
5
6
1
8
4
1
0
1
6
``````
my output (program accepted)
Code: Select all
``````0
1
4
2
7
9
4
5
6
1
4
6
1
1
9
6
``````
xero23xx
New poster
Posts: 1
Joined: Thu Jun 16, 2005 6:47 am
### 10515 --WA
I've tried many times, but I still can't find where there is something wrong......
------------------------------------------
#include<iostream.h>
int main(void)
{
char a[101],b[101];
int f,s,y,m,n;
while(cin>>a>>b)
{
s=1;
for(f=0;f<=101;f++)
{
if(a[f]==0)
{
if(a[f-1]==48 && a[f-2]>=48)
m=10;
else
m=((int)a[f-1])-48;
break;
}
}
for(f=0;f<=101;f++)
{
if(b[f+1]==0)
{
if(b[f-1]==0)
n=((int)b[f])-48;
else if(b[f-1]==48)
n=100;
else
n=((int)b[f])-48+(((int)b[f-1])-48)*10;
break;
}
}
if(m==0 && n==0)
return 0;
if(m==0 || m==10)
s=0;
if(n==0)
s=1;
if(m>0 && n>0)
{
switch(m)
{
case 1:
n=1;
break;
case 5:
n=1;
break;
case 6:
n=1;
default :
n=n%4+4;
break;
}
for(y=1;y<=n;y++)
s=s*m%10;
}
cout<<s<<endl;
}
return 0;
}
zero_cool
New poster
Posts: 27
Joined: Fri Sep 02, 2005 6:33 am
### 10515 - WA
I don't know what's wrong with my program. Can somebody help me?
_____________________________________________________________
#include <iostream>
#include <string>
using namespace std;
void main() {
string x,y;
unsigned short i,c,cycle,temp,tmp;
int base[10] = {1,1,4,4,2,1,1,4,4,2};
cin >> x >> y;
while ((x!="0")||(y!="0")) {
c=x[x.length()-1]-'0';
if (y.length()==1)
temp=(y[y.length()-1]-'0');
else
temp=(y[y.length()-1]-'0')+(y[y.length()-2]-'0')*10;
if (temp==0)
cout << 1 << endl;
else {
cycle=(temp-1)%base[c];
tmp=c;
for (i=0;i<cycle;i++)
c*=tmp;
cout << c%10 << endl;
}
cin >> x >> y;
}
}
_____________________________________________________________
acmmamun
New poster
Posts: 5
Joined: Tue Jul 19, 2005 1:02 pm
Contact:
### DONT UNDERSTAND!!!!!!
IF INPUT IS 3 74
THEN OUTPUT is 1 => 3^4=81%10=1
IN YOUR RESULT THAT IS 9
HOW IS IT POSSIBLE!!!!!
There are nothing to say about me....
acmmamun
New poster
Posts: 5
Joined: Tue Jul 19, 2005 1:02 pm
Contact:
I am Sorry for previous reply...
But I got the same ans that you have shown?
But still wrong Ans...
//HERE MY CODE
#include <stdio.h>
#include <math.h>
#include <string.h>
char s1[200],s2[200];
int m,n,st[12][6];
int main(){
int t,i,j,l1,l2;
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
for(i=0;i<=9;i++){
if(i==0){
for(j=1;j<=4;j++)
st[j]=0;
}
else if(i==1){
for(j=1;j<=4;j++)
st[j]=1;
}
else if(i==2){
st[1]=2;
st[2]=4;
st[3]=8;
st[4]=6;
}
else if(i==3){
st[1]=3;
st[2]=9;
st[3]=7;
st[4]=1;
}
else if(i==4){
st[i][1]=4;
st[i][2]=6;
st[i][3]=4;
st[i][4]=6;
}
else if(i==5){
st[i][1]=5;
st[i][2]=5;
st[i][3]=5;
st[i][4]=5;
}
else if(i==6){
st[i][1]=6;
st[i][2]=6;
st[i][3]=6;
st[i][4]=6;
}
else if(i==7){
st[i][1]=7;
st[i][2]=9;
st[i][3]=3;
st[i][4]=1;
}
else if(i==8){
st[i][1]=8;
st[i][2]=4;
st[i][3]=2;
st[i][4]=6;
}
else if(i==9){
st[i][1]=9;
st[i][2]=1;
st[i][3]=9;
st[i][4]=1;
}
}
while(scanf("%s%s",s1,s2) == 2){
if(s1[0]=='0' && s2[0]=='0')
break;
l1=strlen(s1);
l2=strlen(s2);
m=s1[l1-1]-'0';
n=0;
if(l2>1){
t=s2[l2-2]-'0';
n=t*10;
t=s2[l2-1]-'0';
}
else
t=s2[l2-1]-'0';
n+=t;
if(n==0)
printf("1\n");
else{
n%=4;
if(n==0)
n=4;
printf("%d\n",st[m][n]);
}
}
return 0;
}
There are nothing to say about me....
tuman
New poster
Posts: 24
Joined: Sat Oct 22, 2005 7:30 pm
Location: CUET
Contact:
[quote="Rocky"]I am a C++ Programmer.So I Can't Analysis You'r Code.
You Need Only The Last Two Digit Of m,n & Then make it Power(m,n) And Mod By 10 Output The Result.
Rocky, u dont need last two digit of m, you only need last digit of m and the last 2 digit of n, Then power them and finally mod the output by 10. You should make it clear before posting.Your advice can only result wrong answer.
We the dreamer of the dreamy dream...
jjtse
Learning poster
Posts: 80
Joined: Mon Aug 22, 2005 7:32 pm
Contact:
Hey guys,
I'm having a problem with this problem. And I don't think the problem is trivial. I used the basic well known idea of getting last digit in m and last 2 digit in n. I tried all the possible inputs I can find, and works fine.
i submitted my C program as a c++ program. got WA.
I submitted my C program as a c program. got CE (compile error)
There must be a header of some sort that I'm forgetting to put in. Can someone compile my code with the correct version of the compiler and execute it? thanks.
Code: Select all
``````
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
int main(){
int num, pow;
char s1[2000], s2[2000];
char temp[5];
int i;
int sum;
int cnt;
int len;
int list[10][5] = {
1, 0, 0, 0, 0,
1, 1, 1, 1, 0,
6, 2, 4, 8, 0,
1, 3, 9, 7, 0,
6, 4, 0, 0, 0,
1, 5, 0, 0, 0,
1, 6, 0, 0, 0,
1, 7, 9, 3, 0,
6, 8, 4, 2, 0,
1, 9, 0, 0, 0
};
scanf("%s%s", &s1, &s2);
while ( strcmp(s1, "0") || strcmp(s2, "0")){
len = strlen(s1);
num = atoi(&s1[len-1]);
len = strlen(s2);
cnt = 0;
strcpy (temp, "\0");
if (len > 2){
for (i=len-2; i<len; i++){
temp[cnt++] = s2[i];
}
temp[cnt] = '\0';
}
else {
strcpy(temp, s2);
}
pow = atoi(temp);
switch(num){
case 0:
if (pow != 0)
sum = 0;
else {
sum = 1;
}
break;
case 1:
sum = 1;
break;
case 2: case 3: case 7: case 8:
if (pow == 0)
sum = 1;
else {
pow = pow % 4;
sum = list[num][pow];
}
break;
case 5: case 6:
if (pow == 0)
sum = 1;
else {
sum = num;
}
break;
case 4: case 9:
if (pow == 0)
sum = 1;
else{
pow = pow % 2;
sum = list[num][pow];
}
break;
default: printf("*(#(WUIOJFLSDKFJ\n");
break;
}
printf ("%i\n", sum);
scanf("%s%s", &s1, &s2);
}//end while
return 0;
}
``````
ayon
Experienced poster
Posts: 161
Joined: Tue Oct 25, 2005 8:38 pm | 3,823 | 9,872 | {"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-2020-45 | latest | en | 0.399213 |
https://classroom.thenational.academy/lessons/subtracting-multiples-of-10-from-3-digit-numbers-61k34t?activity=exit_quiz&step=4 | 1,632,210,811,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057199.49/warc/CC-MAIN-20210921070944-20210921100944-00215.warc.gz | 217,397,424 | 35,797 | # Subtracting multiples of 10 from 3-digit numbers
In this lesson, we will use known number facts in order to mentally subtract multiples of 10 from 3-digit numbers. We will look at partitioning strategies and analyse place value to make mental subtraction more efficient.
This quiz includes images that don't have any alt text - please contact your teacher who should be able to help you with an audio description.
Quiz:
# Intro quiz - Recap from previous lesson
Before we start this lesson, let’s see what you can remember from this topic. Here’s a quick quiz!
Q1.Which one of these is a 3 digit number?
1/5
Q2.674 + 20 =
2/5
Q3.654 + 30 = 694 True or false?
3/5
Q4.520 + 80 =
4/5
Q5.666 + 50 =
5/5
This quiz includes images that don't have any alt text - please contact your teacher who should be able to help you with an audio description.
Quiz:
# Intro quiz - Recap from previous lesson
Before we start this lesson, let’s see what you can remember from this topic. Here’s a quick quiz!
Q1.Which one of these is a 3 digit number?
1/5
Q2.674 + 20 =
2/5
Q3.654 + 30 = 694 True or false?
3/5
Q4.520 + 80 =
4/5
Q5.666 + 50 =
5/5
# Video
Click on the play button to start the video. If your teacher asks you to pause the video and look at the worksheet you should:
• Click "Close Video"
• Click "Next" to view the activity
Your video will re-appear on the next page, and will stay paused in the right place.
# Worksheet
These slides will take you through some tasks for the lesson. If you need to re-play the video, click the ‘Resume Video’ icon. If you are asked to add answers to the slides, first download or print out the worksheet. Once you have finished all the tasks, click ‘Next’ below.
This quiz includes images that don't have any alt text - please contact your teacher who should be able to help you with an audio description.
Quiz:
# Subtracting Multiples of 10 from 3-Digit Numbers Quiz
Let's see how much you have learnt about subtracting multiples of 10 from 3-digit numbers
Q1.When we subtract the number we started with gets...
1/5
Q2.356 - 40 = 326 True or false?
2/5
Q3.673 - 60 =
3/5
Q4.532 - 40 =
4/5
Q5.300 - 60 =
5/5
This quiz includes images that don't have any alt text - please contact your teacher who should be able to help you with an audio description.
Quiz:
# Subtracting Multiples of 10 from 3-Digit Numbers Quiz
Let's see how much you have learnt about subtracting multiples of 10 from 3-digit numbers
Q1.When we subtract the number we started with gets...
1/5
Q2.356 - 40 = 326 True or false?
2/5
Q3.673 - 60 =
3/5
Q4.532 - 40 =
4/5
Q5.300 - 60 =
5/5
# Lesson summary: Subtracting multiples of 10 from 3-digit numbers
## It looks like you have not completed one of the quizzes.
To share your results with your teacher please complete one of the quizzes.
## Time to move!
Did you know that exercise helps your concentration and ability to learn?
For 5 mins...
Move around:
Jog
On the spot:
Dance | 808 | 2,998 | {"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} | 3.859375 | 4 | CC-MAIN-2021-39 | latest | en | 0.889665 |
https://www.coursehigh.com/downloads/solved-suppose-start-0-0-cy-plane-turn-consists-following-flip-two-fair-coins-first-coin-comes-he-q42684934/ | 1,696,069,272,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510671.0/warc/CC-MAIN-20230930082033-20230930112033-00318.warc.gz | 779,200,436 | 16,661 | # (Solved) : Suppose Start 0 0 Cy Plane Turn Consists Following Flip Two Fair Coins First Coin Comes He Q42684934 . . .
please solve this problem using python.
Suppose that you start at (0,0) on the cy-plane. A turn consists of the following: • Flip two fair coins. • If the first coin comes up heads, increase your c-coordinate by 1 and decrease it by 1 otherwise . If the second coin comes up heads, increase your y-coordinate by 1 and decrease it by 1 otherwise Estimate the average maximal distance to the origin after 50 turns. Show transcribed image text Suppose that you start at (0,0) on the cy-plane. A turn consists of the following: • Flip two fair coins. • If the first coin comes up heads, increase your c-coordinate by 1 and decrease it by 1 otherwise . If the second coin comes up heads, increase your y-coordinate by 1 and decrease it by 1 otherwise Estimate the average maximal distance to the origin after 50 turns.
Answer to Suppose that you start at (0,0) on the cy-plane. A turn consists of the following: • Flip two fair coins. • If the f…
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http://www.askphysics.com/tag/frictional/ | 1,603,867,347,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107896778.71/warc/CC-MAIN-20201028044037-20201028074037-00111.warc.gz | 119,502,451 | 21,150 | Home » Posts tagged 'frictional'
# Tag Archives: frictional
## CENTRIPETAL FORCE MISCONCEPTION
For a circular motion centripetal force is required. Is there any other force which could replace centripetal force to obtain a circular motion? (Asked Sajin)
Please note that Centripetal Force is the net force that must be acting towards the centre of the circular path. It may be provided by one or more of the forces of different kinds. It is not a kind of force like the frictional force or gravitational force. In different cases the centripetal force is provided by different forces.
For example, when we whirl a stone tied to the end of a rope in a horizontal plane, the tension in the string provides the centripetal force. Here the real force acting is the tension in the string and its magnitude equals the centripetal force mv^2/r.
1. http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html
2. http://en.wikipedia.org/wiki/Centripetal_force
3. http://www.physicsclassroom.com/Class/circles/u6l1c.cfm
## An Idea for Cycle Rickshaw
Sir,
While seeing a rickshaw puller struggling to pull heavy weight,I wondered if the load carried by him can be reduced for carrying same weight people.Since the load carried by him is dependent on the horizontal component of frictional force (i.e,µ.mgsinØ) ,cant we apply a spring in the rickshaw so that the effective weight will decrease and hence the load carried by him?
### Hits so far @ AskPhysics
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https://www.tutorialaicsip.com/cs-xii/class-12-computer-science-answer-key-2024/ | 1,716,889,372,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059085.33/warc/CC-MAIN-20240528092424-20240528122424-00882.warc.gz | 892,593,344 | 55,864 | # Class 12 Computer Science answer key 2024 – A comprehensive Solutions
In this article, I will discuss Class 12 Computer Science Answer Key 2024. The class 12 Computer Science exam was held on 02.04.2024. The paper was moderate. So let us begin.
Topics Covered
## Class 12 Computer Science Answer Key 2024
There are 5 sections.
## Section A – Class 12 Computer Science Answer Key 2024
[1] State True or False:
While defining a function in Python, the positional parameters in the function header must always be written after the default parameters.
[2.] The SELECT statement when combined with ____ clause, returns records without repetition
(a) DISTINCT
(b) DESCRIBE
(c) UNIQUE
(d) NULL
[3.] What will be the output of the following statement:
print (16*5/4*2/5-8)
(a) -3.33
(b) 6.0
(c) 0.0
(d) -13.33
[4.] What possible output from the given options is expected to be displayed when the following Python code is executed?
``````import random
Signal = [ 'RED, 'YELLOW', 'GREEN' ]
for K in range(2, 0, -1):
R = random.randrange(K)
print (Signal[R], end = ' # ')
``````
(a) YELLOW # RED #
(b) RED # GREEN #
(c) GREEN # RED #
(d) YELLOW # GREEN
[5.] In SQL, the aggregate function which will display the cardinality of the table is____
(a) Sum()
(b) Count(*)
(c) Avg()
(d) Sum(*)
[6.] Which protocol out of the following is used to send and receive emails over a computer network?
(a) PPP
(b) HTTP
(c)FTP
(d)SMTP
[8.] Consider the statements given below and then choose the correct output from the given options:
``````myStr=”MISSISSIPPI”
print( myStr[:4] + “#”+myStr [-5:])``````
(a) MISSI#SIPPI
(b) MISS#SIPPI
(c) MISS#IPPIS
(d) MISSI#IPPIS
[9.] Identify the statement from the following which will raise an error:
(a) print(“A”*3)
(b) print (5*3)
(c) print (“15” + 3)
(d) print(“15” + “13”)
[10.] Select the correct output of the following code:
``````event="G20 Presidency@2023"
L=event.split(' ')
print (L[::-2])``````
(a) ‘G20’
(b) [‘Presidency@2023’]
(c) [‘G20’]
(d) ‘Presidency@2023’
[11.] Which of the following options is the correct unit of measurement for network bandwidth?
(a) KB
(b) Bit
(c) Hz
(d) Km
12. Observe the given Python code carefully:
``````a=20
def convert (a):
b=20
a=a+b
convert (10)
print (a)``````
Select the correct output from the given options:
(a) 10
(b) 20
(c) 30
(d) Error
[13.] State whether the following statement is True or False
While handling exceptions in Python, name of the exception has to be compulsorily added with except clause.
[14.] Which of the following is not a DDL command in SQL?
(a) DROP
(b) CREATE
(c) UPDATE
(d) ALTER
[15.] Fill in the blanks:
_________ is a set of rules that needs to be followed by the communicating parties in order to have a successful and reliable data communication over a network.
[16.] Consider the following Python statement.
F=open (‘CONTENT. TXT’)
Which of the following is an invalid statement in Python?
(a) F. seek (1, 0)
(b) F. seek (0, 1)
(c) F. seek (0, -1)
(d) F. seek (0, 2)
Q17 and 18 are ASSERTION AND REASONING based questions. Mark the correct choice as
(a) Both A and R are true and R is the correct explanation for A
(b) Both A and R are true and R is not the correct explanation for A
(c) A is True but R is False
(d) A is false but R is True
[17.] Assertion (A): CSV File is a human readable file where each line has a number of fields, separated by comma or some other delimiter.
Reason (R): writerow() function is used to write a single row in a CSV file.
[18.] Assertion (A) : The expression “HELLO”.sort() in Python will give an error.
Reason (R): sort() does not exist as a method/function for strings in python.
## Section B – Class 12 Computer Science Answer Key 2024
[19.] (A) (i) Expand the following terms: XML, PPP
(ii) Given one difference point between circuit switching and packet switching.
OR
(B) (i) Define the term web hosting.
(ii) Name any two web browsers.
[20.] The code given below accepts five numbers and displays whether they are even or odd. Observe the following code and rewrite it after removing all syntax and logical errors:
``````def EvenOdd()
for i in range(5):
num=int(input("Enter a number")
if num/2==0:
print("Even")
else:
print("Odd")
EvenOdd()``````
Ans.:
``````def EvenOdd(): # Colon at the end of statement
for i in range(5):
num=int(input("Enter a number")) # Closing bracket missing
if num%2==0: # The operator needs to be changed
print("Even")
else:
print("Odd") # Indentation
EvenOdd()``````
[21.] (A) Write a user-defined function in Python named showGrades(S) which takes the dictionary S as an argument. The dictionary, S contains Name:[Eng, Math, Science] as key:value pairs. The function displays the corresponding grade obtained by students according to the following grading rules:
For Example, Consider the following dictionary:
S={“AMIT”:[92,86,64],”NAGMA”:[65, 42, 43],”DAVID”:[92, 90, 88]}
The output should be:
AMIT – B
NAGMA – C
DAVID – A
Ans.:
``````def showGrades(S):
for i in S:
s=0
for j in S[i]:
s+=j
avg=s/3
if avg>=90:
elif avg>=60 and avg<90:
elif avg<60:
S={"AMIT":[92,86,64],"NAGMA":[65, 42, 43],"DAVID":[92, 90, 88]}
(B) Write a user-defined function in Python named Puzzle(W,N) which takes the argument W as an English word and N as an integer and returns the string where every Nth alphabet of the word W is replaced with an underscore(“-“).
For example: if W contains the word “TELEVISION” and N is 3, then the function should return the string “TE_EV_SI_N”. Likewise for the word “TELEVISION” if N is 4, then the function should return “TEL_VIS_ON”.
Ans.:
``````def Puzzle(W,N):
l=list(W)
s1=''
for i in range(0,len(l)):
if i!=0 and (i+1)%N==0:
s1+='_'
else:
s1+=W[i]
return str(s1)
w=input("Enter English Word:")
n=int(input("Enter n to replace:"))
print(Puzzle(w,n))``````
[22.] Write the output displayed on the execution of the following Python code:
``````LS=["HIMALAYA","NILGIRI","ALASKA","ALPS"]
D={}
for S in LS:
if len(S)%4==0:
D[S]=len(S)
for K in D:
print(K,D[K],sep="#")``````
[23.] (A) Write a Python statement for each of the following tasks using built-in functions/methods only:
(i) To remove an item whose key is “NISHA” from a dictionary named Students.
For example, if the dictionary Students contains {“ANITA”:90,”NISHA”:76,”ASHA”:92}
(ii) To display the number of occurrences of the substring “is” in a string named message.
For example, if the string message contains “This is his book”, then the output will be 3.
OR
(B) A tuple named subject stores the names of different subjects. Write the Python commands to convert the given tuple to a list and thereafter delete the last element of the list.
Ans.:
``````subject=("English","Physics","Chemistry","Maths","Biology","Computer Science")
l=list(subject)
l.pop()
print(l)``````
[24.] (A) Ms. Veda created a table named Sports in a MySQL database, containing columns Game_Id, P_Age and G_Name.
After creating the table, she realized that the attribute, Category has to be added. Help her to write a command to add the Category column. Thereafter, write the command to insert the following record in the table:
OR
(B) Write the SQL commands to perform the following tasks:
1. View the list of tables in the database Exam
2. View the structure of the table Term1
[25] Predict the output of the given code:
``````def callon(b=20,a=10):
b=b+a
a=b-a
print(b,'#',a)
return b
x=100
y=200
x=callon(x,y)
print(x,'@',y)
y=callon(y)
print(x,'@',y)``````
## Section C – Class 12 Computer Science Answer Key 2024
[26] Write the output on execution for the following Python code:
``````S="Racecar Car Radar"
L=S.split()
for W in L:
x=W.upper()
if x==x[::-1]:
for I in x:
print(I, end='*')
else:
for I in W:
print(I,end='#')
print()``````
[27] Consider the table ORDERS given below and write the output of the SQL queries that follow.
(I) SELECT ITEM, SUM(QTY) FROM ORDERS GROUP BY ITEM;
(ii) SELECT ITEM, QTY FROM ORDERS WHERE ORDATE BETWEEN ‘2023-11-01’ AND ‘2023-12-31’;
(iii) SELECT ORDNO, ORDATE FROM ORDERS WHERE ITEM = ‘WHEAT’ AND RATE>=60;
[28] (A) Write a user-defined function in Python named showLines() which reads the contents of a text file named STORY.TXT and displays every sentence in a separate line.
Assume that a sentence ends with a full stop (.), a question mark (?), or an exclamation mark(!).
For example, if the content of file STORY.TXT is as follows:
Our parents told us that we must eat vegetables to be healthy. And it turns out, our parents were right! So, what else did our parents tell?
Then the function should display the file contents as follows:
`Our parents told us that we must eat vegetale to be healthy. And it turns out, our parents were right!So, what else did our parents tell?`
Ans.:
Method 1:
``````def showInLines():
f=open("story.txt")
sentence=[]
sentence1=[]
sentence2=[]
for i in l:
if i=='.':
idxdt=l.index(i)
sentence.append(l[:idxdt+1])
elif i=='!':
idxe=l.index(i)
sentence1.append(l[idxdt+1:idxe+1])
elif i=='?':
idxq=l.index(i)
sentence2.append(l[idxe+1:idxq+1])
for i in sentence:
print(i)
for i in sentence1:
print(i)
for i in sentence2:
print(i)
showInLines()
``````
Method 2:
``````def showLines():
f=open("story.txt")
sentence=[]
cur_sen=''
for i in x:
cur_sen+=i
if i in ['.','?','!']:
sentence.append(cur_sen.strip())
cur_sen=''
if cur_sen:
sentence.append(cur_sen.strip())
for i in sentence:
print(i)
showLines()``````
OR
(B) Write a function, c_words() in Python that separately counts and displays the number of uppercase and lowercase alphabets in a text file, words.txt.
Ans.:
``````def c_words():
f=open("story.txt")
uc=0
lc=0
for i in x:
if i.isupper():
uc+=1
if i.islower():
lc+=1
print("Uppercase Letters:",uc)
print("Lowercase Letters:",lc)
c_words()``````
[29] Consider the table projects given below:
Table: Projects
Based on the given table, write SQL queries for the following:
(i) Add the constraint, primary key to column P__id in the existing table Projects.
(ii) To change the language to Python of the project whose id is P002.
(iii) To delete the table Projects from MySQL database along with its data.
[30] Consider a list named Nums which contains random integers:
Write the following user defined functions in Python and perform the specified operations on a stack named BigNums.
(i) PushBig(): It checks every number from the list Nums and pushes all such numbers which have 5 or more digits into the stack, BigNums.
(ii) PopBig(): It pops the numbers from the stack, BigNums, and displays them. The function should also display “Stack Empty” when there are no more numbers left in the stack.
For example: If the list Nums contains the following data:
Nums=[213,10025,167,254923,14,1297653,31498,386,92765]
Then on execution of PushBig(), the stack BigNums should store:
[10025, 254923, 1297653, 311498, 92765]
And on execution of PopBig(), the following output should be displayed:
92765
31498
1297653
254923
10025
Stack Empty
Ans.:
``````Nums=[213,10025,167,254923,14,1297653,31498,386,92765]
BigNums=[]
def PushBig():
for i in Nums:
if i>=10000:
BigNums.append(i)
return BigNums
def PopBig():
if BigNums==[]:
return "Stack is empty"
else:
return BigNums.pop()
print(PushBig())
while True:
if BigNums!=[]:
print(PopBig())
else:
break
if BigNums==[]:
print("Stack Empty")``````
## Section D – Class 12 Computer Science Answer Key 2024
[31] Consider the tables Admin and Transport given below:
Table: Transport
Write SQL queries for the following:
(i) Display the student name and their stop name from the tables Admin and Transport.
(ii) Display the number of students whose S_type is not known.
(iii) Display the details of the students whose names starts with ‘V’
(iv) Display student id and address in alphabetical order of student name from the table admin
Ans.:
[32] Sangeeta is a Python programmer working in a computer hardware company. She has to maintain the records of the peripheral devices. She created a csv file named Peripheral.csv, to store the details. The structure of Peripheral.csv is:
[P_id, P_name, Price]
where
P_id is Peripheral devices ID (integer)
P_name is Peripheral device name (String)
Price is Peripheral device price (integer)
Sangeeta wants to write the following user-defined functions:
Add_Devices(): to accept a record from the user and add it to a csv file, Peripheral.csv
Count_Device(): To count and display number of peripheral devices whose price is less than 1000.
Ans.:
``````import csv
P_id=int(input("Enter Peripheral id:"))
P_name=input("Enter Peripheral Name:")
price=float(input("Enter price:"))
f=open("Peripheral.csv","a",newline='')
wo=csv.writer(f)
wo.writerow([P_id,P_name,price])
f.close()
def Count_device():
cnt=0
f=open("Peripheral.csv","r")
l=list(ro)
for i in l:
if i[2]<1000:
cnt+=1
print("Number of devices:",cnt)
Count_device()``````
## Section E – Class 12 Computer Science Answer Key 2024
[33] Infotainment Ltd. is an event management Ltd. is an event management company with its prime office located in Bengaluru. The company is planning to open it new division at three different locations in Chennai named as – Vajra, Trishula and Sudershana.
You, as a networking expert, need to suggest solutions to the questions in part (i) to (v), keeping in mind the distances and other given parameters.
Distances between various locations:
Number of computers installed at various locations:
(i) Suggest and draw the cable layout to efficiently connect various locations in the Chennai division for connecting the digital devices.
(ii) Which block in Chennai division should host the server? Justify your answer.
(iii) Which fast and effective wired transmission medium should be used to connect the prime office at Begaluru with the Chennai division?
(iv) Which network device will be used to connect the digital devices within each location of the Chennai division so that they may communicate with each other?
(v) A considerable amount of data loss is noticed between different loc
Ans.:
(i)
(ii) Vajra block in Chennai division shoud host server because it has maximum number of computers installed, and according to 80:20 rule the server should be placed in the room where maximum number computers are installed.
(iii) Fibre optical cable should be used to connect the prime office at Bengaluru with the Chennai location.
(iv) Switch will be used to connect the digital devices within each location of Chennai division.
(v) Repeater should be installed to refresh the data loss during transmission to and from different locations of Chennai division.
[34] (A) (i) Differentiate between ‘w’ and ‘a’ file modes in Python.
(ii) Consider a binary file, items.dat, containing records stored in the given format:
{item_id:[item_name, amount]}
Write a function, Copy_new(). that copies all records whose amount is greater than 1000 from items.dat to new_items.dat.
Ans.:
(i)
(ii)
``````def Copy_new():
d1={}
f=open("items.dat","rb")
while True:
try:
for i in dt:
if dt[i][1]>1000:
d1[i]=dt[i]
except EOFError:
break
f.close()
f=open("items.dat","wb")
pickle.dump(d1,f)
f.close()
Copy_new()``````
OR
(B) (i) What is the advantage of using with clause while opening a data file Python? Also give syntax of with clause.
(ii) A binary file EMP.DAT has the following structure:
[Emp_Id, Name, Salary]
where
Emp_Id : Employee id
Name: Employee Name
Salary: Employee Salary
Write a user defined function, disp_Detail(), that would read the contents of the file EMP.DAT and display the details of those employees whose salary is below 25000.
Ans.:
(i) The with clause automatically closes the file after nested block of code. It guarantees to close the file no matter how the nested block exists even exception occurs before the end of the block, the with statement will handle it and close the file.
(ii)
``````import pickle
def disp_Detail():
f=open("emp.dat","rb")
while True:
try:
for i in range(len(dt)):
if dt[2]<25000:
print(dt[i],end=" ")
print()
except EOFError:
break
disp_Detail()``````
[35] (A) (i) Define cartesian product with respect to RDBMS.
(ii) Sunil wants to write a program in Python to update the quantity to 20 of the records whose item code is 111 in the table named shop in MySQL database named Keeper.
The table shop in MySQL contains the following attributes:
• Item_code: Item code (Integer)
• Item_name: Name of item (String)
• Qty: Quantity of item (Integer)
• Price: Price of item (Integer)
Consider the following to establish connectivity between Python and MySQL:
• Host : localhost
Ans.:
(i) Cartesian products refers to the product of two tables of all possible concatenations are formed of all rows of both tables.
(ii)
``````import mysql.connector as m
cr=cn.cursor()
cr.execute("update shop set qty=20 where item_code =111")
cn.commit()``````
OR
(B) (i) Give any two features of SQL.
(ii) Sumit wants to write a code in Python to display all the details of the passengers from the table flight in MySQL database, Travel. The table contains the following attributes:
F_code : Flight code (String)
F_name: Name of flight (String)
Source : Departure city of flight (String)
Destination : Destination city of flight (String)
Consider the following to establish connectivity between Python and MySQL:
• Host: localhost
Ans.:
(i)
• Speed
• Ease of use
• Cost
• Query Language
• Portability
• Data Types
• Scalability and Limits
• Localization
(ii)
``````import mysql.connector as my
cn=my.connect(host='localhost',user='root',passwd='airplane',database='school')
cur=cn.cursor()
cur.execute("select * from shop")
dt=cur.fetchall()
for i in dt:
print(i)
cn.close()`````` | 4,717 | 17,713 | {"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} | 2.5625 | 3 | CC-MAIN-2024-22 | latest | en | 0.675012 |
https://physics.stackexchange.com/questions/322379/boundary-conditions-in-variational-principles | 1,719,208,689,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865074.62/warc/CC-MAIN-20240624052615-20240624082615-00829.warc.gz | 405,090,552 | 39,657 | # Boundary conditions in variational principles
In classical mechanics, the condition to fix the variation of the trajectory at the endpoints has a clear-cut meaning. We want the system to propagate from $x\in\mathcal{C}$ to $y\in\mathcal{C}$, therefore, we only consider curves that have these two points as endpoints, so the variations also have to respect this. It is clear.
Moving on to relativistic field theory and the (covariant) Lagrangian approach of it, these conditions however become much less transparent.
The action is usually defined as $$S[\phi]=\int_{\mathcal{D}}\mathcal{L}(\phi,\nabla\phi...\nabla^{(k)}\phi)\ d^nx,$$ and we consider only variations $\delta\phi$ for which $\delta\phi|_{\partial\mathcal{D}}=0$.
In particular, it is accepted, that the derivatives of the variation $\nabla_\mu\delta\phi$ cannot be set to zero on the boundary.
Sources I have seen, however did not explain any of this, they just postulated.
Questions:
• What is the motivation to postulate the vanishing of the variation at the boundary?
• What is the reason one cannot also postulate the vanishing of the derivative of the variation at the boundary?
• Is there any significance to the domain $\mathcal{D}$ in the action? In particular, I have seen some books demand the integral to be extended to the entire manifold, while some books explicitly said that $\mathcal{D}$ should be a compact or precompact domain.
Further notes:
• I have seen a throwaway note in Wald's General Relativity that, when defined the functional derivative $\delta S/\delta\phi$ as $$\delta S[\phi]=\int_{\mathcal{D}}\frac{\delta S}{\delta\phi}\delta\phi\ d^nx,$$ said that more generally, $S$ is functionally differentiable if there exists a tensor distribution $\frac{\delta S}{\delta\phi}$ such that $$\delta S[\phi]=\langle \frac{\delta S}{\delta\phi},\delta\phi\rangle.$$ This made me think that maybe one should take the variations $\delta\phi$ as test functions. But then, if they are usual test functions and have compact support, then taking $\mathcal{D}=\text{supp}(\delta\phi)$ will reproduce the usual boundary conditions, but if we extend the domain of integration outside $\mathcal{D}$, then because the test function is identically zero outside its support, then we can also set the derivatives zero, right? But if we take the variations to be tempered test functions, then the domain always have to be the entire manifold.
.
• It is possible to derive the Israel junction conditions from variational principles, but in this case, the Gibbons-Hawking-York boundary term must be appended to the action. This provides a direct application of the GHY term, which itself is a consequence of not being able to set the derivatives of the variation to zero, so here I see this claim validated by practical results, yet the underlying reason still eludes me.
1. Disclaimer: We assume that OP only wants to discuss physical systems that have a stationary action principle.
2. Variations of physical systems are in general not limited to have compact support, or satisfy various mathematical regularization conditions, such as, e.g., smoothness. However, in many cases we may make simplifying technical assumptions. Just be careful that we don't kill interesting physics in the pursuit of mathematical idealization!
3. The spacetime integration region may in general reflect the physical spacetime, or a subregion thereof.
4. To derive Euler-Lagrange (EL) equations, it is necessary to impose boundary conditions (BCs), cf. e.g. this Phys.SE post, either essential/Dirichlet BCs or natural BCs.
5. By adding boundary terms (BTs) to the action, the above set of consistent BCs may change.
6. The nature of the physical system under investigation may lead to BCs for some other physical reasons. These physical BCs should agree with either essential/Dirichlet BCs or natural BCs for consistency. | 907 | 3,894 | {"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} | 2.78125 | 3 | CC-MAIN-2024-26 | latest | en | 0.914125 |
https://www.angelfire.com/hi5/ezramann/OldSite/past/psports191.html | 1,621,294,186,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991870.70/warc/CC-MAIN-20210517211550-20210518001550-00115.warc.gz | 665,840,139 | 4,159 | Past Sports
Past Sports from the past week. Past sports article for the week of 2/3/08 Fraction warriors stay undivided in the face of decimals By, Cozmic After Dennis DeTurck stepped into the spotlight with his claims that fractions should be abandoned once again, the “fractal warriors”, as they are called, a super-team of absolute and total math masters, have rebelled strongly against the idea, claiming that fractions are an integral part of math, and, more importantly, competing in math and thus proving you might be a total nerd but at least you're better at it than everyone else. DeTurck's claims that teachers should stop teaching fractions, instead replacing them with decimals such as 1/3 being replaced by .333333333333333333333333333333333333333333333333333333333333333 (to infinity and beyond!) are, according to the leader of the group, known as “The Non-Remainder” in the competitive maths-circuit, and Bob by everyone else, “the most stupidest thing I've ever heard since someone said pi was only 3.14.” Such harsh words have of course led to DeTurck filing a lawsuit against Bob, who's sole comment on the matter was that this was merely the start of the first quarter. DeTurck, of course, was even more infuriated by this. Rather than take it up in court, however, the fractal warriors want to settle the fractions versus decimals fight in a simple game of taking math-tests. Whoever finishes first and has the most correct answers will win the fight. DeTurck has thus far refused to partake, saying that it would be heavily slanted against using decimals, since he refuses to use fractions, while the fractal warriors could use whatever they please. This means that they could answer things with 100% accuracy, something DeTurck frowns upon, as the closest he would get would be to type an infinite amount of decimals, something that would take up far too much time, meaning he would either have an incorrect answer or lose. When the fractal warriors asked if this did not pretty much invalidate his entire point of why fractions should be ignored, DeTurck chose not to respond. Expert commentators, who all are part of the fractal warriors or are their arch-enemies, all agree that DeTurck has pretty much lost the debate entirely now, and that should the whole thing end up in court, he would have to pay four fifths of the legal fees. DeTurck pointed out that four fifths was a staggering 80 per cent, and was immediately patted on the head by Bob's friend “Dividing by zero” for being such a good boy who could figure that out.
Really Pathetic Productions 1997-2007© Menu Bar by Albatross | 585 | 2,617 | {"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-2021-21 | latest | en | 0.966573 |
https://socratic.org/questions/a-firework-is-launched-from-the-ground-at-a-velocity-of-180-feet-per-second-its- | 1,726,192,005,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651506.7/warc/CC-MAIN-20240913002450-20240913032450-00885.warc.gz | 494,861,660 | 6,305 | # A firework is launched from the ground at a velocity of 180 feet per second. Its height after t (t is the variable) seconds is given by the polynomial -16^2 + 180t. How do you find the height of the firework after 2 seconds and after 5 seconds?
Jun 13, 2015
In your equation I think there is a $t$ missing!!!
$h = 180 t - 16 {t}^{2}$
#### Explanation:
$h$ is the height reached starting with an initial velocity of $180 \frac{f t}{s}$ and considering an acceleration of gravity of $32 \frac{f t}{{s}^{2}}$:
$h \left(t\right) = {v}_{i} t - \frac{1}{2} \left(32\right) {\left(t\right)}^{2}$
$h \left(t\right) = 180 t - 16 {t}^{2}$
for:
$t = 2 s$
$h \left(2\right) = \textcolor{red}{296} f t$
$t = 5 s$
$h \left(5\right) = \textcolor{red}{500} f t$ | 263 | 753 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "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} | 4.1875 | 4 | CC-MAIN-2024-38 | latest | en | 0.823349 |
https://www.physicsforums.com/threads/stumped-on-precalc-problem.532485/ | 1,547,914,259,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583671342.16/warc/CC-MAIN-20190119160425-20190119182425-00167.warc.gz | 892,007,441 | 14,790 | # Stumped on precalc problem
1. Sep 21, 2011
### HarveyBullock
1. The problem statement, all variables and given/known data
1. given F(x) = .2x^4 - 2x^2 - 5x
find: XMIN, XMAX, YMIN, YMAX
2. Using F(X) find the following:
a. Domain
b. Range
c. List increasing intervals
d. List decreasing intervals
e. Coordinates of any maximums or minimums
I worked it out mostly on paper and can't get that far. I did figure out though that the function is neither odd nor even. which was for a different question
Last edited: Sep 21, 2011
2. Sep 21, 2011
### symbolipoint
Since you are not looking for roots but want minima and maxima and the problem is for Precalculus, easiest and fastest is to use a graphing calculator.
3. Sep 21, 2011
### HarveyBullock
I entered it on the calculator but did not really see the "hump" do figure out maxima and minima
4. Sep 22, 2011
### Allenman
Did you learn any rules for differentiation?
If you differentiate it, you're finding the equation of the slope of your original function.
Set the new equation equal to zero and solve for different values of x to get the critical points (don't forget the endpoints are also critical points).
Plug in numbers on either side of those points to find whether it's positive or negative (increasing or decreasing).... If the critical point is between a positive and a negative slope, it will be a local max or min (depending on which side has the positive and negative).
5. Sep 22, 2011
### symbolipoint
You will see an inflection, but no other kind of hump. The question is here in the Precalculus section of this category of the forum, so no calculus assumed and none expected. With a graphing program or tool, you will find two Real roots, and there is only one minimum; no other minimum or maximum.
For viewing, you could set to XMIN = ~-10, XMAX = ~+15, YMIN = -20, YMAX = ~+15.
The one obvious root is (0, 0), and the other root just a fraction of a unit greater than x=4 (but you find it yourself using your program or your graphing calculator).
Your function can be transformed into $F(x)=\frac{1}{5}x(x^3-10x-25)$. When you try examining the cubic factor with the Rational Roots method, you may find you cannot obtain another polynomial factor. I suspect that two factors for F(x) could contain either non-rational roots or complex roots.
6. Sep 22, 2011
### HallsofIvy
This makes no sense. First, obviously, there is NO y and so no "YMIN" or "YMAX"! I assume you mean y= F(x). More importantly, unless additional conditions are given, there is not limit in x and so there is no "XMIN" or "XMAX". (Perhaps they intend XMIN= -infinity and XMAX= +infinity.)
Are you sure about that "x" in "-5x"? Without it, we could let $u= x^2$, so the equation becomes $u= .2u^2- 2u- 5= (1/5)(u^2- 10u- 25)=(1/5)(u^2- 10u+ 25- 50)= (1/5)((u- 5)^2- =50)$. In that form, it is relatively easy to determine the values you want.
If it really is $F(x)= .2x^4- 2x^2- 5x= (1/5)x(x^3- 10x- 25)$. Now, you would have to use differentiation to find max and min.
7. Sep 22, 2011
### Swalker
Hi,
It is clear that f(x) will be plotted on an x, y graph so xmin, xmax correspond to the x axis minima and maxima humps, ymin and ymax correspond to the values.
To search for these using your graphing calculator stay with a large range like
Xmin & ymin = -50 and then xmax and ymax = 50.
Once you see humps on the graph zoom in to the ranges to get the actual values.
Your domain will be xmin, xmax.
Your range will be ymin to ymax.
Hope this helps
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook | 1,014 | 3,604 | {"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} | 3.90625 | 4 | CC-MAIN-2019-04 | latest | en | 0.899921 |
https://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-11-section-11-4-partial-sums-of-arithmetic-and-geometric-sequences-exercise-set-page-658/4 | 1,537,529,463,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267157070.28/warc/CC-MAIN-20180921112207-20180921132607-00550.warc.gz | 758,510,887 | 12,693 | ## Intermediate Algebra (6th Edition)
$S_{8} = 85$
Given geometric sequence $-1,2,-4,...$ $a_{1} = -1$ Common ratio $r = \frac{a_{n}}{a_{n-1}}$ $r= \frac{a_{2}}{a_{1}} = \frac{2}{-1} = -2$ Sum of first eight terms is $S_{8} = \frac{-1(1-(-2)^{8})}{1-(-2)}$ [Using $S_{n} =\frac{ a_{1}(1-r^{n})}{1-r}$] $S_{8} = \frac{-1(1-256)}{1+2}$ $S_{8} = \frac{-1(-255)}{3}$ $S_{8} = \frac{255}{3}$ $S_{8} = 85$ | 202 | 400 | {"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} | 4.25 | 4 | CC-MAIN-2018-39 | longest | en | 0.49877 |
https://www.nagwa.com/en/videos/690149832609/ | 1,586,545,990,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370511408.40/warc/CC-MAIN-20200410173109-20200410203609-00040.warc.gz | 1,035,747,504 | 10,465 | # Video: Comparing Energy Transfers Produced by Magnetic and Electric Fields
A student uses a bar magnet to lift some steel paperclips off a table. Figure 1 shows the magnet lifting the paperclips off the table. Explain how the bar magnet lifts a steel paperclip off the table. Iron can be used to make permanent magnets. Which other materials can be used to make permanent magnets? [A] Copper [B] Magnesium [C] Nickel [D] Cobalt. Figure 2 shows two parallel, charged plates. The charged plates create a uniform electric field between them. Use an expression from the box to complete the sentence. As the amount of charge on each metal plate is increased, the potential difference between the positively charged plate and the negatively charged plate ＿. When the potential difference between two charged plates is 50 kv, a spark jumps between the two plates. The spark transfers 0.00004 C of charge between the plates. The equation which relates the energy transferred by a charge that moves across an electric potential difference, the size of the charge, and the potential difference is energy transferred = charge × potential difference. Calculate the energy transferred by the spark. Energy transferred = ＿ J
15:06
### Video Transcript
A student uses a bar magnet to lift some steel paperclips off a table. Figure one shows the magnet lifting the paperclips off the table. Explain how the bar magnet lifts a steel paperclip off the table.
Looking at Figure one, we see an image of something you may have experienced before. If you start out with a group of paperclips sitting in a pile on a table and then bring a bar magnet close to the pile without touching them, the paperclips actually will do what we’re seeing here in Figure one. They will be drawn to the end of the bar magnet and attach in a chain like this, hanging down from the magnet to the table.
Knowing that this does happen, we want to explain just how it is that this happens. We know from experience that most materials don’t act this way. So what is it about the bar magnet and the steel paperclips that’s different?
Part of the explanation for all this comes from the fact that these paperclips are made of steel. That means that this paperclip made of steel is in a class of materials that change or respond when they’re in a magnetic field. Most materials of course aren’t like this. If you bring a bar magnet near to a leaf or to a book or to a cotton shirt, they won’t change in response to the magnetic field from the bar magnet. But objects made of steel — like this paperclip — do.
Let’s consider how this happens. It starts with the fact that a bar magnet like the one we have in Figure one creates a magnetic field around it. That field is invisible to our eye. But if we were to draw in what it might look like, if we could see it, it will look something like this. The magnetic field lines — that’s what each one of these is called — start out at the north pole of the magnet and move to the south pole.
Now, here’s what’s interesting about this. If we take our paperclip and put it in the field created by this magnet, not touching the bar magnet, but just in the field it creates, then our paperclip like we mentioned will be changed by this magnetic field. It will line up so that it is oriented along the magnetic field lines.
When this occurs, the paperclip itself becomes a magnet, not a permanent one like the bar magnet, but a magnet nonetheless whilst in this field. Knowing that with magnets, north poles attract south poles and south poles attract north poles, what do you think are the poles of this paperclip that’s in the magnetic field we’ve drawn?
Well, if we start at the north pole of the bar magnet and follow the field lines until they reach one of the ends of the paperclip, we know that because opposite poles attract one another, that end of the paperclip will be its south pole. And likewise, if we start at the south pole of the permanent bar magnet and move backwards along one of the field lines until we reach the paperclip, then that end of the paperclip will be its north pole.
So the north end of the paperclip is closest to the south end of the bar magnet and the south end of the paperclip is closest to the north end of the bar magnet. The paperclip that we’ve drawn is coming in from the side of the bar magnet. But in our scenario, in Figure one, we have a pile of paperclips right below it. A paperclip that’s lifted this way will end up looking like we see the paperclips in this figure.
One really fascinating thing about this effect is that the magnetic attraction between the paperclip and the bar magnet is stronger than the force of gravity on the paperclip; that’s why it rises up. Let’s put some of what we’ve described here into words as part of our answer.
The first step we mentioned in this process is that the magnetic field of the permanent magnet makes the steel paperclips themselves magnetised; it changes them. Next, we said that the field of the temporary magnet, that is the paperclip that’s changed by the magnetic field of the bar magnet, aligns to the field that created it.
This is what it meant when we said that the north pole of our temporary magnet, the paperclip, faces the south pole of our bar magnet. And it’s the same on the other side too. The relative south pole of our paperclip is aligned towards the north pole of our bar magnet.
Writing all that out, we can say that this means that the end of the paperclip closest to the south pole of the magnet becomes the north pole of the paperclip. We say “becomes” here because our paperclip only turns into a magnet in the presence of the bar magnet’s magnetic field. Without that field, the paperclip is unmagnetised and continues to sit in a pile on the table.
Then, finally, because opposite poles attract and because the north pole of the paperclip is facing the south pole of the bar magnet, the paperclip is lifted off the table against the force of gravity. This is our explanation for just how it is that this physical phenomenon occurs.
In this example, we talked about how an object made of steel is affected by an external magnetic field. Next, let’s consider what other types or materials are affected in a similar way.
Iron can be used to make permanent magnets. Which other materials can be used to make permanent magnets? Tick two boxes. Copper, magnesium, nickel, cobalt.
This question is interesting because it tells us that certain materials which do not start off as magnets can become permanent magnets. We’re told that iron is a material like this and that there are two more in this list for us to identify. Considering a large chunk of iron, let’s consider just how it would be that this chunk could become a permanent magnet.
The idea is that iron and materials likes it are made up of what are called domains. These domains are each like a little region within the larger chunk of material itself. And each region in a material such as iron or one similar has its own overall magnetic field. And the direction of the magnetic field can be represented by an arrow.
If we look at the directions of the magnetic fields in these domains of our chunk of iron, we see that they point in pretty much every single direction: some point up, some point down, some point left, some point right. If we consider the overall magnetic field of this entire chunk of iron, we can’t really tell what that is because the magnetic fields of the domains point in all these different directions.
Remember though we’ve been told that materials made of iron can become permanent magnets. Here’s how that happens. Say we take our chunk of iron and we put it within a magnetic field. We’ve called that field capital 𝐵. This external magnetic field will change the domains of this chunk of iron; it won’t change where their boundaries are, but it will change the direction of the magnetic field in each domain.
Thanks to the magnetic field, look what happens to the magnetic fields in each of the domains. They line up with that external field. If we were to then turn off the external magnetic field so that it’s no longer influencing the domains of this chunk of iron, those domain fields would stay in largely the same direction.
Over time, the magnetic fields of these domains would drift out of alignment. But for quite some time, they would be relatively in line. And that’s why we say that iron can be made into a permanent magnet. The property that iron has of having domains each with their magnetic field and having these magnetic fields respond to an external magnetic field has a name for it.
That name is ferromagnetism, where the prefix ferro refers to iron and magnetism of course refers to magnetism. And it turns out that iron isn’t the only ferromagnetic material there is. There are other elements that behave this way too that are ferromagnetic.
We can find out whether a given element is ferromagnetic by looking up its properties in a table. When we do this for copper, magnesium, nickel, and cobalt, we see that it’s the last two elements listed here, nickel and cobalt, which both themselves are ferromagnetic. That means that these elements like iron can be used to make permanent magnets.
Next, let’s consider a question not about magnetic poles, but about electric poles, that is, electric charges.
Figure two shows two parallel, charged plates. The charged plates create a uniform electric field between them. Use an expression from the box to complete the sentence: decreases, stays the same, increases. As the amount of charge on each metal plate is increased, the potential difference between the positively charged plate and the negatively charged plate blank.
In this question then, we want to work off of Figure two which shows a positively charged plate opposite and negatively charged plate. Based on what’s going on there, we want to choose from this list of possible answers, decreases, stays the same, or increases, to fill in the blank in this sentence.
This sentence that we want to complete talks about the amount of charge that’s on each of our two metal plates. We know from Figure two that our top plate has a positive charge and our bottom plate has a negative charge. And if we were to sketch those charges in on our plates, they might look something like this.
Not only do we have two oppositely charged plates, but we’re told that a uniform electric field exists between these plates. That’s actually to be expected because electric charges of any sign whether positive or negative create an electric field around them. We see those electric field lines drawn in between our positive and negative plates and the arrows represent which direction the field lines point, from positive to negative.
The question is what would happen if we increased the amount of charge on each plate; that is, what would happen if we put more positive charge on the positive plate and more negative charge on the negative plate? Well, for one thing the electric field in between these two plates would change. Just as the charge increased, so will the strength of that electric field.
We could represent that change if we wanted by drawing more electric field lines to indicate that the field is getting stronger. But it’s not the electric field strength that we’re interested in directly, rather it’s the potential difference between the positive and negatively charged plates.
Here’s what we know so far. We’ve increased the charge on each plate and that increase has led to an increase in the strength of the electric field between the plates. The question is how does our increased electric field relate to the potential difference between the plates.
In cases like this, where we have oppositely charged parallel plates facing one another, there is a helpful relationship between electric field and potential difference that we can recall.
If we represent the potential difference between the plates as capital 𝑉, then that potential difference it turns out depends on two factors: one is the distance between the two plates — we can call that distance 𝑑 — and the other is the electric field that’s in between these oppositely charged plates.
If we take the product of that electric field and the distance between the two plates, that product is equal to the potential difference between them. Now, let’s apply this to our situation.
We know that in this instance the distance between our plates isn’t changing; that’s a constant value. But what is changing? Well, the electric field is changing. And it’s increasing because we’re putting more charge on the positively and negatively charged plates.
So if the distance is staying the same and the electric field is increasing, then what must be happening to the potential difference 𝑉? Since the right-hand side of this equation is increasing, that means the left-hand side must be increasing as well. Potential difference must be going up.
This tells us which expression from the box to choose to complete the sentence. As the amount of charge on each metal plate is increased, the potential difference between the positively charged plate and the negatively charged plate increases. That’s how this change in charge affects potential difference.
Finally, let’s work on a calculation involving potential difference.
When the potential difference between two charged plates is 50 kilovolts, a spark jumps between the two plates. The spark transfers 0.00004 coulombs of charge between the plates. The equation which relates the energy transferred by a charge that moves across an electric potential difference, the size of the charge, and the potential difference is energy transferred equals charge times potential difference. Calculate the energy transferred by the spark.
In this example, we have a series of information given to us and then a way to combine that information to give us our desired result: the energy transferred by this spark that moves between two charged plates. To calculate this amount of energy, let’s start out by using symbols to represent the information we’re given as well as this energy transfer equation.
Beginning with the equation, let’s use capital 𝐸 to represent the energy transferred. We’ll use capital 𝑄 to represent charge and we’ll use capital 𝑉 to represent potential difference. Off to the side then, we can summarize this equation as 𝐸 equals 𝑄 times 𝑉. And we’ll now know what that means.
The charge transferred between plates multiplied by the potential difference between them is equal to the energy that’s transferred between the plates. If we looked to our question statement, we see we’re given information about that potential difference 𝑉 as well as the charge 𝑄. We can write those in shorthand too.
Clearing some space, we can say that 𝑉, the potential difference, is equal to 50 kilovolts and that 𝑄, the charge transferred between the plates, is equal to 0.00004 coulombs. We want to combine 𝑉 and 𝑄 according to this equation to solve for 𝐸. But before we do it, there’s a change that we’ll need to make.
That change involves the units of our potential difference 𝑉. Notice that those units are given in kilovolts that is thousands of volts. When we use potential difference in our equation though, we want its units to simply be units of volts. So before we calculate 𝐸, let’s convert our potential difference from units of kilovolts to units of volts.
Here’s how we’ll do that. We’ll recall the conversion between kilovolts and volts. If we take 1000 volts, that’s equal to one kilovolt. In fact, that’s what the prefix kilo refers to, 1000. So this means that our voltage given as 50 kilovolts is actually 50 times 1000 volts.
We can write it this way. We can say that since a kilovolt is equal to 1000 volts, then we can replace kilovolts with that expression, 1000 volts. And we’ll multiply that by 50 to get our potential difference 𝑉 in volts. 50 times 1000 is equal to 50000. So that’s the number of volts of our potential difference let’s use this updated value in place of our previous value for 𝑉.
And realise that both values are the same; they’re just expressed in different units. We’re now ready to solve for the energy transferred by multiplying 𝑄 times 𝑉. We plug in the values for 𝑄 and then for 𝑉 and multiply them together. And when we do, we find a result of 20 joules. That’s the amount of energy transferred by the spark. | 3,450 | 16,438 | {"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} | 4.21875 | 4 | CC-MAIN-2020-16 | latest | en | 0.913497 |
https://nl.mathworks.com/matlabcentral/cody/players/9120510-andy-su/solved | 1,591,204,660,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347435238.60/warc/CC-MAIN-20200603144014-20200603174014-00032.warc.gz | 443,490,731 | 18,563 | Cody
# Andy su
Rank
Score
1 – 31 of 31
#### Problem 94. Target sorting
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Tags sorting, matlab
#### Problem 105. How to find the position of an element in a vector without using the find function
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Tags indexing, find
#### Problem 39. Which values occur exactly three times?
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Tags search
#### Problem 22. Remove the vowels
Created by: Cody Team
Tags regexp, siam
#### Problem 233. Reverse the vector
Created by: Vishwanathan Iyer
#### Problem 30. Sort a list of complex numbers based on far they are from the origin.
Created by: Cody Team
#### Problem 1658. Simple equation: Annual salary
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Tags easy, basics, salary
#### Problem 109. Check if sorted
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#### Problem 20. Summing digits
Created by: Cody Team
Tags strings
#### Problem 11. Back and Forth Rows
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Tags matrices
#### Problem 32. Most nonzero elements in row
Created by: Cody Team
Tags matrices
#### Problem 14. Find the numeric mean of the prime numbers in a matrix.
Created by: Cody Team
Tags easy, matrices
#### Problem 25. Remove any row in which a NaN appears
Created by: Cody Team
#### Problem 189. Sum all integers from 1 to 2^n
Created by: Dimitris Kaliakmanis
Created by: Will
#### Problem 33. Create times-tables
Created by: Cody Team
Tags matrices
#### Problem 12. Fibonacci sequence
Created by: Cody Team
#### Problem 10. Determine whether a vector is monotonically increasing
Created by: Cody Team
#### Problem 19. Swap the first and last columns
Created by: Cody Team
#### Problem 4. Make a checkerboard matrix
Created by: Cody Team
#### Problem 17. Find all elements less than 0 or greater than 10 and replace them with NaN
Created by: Cody Team
#### Problem 5. Triangle Numbers
Created by: Cody Team
Tags math, triangle, nice
#### Problem 7. Column Removal
Created by: Cody Team
#### Problem 6. Select every other element of a vector
Created by: Cody Team
#### Problem 149. Is my wife right?
Created by: the cyclist
Tags easy, silly, fun
#### Problem 167. Pizza!
Created by: the cyclist
Tags fun, pizza, good
#### Problem 26. Determine if input is odd
Created by: Cody Team
#### Problem 8. Add two numbers
Created by: Cody Team
#### Problem 3. Find the sum of all the numbers of the input vector
Created by: Cody Team
#### Problem 2. Make the vector [1 2 3 4 5 6 7 8 9 10]
Created by: Cody Team
Tags basic, basics, colon
#### Problem 1. Times 2 - START HERE
Created by: Cody Team
Tags intro, math, easy
1 – 31 of 31 | 687 | 2,601 | {"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} | 3.09375 | 3 | CC-MAIN-2020-24 | latest | en | 0.743447 |
https://tom.busby.ninja/understanding-cryptography/ex1-13/ | 1,656,318,936,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103329963.19/warc/CC-MAIN-20220627073417-20220627103417-00236.warc.gz | 610,526,952 | 14,282 | # Understanding Cryptography by Christof Paar and Jan Pelzl - Chapter 1 Solutions - Ex1.13
- 1 min
## Exercise 1.13
In an attack scenario, we assume that the attacker Oscar manages somehow to provide Alice with a few pieces of plaintext that she encrypts. Show how Oscar can break the affine cipher by using two pairs of plaintext–ciphertext, $(x_1, y_1)$ and $(x_2, y_2)$. What is the condition for choosing $x_1$ and $x_2$?
Remark: In practice, such an assumption turns out to be valid for certain settings, e.g., encryption by Web servers, etc. This attack scenario is, thus, very important and is denoted as a chosen plaintext attack.
### Solution
This solution is verified as correct by the official Solutions for Odd-Numbered Questions manual.
In order to use the chosen plaintext attack, the plaintexts need to be chosen such that $\mathrm{gcd}(x_2 - x_1, m) = 1$, where $m$ is the size of the alphabet being encrypted. Another way to put this is that $x_2 - x_1$ must have multiplicative inverse in $m$.
The following equations can be derived by trying to solve the two chosen plaintext encryptions as a pair of simultaneous equations:
$a \equiv (x_1 −x_2)^{-1}(y_1 − y_2)\,\mathrm{mod}\,m$ $b \equiv y_1 − ax_1\,\mathrm{mod}\,m$ | 338 | 1,246 | {"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": 2, "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-2022-27 | latest | en | 0.864829 |
https://brilliant.org/problems/whats-the-exponent/ | 1,524,632,678,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125947693.49/warc/CC-MAIN-20180425041916-20180425061916-00381.warc.gz | 573,078,702 | 10,548 | # What's the exponent?
Algebra Level 4
$\large (x^0 + x^1 + x^2 + x^3 )(x^0 + x^1 + x^2 + x^3 + x^4 )^2$
Find the coefficient of $$x^6$$ in above expression.
× | 69 | 163 | {"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} | 2.875 | 3 | CC-MAIN-2018-17 | latest | en | 0.693841 |
http://oeis.org/A007700 | 1,510,992,457,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934804680.40/warc/CC-MAIN-20171118075712-20171118095712-00729.warc.gz | 230,168,012 | 4,731 | This site is supported by donations to The OEIS Foundation.
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A007700 Numbers n such that n, 2n+1, and 4n+3 all prime. (Formerly M1406) 46
2, 5, 11, 41, 89, 179, 359, 509, 719, 1019, 1031, 1229, 1409, 1451, 1481, 1511, 1811, 1889, 1901, 1931, 2459, 2699, 2819, 3449, 3491, 3539, 3821, 3911, 5081, 5399, 5441, 5849, 6101, 6131, 6449, 7079, 7151, 7349, 7901, 8969, 9221, 10589, 10691, 10709, 11171 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS The corresponding primes 2n+1 and 4n+3 respectively have n-1 and 2n primitive roots. - Lekraj Beedassy, Jan 07 2005 At n > 2, a(n) == {11,29} (mod 30). - Zak Seidov, Jan 31 2013 REFERENCES T. Moreau, personal communication. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 L. Blum, M. Blum, and M. Shub, A simple unpredictable pseudorandom number generator, SIAM J. Comput. 15 (1986), no. 2, 364-383. MAPLE A007700 := proc(n) local p1, p2; p1 := 2*n+1; p2 := 2*p1+1; if isprime(n) = true and isprime(p1)=true and isprime(p2)=true then RETURN(n); fi; end; MATHEMATICA Select[Range[10^3*3], PrimeQ[ # ]&&PrimeQ[2*#+1]&&PrimeQ[4*#+3] &] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *) PROG (PARI) is(n)=isprime(n)&&isprime(2*n+1)&&isprime(4*n+3) \\ Charles R Greathouse IV, Mar 21 2013 CROSSREFS Intersection of A005384 and A023213. Cf. A005385, A023272, A023302, A023330, A057331, A005602. Sequence in context: A191029 A106886 A237814 * A071313 A172297 A128231 Adjacent sequences: A007697 A007698 A007699 * A007701 A007702 A007703 KEYWORD nonn AUTHOR STATUS approved
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The OEIS Community | Maintained by The OEIS Foundation Inc. | 800 | 2,192 | {"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} | 3.375 | 3 | CC-MAIN-2017-47 | longest | en | 0.534311 |
https://plainmath.org/precalculus/24333-determine-whether-the-vectors-u-and-are-parallel-orthogonal-or-neither | 1,713,434,461,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817206.28/warc/CC-MAIN-20240418093630-20240418123630-00706.warc.gz | 418,951,318 | 22,498 | pedzenekO
2021-08-18
Determine whether the vectors u and v are parallel, orthogonal, or neither.
$u=⟨-3,4⟩,v-⟨\frac{20}{15}⟩$
$u=⟨-3,4⟩,v-⟨\frac{20}{15}⟩$
pierretteA
Without finding the angle between two vectors, we can determine if they are parallel if they are scalar multiples of each other. If $u=kv\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}v=ku$ for non-zero value of k since we are simply scaling. The two vectors are orthogonal if their dot product is 0: $u×v=0$
Check if they are parallel:
Since $v\ne 5u,⟨20,15⟩\ne 5⟨-3.4⟩$
Then u and v are not parallel.
Check if they are orthogonal:
Find the dot product:
$u×v=\left(-3\right)\left(20\right)+\left(4\right)\left(15\right)=-60+60=0$
Since $u×v=0$, then u and v are orthogonal.
Do you have a similar question? | 286 | 789 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 20, "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-2024-18 | latest | en | 0.757744 |
https://forum.mongoosepublishing.com/threads/pay-thread-again.8687/ | 1,709,311,244,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475422.71/warc/CC-MAIN-20240301161412-20240301191412-00079.warc.gz | 254,818,649 | 15,532 | #### Babylon 5 Aide
##### Mongoose
Pay for EarthForce Officers. I'm looking at the books, and still haven't found anything that lines this out. Now, the new book EarthForce Campaign Guide sounds like it may have it in there, but...
You can't use Profession as a measure, pay would be based on Time in Service, and Pay Grade it seems to me.
A starting Psi Cop makes 80k a year. Interesting sense that doesn't work out with the way to calculate the pay of a telepath in Psi Corps in the same book.
Anyone have a good way of figuring it up? We are starting out old campaign over again and I will be playing a Commander with about 10 years of experience. Unless I find something helpful I am going to just figure it up by the US Navy's pay scale and be done with it. lol
Thanks again for taking a look at another thread on this subject folks. I did the search and got alot of stuff that just didn't help at all, so I thought I'd ring everyone again.
I started working on this: http://www.perturbatio.com/b5/professions.xml
It should work in Firefox 1.0 and IE6 for sure
don't ask me exactly what my intentions were, it was a while ago but I felt the profession rules were too generalized.
I did base it on skill to a certain extent but the idea was to implement a sort of performance related pay.
The players could choose to take the average (assume a roll of 10) or may roll a D20 and calculate based on the formula provided.
I think I intended for the skill to be the player's profession skill or primary skill ranks (whichever is lower) and for the Range column to represent the possible variance with the profession by multiplying the formula result by this value. (i.e. a beggar is likely to have extremes of luck so has a range of 0.1-2.0 or 10% to 200%, whereas a telepath is usually paid a regular wage from an employer)
The plan was to work this out for every major profession.
Well Earth Force pay would be based on rank and time served rather than a PC's skill points.
LBH
Psi Cops' pay doesn't work out with the rules for calculating a commercial telepath's pay because it's totally different work.
There are notes on pay scales in the EarthForce book (based on the Navy pay scales, for that matter). I think my original draft had a ccommander earning about 100k credits a year, but that was before playtesting and sanity checking.
A commander makes almost that much depending on what bonuses (hostile fire pay / aviation pay for example) before taxes now. So that doesn't make a problem for me. Where is this in the EF book anyway?
EarthForce book isn't out yet...
As for bonuses for EA officers, I'm sure Sheridan mentions needing to keep his flight hours up to qualify for flight pay.
LBH
Sorry thought maybe you meant the Earth Alliance book that is out...
Would love a sneak peak of the pay rules for that... :lol:
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447 | 696 | 2,949 | {"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-2024-10 | latest | en | 0.978202 |
http://blackholeformulas.com/files/ebner1_c3_rotation.html | 1,643,285,739,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305260.61/warc/CC-MAIN-20220127103059-20220127133059-00015.warc.gz | 7,421,086 | 4,690 | Chapter 3 - The rotating universe modified 20110924
Introduction
As the light and energy orbit the expanding Cosmos, it takes longer to reach a reference point against the background universe. Newton would call this reference point absolute space. Mach would call it the fixed stars. The Cosmos, galaxy and solar system all rotate, with respect to that which is outside our cosmic dynamic unit. If the background universe has features which are close enough, and these features are not black holes, then they may be visible through the intense orbiting energy and light around the Cosmos. Seeing through this orbital energy seems possible since stars are visible near the sun during an eclipse as starlight perpendicular to the huge energy flow from the sun. We might be seeing such features in the Hubble telescope deep field photographs. It would not be remarkable if the background universe looks the same as it does within our dynamic unit Cosmos.
Rotation or vorticity
The angular velocity = tangent velocity/radius= vt/r = c/(c*age) = 1/age in radians/second or Hubble's constant as a rotation rate or fr*c/(fr*c*age) = 1/age
The rate of change of the angle of rotation is the angular velocity.
The rate of change of the angle of rotation is 1/age.
The rate of change of the ln(age) is 1/age.
The angle of rotation = ln(age) = the natural logarithm of the age = ln(4.73E17) = 40.7 radians.
The base of the natural logarithms is e.
e(angle of rotation) = e40.7 = 4.73E17 = age
ln(age*2) = ln(age) + ln(2). Each time the Cosmos doubles in age or size the angle of rotation of the Cosmos increases by the ln(2) = .693 radians = 39.7 degrees
We are currently at 40.7 radians so 40.7 /(2*pi) = 6.5 revolutions might have been made by the orbiting light and energy in the age of the Cosmos. The last revolution started when the Cosmos was, e(40.7 - 6.28) = 8.88E14_s = 28.1 million years old.
The previous revolution took 15 billion years.
The next revolution will end in, e(40.7 + 6.28) = 2.53E20_s = 8.017E12_years = 8017 billion years.
The next revolution will take 8000 billion years. The slowly stirring Cosmos is slowing down.
The rate of change of the angular velocity (1/age) is the angular acceleration.
angular acceleration = -(1/age2) = -4.46E-36_1/s2. This is the second derivative of the angle of rotation. This very small rate that the Cosmos is decelerating in its rotation is necessary for the equilibrium between rotation and expansion. We are rotating with the Cosmos. Everything has the same universal angular velocity (1/age) as a component of their local angular velocity, as we will see in our galaxy. The Cosmos rotated faster when it was younger. This differential rotation might be detected but the angular acceleration is profoundly slow at (1/age2).
Inertial accelerations
To calculate the path of expansion of a particle we need the vector sum of three accelerations; the centrifugal, tangent and coriolis. These are components of the so called fictitious forces which are more properly called forces due to inertia. They are certainly not fictitious if you take the Machian view that inertia is the acceleration dependant gravitational force exerted by the rest of the Cosmos. See the article on Inertial Inductance.
Centrifugal acceleration
The centrifugal and gravitational forces are equal. m*c2/r equals the centrifugal force and c2/r is the acceleration felt by light or energy in orbit at the perimeter of the Cosmos.
c2/r = c2/(c*age) = c/age = 6.33E-10_m/s2 or c2*fr2 /(c*age*fr) = fr*c/age if fr is less than one
Tangent acceleration
We can calculate the tangent acceleration using the torque formula.
moment of inertia*angular acceleration = force*radius.
m*r2*angular acceleration = m*a*r.
a = r *angular acceleration = tangent acceleration
a = c*age *(1/age2) = c/age,
or
a = fr*c/age if fr is less than one
The direction of deceleration is opposite of rotation. The tangent acceleration can also be calculated from velocity dependent inertial induction with the same result.
Coriolis acceleration
Inertia will cause an outward directed mass, on a rotating platform, to lag behind in a direction opposite to the rotation. This is the reaction. The action which is the coriolis acceleration is in the direction of the rotation. A person in an accelerating car is pushed back against the seat. This is a reaction to the acceleration. The acceleration is in the direction of the velocity. The reaction is in the direction opposite the velocity.
2 *angular velocity *vr = 2 *vt/r *vr = 2 *c/(c*age) *c = coriolis acceleration
vr is the radial velocity which at the perimeter is c.
2*c/age = coriolis acceleration or
fr*2*c/age if fr is less than one
Click to enlarge! Spirals:
Now that we have calculated the inertial accelerations, we can look at the way the Cosmos expands. We have the centrifugal acceleration of c/age, directed radially out. We have the coriolis acceleration of 2*c/age, in the direction of rotation, and the deceleration of c/age, in the direction opposite of rotation. The resultant of these accelerations, is 45 degrees between the direction of rotation and the outward directed radius. It has a value of 21/2 *c/age = 8.96E-10_m/s2, quite close to that of the Pioneer Anomaly. A particle moving in this way traces out a logarithmic spiral. We have seen that the
angle of rotation = ln(age). This can be written as
age = e(angle of rotation). Now
r = c*age, can be written as
r = c*e(angle of rotation). This is the equation of a logarithmic spiral. It is no coincidence that many galaxies have a spiral shape. Indeed, it is not that space expands, but that the distance between orbiting masses increases as they spiral out and apart from each other, as the Cosmos expands and slows in its rotation. The tangent velocity of the stars orbiting in galaxies, stays the same as the galaxies expand and the orbital periods increase. Any velocity change would require force and energy which are absent.
Torque of a spinning black hole
moment of inertia *angular acceleration = torque
M *r2*angular acceleration =
M *vr2 *age2*angular acceleration,
but
vr/c = M/Mc, so vr2 = c2*M2/Mc2, therefore substituting for vr2
M *{c2*M2/Mc2} *age2 *angular acceleration =
M3 *c2/Mc2 *age2 *angular acceleration = torque.
If the mass of the black hole is, M = Mc, the mass of the Cosmos, then
Mc *c2 *age2 *(1/age2) = Mc *c2
We see that the age2, in the square of the radius, in the moment of inertia, increases at the same rate the angular acceleration 1/age2 decreases so that the age2 in each cancels and the energy stays constant. We will see the same thing in the torque of a spinning galaxy.
The radius of the Cosmos increases while the rotation of the Cosmos slows down, and with it all the blackholes and galaxies, without a change in energy or use of power, always in dynamic equilibrium. Orbits spiral out as the gravitational force decreases with the age of the Cosmos.
References
http://blackholeformulas.com/files/GSJRotation.docx
1. Machian view @ http://www.bun.kyoto-u.ac.jp/~suchii/mach.pr.html
2. Inertial inductance @ http://blackholeformulas.com/files/InertialInductance.html
3. Spiral png @ http://blackholeformulas.com/files/unfigspiral2.png
Go to Chapter 4 - Dark matter | 1,786 | 7,247 | {"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} | 3.515625 | 4 | CC-MAIN-2022-05 | latest | en | 0.91219 |
https://chem.libretexts.org/LibreTexts/Bellarmine_University/BU%3A_Chem_103_(Christianson)/Phase_3%3A_Atoms_and_Molecules_-_the_Underlying_Reality/8%3A_Periodic_Trends_in_Elements_and_Compounds/8.2%3A_Atomic_and_Ionic_Radius | 1,544,486,651,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823516.50/warc/CC-MAIN-20181210233803-20181211015303-00449.warc.gz | 579,266,246 | 24,910 | # 8.2: Atomic and Ionic Radius
Skills to Develop
• To understand periodic trends in atomic radii.
• To predict relative ionic sizes within an isoelectronic series.
Although some people fall into the trap of visualizing atoms and ions as small, hard spheres similar to miniature table-tennis balls or marbles, the quantum mechanical model tells us that their shapes and boundaries are much less definite than those images suggest. As a result, atoms and ions cannot be said to have exact sizes; however, some atoms are larger or smaller than others, and this influences their chemistry. In this section, we discuss how atomic and ion “sizes” are defined and obtained.
Recall that the probability of finding an electron in the various available orbitals falls off slowly as the distance from the nucleus increases. This point is illustrated in Figure $$\PageIndex{1}$$ which shows a plot of total electron density for all occupied orbitals for three noble gases as a function of their distance from the nucleus. Electron density diminishes gradually with increasing distance, which makes it impossible to draw a sharp line marking the boundary of an atom.
Figure $$\PageIndex{1}$$: Plots of Radial Probability as a Function of Distance from the Nucleus for He, Ne, and Ar. In He, the 1s electrons have a maximum radial probability at ≈30 pm from the nucleus. In Ne, the 1s electrons have a maximum at ≈8 pm, and the 2s and 2p electrons combine to form another maximum at ≈35 pm (the n = 2 shell). In Ar, the 1s electrons have a maximum at ≈2 pm, the 2s and 2p electrons combine to form a maximum at ≈18 pm, and the 3s and 3p electrons combine to form a maximum at ≈70 pm.
Figure $$\PageIndex{1}$$ also shows that there are distinct peaks in the total electron density at particular distances and that these peaks occur at different distances from the nucleus for each element. Each peak in a given plot corresponds to the electron density in a given principal shell. Because helium has only one filled shell (n = 1), it shows only a single peak. In contrast, neon, with filled n = 1 and 2 principal shells, has two peaks. Argon, with filled n = 1, 2, and 3 principal shells, has three peaks. The peak for the filled n = 1 shell occurs at successively shorter distances for neon (Z = 10) and argon (Z = 18) because, with a greater number of protons, their nuclei are more positively charged than that of helium. Because the 1s2 shell is closest to the nucleus, its electrons are very poorly shielded by electrons in filled shells with larger values of n. Consequently, the two electrons in the n = 1 shell experience nearly the full nuclear charge, resulting in a strong electrostatic interaction between the electrons and the nucleus. The energy of the n = 1 shell also decreases tremendously (the filled 1s orbital becomes more stable) as the nuclear charge increases. For similar reasons, the filled n = 2 shell in argon is located closer to the nucleus and has a lower energy than the n = 2 shell in neon.
Figure $$\PageIndex{1}$$ illustrates the difficulty of measuring the dimensions of an individual atom. Because distances between the nuclei in pairs of covalently bonded atoms can be measured quite precisely, however, chemists use these distances as a basis for describing the approximate sizes of atoms. For example, the internuclear distance in the diatomic Cl2 molecule is known to be 198 pm. We assign half of this distance to each chlorine atom, giving chlorine a covalent atomic radius ($$r_{cov}$$), which is half the distance between the nuclei of two like atoms joined by a covalent bond in the same molecule, of 99 pm or 0.99 Å (Figure $$\PageIndex{2a}$$). Atomic radii are often measured in angstroms (Å), a non-SI unit: 1 Å = 1 × 10−10 m = 100 pm.
Figure $$\PageIndex{2}$$: Definitions of the Atomic Radius. (a) The covalent atomic radius, rcov, is half the distance between the nuclei of two like atoms joined by a covalent bond in the same molecule, such as Cl2. (b) The metallic atomic radius, rmet, is half the distance between the nuclei of two adjacent atoms in a pure solid metal, such as aluminum. (c) The van der Waals atomic radius, rvdW, is half the distance between the nuclei of two like atoms, such as argon, that are closely packed but not bonded. (d) This is a depiction of covalent versus van der Waals radii of chlorine. The covalent radius of Cl2 is half the distance between the two chlorine atoms in a single molecule of Cl2. The van der Waals radius is half the distance between chlorine nuclei in two different but touching Cl2 molecules. Which do you think is larger? Why?
In a similar approach, we can use the lengths of carbon–carbon single bonds in organic compounds, which are remarkably uniform at 154 pm, to assign a value of 77 pm as the covalent atomic radius for carbon. If these values do indeed reflect the actual sizes of the atoms, then we should be able to predict the lengths of covalent bonds formed between different elements by adding them. For example, we would predict a carbon–chlorine distance of 77 pm + 99 pm = 176 pm for a C–Cl bond, which is very close to the average value observed in many organochlorine compounds. A similar approach for measuring the size of ions is discussed later in this section.
Covalent atomic radii can be determined for most of the nonmetals, but how do chemists obtain atomic radii for elements that do not form covalent bonds? For these elements, a variety of other methods have been developed. With a metal, for example, the metallic atomic radius ($$r_{met}$$) is defined as half the distance between the nuclei of two adjacent metal atoms in the solid (Figure $$\PageIndex{2b}$$). For elements such as the noble gases, most of which form no stable compounds, we can use what is called the van der Waals atomic radius ($$r_{vdW}$$), which is half the internuclear distance between two nonbonded atoms in the solid (Figure $$\PageIndex{2c}$$). This is somewhat difficult for helium which does not form a solid at any temperature. An atom such as chlorine has both a covalent radius (the distance between the two atoms in a $$\ce{Cl2}$$ molecule) and a van der Waals radius (the distance between two Cl atoms in different molecules in, for example, $$\ce{Cl2(s)}$$ at low temperatures). These radii are generally not the same (Figure $$\PageIndex{2d}$$).
Because it is impossible to measure the sizes of both metallic and nonmetallic elements using any one method, chemists have developed a self-consistent way of calculating atomic radii using the quantum mechanical functions. Although the radii values obtained by such calculations are not identical to any of the experimentally measured sets of values, they do provide a way to compare the intrinsic sizes of all the elements and clearly show that atomic size varies in a periodic fashion (Figure $$\PageIndex{3}$$).
Figure $$\PageIndex{3}$$: A Plot of Periodic Variation of Atomic Radius with Atomic Number for the First Six Rows of the Periodic Table
In the periodic table, atomic radii decrease from left to right across a row and increase from top to bottom down a column. Because of these two trends, the largest atoms are found in the lower left corner of the periodic table, and the smallest are found in the upper right corner (Figure $$\PageIndex{4}$$).
Figure $$\PageIndex{4}$$ Calculated Atomic Radii (in Picometers) of the s-, p-, and d-Block Elements. The sizes of the circles illustrate the relative sizes of the atoms. The calculated values are based on quantum mechanical wave functions. Source: http://www.webelements.com. Web Elements is an excellent online source for looking up atomic properties.
Trends in atomic size result from differences in the effective nuclear charges ($$Z_{eff}$$) experienced by electrons in the outermost orbitals of the elements. For all elements except H, the effective nuclear charge is always less than the actual nuclear charge because of shielding effects. The greater the effective nuclear charge, the more strongly the outermost electrons are attracted to the nucleus and the smaller the atomic radius.
Atomic radii decrease from left to right across a row and increase from top to bottom down a column.
The atoms in the second row of the periodic table (Li through Ne) illustrate the effect of electron shielding. All have a filled 1s2 inner shell, but as we go from left to right across the row, the nuclear charge increases from +3 to +10. Although electrons are being added to the 2s and 2p orbitals, electrons in the same principal shell are not very effective at shielding one another from the nuclear charge. Thus the single 2s electron in lithium experiences an effective nuclear charge of approximately +1 because the electrons in the filled 1s2 shell effectively neutralize two of the three positive charges in the nucleus. (More detailed calculations give a value of Zeff = +1.26 for Li.) In contrast, the two 2s electrons in beryllium do not shield each other very well, although the filled 1s2 shell effectively neutralizes two of the four positive charges in the nucleus. This means that the effective nuclear charge experienced by the 2s electrons in beryllium is between +1 and +2 (the calculated value is +1.66). Consequently, beryllium is significantly smaller than lithium. Similarly, as we proceed across the row, the increasing nuclear charge is not effectively neutralized by the electrons being added to the 2s and 2p orbitals. The result is a steady increase in the effective nuclear charge and a steady decrease in atomic size (Figure $$\PageIndex{5}$$).
Figure $$\PageIndex{5}$$: The Atomic Radius of the Elements. The atomic radius of the elements increases as we go from right to left across a period and as we go down the periods in a group.
The increase in atomic size going down a column is also due to electron shielding, but the situation is more complex because the principal quantum number n is not constant. As we saw in Chapter 2, the size of the orbitals increases as n increases, provided the nuclear charge remains the same. In group 1, for example, the size of the atoms increases substantially going down the column. It may at first seem reasonable to attribute this effect to the successive addition of electrons to ns orbitals with increasing values of n. However, it is important to remember that the radius of an orbital depends dramatically on the nuclear charge. As we go down the column of the group 1 elements, the principal quantum number n increases from 2 to 6, but the nuclear charge increases from +3 to +55!
As a consequence the radii of the lower electron orbitals in Cesium are much smaller than those in lithium and the electrons in those orbitals experience a much larger force of attraction to the nucleus. That force depends on the effective nuclear charge experienced by the the inner electrons. If the outermost electrons in cesium experienced the full nuclear charge of +55, a cesium atom would be very small indeed. In fact, the effective nuclear charge felt by the outermost electrons in cesium is much less than expected (6 rather than 55). This means that cesium, with a 6s1 valence electron configuration, is much larger than lithium, with a 2s1 valence electron configuration. The effective nuclear charge changes relatively little for electrons in the outermost, or valence shell, from lithium to cesium because electrons in filled inner shells are highly effective at shielding electrons in outer shells from the nuclear charge. Even though cesium has a nuclear charge of +55, it has 54 electrons in its filled 1s22s22p63s23p64s23d104p65s24d105p6 shells, abbreviated as [Xe]5s24d105p6, which effectively neutralize most of the 55 positive charges in the nucleus. The same dynamic is responsible for the steady increase in size observed as we go down the other columns of the periodic table. Irregularities can usually be explained by variations in effective nuclear charge.
Not all Electrons shield equally
Electrons in the same principal shell are not very effective at shielding one another from the nuclear charge, whereas electrons in filled inner shells are highly effective at shielding electrons in outer shells from the nuclear charge.
Example $$\PageIndex{1}$$
On the basis of their positions in the periodic table, arrange these elements in order of increasing atomic radius: aluminum, carbon, and silicon.
Given: three elements
Strategy:
1. Identify the location of the elements in the periodic table. Determine the relative sizes of elements located in the same column from their principal quantum number n. Then determine the order of elements in the same row from their effective nuclear charges. If the elements are not in the same column or row, use pairwise comparisons.
2. List the elements in order of increasing atomic radius.
Solution:
A These elements are not all in the same column or row, so we must use pairwise comparisons. Carbon and silicon are both in group 14 with carbon lying above, so carbon is smaller than silicon (C < Si). Aluminum and silicon are both in the third row with aluminum lying to the left, so silicon is smaller than aluminum (Si < Al) because its effective nuclear charge is greater.
B Combining the two inequalities gives the overall order: C < Si < Al.
Exercise $$\PageIndex{1}$$
On the basis of their positions in the periodic table, arrange these elements in order of increasing size: oxygen, phosphorus, potassium, and sulfur.
O < S < P < K
### Ionic Radii and Isoelectronic Series
An ion is formed when either one or more electrons are removed from a neutral atom to form a positive ion (cation) or when additional electrons attach themselves to neutral atoms to form a negative one (anion). The designations cation or anion come from the early experiments with electricity which found that positively charged particles were attracted to the negative pole of a battery, the cathode, while negatively charged ones were attracted to the positive pole, the anode.
Figure $$\PageIndex{6}$$: Definition of Ionic Radius. (a) The internuclear distance is apportioned between adjacent cations (positively charged ions) and anions (negatively charged ions) in the ionic structure, as shown here for Na+ and Cl in sodium chloride. (b) This depiction of electron density contours for a single plane of atoms in the NaCl structure shows how the lines connect points of equal electron density. Note the relative sizes of the electron density contour lines around Cl and Na+.
Ionic compounds consist of regular repeating arrays of alternating positively charged cations and negatively charges anions. Although it is not possible to measure an ionic radius directly for the same reason it is not possible to directly measure an atom’s radius, it is possible to measure the distance between the nuclei of a cation and an adjacent anion in an ionic compound to determine the ionic radius (the radius of a cation or anion) of one or both. As illustrated in Figure $$\PageIndex{6}$$, the internuclear distance corresponds to the sum of the radii of the cation and anion. A variety of methods have been developed to divide the experimentally measured distance proportionally between the smaller cation and larger anion. These methods produce sets of ionic radii that are internally consistent from one ionic compound to another, although each method gives slightly different values. For example, the radius of the Na+ ion is essentially the same in NaCl and Na2S, as long as the same method is used to measure it. Thus despite minor differences due to methodology, certain trends can be observed.
A comparison of ionic radii with atomic radii (Figure $$\PageIndex{7}$$) shows that a cation, having lost an electron, is always smaller than its parent neutral atom, and an anion, having gained an electron, is always larger than the parent neutral atom. When one or more electrons is removed from a neutral atom, two things happen: (1) repulsions between electrons in the same principal shell decrease because fewer electrons are present, and (2) the effective nuclear charge felt by the remaining electrons increases because there are fewer electrons to shield one another from the nucleus. Consequently, the size of the region of space occupied by electrons decreases and the ion shrinks (compare Li at 167 pm with Li+ at 76 pm). If different numbers of electrons can be removed to produce ions with different charges, the ion with the greatest positive charge is the smallest (compare Fe2+ at 78 pm with Fe3+ at 64.5 pm). Conversely, adding one or more electrons to a neutral atom causes electron–electron repulsions to increase and the effective nuclear charge to decrease, so the size of the probability region increases and the ion expands (compare F at 42 pm with F at 133 pm).
Figure $$\PageIndex{7}$$: Ionic Radii (in Picometers) of the Most Common Ionic States of the s-, p-, and d-Block Elements.Gray circles indicate the sizes of the ions shown; colored circles indicate the sizes of the neutral atoms. Source: Ionic radius data from R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallographica 32, no. 5 (1976): 751–767.
Cations are always smaller than the neutral atom and anions are always larger.
Because most elements form either a cation or an anion but not both, there are few opportunities to compare the sizes of a cation and an anion derived from the same neutral atom. A few compounds of sodium, however, contain the Na ion, allowing comparison of its size with that of the far more familiar Na+ ion, which is found in many compounds. The radius of sodium in each of its three known oxidation states is given in Table $$\PageIndex{1}$$. All three species have a nuclear charge of +11, but they contain 10 (Na+), 11 (Na0), and 12 (Na) electrons. The Na+ ion is significantly smaller than the neutral Na atom because the 3s1 electron has been removed to give a closed shell with n = 2. The Na ion is larger than the parent Na atom because the additional electron produces a 3s2 valence electron configuration, while the nuclear charge remains the same.
Table $$\PageIndex{1}$$: Experimentally Measured Values for the Radius of Sodium in Its Three Known Oxidation States
Na+ Na0 Na
Electron Configuration 1s22s22p6 1s22s22p63s1 1s22s22p63s2
*The metallic radius measured for Na(s). †Source: M. J. Wagner and J. L. Dye, “Alkalides, Electrides, and Expanded Metals,” Annual Review of Materials Science 23 (1993): 225–253.
Ionic radii follow the same vertical trend as atomic radii; that is, for ions with the same charge, the ionic radius increases going down a column. The reason is the same as for atomic radii: shielding by filled inner shells produces little change in the effective nuclear charge felt by the outermost electrons. Again, principal shells with larger values of n lie at successively greater distances from the nucleus.
Because elements in different columns tend to form ions with different charges, it is not possible to compare ions of the same charge across a row of the periodic table. Instead, elements that are next to each other tend to form ions with the same number of electrons but with different overall charges because of their different atomic numbers. Such a set of species is known as an isoelectronic series. For example, the isoelectronic series of species with the neon closed-shell configuration (1s22s22p6) is shown in Table $$\PageIndex{3}$$.
The sizes of the ions in this series decrease smoothly from N3− to Al3+. All six of the ions contain 10 electrons in the 1s, 2s, and 2p orbitals, but the nuclear charge varies from +7 (N) to +13 (Al). As the positive charge of the nucleus increases while the number of electrons remains the same, there is a greater electrostatic attraction between the electrons and the nucleus, which causes a decrease in radius. Consequently, the ion with the greatest nuclear charge (Al3+) is the smallest, and the ion with the smallest nuclear charge (N3−) is the largest. The neon atom in this isoelectronic series is not listed in Table $$\PageIndex{3}$$, because neon forms no covalent or ionic compounds and hence its radius is difficult to measure.
Table $$\PageIndex{3}$$: Radius of Ions with the Neon Closed-Shell Electron Configuration. Source: R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallographica 32, no. 5 (1976): 751–767.
N3− 146 7
O2− 140 8
F 133 9
Na+ 98 11
Mg2+ 79 12
Al3+ 57 13
Example $$\PageIndex{2}$$
Based on their positions in the periodic table, arrange these ions in order of increasing radius: Cl, K+, S2−, and Se2−.
Given: four ions
Strategy:
1. Determine which ions form an isoelectronic series. Of those ions, predict their relative sizes based on their nuclear charges. For ions that do not form an isoelectronic series, locate their positions in the periodic table.
2. Determine the relative sizes of the ions based on their principal quantum numbers n and their locations within a row.
Solution:
A We see that S and Cl are at the right of the third row, while K and Se are at the far left and right ends of the fourth row, respectively. K+, Cl, and S2− form an isoelectronic series with the [Ar] closed-shell electron configuration; that is, all three ions contain 18 electrons but have different nuclear charges. Because K+ has the greatest nuclear charge (Z = 19), its radius is smallest, and S2− with Z = 16 has the largest radius. Because selenium is directly below sulfur, we expect the Se2− ion to be even larger than S2−.
B The order must therefore be K+ < Cl < S2− < Se2−.
Exercise $$\PageIndex{2}$$
Based on their positions in the periodic table, arrange these ions in order of increasing size: Br, Ca2+, Rb+, and Sr2+. | 4,980 | 21,898 | {"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} | 3.125 | 3 | CC-MAIN-2018-51 | latest | en | 0.919585 |
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# Data - Range
For a test which is scored out of 100, half of the students scored 70 and the other half of the students scored 81. What is the range of their scores?
$\{ 4, 7, 10, 18, 26 \}$
What is the range of the above set?
$\begin{array} &-14, &21, &-17, &25, &0, &-19, &11, &-20, &18\end{array}$
The above are the points by which Jack's basketball team won/lost against his rival team in the last 9 games. What is the range of these points?
$\{ -3, 7, 10, -25, 35 \}$
What is the range of the above set?
10 students took a test that was scored out of 10.
1 of them got a score of 3,
3 of them got a score of 5,
and 6 of them got a score of 7.
What is the range of scores?
× | 228 | 701 | {"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} | 2.984375 | 3 | CC-MAIN-2023-23 | latest | en | 0.974048 |
http://www1.rmit.edu.au/browse;ID=C3305MATH53411345tafecombined | 1,540,298,331,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583516135.92/warc/CC-MAIN-20181023111223-20181023132723-00144.warc.gz | 582,049,298 | 9,553 | # Course Title: Use a range of techniques to solve mathematical problems
## Part B: Course Detail
Teaching Period: Term2 2013
Course Code: MATH5341
Course Title: Use a range of techniques to solve mathematical problems
School: 155T Vocational Health and Sciences
Campus: City Campus
Program: C3305 - Certificate III in Science
Course Contact: Namrita Kaul
Course Contact Phone: +61 3 9925 4713
Course Contact Email: namrita.kaul@rmit.edu.au
Name and Contact Details of All Other Relevant Staff
+61 3 99254932
Nominal Hours: 110
Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.
Pre-requisites and Co-requisites
None.
Course Description
The purpose of this unit is to provide learners with the knowledge and skills to use a range of specialist techniques and concepts to solve mathematical problems.
National Codes, Titles, Elements and Performance Criteria
National Element Code & Title: VU21058 Use a range of techniques to solve mathematical problems Element: 1. Use ratio, proportion and percent to solve problems Element: 2 Use trigonometry to determine lengths and angles Element: 3 Use basic indices to solve problems Element: 4 Use measurements to solve mensuration problems in two and three dimensions Element: 5 Substitute into and transpose simple equations and formulae Element: 6 Solve problems by plotting points Element: 7 Present and evaluate statistical information Element: 8 Identify connections between formulae and graphical representations Element: 9 Use algebraic techniques to analyse and solve problems
Learning Outcomes
Details of Learning Activities
Students are expected to participate actively in all learning activities that include
discussion of mathematical concepts relevant to each topic
discussion of the mathematical routines and procedures for solving problems related to each topic
working independently or in groups in solving problems on exercise and work sheets
working in groups to solve more challenging problems requiring interpretation and evaluation of results
Teaching Schedule
Week beginning Topic/Assessment Exercises 8/7 Induction and Numeracy Assessment Number Skills -Order of operations - Directed number Order of operations Exercise Directed number Exercise 15/7 Calculations involving fractions Fractions Exercise 1. 22/7 Word problems involving fractions Decimal places and significant figures Calculations involving decimals Fractions Exercise 2. Decimal places and significant figures Exercise Decimals Exercise 29/7 Ratio and proportion QUIZ 1. Ratio and proportion Exercise 1. Ratio and proportion Exercise 2. 5/8 Introduction to percentages Calculations involving percentages Introduction to algebra Percentages Exercise Basic Albegra Exercise 1. 12/8 Simplifying algebraic expressions Working with indices Basic Albegra Exercise 2. Basic Albegra Exercise 3. Indices Exercises 19/8 Scientific notation Solving linear equations QUIZ 2. Scientific notation Exercise Linear Equations Exercise 0. Linear Equations Exercise 1. 26/8 Revision MID-SEMESTER TEST 2/9 Solving linear equations Linear Equations Exercise 2. Linear Equations Exercise 3. 9/9 Working with formulae Formulae Exercise 1. Formulae Exercise 2. Formulae Exercise 3. 16/9 Metric conversion Calculating perimeter Calculating area Metric Conversion Exercise Perimeter Exercise 1. Perimeter Exercise 2. Area Exercise 1. Area Exercise 2. 23/9 MID-SEMESTER BREAK 30/9 Calculating volume Calculations involving the Theorem of Pythagoras QUIZ 3. Volume Exercise Theorem of Pythagoras Exercise 1. Theorem of Pythagoras Exercise 1. 7/10 Introduction to trigonometric ratios Calculations involving trigonometric ratios Trigonometric Ratios Exercise 1 Trigonometric Ratios Exercise 2 14/10 Calculations involving trigonometric ratios Analysis of univariate data QUIZ 4. Trigonometric Ratios Exercise 3. Statistics Exercise 1. Statistics Exercise 2. 21/10 Further analysis of univariate data STATISTICS ASSIGNMENT Introduction to linear relations Working with linear relations Linear Relations Exercise 1. Linear Relations Exercise 2. Linear Relations Exercise 3. 28/10 Analysis of bivariate data Statistics Exercise 3. 4/11 Revision FINAL EXAMINATION
Learning Resources
Prescribed Texts
References
Any Year 10 or Year 11 Mathematics textbook. MATHEMATICS for Biology/Pathology Technicians by Carly Marshall and Sue van Megen 0 7035 8505 0
Other Resources
Students are required to purchase:
- a scientific calculator for use in class and when completing assessment tasks
- lined exercise book in which to complete Exercises
- binder with plastic sleeves for storing Exercises and Worksheets
- writing materials.
Overview of Assessment
Assessment in this course may include:
Worksheets
Quizzes
Assignments
Tests
4 Quizzes(best 3 results of 4 quizzes) 20%
Statistics Assignment 15%
Mid-semester Test 25%
Final Test 40%
Assessment Matrix
Other Information
1. Classroom lessons 17 x 4 hours = 72 hours
Tutorials 17 x 1 hour = 17 hours
Work outside class on Exercises, Worksheets etc = 6 hours
Assignment work = 5 hours
Revision and preparation for assessment tasks = 10 hours
TOTAL 110 hours
2. Students who are absent on the day of an assessment task, whose performance in an assessment task has been severely affected by some unforeseen circumstance or who are unable to submit an assignment by the due date, should refer to the assessment procedures described on the C3305 Certificate III in Science webpage of myRMIT Studies(Blackboard) Program Information/General information for new students.
Course Overview: Access Course Overview | 1,259 | 5,955 | {"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-2018-43 | latest | en | 0.862764 |
https://mathoverflow.net/questions/356656/variational-problem-how-to-minimise-the-second-moment | 1,611,139,463,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703519984.9/warc/CC-MAIN-20210120085204-20210120115204-00745.warc.gz | 472,028,566 | 27,886 | # Variational problem: how to minimise the second moment?
This is a neater version of a question I posted here, on which I'm also stuck.
The problem: Say I have a probability density function $$f(x)$$, defined for positive $$x$$, and let's note its $$n$$th non-centred moment $$x_{n}$$. Now, if the mean $$x_{1}$$ is fixed, what $$f(x)$$ minimises the second moment $$x_{2}$$? My intuition says it should be an exponential distribution (or similar shape).
My attempt: I want to minimise the functional
$$J(y)=\int x^{2}f(x)dx$$
with the constraints of mean and unit integral:
$$\int xf(x)dx=x_{1}$$
$$\int f(x)dx=1$$
So I need to minimise the modified functional:
$$J^{\ast}(y)=\int x^{2}f(x)dx+\alpha \int xf(x)dx + \beta \int f(x)dx$$
$$J^{\ast}(y)=\int (x^{2}f(x) +\alpha xf(x) + \beta f(x))dx$$
$$J^{\ast}(y)=\int (x^{2} +\alpha x + \beta )f(x)dx$$
Applying Euler-Lagrange gives $$x^{2}+\alpha x +\beta =0$$, where $$f(x)$$ doesn't appear!
So I don't know how to do, especially for finding the values of $$\alpha$$ and $$\beta$$. I also tried adding a constraint of positivity on $$f(x)$$, by substituting it with $$u(x)^{2}$$ (always positive by construction), but it leads to the same Euler-Lagrange equation.
Could anyone help me on that? Many thanks!
• I think it does not satisfy the conditions for applying the E-L equation. – Ryan Chen May 6 '20 at 2:43
Let $$X$$ be a positive random variable (r.v.) with probability density function $$f$$. By the Cauchi--Schwarz inequality, $$x_1^2=(EX)^2$$ is a lower bound on $$x_2=EX^2$$, and this lower bound is attained if and only if the r.v. $$X$$ is a constant. Since $$X$$ has a pdf $$f$$, it is not discrete and hence not a constant. So, the lower bound $$x_1^2$$ on $$EX^2$$ is not attained here. However, by considering e.g. a r.v. $$X$$ uniformly distributed on the interval $$[x_1-h,x_1+h]$$ with $$h\in(0,x_1)$$, we see that here $$x_2=x_1^2+h^2/3$$, which converges to $$x_1^2$$ as $$h\to0$$.
We conclude that $$x_1^2$$ is the exact lower bound on $$x_2$$.
• Thanks! So $f(x)$ should be a Dirac? – user655870 Apr 5 '20 at 15:50
• For the lower bound to be attained, the distribution of $X$ should indeed be Dirac at the point $x_1$. – Iosif Pinelis Apr 5 '20 at 16:06 | 734 | 2,246 | {"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": 36, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2021-04 | longest | en | 0.816908 |
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0 Basic Vocational Knowledge Introduction to Electrical Engineering
Introduction to Electrical Engineering Preface 1. Importance of Electrical Engineering 2. Fundamental Quantities of Electrical Engineering 2.1. Current 2.2. Voltage 2.3. Resistance and Conductance
3. Electric Circuits 3.1. Basic Circuit 3.2. Ohm’s Law 3.3. Branched and Unbranched Circuits 3.3.1. Branched Circuits 3.3.2. Unbranched Circuits 3.3.3. Meshed Circuits 4. Electrical Energy 4.1. Energy and Power 4.2. Efficiency 4.3. Conversion of Electrical Energy into Heat 4.4. Conversion of Electrical Energy into Mechanical Energy 4.5. Conversion of Electrical Energy into Light 4.5.1. Fundamentals of Illumination Engineering 4.5.2. Light Sources 4.5.3. Illuminating Engineering 4.6. Conversion of Electrical Energy into Chemical Energy and Chemical Energy into Electrical Energy 5. Magnetic Field 5.1. Magnetic Phenomena 5.2. Force Actions in a Magnetic Field 5.3. Electromagnetic Induction 5.3.1. The General Law of Induction 5.3.2. Utilisation of the Phenomena of Induction 5.3.3. Inductance 6. Electrical Field 6.1. Electrical Phenomena in Non-conductors 6.2. Capacity 6.2.1. Capacity and Capacitor 6.2.2. Behaviour of a Capacitor in a Direct Current Circuit Introduction to Electrical Engineering 2 6.2.3. Types of Capacitors 7. Alternating Current 7.1. Importance and Advantages of Alternating Current 7.2. Characteristics of Alternating Current 7.3. Resistances in an Alternating Current Circuit 7.4. Power of Alternating Current 8. Three-phase Current 8.1. Generation of Three-phase Current 8.2. The Rotating Field 8.3. Interlinking of the Three-phase Current
hoisting gear and lifts is enabled in a simple form by the electromotor which in railway transport also has the advantage over internal combustion engines. Measures for the Protection of Man from Electric Shock 9. Connection to the Neutral 9. We wish all readers a successful completion of their vocational training and hope this textbook will be instrumental to this end.2. The practical use of the formulas is shown by demonstrations of examples of solutions and the trainee will thus be enabled to solve the problems presented without assistance. offices. Power of Three-phase Current 9. Thus. Protective Isolation 9. A few examples will show the importance of electrical energy.8.2.4.7. The drive of machines. a growing proportion of electrical energy is used for the lighting of shops. It is also suitable for electricians who want to make themselves again acquainted with the theoretical fundamentals of electrical engineering by private study and qualify for higher positions.2. The grasping of the subject-matter is facilitated by the inclusion in this book of numerous sketches and illustrations. cooling and ventilation is installed for the operation of which electrical . and we ask them to send suggestions for improving the textbook to the Institute for Vocational Development.2.1. Extra-low Protective Voltage 9. Introduction to Electrical Engineering 4 1. We are indepted to the experts for their valuable suggestions.5.1.4. Protective Measures in Electrical Installations 9. With increasing industrialisation.2. electrical lighting is indispensable for working during the dark hours of the day.2. The growing utilisation of the latter is a decisive prerequisite for a rapid development of industry and agriculture. Fault-current Protection 9. dwellings and for outdoor lighting.6. There are many buildings where an air-conditioning system including heating. Protective Earthing 9. Each Section is followed by a summary of the subjects and problems for exercise and recapitulation. The authors have spared no effort to represent the subject-matter scientifically exact and at the same time so that it is easily understood.2. Protective Wire System 9.2. Checking the Protective Measures Introduction to Electrical Engineering 3 Preface The present textbook is intended for trainees in the field of electrical engineering.3.3. Protective Insulation 9.2. For the derivation of formulas only fundamental knowledge of mathematics is required on the part of the reader. Man is relieved from heavy physical labour by the use of electrical devices. Danger to Man by Electric Shock 9. Importance of Electrical Engineering Our life would be unthinkable without the use of electrical energy.
Table 1. their prices have been increased continuously. Water power is not in all countries available to a sufficient degree. are driven almost exclusively by electrical energy. the initial cost of a thermal power station. there would be no broadcasting and television systems. shows a survey of the two large fields of electrical engineering. Without electrical energy. For this purpose. very large amounts of electrical energy are required. Sections of Electrical Engineering . power electrical engineering and information electrical engineering. The chemical industry and metallurgy have a particularly high consumption. it is absolutely necessary to use electrical energy sparingly. the consumption of electrical energy increases by 4 % to 7 % per year. no telephone communication or telegraphy. devices of control an regulation engineering are required which.energy is required. According to the present developmental stage of engineering. For the production of the electrical conductor materials electrolytic copper and aluminium. In order to arrange automatic sequences of operation in production. In industrial countries.1. Therefore. a reduction of the resources of primary energy carriers takes place. considerable amounts of primary energy carriers such as coal. today. All over the world. This also means that Introduction to Electrical Engineering such devices and installations have to be developed and used which ensure a high net efficiency with as small a consumption of electrical energy as possible. The initial cost for the construction of a hydroelectric power station by far exceed. nuclear power stations represent not yet a final solution of the problem. petroleum or natural gas must be provided. foodstuffs can only be kept for a prolonged period of time in refrigerators or cold-storage rooms which usually are also operated with electrical energy. At the same time. The consumption of electrical energy by the various branches of economy is quite different.1. At higher ambient temperatures. Table 1.
mention should be made of the fact that electrical energy can be transported conveniently through large distances at low losses. telephone. telegraph. cables Communicationengineering Broadcasting. telewriter Conversion of electrical energy Motors. thermal devices. light sources. Production and consumption must take place . On the other hand. galvanic stations Control and regulation engineering Control of airconditioning plants. control and regulation of production processes Storage of electrical energy accumulators Electronic computer engineering Pocket computers. refrigerators.Power Electrical Engineering Information Electrical Engineering Section Examples Section Examples Generation of electrical energy Transmission of electrical energy Power stations Overhead lines. television. data processing Finally. there is the disadvantage that electrical energy can be stored only in small amounts at high cost. other telecommunication.
i. copper.1. then it is called negatively charged. Fundamental Quantities of Electrical Engineering 2. flowing quantities of water a water current. whereas the current flowing through electrolytes is called ion current because the flowing charge carriers are ions. As a current consists of flowing quantities of electricity (charge quantities). it is called positively charged.largely at the same time. therefore. Ions are charge carriers having mass. in rare cases ions.Conductor electrons . The carriers of the quantities of electricity are called charge carriers. the phenomenon of flowing quantities of electricity is called electrical current. As the current in metals is carried by electrons. the basic units of which the material world is constructed. Mostly the latter are electrons. Atoms or groups of atoms which have lost or gained one or more electrons are called ions. Electrons are constituents of atoms. in electrical engineering. An electron has the smallest imaginable charge which. They include all metals (especially silver. aluminium and iron) and electrolytes (salt solutions). The electron itself has a negative charge. electrons are considered as practically massless charge carriers because of their small volume and extremely small mass. Substances with many mobile charge carriers are called conductors.has more electrons.1. Since flowing quantities of air are called an air current. When an ion .as compared with the chargelss neutral atom .Atomic union 2 . when it has less electrons. An atom consists of a nucleus and the electrons surrounding it. is called elementary charge. Fig. Current Flowing quantities of electricity cause effects which are utilised in practice.technology. non-stationary charge carriers. In electro. it can only flow in such substances which possess freely mobile. the free electrons move through the atomic lattice of the conductor 1 . Electron current.e. it is called electron current. 2. Introduction to Electrical Engineering 6 2.
These are 1. that is to say. the generation of heat in conductors through which current flows 2. they are not freely mobile. The generation of electric heat can be imagined in such a way that the flowing . the magnetic field associated with the current 3. are called non-conductors or insulators.Electrolyte 3 . plastics.7 Fig.Negative ions 5 . 2. They conduct current so badly that they cannot be termed as conductor but they allow a small current to flow so that they cannot be used as a non-conductor. transport of substance by ion currents Re 1. There are substances whose electrical conductivity is such that they are between conductor and nonconductor. We cannot perceive electrical currents directly but only indirectly we become aware of three characteristic effects of current.Positive ions 6 .Electrons 4 .Neutral molecules Substances in which the charge carriers are fixed or stationary. . Semiconductors are of particular practical importance to electrical engineering. It is utilised in electric heating engineering.Every electric current generates electric heat in conductors. Ion current 1 . The most important nonconductors are porcelain. germanium and selenium. flat iron.2. The most important semiconductors are silicon. cooking plate. glass. These substances are called semiconductor. Current cannot flow through them. for example.Metallic feed lines 2 .
Introduction to Electrical Engineering .
This process is called electrolysis. material changes will take place at the two feed wires when current flows. When. From the ions. it is independent of the place of the line. The mutual coupling of current and magnetic field is of eminent practical importance. Proof of this can easily be given by means of a magnetic needle which with initial direction parallel to the current will be turned so that it is across to the current. for an economic production of electrical energy (see Section 5). In order to define the intensity of a current.North pole 2 . in other words. for the deposition of metallic coats and protective coverings (galvanisation). especially metals in a pure state. the copper particles are separated at one electrode in the form of a metallic coat. . 2. Magnetic field associated with the current 1 . then . Development of heat in the current carrying conductor Re 2. Obviously. There is no current without a magnetic eddy and no magnetic field eddy without current.4. are deposited at these leads. Fig. the line material and the line cross-sectional area but it is only determined by the number of charge carriers (quantity of charge Q) flowing through the line in a certain time t. a consequence of the transport of substance associated with the current. the energy of the braked charge carriers is converted into irregular oscillatory energy. 2. for example. the term current intensity (formula sign I) has been introduced.When a fluid conductor with ions is interposed in a metallic current path. many charge carriers flow through the conductor.3.8 charge carriers collide with the stationary particles forming the skeleton of the material or substance. for example. As a consequence. Fig. namely thermal energy. It surrounds the current spatially like an eddying fluid its axis of eddy. . of the stationary particles. the fluid conductor is a copper sulphate solution. consequently.Every electric current is accompanied by a magnetic field. It is used for the winning of metals. in a certain time. the electrons can migrate into the 9 current supply leads or out of them.South pole Re 3. this cannot be effected by the material particles which. If. These material changes are the result of the material particles flowing with the ions.
).1. namely Q=I·t [Q] = [I] · [t] .2 A = 200 mA After the establishment of the basic unit for the current intensity. Current Intensities for a Few Applications Melting furnace 100. current intensities may occur in largely different magnitudes.5 A = 500 mA Torch lamp 0. 2.5.000 A = 10 kA Welding 1.1836).000 A 1 mA = 1 milliampere = 10-3 A = 0.1.1.1. [I] = A Other usually used units of the ampere are 1 kA = 1 kiloampere = 103 A = 1. The unit of current intensity is called ampere = A in honour of the French physicist Marie Andr Ampre (1775 .000 A = 100 kA Aluminium production 10.) I = current intensity Q = charge quantity t = time The sign of the current intensity indicates the current direction. Transport of matter in case of conduction by ions The following holds: where I = Q/t (2. Table 2. vice versa it is low.000001 A In electrical engineering.the current intensity is high. units for the quantity of electricity can be derived from equation (2. One has defined: Introduction to Electrical Engineering 10 The current intensity is positive when the current direction is equal to the direction of flow of the positive charge carriers or when it is opposite to the direction of flow of negative carriers (e. Fig. Table 2.000 A = 1 kA Starter for motor-car 100 A Household appliances up to 6 A Refrigerator 0.001 A 1µA = 1 microampere = 10-6 A = 0.g. shows a few values. It is an arbitrarily established mathematical direction of counting and should not be confused with the actual flowing direction of the moved charge carriers. electrons).
Voltage In order that a current flows through a conductor.1806). From the definition equation of the current intensity.h. How many C are 1. The carriers of the quantities of electricity are called charge carriers. . the most frequently used sub-units are kA. As to their conductivity for electrical current. 3. it is the ampere-second (A. 84 A. It imparts energy to the charge carriers which thus are driven through the conductor. As 1 hour has 3. Introduction to Electrical Engineering 12 2. Calculate the transported quantity of electricity in the units C and A. these are electrons and ions. It is generated in a voltage source. A quantity of electricity of 108.h). the basic unit for the quantity of electricity is derived.000278 A.[Q] = A · s and from 1A · 1s = 1C = 1 coulomb follows [Q] = C The product of A · s is called coulomb in honour of the French physicist Charles Auguste de Coulomb (1736 . How many A are 27 mA.600 seconds.h: 1 A · h = 1 A · 3600 s = 3600 A · s = 3600 C Introduction to Electrical Engineering 11 The electrical current is the phenomenon of flowing quantities of electricity. The unit of current intensity is the ampere = A. The three characteristic effects of current are generation of heat in conductors through which current passes the magnetic field associated with the current transport of substance by ion currents The current intensity is determinded by the quantity of charge flowing through the conductor during a certain time. non-conductors (insulators) and semiconductors. 80µA.s) = coulomb (C).h. An electric current having the intensity of 2 A flows through a line for a period of 2 hours. 5. the following relation holds for the conversion of A. mA andµA.000 C is flowing through a line within 5 hours. 6. an electrical “pressure” must be exerted on the freely mobile charge carriers.h.04 kA 2.s into A.h). This “pressure” is the electrical drive phenomenon on the charge carriers which is called voltage.000 mA.500µA. 0.5 A.2. the various substances are divided into conductors. It results from the relation I = Q/t. 0. 0.h? 2. There is no current without an electrical voltage. A frequently used sub-unit is the ampere-hour (A. Questions and problems: 1. The original drive phenomenon for current is called primary electromotive force.1 kA. Find the current intensity. A larger unit of the quantity of electricity is the ampere-hour (a. 1.
For the winning of electrical energy. Table 2.000 V = 600 kV High-voltage lines 60.000 V = 15 kV Lighting network 220 V Motor-car battery 12 V Receiving voltage of a wireless set 0. the current path formed by the conductor must be closed. This loss can be characterised as voltage drop. Primary electromotive force and voltage drop have the same unit which is called volt .2.001 V 1µV = 1 microvolt = 10-6 V = 0. On principle.000. the designations of the respective voltage sources and their main applications.000. that is to say. voltages may occur in quite different magnitudes. these voltage sources operate as follows . A current can only flow through a conductor. Introduction to Electrical Engineering 13 Table 2. shows the various possibilities of producing a primary electromotive force.01 V = 10µV The primary electromotive force is a prerequisite for an electrical current. the charge carrier differs by nothing from its state before it started the circulation. it passes through the conductor.000 V = 60 kV Sparking-plug in an internal combustion engine 15.000 V 1 mV = 1 millivolt = 10-3 V = 0.2. In practice. [E] = V [U] = V Frequently used sub-units of volt are 1 MV = 1 megavolt = 106 V = 1. Table 2. completely transferring the energy taken up to this conductor.1827). When a charge carrier has received drive energy from a voltage source. After exactly one circulation.Since every conductor offers resistance more or less to the passage of current. the voltage drop by U. Voltage Values for a Few Applications Lightning up to 10.000 V = 10 MV Extra-high voltage lines 600.5. The primary electromotive force is designated by the formula sign E. therefore. the charge carriers lose energy when passing through. the generation of the primary electromotive force by chemical and magnetic-field actions is of particular importance.000. it cannot have stored energy.V in honour of the Italian physicist Alessandro Volta (1745 . shows some values. no difference is made between these two terms and they are called voltage in short.000001 V In electrical engineering.000 V 1 kV = 1 kilovolt = 103 V = 1.
Diluted sulphuric acid H2SO4 is suitable as electrolyte. copper Cu and zinc Zn are particularly suitable (Fig. This charge carrier difference externally acts as electrical primary electromotive force. 2. as conductor rods (electrodes).). then one will find an excess of electrons at one conductor (negative pole) and an electron deficit at the other conductor (positive pole).6. .· Primary electromotive force by chemical action When immersing two conductors of different kinds into an electrolyte.
Introduction to Electrical Engineering .
for example.conductor by means of pressure piezoelectric element measurement of pressure. the properties of insulating materials are tested . battery. accumulator voltage supply to portable devices. Ways of Producing Primary Electromotive Forces Causes of the production of the electromotive force Designation of the voltage source Examples of use chemical action galvanic cell.3. solar cell measuring the intensity of illumination charge separation by . microphone . sound pick-up for records. remote temperature measurement action of magnetic field (induction) generator economical generation of electrical energy in power stations action of light photovoltaic cell.influence influence machine generation of high and extrahigh voltages by means of which.14 Table 2. starting battery in motor-cars thermal action thermoelectric element (thermocouple) measuring the temperature at points which are not readily accessible.mechanical charge movement belt-type generator displacement of charge (polarisation) on a non.
Lead accumulators and nickeliron or nickel-cadmium accumulators are of particular importance. a primary electromotive force acts externally.Direction of the primary electromotive force 3 .South pole . the charge carriers in the conductor are subjected to an impetus to move. The change of the magnetic flux may. This impetus of motion is different in the different conductor materials so that. In accordance with the general tendency to balance differences in concentration. Primary electromotive force 2 generated by induction 1 . According to a law of nature (law of induction) the following happens: When the magnetic flux enclosed by a conductor loop is changed. for example.7. When current flows. Then. as a result. they are called accumulators (storage batteries). this is also occurring when stored too long. · Primary electromotive force by magnetic-field action (induction) This production of voltage is of greatest technical importance and it is used in all cases when primary electromotive force is to be generated by mechanical motion. be due to the fact that the conductor loop is turned inside the magnetic field or the magnet is approached to are moved away from this loop. Galvanic element also known as galvanic cell 15 Other substances are also suitable (especially coal and zinc in a thickened ammonium chloride solution). these voltage sources disintegrate due to the transport of substance and become useless. the electrolyte tries to press its ions into the solid conductor. the entire conductor loop is a primary electromotive force source. Rechargeable voltages sources do not show this disadvantage. Fig. therefore. On the other hand.Fig. the basic units of construction of the solid conductors are eager to migrate as ions in the electrolyte.Direction of motion 2 . 2.6. 2.North pole 4 .
electromotor. heater. the loss in voltage caused when current flows through a conductor is called voltage drop U. 2. It is easily understood and can Introduction to Electrical Engineering . the generation of the primary electromotive force by chemical action and by the action of the magnetic field is of particular importance.8. the electrode with an electron deficit is called positive pole (+).6 MV? 2. the most frequently used sub-units are MV. This property is called electrical resistance (formula sign B). 2. is used. Graphical symbol of a (direct) voltage source. How many V are 500 mV.to + whereas the voltage drop U runs from + to -.V .8.. 0. Questions and problems: 1. As unit of the voltage. The drive phenomenon originally generated in a voltage source is called primary electromotive force E. the geometrical dimensions and the conductor material are decisive for the value of the resistance. 350µV. the primary electromotive force E is directed from . thus.3. Fig.) has the property of resisting any current passage. the graphical symbol shown in Fig. For the winning of electrical energy. The formula for calculating the resistance is called resistance rating formula. it has a different magnitude. the volt . the arrow indicating the direction may be omitted The direction of voltage corresponds to the direction of current defined in Section 2. Resistance and Conductance Every conductor and every electrical device (electric bulb.5 kV.1. The voltage direction is indicated by an arrow. kV andµV. etc. wireless reciever.16 As symbol of a voltage source. The electrical drive exerted on the charge carriers is called voltage. Give reasons for the fact why in a current passage the sum of all voltage drops must be equal to the entire primary electromotive force! 2.has been laid down. For a conductor. 2. The electrode with an excess of electrons is called negative pole (-). Depending on the material used and the design of the conductor or the device.
R ~ 1/A Finally.2) where R = resistance r = specific resistance l = length of the conductor A = cross-sectional area of the conductor The higher the resistance. G = 1/R (2.) and (2. In the place of the specific resistance. for example.1854) and abbreviated by the Greek letter W 2) 2) W Greek letter omega [R] = W A conductor has a resistance of 1W if a voltage of 1 V drops when a current of 1 A passes this conductor. hence.3) where G = conductance R = resistance Similar relations apply to the material constant. When designating the line length by 1 and the line cross-sectional area by A.2.3). 1) r Greek letter rho (2. Hence. k=1/r. From the equations (2. The permeability to current of a conductor is called conductance (formula sign G) and. the specific conductance (formula k 1)) can be stated as reciprocal value. the resistance is dependent on the conductor material. This dependence on material is covered by a material constant which is termed as specific resistance or resistivity (formula sign r 1)).17 be checked by experiment that a long thin wire will offer a higher resistance to the current passage than a short thick one. the rating equation for the electrical conductance is obtained as follows 1) k Greek letter kappa where G = conductance 18 k = specific conductance. the poorer the conduction of the current. The unit of the conductance is called siemens = S in honour of the German physicist Werner von . iron as a conductor is inferior to copper (iron has a higher resistance). hence. is inversely proportional to the resistance. then the resistance R is proportional to 1/A. k=1/r A = cross-sectional area of the conductor l = length of the conductor The unit of the resistance is called ohm in honour of the German physicist Georg Simon Ohm (1789 .
the unit siemens has not been generally adopted.1892).000.5 mm2 = 1. Calculate the resistance and conductance of a copper wire having a length of 175 m and a cross-sectional areas of 2.246 W G = 1/1.2.) we have r = R · A/I [r] = W · m²/m = W · m A frequently used sub-unit is W · mm²/m = 10-6 W·m From equation (2.5 mm2. shows for a few substances the values of r and k. [G] = S = 1/W Frequently used sub-units of ohm (W) and siemens (S) are 1 MW = 1 megaohm = 106 W = 1. units can be given also for the specific resistance and the specific conductance by rearranging the equations (2.000 S 1 mS = 1 millisiemens = 10-3 S = 0.001 S 1µS = 1 microsiemens = 10-6 S = 0.000001 S Now. A copper conductor having a cross-sectional area of 6 mm is to be replaced by an aluminium conductor of the same resistance. for k we have 19 k = G l/A [k] = S · m/m² = S/m = 1/(W · m) Table 2.Siemens (1816 .5 mm2 rCu = 0.3). (In English-speaking countries.001W 1 kS = 1 kilosiemens = 103 S = 1. What is the size of the cross-sectional area of the aluminium conductor? .4).1.2.000 W 1 mW = 1 milliohm = 10-3 = 0.2) and (2. Example 2.246 W = 0.4.804 S Example 2.0178 (W · mm2)/m (kCu = 1/rCu » 56 · 106 S/m) To be found: RGSolution: R= r · l/A G=1/R R=0. Given: l = 175 mm A = 2.) The correlation between the units siemens and ohm is given by equation (2.000 W 1 kW = 1 kiloohm = 103 = 1. For r from equation (2.0178 · (W · mm2)/m 175 m/2.4).
This is due to the fact that the more intensively oscillating crystal lattices offer a higher resistance to the electron current. hence.0286/0. the following approximate values of the temperature coefficient . the resistance diminishes with increasing temperature.64 mm2 For the aluminium conductor. the resistance increases with increasing temperature. hence. The most striking influence on the resistance of a conductor or device is exerted by the temperature.5) where a = temperature coefficient D 2) = R/R change in resistance related to the initial resistance Du 3) = temperature change 2) D Greek letter delta 3) u Greek letter theta The unit of the temperature coefficient is [a] = 1/K (K = Kelvin) In metallic conductors.0178 (W · mm2)/m rAl = 0. the standardised cross-sectional o area of 10 mm2 is selected.0178 · 6 mm2 = 9.Given: ACu = 6 mm2 rCu = 0. This is due to the fact that with rise in temperature more charge carriers are released which then are available as free charge carriers for the transport of electricity. The temperature dependence of the electrical resistance can be quantitatively expressed by the temperature coefficient a1) 1) a Greek letter alpha The temperature coefficient states the fraction by which the resistance changes with a change in temperature of 1 K: a = (DR/R) · 1/Du (2. a is positive. a is negative. For practice.0286 (W · mm2)/m To be found: AAl Solution: RCu = RAl 20 RCu = rCu · 1/Acu RAl = rCu · 1/AAl rCu · 1/Aal = rAl · 1/AAl AAl = rAl/rCu · Acu AAl = 0. In electrolytes and semiconductors.
0286 55 » + 0.02 1/K · Semiconductors a is negative and largely dependent on temperature.004 copper 0.004 zinc 0.004 aluminium 0.004 lead 0.016 62. · Ferromagnetic metals (iron. Specific Resistance r. it should be drawn from special Tables for the temperatures involved. for example. constantan) a»0 These special metal alloys are of particular importance to measuring techniques if resistors independent of temperature are required.g. a numerical value cannot be stated. will increase by 0.21 4.0.4W in the event of an increase in temperature of 1 K. Conductance k and Temperature Coefficient a of a Few Conductor Materials r k a Conductor Material W · mm2/m S · m/mm2 1/K silver 0.004 nickel .4W to 100.004 1/K The resistance of a copper conductor of 100W.4): · Non-ferromagnetic pure metals (no metal alloys) a » + 0. Table 2.4.063 16 » + 0. from 20 °C to 100 °C) it will increase by 32 W to 132 W. in case of a rise in temperature of 80 K (e.5 » + 0.0178 56 » + 0. · Electrolytes a » . nickel) a » + 0.will suffice (see also Table 2.8 » + 0.006 1/K · Metal alloys of a special composition (novoconstant.
10 10 » + 0. 4 % Al. the temperature rises to 85 °C.26 R85 = 22. R85 = R20 + DR R85 = R20 + aR20Du R85 = R20 (1 + aDu) R85 = 18W (1 + 0.45 2. pure 0.68W Components which are used to limit the current by means of certain resistance values and which are constructed specifically for this purpose are called resistors.10 10 » + 0. 1.5) we obtain by transposing a value for the change of resistance DR = a R20 Du This amount must be added to the resistance R20 in order to determine the final resistance R85.26) R85 = 18W · 1. 12 % Mn.20 °C = 65 K a » +0.004 1/K To be found: R85 Solution: From equation (2.5 % Cu. During operation.004 1/K · 65K) R85 = 18W (1 + 0.5 2 »0 22 1) Novokonstant: 82.3. A coil of copper wire has a resistance of 18 W at room temperature (20 °C).3 »0 constantan 2) 0. Resistor is a component for the realisation . 1 % Mn Example 2.006 iron.006 Novokonstand 1) 0. Given: R20 = 18 W D u = 85 °C .0. 45 % Ni. Find the resistance of the coil at this temperature.5 % Fe 2) constantan: 54 % Cu.
Graphical symbol of a resistor Introduction to Electrical Engineering 23 Resistance and conductance are properties of electrical conductors and devices. 350 mW. a 2-core copper line with a cross-sectional area of 2. Calculate the temperature (related to a reference temperature of 20 °C) at which the resistance of a copper wire will double. 2. this means that the resistance of these materials increases with increasing temperature. the most frequently used subunits are kS. .9. 3. 4 S. For the supply of energy to a consumer situated at a distance of 150 m. 2 mS? 2. The correlation between resistance and conductance results from the relation R = 1/G The rating equation of the resistance and of the conductance is R = r · l/A and G = k · A/l The material constant r is called specific resistance. Questions and problems: 1. Calculate the resistance and the conductance of the line (take into consideration the outgoing and the return conductors). k is called specific conductance. The resistance characterises the resistance offered to the passage of current. The general graphical symbol of a resistor is shown in Fig. Fig. The magnitude of the temperature dependence is covered by the temperature coefficient a which indicates the relative change in resistance per degree of change in temperature. A component which is specially built to realise a certain resistance value is called resistor. the conductance indicates how well the conductor or device in question allows the current to pass. a = +0. the ohm = W is specified. KW. the most frequently used sub-units are MW.of a certain resistance value. The unit of conductance is siemens = S = 1/W. too) is primarily depending on temperature.5 mm2 per conductor is used.9. 2. mS.004 1/K. How many W are 2 MW 15 kW. As unit of the resistance.5µS. For non-ferromagnetic metals. The resistance (and the conductance.µS. mW. 0.
Plug socket 4 . 5. A fuse is interposed in each line as overcurrent protection. transfer their energy to the lamp and return to the source where they receive again drive energy.Voltage source 2 .1.Table lighting fitting 3 . This is a circulatory process and. For conveniently switching on and off. Electric Circuits 3. 3. Basic Circuit If an incandescent lamp for illuminating a working place is to be caused to light.g.2 the schematic representation with symbols which is called wiring diagram. The charge carriers driven from the source pass through the conductor. a switch is interposed. · A voltage source whose voltage is available at the point of connection (socket outlet). therefore. in a power station). the following pre-conditions are required.Introduction to Electrical Engineering 24 3. Fig.Plug 5 . 5. Fig. The voltage source may be far away from the point of connection (e.1.Switch This shows that a closed connection from the voltage source to the incandescent lamp is essential for operation. Fig. Simplified representation of the arrangement voltage source/table lighting fitting 1 . such an arrangement is called circuit.1. shows the described arrangement.Fuses 6 . · A 2-core line leading to the incandescent lamp which conducts the voltage via a plug to the lamp. .
Sign up to vote on this title | 7,920 | 34,458 | {"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-2018-13 | latest | en | 0.734299 |
https://mathleaks.com/study/combining_linear_functions | 1,642,361,816,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300010.26/warc/CC-MAIN-20220116180715-20220116210715-00158.warc.gz | 457,238,207 | 24,465 | mathleaks.com mathleaks.com Start chapters home Start History history History expand_more Community
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# Combining Linear Functions
## Function Operation
Functions can be combined, through addition, subtract, multiplication, and division to create a new function. The resulting function can have similar or new characteristics, depending on the original functions and which function operation is used.
## Combining Functions
Functions behave similar to numbers when they are combined to create new functions. Common ways of combining functions include addition, subtraction, multiplication and division.
### Method
When adding or subtracting functions, it is possible to find the resulting function by combining like terms. If two functions, f(x) and g(x), are combined through addition or subtraction and one or both have a restricted domain, the domain of the resulting function is restricted to interval(s) where both f(x) and g(x) are defined.
### Multiplication
When multiplying two functions, the Distributive Property can be used. Meaning, every term in one function is multiplied with every term in the other. If two functions, f(x) and g(x), are combined through multiplication and one or both have a restricted domain, the domain of the resulting function is restricted to interval(s) where both f(x) and g(x) are defined.
### Division
When two functions are combined through division it is necessary to take into account that division by zero is undefined. As a consequence the domain of the resulting function is restricted to interval(s) where both functions are defined and where the denominator does not equal zero.
fullscreen
Exercise
Given the linear functions f(x)=3x+5 and g(x)=-x+2, find the function
h(x)=f(x)+g(x).
Show Solution
Solution
We add functions by combining like terms. Since g(x) begins with a negative term, we can put parentheses around it before adding.
h(x)=f(x)+g(x)
h(x)=3x+5x+2
h(x)=3xx+5+2
h(x)=2x+7
The new function, h(x), can be written as h(x)=2x+7.
fullscreen
Exercise
The functions f and g are given as f(x)=x4 and g(x)=2x1. Find h(2) if
h(x)=f(x)g(x).
Show Solution
Solution
To begin, we can write the rule of h(x) by multiplying f and g.
h(x)=f(x)g(x)
h(x)=(x4)(2x1)
h(x)=2x2x8x+4
h(x)=2x29x+4
Next, to find h(2), we'll substitute x=2 into the rule of h and simplify.
h(x)=2x29x+4
h(2)=22292+4
h(2)=2492+4
h(2)=818+4
h(2)=-6
Thus, h(2)=-6. | 664 | 2,626 | {"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} | 4.84375 | 5 | CC-MAIN-2022-05 | latest | en | 0.8565 |
https://study.com/academy/topic/square-roots-help-and-review.html | 1,569,096,419,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514574662.80/warc/CC-MAIN-20190921190812-20190921212812-00133.warc.gz | 678,499,779 | 26,775 | # Ch 2: Square Roots: Help and Review
The Square Roots chapter of this SAT Mathematics Level 2 Help and Review course is the simplest way to master square roots for the SAT test. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of square roots.
## Who's it for?
Anyone who needs help learning or mastering SAT mathematics level 2 material will benefit from taking this course. There is no faster or easier way to prepare for this SAT math subject test. Among those who would benefit are:
• Students who have fallen behind in understanding how to evaluate and simplify square roots
• Students who struggle with learning disabilities or learning differences, including autism and ADHD
• Students who prefer multiple ways of learning math (visual or auditory)
• Students who have missed class time and need to catch up
• Students who need an efficient way to learn about square roots for the SAT test
• Students who struggle to understand their teachers
• Students who attend schools without extra math learning resources
## How it works:
• Find videos in our course that cover what you need to learn or review.
• Press play and watch the video lesson.
• Refer to the video transcripts to reinforce your learning.
• Test your understanding of each lesson with short quizzes.
• Verify you're ready by completing the Square Roots chapter exam.
## Why it works:
• Study Efficiently: Skip what you know, review what you don't.
• Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
• Be Ready on Test Day: Use the Square Roots chapter exam to be prepared.
• Get Extra Support: Ask our subject-matter experts any square roots question. They're here to help!
• Study With Flexibility: Watch videos on any web-ready device.
## Students will review:
This chapter helps students review the concepts in a square roots unit of a standard math course. Topics covered include:
• Evaluating square roots
• Estimating square roots
• Simplifying square roots
10 Lessons in Chapter 2: Square Roots: Help and Review
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken
### Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. | 563 | 2,762 | {"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} | 2.765625 | 3 | CC-MAIN-2019-39 | longest | en | 0.892923 |
https://www.teacherspayteachers.com/Product/Turkey-Trot-factor-multiple-math-game-Thanksgiving-fall-theme-391201 | 1,529,805,678,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267865995.86/warc/CC-MAIN-20180624005242-20180624025242-00547.warc.gz | 921,791,551 | 17,947 | # Turkey Trot – factor & multiple math game – Thanksgiving, fall theme
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Build students' understanding of factors and multiples with this simple game that provides for differentiation based on student need. Students will be able to practice identifying factors of given two-digit numbers. These games will also help students recognize that some numbers have more factors than others.
Math Common Core State Standards addressed –
Operations and Algebraic Thinking (4.OA)
Gain familiarity with factors and multiples. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. (4.OA.4)
Included:
• teacher directions and student directions
• "Thinking Questions" for guiding student discussion
• graphic reference sheet (color and grayscale)
• two gameboards
• four spinners
• two recording sheets
This games requires minimal prep – just provide game pawns and a paper clip or plastic spinner. Students spin one of two provided spinners and then find a factor of the number spun. Once a student reaches the final space, that player wins.
The game comes with two gameboards and four spinners. Of the four spinners, two are designed for use with the first gameboard, while the other two spinners – which use larger numbers – are made to be used with the second gameboard. The varied spinners allow for differentiation within your class while they play. Assign the gameboards and spinners based on your students' proficiency with factors and multiples.
The provided recording sheets require students to write the numbers landed on and spun, practicing how to accurately use the word "multiple" and "factor" to describe the relationship between the numbers. One recording sheet uses the word "multiple" and the other uses the word "factor", allowing you to choose the recoding sheet based on the concepts you want students to practice.
Also included is a full-page reference sheet, available in both color and grayscale, that describes factors and mutliples, as well as giving the first 15 multiples of the numbers 2 through 9. Before you have your students play the game, you can have them review the reference sheet and glue it in their journals. Your students can use the journal insert as a guide while they play the game, as well as when they complete other tasks that relate to factors and multiples.
For more practice with factors and multiples, please check out these other resources I have available –
Buzzing About Factors - task cards + printables set
Bumblebee Paths, Frog Pond Frenzy - factors & multiples math games bundle
Polar Paths, Penguin Power factors multiples game, task cards, printables bundle
Factor Flip prime & composite game
I hope these materials are helpful (and fun!) for your students – Dennis McDOnald
Total Pages
9 pages
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Sign Up | 672 | 3,271 | {"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} | 3.796875 | 4 | CC-MAIN-2018-26 | latest | en | 0.913036 |
https://math.stackexchange.com/questions/34193/help-finding-solution-for-trigonometric-equation | 1,621,169,673,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991269.57/warc/CC-MAIN-20210516105746-20210516135746-00619.warc.gz | 397,828,494 | 38,746 | # Help finding solution for trigonometric equation
I have a flat mirror and a target. Given the sun's light angle of incidence, I must calculate how much to spin my mirror to hit the target with the light. The problem is shown in the following figure.
Given $a$, the angle of sun's light incidence, and $b$, the angle the reflected light must have in order to reach the target (from the center of the mirror), I must calculate $c$, the angle the mirror must spin. Simple enought, the solution is given by:
$c = {a + b \over 2}$
But there is a variation of this situation where it is not possible to rotate the mirror from it's center. The mirror is attached on the surface of a cylinder, and the spin is relative to the cylinder's center. In this new situation, $b$ is function of $c$.
Considering I had the brilliant idea of using positive y-axis for angle reference, I soon figured out that
\begin{aligned} & x' = x - (- r \sin c) \\ & y' = y - r \cos c \\ & \tan b = {x' \over y'} \end{aligned}
thus
\begin{aligned} & c = {a + b(c) \over 2} \\ & c = {a + \arctan {x + r \sin c \over y - r \cos c} \over 2} \\ & 2 c = a + \arctan {x + r \sin c \over y - r \cos c} \\ & \tan (2 c - a) = {x + r \sin c \over y - r \cos c} \\ & {\sin (2 c - a) \over \cos (2 c - a)} = {x + r \sin c \over y - r \cos c} \end{aligned}
This is as far as I could get finding $c$. I was not able to isolate $c$ in the equation, nor could I find a simpler relation between $c$ and $b$. How can I find $c$? Is there a simpler way to define $b(c)$, that does not resort to trigonometry? If not, how can I isolate $c$ in that last equation?
I need to program it, and I'd rather not resort to numerical methods because I can't remember a damn thing about it.
• I believe you have a mistake there, it should be c = (b−a)/2 – JackKalish Dec 12 '18 at 15:47
I believe it is possible to isolate $c$ in your last equation, although I haven't written it all out, and I suspect that if I did I'd find the result too messy to be of much use. You can use $\sin(2c-a)=\sin2c\cos a-\cos2c\sin a$ and $\cos(2c-a)=\cos2c\cos a+\sin2c\sin a$, then $\sin2c=2\sin c\cos c$ and $\cos2c=2\cos^2c-1=1-2\sin^2c$ to get everything in terms of $\sin c$ and $\cos c$. Then you can use $\sin^2c+\cos^2c=1$ to express everything in terms of $\sin c$ or $\cos c$, whichever you prefer. You may have to juggle some square roots, but eventually you'll get to a polynomial, possibly of very high degree, in $\sin c$ (or $\cos c$).
• 9 years too late : After expanding, using the tangent half-angle subsitution avoid to juggle some square roots and leads to a sixtic polynomial in $t$. Cheers :-) – Claude Leibovici Oct 31 '20 at 10:03 | 822 | 2,689 | {"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} | 4.4375 | 4 | CC-MAIN-2021-21 | latest | en | 0.925308 |
https://gmatclub.com/forum/1st-gmat-practise-test-155028.html | 1,487,928,855,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501171418.79/warc/CC-MAIN-20170219104611-00417-ip-10-171-10-108.ec2.internal.warc.gz | 719,483,258 | 50,306 | 1st GMAT practise Test : Ask GMAT Experts
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# 1st GMAT practise Test
Author Message
Verbal Forum Moderator
Status: Getting strong now, I'm so strong now!!!
Affiliations: National Institute of Technology, Durgapur
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28 Jun 2013, 00:18
Guys,
I have appeared for my 1st Mock Test from Veritas Prep. I scored 530. q36v16. It has completely demoralized me. I read somewhere that mostly people improve by 100 points max. I need some feedback on this. Any sort of guidance/experience sharing is most welcome.
Regards,
Subhojyoti
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Re: 1st GMAT practise Test [#permalink]
### Show Tags
28 Jun 2013, 22:13
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Expert's post
There is a great deal of variation in student improvement. For one thing, your improvement depends a great deal upon why you got the initial score that you did. If you ran out of time at the end, you may see a significant jump just from learning to finish on time. Also, have you studied at all, or are you brand new to the test? Are you comfortable with English grammar, with reading passages in different subject areas, etc.? How about math? Did you miss problems because of small errors that can easily be controlled for, or did you consistently find the problems difficult to understand or manipulate?
I often see students improve by much more than 100 points, but it takes a lot of hard work. You have to be very consistent at looking at what you're doing that is and isn't working and then targeting your practice to build on your strengths and address your weaknesses.
Good luck!
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Verbal Forum Moderator
Status: Getting strong now, I'm so strong now!!!
Affiliations: National Institute of Technology, Durgapur
Joined: 04 Jun 2013
Posts: 638
Location: India
GPA: 3.32
WE: Information Technology (Computer Software)
Followers: 98
Kudos [?]: 546 [0], given: 80
Re: 1st GMAT practise Test [#permalink]
### Show Tags
28 Jun 2013, 22:28
Thanks a lot for the insight. I could not complete ir on time. In fact I could only completely few questions. I was completely unprepared for the test. I considered it to be the first diagnostic test. English is not my native language but I have a decent enough grasp on it. Rc was quite difficult for me to get the feel. I bought few mgmat materials and of to master the verbal section. Could you suggest few good books apart from mgmat, though I feel mgmat has covered topics quite well. For cr I intend to buy cr bible by David killoran
Thanks
Subho
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Re: 1st GMAT practise Test [#permalink]
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28 Jun 2013, 22:46
That depends on what you want the other books for. Our 8 books are meant to cover the complete range of material on the test, but you will of course want to apply those skills by practicing in the Official Guide. I'll leave it to others to discuss whether our books are the best for your needs, but are you looking for *supplemental* material? If so, in what area, and are you sure you need more books? Most people find the three Official Guides and our set to be *more* material than they want to work through!
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Re: 1st GMAT practise Test [#permalink] 28 Jun 2013, 22:46
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Display posts from previous: Sort by | 1,346 | 5,197 | {"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-2017-09 | longest | en | 0.88519 |
https://de.zxc.wiki/wiki/Magnetische_Feldkonstante | 1,726,861,041,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725701423570.98/warc/CC-MAIN-20240920190822-20240920220822-00409.warc.gz | 166,241,617 | 12,246 | # Magnetic field constant
Physical constant
Surname Magnetic field constant
Formula symbol ${\ displaystyle \ mu _ {0} \,}$
Size type Magnetic permeability
value
SI 1.256 637 062 12 (19)e-6th ${\ displaystyle \ textstyle {\ frac {\ mathrm {N}} {\ mathrm {A ^ {2}}}}}$
Uncertainty (rel.) 1.5e-10
Relation to other constants
${\ displaystyle \ mu _ {0} = {\ frac {1} {\ varepsilon _ {0} \, c ^ {2}}}}$
Electric field constant speed of light${\ displaystyle \ varepsilon _ {0} \,}$
${\ displaystyle c \,}$
Sources and Notes
Source SI value: CODATA 2018 ( direct link )
The magnetic field constant , also magnetic constant , vacuum permeability or induction constant , is a physical constant that plays a role in the description of magnetic fields . It indicates the ratio of the magnetic flux density to the magnetic field strength in a vacuum. The reciprocal of the magnetic field constant (with a prefactor ) appears as a proportionality constant in the magnetostatic force law . In the International System of Units (SI) the magnetic field constant has the value: ${\ displaystyle \ mu _ {0}}$${\ displaystyle 4 \ pi}$
${\ displaystyle \ mu _ {0} \; = \; 1 {,} 2566 \ ldots \ cdot 10 ^ {- 6} {\ frac {\ mathrm {N}} {\ mathrm {A} ^ {2}} } \; \ approx \; 4 \ pi \ cdot 10 ^ {- 7} {\ frac {\ mathrm {N}} {\ mathrm {A} ^ {2}}}}$
with the units Newton (N) and Ampere (A).
## terminology
Historically, the constant has had different names. Until 1987 one spoke of the "magnetic permeability of the vacuum". Now in physics and electrical engineering it is called the magnetic field constant . ${\ displaystyle \ mu _ {0}}$
In denotes the magnetic field constant and the relative permeability. ${\ displaystyle \ mu = \ mu _ {r} \ mu _ {0}}$${\ displaystyle \ mu _ {0}}$${\ displaystyle \ mu _ {r}}$
## Relationship with other fundamental constants
From the Maxwell equations in the SI there is a simple relationship between the magnetic field constant, the electric field constant and the speed of light : ${\ displaystyle \ varepsilon _ {0}}$ ${\ displaystyle c}$
${\ displaystyle \ mu _ {0} \ varepsilon _ {0} \, c ^ {2} = 1}$
${\ displaystyle \ mu _ {0} = {\ frac {1} {\ varepsilon _ {0} \, c ^ {2}}}}$
## value
Until 2019, the value of the magnetic field constant was determined by the definition of the unit of measurement amperes . According to this definition, two parallel, infinitely long conductors in a vacuum, through which an electric current with a current of 1 ampere flows, exert a force of 2 · 10 −7 Newtons on each other. The exact value of the magnetic field constant of was derived from Ampère's law of force
${\ displaystyle \ mu _ {0} ^ {\ mathrm {old}} = 4 \ pi \ cdot 10 ^ {- 7} \ mathrm {\ frac {N} {A_ {old} ^ {2}}}}$.
As a result of the revision of the SI units resolved by the 26th General Conference on Weights and Measures (CGPM), the ampere has been defined on the basis of the elementary charge and the definition of the second since May 20, 2019 . As a result, the magnetic field constant is now (again) a variable that has to be determined experimentally and is subject to measurement uncertainty . ${\ displaystyle e}$
The exact relationship still applies . Therefore, the fine structure constant (which is subject to measurement uncertainty) and three further, firmly defined natural constants can be determined: ( = Planck constant ) ${\ displaystyle \ mu _ {0} \ varepsilon _ {0} \, c ^ {2} = 1}$${\ displaystyle \ mu _ {0}}$ ${\ displaystyle \ alpha}$${\ displaystyle h}$
${\ displaystyle \ mu _ {0} = {\ frac {2 \ cdot h \ cdot \ alpha} {c \ cdot e ^ {2}}}}$
When it was decided to change the SI units, the value was initially updated with the relative measurement uncertainty of 2.3 · 10 −10 . At the time of entry into force on May 20, 2019, the value was ${\ textstyle \ mu _ {0} = 4 \ pi \ cdot 10 ^ {- 7} \, \ mathrm {N / A ^ {2}}}$${\ displaystyle \ alpha}$
${\ displaystyle \ mu _ {0} \; = \; 1 {,} 256 \, 637 \, 062 \, 12 (19) \ cdot 10 ^ {- 6} {\ frac {\ mathrm {N}} { \ mathrm {A} ^ {2}}}}$
specified. With a relative measurement uncertainty of 1.5 · 10 −10 , it is currently generally recognized as the most accurate available value.
## unit
The unit of is expressed in different SI units depending on the use, e.g. B .: ${\ displaystyle \ mu _ {0}}$
${\ displaystyle \ left [\ mu _ {0} \ right] = {\ frac {\ mathrm {N}} {\ mathrm {A} ^ {2}}} = {\ frac {\ mathrm {V \, s }} {\ mathrm {A \, m}}} = {\ frac {\ mathrm {kg \, m}} {\ mathrm {A ^ {2} \, s ^ {2}}}}}$
## Individual evidence
1. SUNAMCO Commission: Recommended values of the fundamental physical constants . In: Symbols, Units, Nomenclature and Fundamental Constants in Physics . 1987, p. 52–61 , here p. 54 (English, metrology.files.wordpress.com [PDF; 624 kB ; accessed on August 14, 2018]).
2. ^ Leaflet: The legal units in Germany . June 2015 ( ptb.de [PDF; 1.6 MB ; accessed on August 14, 2018]). ptb.de ( Memento of the original from October 10, 2017 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
3. 26th CGPM (2018) - Resolutions adopted / Résolutions adoptées. (PDF; 1.2 MB) Versailles 13–16 November 2018. In: bipm.org. Bureau International des Poids et Mesures, November 19, 2018, pp. 2–5 , accessed on August 12, 2019 (English, French).
4. CODATA Recommended Values. National Institute of Standards and Technology, accessed August 12, 2019 . Value for the magnetic permeability in a vacuum. | 1,604 | 5,594 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 28, "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} | 2.9375 | 3 | CC-MAIN-2024-38 | latest | en | 0.76177 |
https://www.jiskha.com/display.cgi?id=1347839837 | 1,510,946,748,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934803906.12/warc/CC-MAIN-20171117185611-20171117205611-00218.warc.gz | 819,592,490 | 3,223 | # Physics
posted by .
A speeder passes a parked police car at a constant speed of 24.8 m/s. At that instant, the police car starts from rest with a uniform acceleration of 2.45 m/s2.
How much time passes before the speeder is overtaken by the police car?
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More Similar Questions | 705 | 2,740 | {"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} | 3.328125 | 3 | CC-MAIN-2017-47 | latest | en | 0.937028 |
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Document Sample
``` Floating
The density of a material governs whether it will sink or float in different liquids or gases.
An object floats in a fluid if its density is less than the density of the fluid.
So a wooden block floats in water while an iron one sinks. A hydrogen-filled balloon will rise
in the air but one filled with carbon dioxide sinks to the ground.
This is best explained by Archimedes principle.
When an object floats in a liquid the upthrust is equal to the weight of the object itself—
the net force on the object is zero.
A floating object displaces its
own weight of liquid.
upthrust
Small weight
Small upthrust
Small displacement Large weight
weight Large upthrust
Large displacement
A ship will float because the weight of water displaced is equal to the weight of the ship. The
ship will sink deeper into the water until this is true.
………
……… …
…
Fresh water Salty water
The density of the liquid is also very important. A ship will float lower in low density fresh
water than it will in higher density salt water. The weight of liquid displaced each time is the
same - the weight of the ship itself.
Increasing density
1
```
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# Golden Search Method
Not what you're looking for?
The attached file has the problem, and an example.
##### Solution Summary
The solution discusses how to solve the problem using the Golden Search method.
Solution provided by:
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• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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##### Exponential Expressions
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Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
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# MAS111_09_assignment_02_hints - NANYANG TECHNOLOGICAL...
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Unformatted text preview: NANYANG TECHNOLOGICAL UNIVERSITY MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 2 HINTS 1. For any positive odd numbers m,n , prove that m 2 + n 2 is even, but not a multiple of 4. Hint : Let m = 2 k + 1 and n = 2 l + 1, and calculate m 2 + n 2 . 2. Prove that for any natural number n, 3 does not divide n 2 + 1. Hint : Consider the cases when n = 3 k + i for integer k and i = 0 , 1 , 2. 3. Prove that √ 5 + √ 7 is an irrational number. Hint : Prove it by contradiction. Suppose that √ 5+ √ 7 is a rational number then √ 5- √ 7 is also rational (why?). Now √ 5 = 1 2 (( √ 5 + √ 7) + ( √ 5- √ 7)) is again rational, which is not true (you may prove here that √ 5 cannot be rational by one more contradiction proof). 4. Prove that for any natural number n , 2 2 n- 1 is divisible by 3. Hint : Prove it by induction. Note that 2 2( k +1)- 1 = 2 2( k +1)- 2 2 k + 2 2 k- 1 = 3 · 2 2 k + 2 2 k- 1....
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Ask a homework question - tutors are online | 504 | 1,568 | {"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} | 3.53125 | 4 | CC-MAIN-2018-09 | latest | en | 0.809442 |
https://www.hackmath.net/en/math-problem/1266 | 1,603,501,913,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107881551.11/warc/CC-MAIN-20201023234043-20201024024043-00416.warc.gz | 733,134,895 | 11,541 | John decorated 29 gingerbread and Annie 8 more. How many gingerbread decorated Annie?
Correct result:
A = 37
#### Solution:
$A=29+8=37$
We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!
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https://web2.0calc.com/questions/help-6 | 1,521,886,417,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257650188.31/warc/CC-MAIN-20180324093251-20180324113251-00259.warc.gz | 715,417,344 | 5,840 | +0
# Help 6
0
56
1
+2126
Help 6
NotSoSmart Feb 20, 2018
#1
+6616
+1
$$0.12\,=\,\frac{100(0.05)+x(0.2)}{100+x} \\~\\ 0.12(100+x)\,=\,100(0.05)+x(0.2) \\~\\ 12+0.12x\,=\,5+0.2x \\~\\ 12-5=0.2x-0.12x \\~\\ 7\,=\,0.08x \\~\\ 87.5=x$$
the amount of 20% dye to add is 87.5 mL .
hectictar Feb 21, 2018
Sort:
#1
+6616
+1
$$0.12\,=\,\frac{100(0.05)+x(0.2)}{100+x} \\~\\ 0.12(100+x)\,=\,100(0.05)+x(0.2) \\~\\ 12+0.12x\,=\,5+0.2x \\~\\ 12-5=0.2x-0.12x \\~\\ 7\,=\,0.08x \\~\\ 87.5=x$$
the amount of 20% dye to add is 87.5 mL .
hectictar Feb 21, 2018
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We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners. See details | 400 | 816 | {"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} | 3.546875 | 4 | CC-MAIN-2018-13 | longest | en | 0.649741 |
https://ask.sagemath.org/users/29826/user2749584820/?sort=recent | 1,627,969,255,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154420.77/warc/CC-MAIN-20210803030201-20210803060201-00431.warc.gz | 120,188,545 | 5,755 | 2021-01-27 13:15:30 +0200 received badge ● Student (source) 2021-01-27 13:15:13 +0200 asked a question Definite Integral of loglikelihood function multipled by Gaussian I am trying to calculate definite_integral((-ln(2*pi)-ln(sigma)-1/2*((x-mu)/sigma)^2)*f, x, -infinity, infinity) where f=1/(sqrt(2*pi)*sigmaprime)*exp(-1/2*((x-muprime)/sigmaprime)^2) using sagemath. I have done from sage.symbolic.integration.integral import definite_integral And I have also done assume(sigma>0) assume(sigmaprime>0) however I obtain this error ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(muprime>0)', see assume? for more details) Is muprime positive, negative or zero? However muprime can be positive, negative or zero. So I don't know how to proceed. | 249 | 870 | {"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-2021-31 | latest | en | 0.74394 |
http://www-sop.inria.fr/members/Claude.Stolze/publications.html | 1,527,456,612,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794870470.67/warc/CC-MAIN-20180527205925-20180527225925-00493.warc.gz | 311,717,286 | 3,768 | [1] Daniel J. Dougherty, Ugo de'Liguoro, Luigi Liquori, and Claude Stolze. A realizability interpretation for intersection and union types. In Programming Languages and Systems - 14th Asian Symposium, APLAS 2016, pages 187-205, October 2016. [ bib | DOI | http | .pdf ] Proof-functional logical connectives allow reasoning about the structure of logical proofs, in this way giving to the latter the status of first-class objects. This is in contrast to classical truth-functional connectives where the meaning of a compound formula is dependent only on the truth value of its subformulas. In this paper we present a typed lambda calculus, enriched with products, coproducts, and a related proof-functional logic. This calculus, directly derived from a typed calculus previously defined by two of the current authors, has been proved isomorphic to the well-known Barbanera-Dezani-Ciancaglini-de'Liguoro type assignment system. We present a logic L featuring two proof-functional connectives, namely strong conjunction and strong disjunction. We prove the typed calculus to be isomorphic to the logic L and we give a realizability semantics using Mints' realizers and a completeness theorem. A prototype implementation is also described. [2] Luigi Liquori and Claude Stolze. A Decidable Subtyping Logic for Intersection and Union Types (full version). Research report, Inria, March 2017. [ bib | http | .pdf ] Proof-functional logical connectives allow reasoning about the structure of logical proofs, in this way giving to the latter the status of first-class objects. This is in contrast to classical truth-functional connectives where the meaning of a compound formula is dependent only on the truth value of its subformulas. We present a proof-functional logic and we give a semantics using Mints' realizers accounting for intersection types, union types, and subtyping. The semantics interprets the type ω as the set universe, the -> type as a function space, the /\ and V types as set intersection and set union, respectively, and the subtype relation as a subset operator. Using the proof-as-types and terms-as-propositions paradigms, we extend the typed calculus previously defined by the authors with a decidable subtyping relation and we show this calculus to be isomorphic to the Barbanera-Dezani-Ciancaglini-de'Liguoro type assignment system. A subtyping algorithm is presented and proved to be sound and complete. Hindley gave a subtyping algorithm for intersection types but, as far as we know, there is no system in the literature also including union types. [3] Luigi Liquori and Claude Stolze. A Decidable Subtyping Logic for Intersection and Union Types. In 2nd International Conference on Topics in Theoretical Computer Science, TTCS 2017, pages 74-90, September 2017. [ bib | DOI | http | .pdf ] Using Curry-Howard isomorphism, we extend the typed lambda-calculus with intersection and union types, and its corresponding proof-functional logic, previously defined by the authors, with subtyping and explicit coercions.We show the extension of the lambda-calculus to be isomorphic to the Barbanera-Dezani-de'Liguoro type assignment system and we provide a sound interpretation of the proof-functional logic with the NJ(β) logic, using Mints' realizers.We finally present a sound and complete algorithm for subtyping in presence of intersection and union types. The algorithm is conceived to work for the (sub)type theory Ξ. [4] Claude Stolze, Luigi Liquori, Furio Honsell, and Ivan Scagnetto. Towards a Logical Framework with Intersection and Union Types. In 11th International Workshop on Logical Frameworks and Meta-languages, LFMTP 2017, pages 1 - 9, September 2017. [ bib | http | .pdf ] We present an ongoing implementation of a dependent-type theory (Δ-framework) based on the Edinburgh Logical Framework LF, extended with Proof-functional logical connectives such as intersection , union, and strong (or minimal relevant) implication. Proof-functional connectives take into account the shape of logical proofs, thus allowing to reflect polymorphic features of proofs in formulae. This is in contrast to classical Truth-functional connec-tives where the meaning of a compound formula is only dependent on the truth value of its subformulas. Both Logical Frameworks and proof functional logics consider proofs as first class citizens. But they do it differently namely, explicitly in the former while implicitly in the latter. Their combination opens up new possibilites of formal reasoning on proof-theoretic semantics. We provide some examples in the extended type theory and we outline a type checker. The theory of the system is under investigation. Once validated in vitro, the proof-functional type theory can be successfully plugged in existing truth-functional proof assistants. [5] Furio Honsell, Luigi Liquori, Ivan Scagnetto, and Claude Stolze. The Δ-framework. working paper or preprint, February 2018. [ bib | http | .pdf ] We introduce a dependent-type theory Δ-framework, LF-Δ , based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives intersection, union, and relevant implication. Proof-functional connectives take into account the shape of logical proofs, thus allowing the user to reflect polymorphic features of proofs in formulae. This is in contrast to classical and intuitionistic connectives where the meaning of a compound formula is dependent only on the truth value or the provability of its subformulae. Both Logical Frameworks and Proof Functional Logics consider proofs as first class citizens albeit differently. The former mention proofs explicitly, while the latter mention proofs implicitly. Their combination therefore opens up new possibilites of formal reasoning on proof-theoretic semantics. We study the metatheory of LF-Δ and provide various examples of applications. Moreover, we discuss a prototype implementation of a type checker and a refiner allowing the user to accelerate and possibly automate, the proof development process. This proof-functional type theory can be plugged in existing common proof assistants. [6] Luigi Liquori and Claude Stolze. The Delta-calculus: syntax and types. working paper or preprint, March 2018. [ bib | http | .pdf ] We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the Coppo-Dezani-Sallé, the Coppo-Dezani-Venneri and the Barendregt-Coppo-Dezani ones, producing a family of Delta-calculi with related intersection type systems. We prove the main properties like Church-Rosser, unicity of type, subject reduction, strong normalization, decidability of type checking and type reconstruction. We state the relationship between the intersection type assignment systems à la Curry and the corresponding intersection type systems à la Church by means of an essence function translating an explicitly typed Delta-term into a pure lambda-term one. We finally translate a Delta-term with type coercions into an equivalent one without them; the translation is proved to be coherent because its essence is the identity. The generic Delta-calculus can be parametrized to take into account other intersection type theories as the ones in the Barendregt et al. book.
This file was generated by bibtex2html 1.97. | 1,593 | 7,421 | {"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-2018-22 | latest | en | 0.894185 |
http://www.parsonsmatt.org/2017/09/22/what_does_free_buy_us.html | 1,537,931,134,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267163146.90/warc/CC-MAIN-20180926022052-20180926042452-00467.warc.gz | 380,286,717 | 11,774 | # What does Free buy us?
Why are they free? Do monads ordinarily cost us something?
The category theory intuition for “free” roughly expands to:
This structure gives you a free X when given a Y
data Free f a
= Pure a
| Free (f (Free f a))
this really expands to:
This structure gives you a free monad for a given functor
This expansion is witnessed by the instance:
instance (Functor f) => Monad (Free f) where
return = Pure
Pure a >>= k = k a
Free m >>= k = Free ((>>= k) <$> m) The instance says: “If your f is a Functor, then a Free f is a Monad.” The exact implementation is less important. # Free Monoids We say that “List is the free monoid.” What we mean is that: This structure gives you a free monoid for a given type. So we can equip any value with list and it becomes a monoid, for free. This expansion is witnessed by the instance: instance Monoid [a] where mempty = [] mappend xs ys = xs ++ ys Are there other free monoids? Yes! We have a free monoid for a given semigroup. This is the more moral instance of Monoid for Maybe: instance (Semigroup a) => Monoid (Maybe a) where mempty = Nothing mappend (Just a) (Just b) = Just (a <> b) mappend Nothing (Just b) = Just b mappend (Just a) Nothing = Just a mappend Nothing Nothing = Nothing -- where <> comes from Data.Semigroup # What’s the point? Great question! What do these constructs buy us? What is the alternative to using Free’s Monad instance for a given Functor? The common motivation for Free is writing a data structure that we can build up specialized programs in, and then vary the interpretation. So let’s do this without free. We’ve been tasked with writing our billing logic system for our SaaS billing system. We’re going to construct a data type that represents a program where we check a user’s balance and either charge them, notify them, or cancel their subscriptions based on various factors. We absolutely need to get this right, so we’re doing this weird heavy weight technique to improve our confidence in it’s correctness. # Sum Commands First, we need to represent the various things we want to do: data BillingProgram = GetUserBalance | GetUserLastPaymentDate | CancelSubscription | ChargeUser | SendLateNotice These are the commands we need to do: 1. We need a way to get the user’s current account balance. 2. We need a way to get the user’s last successful payment date. 3. We need a way to cancel a user’s subscription. 4. We need to be able to charge the user. 5. We need to be able to send the user a late notice. This data type is a sum type that represents the possible commands we can issue to the system. Now, we can construct “programs” using just this type! Here is a basic interpreter for this data type: data BillingState = BillingState { userId :: UserId , userBalance :: Double , userSubscription :: SubscriptionId , lastPaymentDate :: Day } interpret :: BillingProgram -> StateT BillingState IO () interpret GetUserBalance = do id <- gets userId balance <- liftIO$ Stripe.getUserBalance id
modify (\s -> s { userBalance = balance })
interpret GetUserLastPaymentDate =
-- etc...
We can have our logic construct a [BillingProgram] value, and then use mapM_ interpret over that. However, this is really inflexible. We’re required to store every bit of state in the interpreter, as well as the current user and subscription that we’re working on. Let’s delegate some of that work to our command type.
In a sense, this is sort of like the code we might write in a highly stateful, imperative OOP context:
class BillingProgram {
private UserId userId;
private double userBalance;
private SubscriptionId userSubscription;
private Day lastPaymentDate;
public BillingProgram(UserId u) { /* etc... */ }
public void runLogic() {
getUserBalance();
if (this.userBalance > 100) {
chargeUser();
} else {
sendBalanceNotice();
}
}
}
The command data type has no way of communicating arguments, and it has no way of communicating a return value. This is no fun.
# Commands, with info!
We want our commands to contain the information they need in order to be able to do work. Rather than a simple signal to our interpreter on what action to take, we’ll also include the parameters that we wish to act on.
data BillingProgram
= GetUserBalance UserId
| GetUserLastPaymentDate UserId
| CancelSubscription UserId PlanId
| ChargeUser UserId Double
| SendLateNotice PlanId Email
Now, we’ve augmented our data type. Interpreting this has become a lot easier – we no longer need to carry the user ID in the state, or the last payment date. These are just things we can interpret and request.
interpret :: BillingProgram -> IO ()
interpret (GetUserBalance userId) =
Stripe.getUserBalance userId
interpret (GetUserLastPaymentDate userId) =
Stripe.getLastPaymentDate userId
interpret (CancelSubscription userId planId) = do
subscriptions <- Stripe.getSubscriptionsFor userId
for_ subscriptions $\sub -> do when (sunPlan sun == planId)$ do
Stripe.cancelSubscription (subId sub)
-- etc...
This implementation is pretty clean. Just like the previous type, we can have our logic functions create a list of these commands, and we can use mapM_ interpret to interpret them meaningfully.
However, we have a problem: the two commands GetUserBalance and GetUserLastPaymentDate are queries. These queries have a meaningful return value. And we don’t have a way to vary behavior. The interpret function won’t type check: Stripe.getUserBalance doesn’t return (), it returns a Double that we want to use!
So, we have two choices:
1. Refactor the data type to not have queries.
2. Refactor the data type to be able to use queries.
Let’s explore #1 first.
# No Queries No Masters
So, we can’t have queries in our data type. That means we need to factor all of the logic that we’d do on those queries into the individual commands.
data BillingProgram
= CancelSubscriptionIfUserPaymentTooOld UserId SubscriptionId
| IfBalanceGreatEnoughThenChargeUserElseSendNotice UserId SubscriptionId Email
Ugh. Let’s write the interpreter:
interpret :: BillingProgram -> IO ()
interpret (CancelSubscriptionIfUserPaymentTooOld userId subscriptionId) = do
date <- Stripe.getLastPaymentDate userId
now <- getCurrentTime
when (now diffTime date > days 60) $do Stripe.cancelSubscription userId subscriptionId interpret (IfBalanceGreatEnoughThenChargeUserElseSendNotice userId subscriptionId email) = do balance <- Stripe.getUserBalance userId subscription <- Stripe.getSubscriptions subscriptionId if balance > subPrice subscription then Stripe.chargeUser userId (subPrice subscription) else Email.sendBalanceNotice email subscription Ugh! This is horrible. OK, this approach was a mistake. Let’s try refactoring the data type to be able to use queries. # The question of next A query is “something that informs what we might want to do next.” But our command data type doesn’t have any concept of “next” or “previous,” only “now”: Charge the user money! Send a billing email! We’d previously used lists to have a sequence of commands, and we’d execute each of them individually. Lists are a fine way to express iteration and sequencing, but they don’t allow previous commands to affect future commands. So, if we want to incorporate the idea of “next” into our data type, then we can’t use lists. We have to make it part of the type. We’ll include another field on each command: this will have the BillingProgram to execute after the current program. data BillingProgram = GetUserBalance UserId BillingProgram | GetUserLastPaymentDate UserId BillingProgram | CancelSubscription UserId PlanId BillingProgram | ChargeUser UserId Double BillingProgram | SendLateNotice PlanId Email BillingProgram Now, these commands all have a way of expressing “Once you’re done with this command, here’s the next command you’ll want to execute.” However, we’re still not using the information from the UserBalance and LastPaymentDate commands. We can express that as a function where the construction of the next BillingProgram depends on the value that the interpreter returns. data BillingProgram = GetUserBalance UserId (Double -> BillingProgram) | GetUserLastPaymentDate UserId (Day -> BillingProgram) | CancelSubscription UserId PlanId BillingProgram | ChargeUser UserId Double BillingProgram | SendLateNotice PlanId Email BillingProgram That does it! Now, we can express complex logic in our billing program. Let’s construct our billing program that expresses “If the user has enough balance, then charge them, otherwise send a balance notice.” chargeOrEmail :: User -> Subscription -> BillingProgram chargeOrEmail user sub = GetUserBalance (userId user)$ \userBalance ->
if userBalance >= subPrice sub
then ChargeUser (userId user) (subPrice sub) ???
else SendLateNotice (subPlan sub) (userEmail user) ???
Errr, this doesn’t quite work. We need something in our command data type to indicate “This program is complete.” Let’s add that constructor:
data BillingProgram
= GetUserBalance UserId (Double -> BillingProgram)
| GetUserLastPaymentDate UserId (Day -> BillingProgram)
| CancelSubscription UserId PlanId BillingProgram
| ChargeUser UserId Double BillingProgram
| SendLateNotice PlanId Email BillingProgram
| Done
The Done constructor is the only constructor that doesn’t contain a BillingProgram, which means that every BillingProgram must end with a Done (or loop infinitely). Alright, we can finish our program now:
chargeOrEmail :: User -> Subscription -> BillingProgram
chargeOrEmail user sub =
GetUserBalance (userId user) $\userBalance -> if userBalance >= subPrice sub then ChargeUser (userId user) (subPrice sub) Done else SendLateNotice (subPlan sub) (userEmail user) Done # Meaningful return values But, hmm, what if we want to report on whether or not we could successfully bill the user? The command data type has no way of “returning” a value. That’s kind of unfortunate. We can change the Done constructor to take a value, but we don’t want to constrain the type of the value – we could potentially return all kinds of things! That means we need to add a type variable to the command data type: data BillingProgram ret = GetUserBalance UserId (Double -> BillingProgram ret) | GetUserLastPaymentDate UserId (Day -> BillingProgram ret) | CancelSubscription UserId PlanId (BillingProgram ret) | ChargeUser UserId Double (BillingProgram ret) | SendLateNotice PlanId Email (BillingProgram ret) | Done ret Alright, now we can rewrite our program to return whether or not we successfully billed the customer: chargeOrEmail :: User -> Subscription -> BillingProgram Bool chargeOrEmail user sub = GetUserBalance (userId user)$ \userBalance ->
if userBalance >= subPrice sub
then ChargeUser (userId user) (subPrice sub) (Done True)
else SendLateNotice (subPlan sub) (userEmail user) (Done False)
Very cool. We’re starting to have a reasonably fully featured language for billing our customers. However, we don’t have any tools for taking an existing program and extending it, or composing it with another one.
# Extending programs
So, we want to extend a preexisting program. What does it mean to extend a program? To me, that suggests that we’ll start running a new program with the output of the old program. In order to get the output of the old program, we need to run it until we get to a Done constructor. Then, we can use the value from Done to continue the program. We’ll start with the Done case:
andThen
:: BillingProgram a
-> (a -> BillingProgram b)
-> BillingProgram b
andThen (Done ret) mkProgram = mkProgram ret
We take the return value from the previous program, and use it to construct the next bit of the program. Now, we just need to plumb this through the other constructors:
andThen (GetUserBalance userId next) mkProgram =
GetUserBalance userId (\balance -> andThen (next balance) mkProgram)
andThen (GetUserLastPaymentDate userId next) mkProgram =
GetUserLastPaymentDate userId (\date -> andThen (next date) mkProgram)
andThen (CancelSubscription userId planId next) =
CancelSubscription userId planId (andThen next mkProgram)
andThen (ChargeUser userId amount next) =
ChargeUser userId amount (andThen next mkProgram)
andThen (SendLateNotice planId email next) =
SendLateNotice planId notice (andThen next mkProgram)
We want to not change the existing command structure. The only thing we do here is use andThen to recursively walk the program until we hit Done, at which point we extend the program with the new program using the output of the old program.
# huh
## that looks familiar
Let’s write a non-trivial program that uses these commands:
billingProgram :: User -> [Subscription] -> BillingProgram ()
billingProgram _ [] =
Done ()
billingProgram user (sub:subs) =
GetUserBalance uid $\balance -> if balance > price then ChargeUser uid price theRest else SendLateNotice plan (userEmail user)$ GetUserLastPaymentDate uid
$\day -> if day < 60daysago then CancelSubscription uid plan theRest else theRest where uid = userId user price = subPrice sub plan = subPlan sub theRest = billingProgram user subs This is super clumsy and ugly to write. We have to manually iterate over the list, and we have these weird uppercase constructors everywhere. We need to manually handle lambda scopes and other such nonsense. Let’s factor out some of the common patterns here, and use the andThen function we wrote earlier to build programs rather than manually grafting this stuff together. getUserBalance :: UserId -> BillingProgram Double getUserBalance userId = GetUserBalance userId (\amount -> Done amount) end :: BillingProgram () end = Done () getLastPaymentDate :: UserId -> BillingProgram Day getLastPaymentDate userId = GetUserLastPaymentDate userId (\day -> Done day) cancelSubscription :: UserId -> PlanId -> BillingProgram () cancelSubscription userId planId = CancelSubscription userId planId end -- etc, this gets pretty repetitive Alright, let’s use these and the andThen to write the above logic out: billingProgram :: User -> [Subscription] -> BillingProgram () billingProgram _ [] = end billingProgram user (sub:subs) = getUserBalance uid andThen \balance -> if balance > price then chargeUser uid price andThen \_ -> theRest else sendLateNotice plan (userEmail user) andThen \_ -> getUserLastPaymentDate uid andThen \day -> if day < 60daysago then cancelSubscription uid plan andThen \_ -> theRest else theRest where uid = userId user price = subPrice sub plan = subPlan sub theRest = billingProgram user subs This looks quite a bit nicer! # ah yes, i’ve seen this before This is strongly reminding me of Monad at this point. Let’s write an instance of Monad for our type: instance Monad BillingProgram where return = Done (>>=) = andThen Huh. That was easy. Now we can take advantage of do notation and all the functions that are generic over the monad. I’m specifically thinking of these friends: forM_ :: (Monad m) => (a -> m b) -> [a] -> m [b] when :: (Monad m) => Bool -> m () -> m () Let’s rewrite our program with this new fanciness: billingProgram :: User -> [Subscription] -> BillingProgram () billingProgram user subs = forM_ subs$ \sub -> do
let uid = userId user
price = subPrice sub
plan = subPlan sub
balance <- getUserBalance uid
if balance > price
then do
chargeUser uid price
else do
day <- getUserLastPaymentDate uid
when (day < 60daysago) $do cancelSubscription uid plan Now this is some nice, readable, and idiomatic code. We’ve used the Monad instance to get sweet, sweet do notation. We haven’t tried to interpret it, yet – is this going to suck? # interpreting the monad It’s fairly straightforward. Let’s do a Stripe interpreter: interpret :: BillingProgram a -> IO a interpret (Done a) = pure a interpret (ChargeUser uid price next) = do Stripe.chargeUser uid price interpret next interpret (SendLateNotice plan email next) = do Email.sendLateNoticeFor plan email interpret next interpret (GetUserBalance uid next) = do balance <- Stripe.getBalance uid interpret (next balance) interpret etcccc = do putStrLn "you could finish me" This interpreter just walks down the command tree. It interprets the command, and then calls the interpreter on the next command recursively. Where the next command is a function, we first aquire the value, pass it to the function to generate the next command, and the interpret the result. Can we write a test interpreter? Yes! interpretTest :: BillingProgram a -> State Mock a interpretTest (Done a) = pure a interpretTest (ChargeUser uid price next) = do modify (subtractBalance uid price) interpret next interpretTest (SendLateNotice plan email next) = do modify (addBillingEmail plan email) interpret next interpretTest (GetUserBalance uid next) = do balance <- gets (userBalance uid) interpret (next balance) interpretTest etc = error "finish meeee" This one doesn’t use any IO. It operates in the State monad, so we can keep it entirely pure. We can provide an initial Mock state and then make assertions on what the Mock looks like after we run a program. This lets us write tests without needing to mock out any IO or anything else nasty. # what have we done?! You might be satisfied to stop here. We’ve accomplished a lot, after all! You might think: Dang, that was a lot of boilerplate. There was a lot of repetition in the definition of andThen, and the definition of the interpreter seemed awfully repetitive as well. What if I write another EDSL (embedded domain specific language)? Will I have to write all this boilerplate again? Let’s go deeper. Let’s write another data type for an EDSL. This one describes a terminal interaction: data Terminal a = GetLine (String -> Terminal a) | Done a | PrintLine String (Terminal a) instance Monad Terminal where return = Done t >>= mk = case t of GetLine next -> GetLine$ \s -> next s >>= mk
PrintLine str next ->
PrintLine str (next >>= mk)
Done a ->
mk a
interpret :: Terminal a -> IO a
interpret (Done a) = pure a
interpret (GetLine next) = do
str <- getLine
interpret (next str)
interpret (PrintLine str next) = do
putStrLn str
interpret next
There’s definitely a fair amount of boilerplate here. The structure is very similar. Let’s look at these two types and see what we can factor out:
data Terminal a
= GetLine (String -> Terminal a)
| PrintLine String (Terminal a)
| Done a
data BillingProgram ret
= GetUserBalance UserId (Double -> BillingProgram ret)
| GetUserLastPaymentDate UserId (Day -> BillingProgram ret)
| CancelSubscription UserId PlanId (BillingProgram ret)
| ChargeUser UserId Double (BillingProgram ret)
| SendLateNotice PlanId Email (BillingProgram ret)
| Done ret
Both of these types have a Done constructor, so we should be able to factor that out. Both of these types are also recursive, so we should be able to factor the recursion out.
That means our type should have two components:
1. Factored out recursion (aka, Fix)
2. A Done constructor.
data Free f a
= Free (f (Free f a))
| Done a
This actually looks really similar to a list, except the recursion has an intermediate step, the Free doesn’t take a value, and the Done constructor takes a value. Let’s lay them side by side:
data Free f a
= Free (f (Free f a))
| Done a
data List a
= Cons a (List a)
| Nil
In fact, Free is more general than list! We can recover singly linked lists by providing an appropriate f and a, specifically, (,) n and ():
type List a = Free ((,) a) ()
totallyAList :: List Int
totallyAList = Free (1, Free (2, Free (3, Done ())))
Anyway, back to stuff people actually care about.
Now that we’ve factored out the common stuff between our two program types, let’s get some common machinery between them:
data TerminalF next
= GetLine (String -> next)
| PrintLine String next
type Terminal = Free TerminalF
getLine :: Terminal String
getLine = Free (GetLine (\str -> Done str))
printLine :: String -> Terminal ()
printLine str = Free (PrintLine str (Done ()))
The new command data type only has the commands we care about. We replace the explicit recursion with a next type variable, which the Free type fills in.
data BillingF next
= GetUserBalance UserId (Double -> next)
| ChargeUser UserId Double next
| etc you get it
type Billing = Free BillingF
getUserBalance :: UserId -> Billing Double
getUserBalance userId = Free (GetUserBalance userId Done)
chargeUser :: UserId -> Double -> Billing ()
chargeUser uid amt = Free (ChargeUser uid amt (Done ()))
Same – the new command data type doesn’t have to worry about Done, or anything else. Because Free has an instance of Monad for any Functor, we only have to write a Functor instance to make this work.
I lied.
We don’t even have to write that instance.
We just have to ask for it!
{-# LANGUAGE DeriveFunctor #-}
data TerminalF next
= GetLine (String -> next)
| PrintLine String next
deriving Functor
Haskell lets us derive Functor for types where it can figure it out.
So, the free monad instance makes it easy to write programs, but does it make interpreters easy? Yes!
We can define this function:
foldFree
=> (forall a. f a -> m a)
-> Free f a
-> m a
foldFree morph (Done a) = return a
foldFree morph (Free f) = do
a <- morph f
foldFree morph a
Give me a way to interpret your commands into some monad. Then give me a program built of these commands. I’ll interpret all of the commmands for you.
So we can write our terminal program as:
data TerminalF next
= GetLine (String -> next)
| PrintLine String next
deriving Functor
type Terminal = Free TerminalF
interpret :: Terminal a -> IO a
interpret = foldFree morph
where
morph :: TermF a -> IO a
morph (GetLine next) =
next <\$> getLine
morph (PrintLine s n) = do
putStrLn s
pure n
Note the really interesting bit of this interpreter – we don’t have to specify any recursion, at all. foldFree handles all of that for us. We just need to specify the bits that should happen at each step of the recursion.
# Wrap it up
We’ve implemented a data type to represent a primitive set of commands. We’ve then extended those commands with arguments, which allowed us to shift complexity from the interpreter into the commands themselves. Then, we factored the question of “what to do next” from the list data structure into the command data type. This increased the complexity of both the data type and the interpreter. However, we were able to get a Monad instance for our programs, which gave us a lot of awesome flexibility for writing the EDSLs.
To tame that complexity, we factored the “what to do next” back out into a new data type, this time called Free instead of List. Free and List are similar; and we can use Free to write List and other interesting data structures. The only requirement that Free has to give a monad to the whole type is that the f type parameter be a Functor.
I did a similar dive into recursive types in Recursion Excursion, which you may find interesting. | 5,157 | 22,867 | {"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} | 2.90625 | 3 | CC-MAIN-2018-39 | latest | en | 0.897737 |
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Question From class 12 Chapter CIRCLES - FOR BOARDS
Find the equation of the circle of radius 5 whose centre lies on y-axis and which passes through the point (3, 2).
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Find the equation of the circle which passes through the points , and (3,4) and whose centre lies on the line .
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A circle has radius and its centre lies on the line Find the equation of the circle, if it passes through
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The equation of the circle with radius 3 units, passing through the point (2, 1) and whose centre lies on the line y + x = 0 can be
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20-12-2019 | 859 | 3,312 | {"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-2020-10 | latest | en | 0.928668 |
https://spreadsheetcenter.com/excel-functions/gammadist/ | 1,718,548,627,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861665.97/warc/CC-MAIN-20240616141113-20240616171113-00271.warc.gz | 481,879,635 | 8,894 | The GAMMADIST function is used to calculate the gamma distribution probability for a given value. It is commonly applied in statistical analysis to model continuous random variables with positive skewness.
## Syntax
=GAMMADIST(X, Alpha, Beta, Cumulative)
When diving into the realm of probability distributions and seeking a tool to analyze random variables exhibiting positive skewness, the GAMMADIST function in Excel proves to be a valuable asset. It aids in calculating the probability associated with specific values in a gamma distribution, offering insights into the distribution's characteristics and behavior. Ideal for statistical modeling and risk assessment, GAMMADIST facilitates precise computations by incorporating essential parameters like shape and scale to tailor the output according to the desired context. Whether exploring financial data, biological processes, or engineering phenomena, this function equips users with the means to gauge the likelihood of observing particular outcomes within a gamma distribution with defined alpha and beta parameters.
## Examples
Consider a gamma distribution with Alpha = 2 and Beta = 3. You want to find the cumulative probability of observing a value less than or equal to 5. The GAMMADIST formula would be as follows: =GAMMADIST(5, 2, 3, TRUE) This will return the cumulative probability associated with the gamma distribution for X = 5.
Suppose you have a gamma distribution with alpha = 3 and beta = 2. You wish to determine the probability density at X = 4. The GAMMADIST formula for this scenario would be: =GAMMADIST(4, 3, 2, FALSE) This will provide the probability density at X = 4 in the specified gamma distribution.
## Questions
How does the GAMMADIST function differ from other probability distribution functions in Excel?
The GAMMADIST function specifically calculates the probability associated with a gamma distribution, which is characterized by positive skewness. In contrast, functions like NORM.DIST handle normal distributions, while others like BINOM.DIST focus on binomial distributions.
What role do the shape and scale parameters (Alpha and Beta) play in the GAMMADIST function?
The Alpha parameter influences the shape of the gamma distribution, determining how peaked or spread out the distribution appears. The Beta parameter, known as the rate parameter in some contexts, influences the rate of change in the distribution.
When should one use the cumulative form of the GAMMADIST function?
The cumulative form, selected by setting the Cumulative parameter to TRUE, is useful when analyzing the accumulation of probabilities up to a specific value in the distribution curve. It provides insights into the overall probability of observing values equal to or less than the given X.
GAMMAINV
GAMMALN
BETA.DIST
EXPONDIST
NORM.DIST
BINOM.DIST
CHIDIST
POISSON.DIST | 585 | 2,861 | {"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} | 3.703125 | 4 | CC-MAIN-2024-26 | latest | en | 0.864572 |
http://encyclopediajr.com/the-activity-on-denise-hellings-sears-account-for-one-billing-period-is-shown-below-find-the-average-daily-balance-and-the-finance-charge-if-the-billing-period-is-march-1-through-march-31-the-previ/ | 1,695,610,975,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506676.95/warc/CC-MAIN-20230925015430-20230925045430-00506.warc.gz | 17,268,132 | 32,396 | 19.07.2022 - 13:59
# The activity on Denise Hellings’ Sears account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is March 1 through March 31, the previ
Question:
The activity on Denise Hellings’ Sears account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is March 1 through March 31, the previous balance was $157.65, and the annual simple interest rate is 21%. March 5 payment$25.00 March 17 tools $37.87 Answers (1) • April 7, 2023 в 05:15 To find the average daily balance, we need to calculate the balance at the end of each day in the billing period, add them up, and divide by the number of days in the billing period. March 1 - Previous balance:$157.65 March 2 - Balance: $157.65 March 3 - Balance:$157.65 March 4 - Balance: $157.65 March 5 - Payment: -$25.00, Balance: $132.65 March 6 - Balance:$132.65 March 7 - Balance: $132.65 March 8 - Balance:$132.65 March 9 - Balance: $132.65 March 10 - Balance:$132.65 March 11 - Balance: $132.65 March 12 - Balance:$132.65 March 13 - Balance: $132.65 March 14 - Balance:$132.65 March 15 - Balance: $132.65 March 16 - Balance:$132.65 March 17 - Purchase: $37.87, Balance:$170.52 March 18 - Balance: $170.52 March 19 - Balance:$170.52 March 20 - Balance: $170.52 March 21 - Balance:$170.52 March 22 - Balance: $170.52 March 23 - Balance:$170.52 March 24 - Balance: $170.52 March 25 - Balance:$170.52 March 26 - Balance: $170.52 March 27 - Balance:$170.52 March 28 - Balance: $170.52 March 29 - Balance:$170.52 March 30 - Balance: $170.52 March 31 - Balance:$170.52 To find the average daily balance, we add up all the balances and divide by the number of days in the billing period: (157.65 x 4) + (132.65 x 19) + (170.52 x 8) = 4,417.54 Average daily balance = 4,417.54 / 31 = $142.51 Now that we have the average daily balance, we can calculate the finance charge. We need to first find the interest rate for the billing period by dividing the annual interest rate by the number of days in a year: 21% / 365 = 0.0575 We then multiply the daily balance by the daily interest rate to get the daily finance charge:$142.51 x 0.0575 = $8.19 Finally, we multiply the daily finance charge by the number of days in the billing period to get the total finance charge:$8.19 x 31 = $253.89 Therefore, the average daily balance is$142.51 and the finance charge for the billing period is \$253.89.
Find the right answer to the question The activity on Denise Hellings’ Sears account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is March 1 through March 31, the previ by subject Business, and if there is no answer or no one has given the right answer, then use the search and try to find the answer among similar questions.
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* | 809 | 2,891 | {"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} | 3.765625 | 4 | CC-MAIN-2023-40 | latest | en | 0.946953 |
https://ltwork.net/write-the-algebraic-expression-for-the-quotient-of-79-and--5126674 | 1,660,642,294,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572286.44/warc/CC-MAIN-20220816090541-20220816120541-00394.warc.gz | 340,813,435 | 10,479 | # Write the algebraic expression for the quotient of 79 and x
###### Question:
Write the algebraic expression for the quotient of 79 and x
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I need to explain the meme in 3 sentences or more halp pls. $I need to explain the meme in 3 sentences or more halp pls.$... | 958 | 4,211 | {"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": 2, "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} | 3.078125 | 3 | CC-MAIN-2022-33 | latest | en | 0.904325 |
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# Measurement - Essay Example
Summary
The prehistoric societies inclusive of the primitive humans used different measurements for purposes such as construction of their dwellings to ensure that they were of apposite shape and size. With time, man has…
## Extract of sample"Measurement"
Download file to see previous pages neers observe measurements, why measurements are much needed in the world, the role of measurements in quality control, and different type of measurements techniques used in engineering will be discussed.
The term “measurement” is derived from the Greek word metron which means limited proportion. The first measurement systems were astronomical objects. Babylonians and Egyptians are believed to have invented use of measurement. However, they mainly used comparisons to measure things. For example, they would compare capacity of containers by filling the smaller container and emptying it into the bigger one to measure the volumes (Manseau & Shields, 2005).
However, Gabriel Mouton, who was an astronomer, invented the metric system. He also suggested the swing length of pendulum, which is used as a unit of measuring length. In engineering and construction, there are different metric systems depending on what is being measured. For example, construction materials that are in liquid form are measured using measures such as gallons and liters. In case of length, units such as inches, meters, and feet are used depending on the size being measured. While measuring mass, unit such as pounds, kilograms, and grams are applied (Manseau & Shields, 2005). Although scientists make use of standardized metric units, there are two different types of metric systems. The type of metric system being used depends on the application. When measuring small units of length or mass, engineers make use of the CGS (centimeter-gram-second) system. However, MKS (meter-kilogram-second) system is used while measuring large quantities (Manseau & Shields, 2005).
With globalization, metric system is becoming widely acceptable worldwide though some countries such as United States are resistant to switch to the metric system. US makes use of a mixture of different systems of measurement. In 1960, the General Conference of Weights and Measures revised and simplified the measurement system. Seven ...Download file to see next pagesRead More
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+16312120006 | 1,324 | 6,770 | {"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-2018-43 | latest | en | 0.956705 |
https://www.jiskha.com/questions/1264076/1-what-trig-function-has-an-amplitue-of-1-and-negative-values-for-angles-between | 1,534,632,049,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221213794.40/warc/CC-MAIN-20180818213032-20180818233032-00322.warc.gz | 891,331,760 | 5,353 | # calculus
1. what trig function has an amplitue of 1 and negative values for angles between π/2 and π?
2. what trig function never crosses the x-axis and has a value of 2 at π/6?
are these correct?
3. what trig function has a period of π and is undefined for -π/2, π/2, 3π/2...
4. what trig function has a period of 2π, is continuous, and is increasing for 0 < x < π/2?
1. 1. An amplitude of 1 applies to only the sine or cosine function.
the given domain puts the angle in the 2nd quadrant.
in that quad, the sine is positive and the cosine is negative, so it has to be
y = cosx
2. I know that sin30° = sin(π/6) = 1/2
so csc (π/6) = 2
and we know that the cosecant has values ≥1 or ≤-1 , never crossing the x-axis
so y = cscx
3. you are correct
4. you are correct
posted by Reiny
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How do I find the critical values? y= 4/x + tan(πx/8) What I did is I simplified it to y= 4x^-1 + tan(πx/8) then I took the derivative y'= -4x^-2 + (π/8)(sec(πx/8))^2 Then I simplied it y'= -4/x^2 +
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Mark any solutions to the equation 2cos2x - 1 = 0. The answer can be more than one. Thank you π/8 -7π/4 15π/4 3π/4
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More Similar Questions | 931 | 2,783 | {"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-2018-34 | latest | en | 0.895486 |
https://mt-rca.org/roof-types/how-do-you-work-out-the-area-of-a-roof-australia.html | 1,653,743,302,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663016853.88/warc/CC-MAIN-20220528123744-20220528153744-00668.warc.gz | 480,749,572 | 19,275 | # How do you work out the area of a roof Australia?
Contents
## How is roof area calculated in Australia?
If your house is rectangular, all you need to do is multiply the length and width of the building. If the shape of your house is more complex, simply enter the total area (after measuring the exterior dimensions) into the appropriate box.
## How do you calculate the area of a roof?
Multiply your house length by your house width to get the area. (For example, 40 feet x 30 feet = 1,200 square feet.) Next, multiply the area by your roof’s pitch. (1,200 x 1.05 = 1,260 square feet.)
## What is the standard roof pitch in Australia?
Standard roof pitches in Australia are usually either 15 degrees or 22.5 degrees, depending on the materials used in the roof.
## What is the most common roof pitch?
The most commonly used roof pitches fall in a range between 4/12 and 9/12. Pitches lower than 4/12 have a slight angle, and they are defined as low-slope roofs. Pitches of less than 2/12 are considered flat roofs, even though they may be very slightly angled.
IT IS INTERESTING: What colors go with a GREY roof?
## How many square feet do I need calculator?
If you are measuring a square or rectangle area, multiply length times width; Length x Width = Area. For other area shapes, see formulas below to calculate Area (ft2) = Square Footage.
## How many squares are in a 1200 square foot roof?
To determine the number of squares on the gable roof above, divide its total of 24,000 square feet by 100 (24,000 ÷ 100 = 240).
How many shingles do I need for 1000 square feet?
House by Square Foot Roof by Square Foot Re-Roofing Cost*
1,000 1,054 \$4,000 – \$5,500
1,100 1,160 \$4,200 – \$6,000
1,200 1,265 \$4,500 – \$6,500
1,500 1,581 \$5,500 – \$8,000
## How do I calculate shingles for my garage?
Calculate the square footage by multiplying the width by the length. For example, a 20 foot long by 15 foot wide section will come to 300 square feet. Add the square footage together from all of the areas measured to get total square footage. This is the figure you will use for a shingle estimation.
## What roof pitch is 25 degrees?
Roof Slope in Degrees to Standard Roof Pitch Conversion Tables
Convert Roof Slope from Degrees to Rise-in-Run
Roof Angle in Degrees Roof Slope as Rise-in-Run (X-in-12)
25° 5.596 in 12
26° 5.853 in 12
27° 6.114 in 12
## Is there a minimum roof pitch?
Traditionally, a minimum roof pitch of 20° was recommended in BS 5534, but modern tiles and slates have now been designed for applications as low as 15°. It is uncommon to find a roof below 15° but for those very low pitch applications, there are interlocking clay pantiles available, suitable for use down to 12.5°.
IT IS INTERESTING: How heavy is too heavy for a roof?
## What is the best roof in Australia?
Here are Australia’s top types of roofing.
1. Solar Tiles. An increasingly popular option for those seeking to cut costs and increase green points – solar tiles are ideal for most Australian climates. …
2. Metal Sheeting. …
3. Brickwork. …
4. Terracotta Roof Tiles. …
5. Concrete Tiles.
1.11.2020
## Is a 4/12 roof pitch good?
As well, a slope of 4:12 is most commonly considered the lowest slope for “standard shingle installations”. Most manufacturer and industry recommendations require, or at the very least recommend, special underlayment or other considerations on roofs between 2:12 and 4:12.
## How does roof pitch affect cost?
A slope of 6/12 could add nearly another thousand dollars to the price. If you were to choose a 9/12 slope, the national average for a 40 by 50-foot roof would be more than \$8,300. A high slope of 12/12 could cost \$10,000 or more.
## What roof pitch is 30 degrees?
What roof pitch is 30 degrees? A 30° roof pitch is roughly the same as a 7/12 roof pitch. To convert from degrees to the American ratio: Find the tangent of the angle, tan(angle). | 1,013 | 3,914 | {"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-2022-21 | latest | en | 0.911672 |
http://www.sigmainfy.com/blog/leetcode-trapping-rain-water.html | 1,487,933,491,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501171463.89/warc/CC-MAIN-20170219104611-00199-ip-10-171-10-108.ec2.internal.warc.gz | 594,266,537 | 3,798 | LeetCode Trapping Rain Water: O(N) Time and O(1) Space with Two Pointers
Overview
LeetCode Trapping Rain Water: O(N) Time and O(1) Space with Two Pointers by keeping the left and right bound for each bar so we get the rain each bar can hold
LeetCode Trapping Rain Water
Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it is able to trap after raining.
For example,
Given `[0,1,0,2,1,0,1,3,2,1,2,1]`, return `6`.
The above elevation map is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped. Thanks Marcos for contributing this image! (Image from leetcode.com)
Solution and Precautions: O(N) Time and O(1) Space with Two Pointers
If you do the problem of “leetcode: Largest Rectangle in Histogram” before this problem, then it is not difficult to come up with the solution. For each bar we get the highest bar on its left and right side. Then the water for this bar to hold only depends on these two bounds which is min(leftboud, rightboud) – its own height. So basically three linear scan is enough to get the total sum. The following code uses O(N) space to implement this idea and it can pass the LeetCode OJ for this Trapping Rain Water problem based on which I will give the real O(1) Space solution with two pointers:
```public class Solution {
public int trap(int[] A) {
int n = A.length;
if (n < 2)
return 0;
int [] lBound = new int[n];
int [] rBound = new int[n];
int h = A[0];
for (int i = 0; i < n; ++i)
lBound[i] = h = Math.max(h, A[i]);
h = A[n-1];
for (int i = n-1; i >= 0; --i)
rBound[i] = h = Math.max(h, A[i]);
int ret = 0;
for (int i = 0; i < n; ++i)
ret += Math.min(lBound[i], rBound[i]) - A[i];
return ret;
}
}
```
It turns out that the O(N) space is not necessary as long as we maintain two pointers and scan the bars from both head and tail towards each other, see the following code first which can pass this LeetCode Trapping Rain Water problem:
```public class Solution {
public int trap(int[] A) {
int i = 0, j = A.length - 1;
int lMax = 0;
int rMax = 0;
int ret = 0;
while (i <= j) {
lMax = Math.max(lMax, A[i]); // max within [0..i]
rMax = Math.max(rMax, A[j]); // max within [j..n-1]
if (lMax < rMax) {
ret += lMax - A[i++];
}
else {
ret += rMax - A[j--];
}
}
return ret;
}
}
```
You see the key fact is that we only need constant memory to keep the maximum height among [0..i] and [j..n-1], and if lMax < rMax, it means for the bar i, the left bound must be lMax, and the right bound does not affect how much rain bar i can hold! So we directly calculate the amount of water and add it to the results, the similar reasoning applies to the right side j.
Summary
LeetCode Trapping Rain Water: O(N) Time and O(1) Space with Two Pointers by keeping the left and right bound for each bar so we get the rain each bar can hold
Written on May 26, 2013 | 856 | 2,932 | {"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} | 3.890625 | 4 | CC-MAIN-2017-09 | latest | en | 0.838402 |
http://math4finance.com/general/8-which-box-and-whisker-plot-shows-the-high-temperatures-in-philadelphia-pennsylvania-during-the-first-two-weeks-of-march-39-41-33-57-34-30-47-33-49-52-32-53-37-43-1-point-a-a-box-and-whisker-plot-is-shown-above-a-number-line | 1,723,663,991,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641121834.91/warc/CC-MAIN-20240814190250-20240814220250-00826.warc.gz | 18,015,389 | 7,878 | Q:
# 8. Which box-and-whisker plot shows the high temperatures in Philadelphia, Pennsylvania, during the first two weeks of March: 39, 41, 33, 57, 34, 30, 47, 33, 49, 52, 32, 53, 37, 43 (1 point) A.A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to 49 with a division at 39. There is also a point marked at 39. The whisker on the left extends from 30 to 33. The whisker on the right extends from 49 to 57. B.A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to between 50 and 51 with a division at 41. There is also a point marked at 41. The whisker on the left extends from 30 to 33. The whisker on the right extends from between 50 and 51 to 57. C.A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to 49 with a division at 40. There is also a point marked at 40. The whisker on the left extends from 30 to 33. The whisker on the right extends from 49 to 57. D.A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to between 50 and 51 with a division at 40. There is also a point marked at 40. The whisker on the left extends from 30 to 33. The whisker on the right extends from between 50 and 51 to 57.I am saying this is D.
Accepted Solution
A:
39, 41, 33, 57, 34, 30, 47, 33, 49, 52, 32, 53, 37, 43
Step 1: Order the data from least to greatest:
30, 32, 33, 33, 34, 37, 39, | 41, 43, 47, 49, 52, 53, 57
40
Find the median: 40 (use | to mark this on the box plot)
Find the lower and upper extremes: 30 and 57
Find the middles of the lower and upper halves (called lower and upper quartiles) (see bold): 33 and 49; This is where the box is formed.
These are the 5 numbers used to create the box plot.
Choice C uses these number to create the box plot. | 620 | 1,960 | {"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-2024-33 | latest | en | 0.902977 |
https://www.naukri.com/code360/library/understanding-the-map-function | 1,721,214,747,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514759.39/warc/CC-MAIN-20240717090242-20240717120242-00882.warc.gz | 826,877,361 | 59,998 | 1.
Introduction
2.
3.
Map Function
4.
Reduce Function
5.
What is MapReduce?
5.1.
MapReduce Data Flow
5.2.
Let’s understand MapReduce with a word count example
6.
FAQs
6.1.
What is the Map function?
6.2.
What is Reduce function?
6.3.
What are the steps involved in MapReduce dataflow?
7.
Conclusion
Last Updated: Mar 27, 2024
Easy
# Understanding The Map Function
Master Python: Predicting weather forecasts
Speaker
Ashwin Goyal
Product Manager @
## Introduction
In this modernistic world, information is a crucial element that eases the lives of the masses, and storing this information is one of the biggest challenges we face. As a developer, we don’t deal with single data but clusters of a wide variety of data. We will understand the MapReduce framework, which processes large amounts of unstructured data across a distributed group of processors into a structured unit.
We will start our discussion from when we used to do things manually; here, we will discuss the manual approach and the shortcoming we faced while using the manual method.
Afterwards, we will discuss our approach to doing such a task after developing an algorithm.
Let's look at how parallel and distributed processing used to work before the MapReduce framework. So, let’s say I have a weather log containing the daily average temperature for 2012 to 2022. I'm trying to figure out which day of the year has the highest temperature.
As a result, we'll divide the data into smaller portions or blocks and store them in multiple machines, much as in the old days. Then, we’ll find the highest temperature for each part stored in the associated device. Finally, I will aggregate the results from each machine to produce the final product. Let's have a look at the drawbacks of the standard approach:
• The length of time it takes to complete the project without postponing the following milestone or the actual completion date is known as the critical path problem. As a result, if one of the machines causes a delay, the entire process will be delayed.
• The problem of reliability: What if one of the machines handling a portion of the data fails? It becomes challenging to manage this failover.
• How will I divide the data into smaller chunks so that each computer has an equal amount of data to work with? In other words, how to distribute the data evenly so that no single system is overburdened or underutilized.
• A single split could go wrong: I won't be able to calculate the outcome if any of the machines fails to produce output. As a result, there should be a method to assure the system's fault tolerance capability.
• Compilation of the data: To have a final output, a method should be in place to aggregate the units’ results.
Source
These are the challenges that we'll have to deal with on our own while undertaking parallel processing on large datasets using standard methods.
We have the MapReduce framework to address these concerns, which enables us to do parallel computations without worrying about issues like reliability and fault tolerance. As a result, MapReduce allows us to build code logic without worrying about the system's architecture difficulties.
Now to build the MapReduce framework, we will understand what “map” and “reduce” functions are and how their coexistence gives the MapReduce framework.
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## Map Function
For years, the map function has been a feature of many functional programming languages, with LISP, an artificial intelligence language, being the first to popularise it. The “map” has been revived as a primary technology for processing lists of data pieces by good software developers who recognize the importance of reuse (keys and values).
In the Map function, unction, the user defines a function to apply to each key-value pair, resulting in other key-value pairs known as intermediate key-value pairs.
Source
## Reduce Function
Like the map function, Reduce has long been a part of functional programming languages. It's called fold in different languages, but the behavior is the same. The reduce function takes the result of a map function and "reduces" it in any way the programmer wants. The reduce function requires the first step of entering a value into an accumulator, which stores an initial value. The reduction function processes each element of the list and performs the operation you need across the list after saving a beginning value in the accumulator. The reduction function returns a value at the end of the list based on the operation you wish to execute on the output list.
The intermediate key-value pairs are grouped by key in this phase, and the user applies a “reduce” function to each group, resulting in other key-value pairs, which comprise the round's output.
Source
## What is MapReduce?
MapReduce is a programming framework that allows us to do distributed and parallel processing on massive data sets in a distributed environment.
• As the name implies, the reducer phase occurs after the completion of the mapper phase.
• The first is a “map” job, which reads and processes data blocks to produce key-value pairs as intermediate outputs.
• The reducer receives the output of a Mapper or a “map” job (key-value pairs).
• The reducer then condenses those intermediate data tuples (intermediate key-value pair) into a smaller collection of tuples or key-value pairs, which serves as the final output.
Source
### MapReduce Data Flow
Now we will understand the algorithm's core, and the implementation of a particular round.
1. When we divide the file into chunks, each becomes a map task's input. Each map task is allocated to a worker node, which uses the map function to apply to each key-value pair in the relevant input chunk.
2. The intermediate key-value pairs are saved on the workers' local drives. Each intermediate key-value pair is placed in the local disc into buckets through a hash function h to speed up the procedure and balance the load of workers.
(key,value)->Bucket I = h(k) mod (N° Buckets)
Each bucket is assigned to a distinct worker who uses the user-specified reduce function.
During these three phases, two key functions are performed.
• The shuffle function is used to transmit information from mappers to reducers. This function can start even before the map phase has ended to speed up the algorithm. Shuffle is frequently the most expensive round procedure.
• The sorting function is used to sort a list of values with the same key. If you don't supply any reducers, the result will be zero. The MapReduce job then comes to a halt at the map phase.
### Let’s understand MapReduce with a word count example
Let's look at how a MapReduce works using an example: I have a text file called example.txt with the following contents:
Dear, Bear, River, Car, Car, River, Deer, Car, and Bear
Assume we need to use MapReduce to do a word count on example.txt. As a result, we'll be looking for unique terms and the number of times they appear.
Source
• First, we partition the input into three sections, as shown in the diagram. This will evenly spread the workload across all map nodes.
• Then we tokenize the words in each mapper and assign a hardcoded value (1) to each token or word. Setting the hardcoded value to 1 is that each word will only appear once.
• A list of key-value pairs will now be produced, with the key being the individual words and the value being one. So we have three key-value combinations for the first line (Dear Bear River) — Dear, 1; Bear, 1; River, 1. On all nodes, the mapping procedure is the same.
• Following the mapper phase, a partition process occurs, sorting and shuffling tuples with the same key and sending them to the matching reducer.
• As a result, each reducer will have a unique key and a list of values corresponding to that key after the sorting and shuffling step. For instance, Bear [1,1], Car [1,1,1], and so on.
• Each reducer now counts the number of values in that list of values. Reducer receives a list of values for the key Bear, as illustrated in the diagram. After that, it counts the number of ones throughout the entire list and outputs Bear, 2.
• After that, the output key/value pairs are collected and written to the output file.
## FAQs
### What is the Map function?
In the map function, the user defines a function to apply to each key-value pair, resulting in other key-value pairs known as intermediate key-value pairs.
### What is Reduce function?
The intermediate key-value pairs that we find in the map function are grouped by key in this phase, and the user applies a “reduce” function to each group, resulting in other key-value pairs, which comprise the round's output.
### What are the steps involved in MapReduce dataflow?
The steps involved in MapReduce are input, split, map, combine, shuffle and sort, reduce then output.
## Conclusion
In this article, we have extensively discussed what “map” and “reduced” functions are and why we need MapReduce. We hope that this blog has helped you enhance your knowledge and aspects that you should keep in mind while dealing with the MapReduce framework and if you would like to learn more, check out our articles here. You can also check the introduction to Hadoop and its ecosystem here, and the difference between Sparks and Hadoop here. If you want to explore and learn big data, make sure to check out this. Do upvote our blog to help other ninjas grow.
Learning never stops, and to feed your quest to learn and become more skilled, head over to our practice platform Coding Ninjas Studio to practice top problems, you can check SQL problems here, attempt mock tests, read interview experiences, and you can also check our guided path for the coding interview and much more!
Happy Learning!
Live masterclass | 2,152 | 10,098 | {"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-2024-30 | latest | en | 0.904177 |
https://math.stackexchange.com/questions/3175149/prove-that-if-x-is-odd-and-y-is-even-then-gcdxy-x-y-gcdx-y | 1,558,391,664,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232256163.40/warc/CC-MAIN-20190520222102-20190521004102-00124.warc.gz | 556,030,430 | 32,536 | Prove that if x is odd and y is even, then gcd(x+y,x-y)=gcd(x,y)
It is trivial to prove that gcd(x,y) divides gcd(x+y,x-y). How is it possible to prove gcd(x+y,x-y) divides gcd(x,y)? I don´t know how to use the fact that x is odd and y is even. Can anybody help me prove the statement?
Suppose $$d\,|\,\gcd (x+y,x-y)$$. Then $$d\,|\,(x+y+x-y)=2x$$. Now, the parity assumptions tell us that both $$x\pm y$$ are odd so $$d$$ must be odd. Hence $$d\,|\,2x\implies d\,|\,x$$.
• Well, $\gcd(x+y,x-y)$ is a divisor of $\gcd(x+y,x-y)$. – lulu Apr 4 at 21:01
• I can't understand your confusion. In my post, I proved that any $d$ which divides $\gcd(x+y,x-y)$ also must divide $\gcd(x,y)$. So, just take $d=\gcd(x+y,x-y)$ and you are done. – lulu Apr 4 at 21:16 | 263 | 755 | {"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": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2019-22 | latest | en | 0.862819 |
https://www.doorsteptutor.com/Exams/NSTSE/Class-4/Questions/Topic-Mathematics-0/Subtopic-Addition-and-Subtraction-2/Part-14.html | 1,508,536,734,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824357.3/warc/CC-MAIN-20171020211313-20171020231313-00221.warc.gz | 913,371,922 | 16,662 | # Mathematics-Addition and Subtraction (NSTSE (National Level Science Talent Search Examination) Class 4): Questions 93 - 100 of 100
Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 1791 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.
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## Question number: 93
» Mathematics » Addition and Subtraction
MCQ▾
### Question
The difference between two numbers is. If the smaller number is what is the greater number?
### Choices
Choice (4) Response
a.
2, 564
b.
3, 810
c.
5, 066
d.
1, 256
## Question number: 94
» Mathematics » Addition and Subtraction
MCQ▾
### Question
What must be subtracted to 7536 to get 3680?
### Choices
Choice (4) Response
a.
3680
b.
7536
c.
3856
d.
0
## Question number: 95
» Mathematics » Addition and Subtraction
MCQ▾
________
### Choices
Choice (4) Response
a.
1946
b.
1994
c.
1990
d.
1949
## Question number: 96
» Mathematics » Addition and Subtraction
MCQ▾
### Question
3 thousands 10 tens more than 198 is:
### Choices
Choice (4) Response
a.
3298
b.
198
c.
3002
d.
3100
## Question number: 97
» Mathematics » Addition and Subtraction
MCQ▾
### Question
Urvisha is arranging her clothes in a new cupboard, which has 5 drawers. After putting 7 pairs of clothes in each drawer, she finds that 3 pairs of clothes are still left outside. How many pairs of clothes are there in total?
### Choices
Choice (4) Response
a.
38
b.
32
c.
35
d.
40
## Question number: 98
» Mathematics » Addition and Subtraction
MCQ▾
### Question
Find the sum of the numbers shown on the abacus.
### Choices
Choice (4) Response
a.
2467
b.
432
c.
2035
d.
2476
## Question number: 99
» Mathematics » Addition and Subtraction
MCQ▾
### Question
When zero is subtracted from a number the difference is:
### Choices
Choice (4) Response
a.
Number itself
b.
Zero
c.
1
d.
None of the above
## Question number: 100
» Mathematics » Addition and Subtraction
MCQ▾
### Question
If these number sentences are true, which of the following may be correct?
### Choices
Choice (4) Response
a.
b.
c.
d.
f Page | 628 | 2,245 | {"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-2017-43 | longest | en | 0.673706 |
https://www.shaalaa.com/question-bank-solutions/find-principal-value-cos-1-sqrt3-2-basic-concepts-trigonometric-functions_11811 | 1,576,291,659,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540579703.26/warc/CC-MAIN-20191214014220-20191214042220-00323.warc.gz | 874,924,360 | 11,544 | Share
# Find the Principal Value Of Cos^(-1) (Sqrt3/2) - CBSE (Commerce) Class 12 - Mathematics
ConceptBasic Concepts of Trigonometric Functions
#### Question
Find the principal value of cos^(-1) (sqrt3/2)
#### Solution
Let cos^(-1) (sqrt3/2) = y, " Then " cos y = sqrt3/2 = cos (pi/6)
We know that the range of the principal value branch of cos−1 is
[0, pi] and cos (pi/6) = sqrt3/2
Therefore the priciple value of cos^(-1) (sqrt3/2) is pi/6
Is there an error in this question or solution?
#### APPEARS IN
NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 2: Inverse Trigonometric Functions
Q: 2 | Page no. 41
#### Video TutorialsVIEW ALL [3]
Solution Find the Principal Value Of Cos^(-1) (Sqrt3/2) Concept: Basic Concepts of Trigonometric Functions.
S | 250 | 797 | {"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} | 3.765625 | 4 | CC-MAIN-2019-51 | latest | en | 0.663241 |
http://math.stackexchange.com/questions/334041/what-is-the-intuition-behind-the-lagrange-multiplier/334139 | 1,469,514,767,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824756.90/warc/CC-MAIN-20160723071024-00224-ip-10-185-27-174.ec2.internal.warc.gz | 165,080,102 | 17,143 | # What is the intuition behind the Lagrange multiplier?
I know that the minimum or maximum point is achieved when the gradient in the constraint function is parallel to the gradient on the $f$ function. But why the Lambda is called the Lagrange multiplier?
-
Not a direct answer, but this may help you remember the content of the theorem: A function will have a critical point at a set of constraints when its derivative is a linear combination of the derivatives of the constraints. – Lepidopterist Mar 18 '13 at 19:10
Are you asking for intuition or the naming origin? – copper.hat Mar 18 '13 at 19:12
I think that the terminology comes from statics, when the $f$ function is potential energy and the mechanical constraint is smooth (meaning that friction doesn't do work). The function $f$ has a critical point exactly when energy is stationary, that is, at equilibrium positions. In this case $\nabla f$ is a force and $\nabla g$, the gradient of the constaint function, is the force exerted by the constraint to compensate for $\nabla f$. The Lagrange multiplier measures the amount of stress the constraint is subjected to. – Giuseppe Negro Mar 18 '13 at 19:16 | 270 | 1,168 | {"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} | 2.890625 | 3 | CC-MAIN-2016-30 | latest | en | 0.884622 |
https://chandoo.org/forum/threads/monthly-totals.41910/ | 1,566,436,278,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027316555.4/warc/CC-MAIN-20190822000659-20190822022659-00312.warc.gz | 407,521,737 | 11,405 | # Monthly totals
#### derek davis
##### New Member
Could I ask for some help and steer me in the right direction. I am looking to acheive three results all in Column "O"
1. create a monthly total.
2. create monthly positive result.
3. create monthly negative result.
I have tried using SUMIFS and trying to include EOMONTH functions. I would like to capture the monthly results using funtions. I have included a development sheet for your perusal please see cells O 7,8,9
Thanks
Del.
#### Attachments
• 22.8 KB Views: 9
#### Hui
##### Excel Ninja
Staff member
Derek
Firstly, Welcome to the Chandoo.org Forums
Have a try of these
O7: =SUMPRODUCT((\$E\$7:\$E\$69>=DATEVALUE("1"&N\$7&\$N\$6))*(\$E\$7:\$E\$69<=EOMONTH(DATEVALUE(1&N\$7&\$N\$6),0))*\$K\$7:\$K\$69)
O8: =SUMPRODUCT((\$E\$7:\$E\$69>=DATEVALUE("1"&N\$7&\$N\$6))*(\$E\$7:\$E\$69<=EOMONTH(DATEVALUE(1&N\$7&\$N\$6),0))*(\$K\$7:\$K\$69>0)*(\$K\$7:\$K\$69))
O9: =SUMPRODUCT((\$E\$7:\$E\$69>=DATEVALUE("1"&N\$7&\$N\$6))*(\$E\$7:\$E\$69<=EOMONTH(DATEVALUE(1&N\$7&\$N\$6),0))*(\$K\$7:\$K\$69<0)*(\$K\$7:\$K\$69))
#### derek davis
##### New Member
Hi Hui, thanks for your quick response to my question. On testing all three formulas I noticed that when I enter a new line of data in columns A-G row 70 onwards that the data is not included in the final tally. I can see why this has occurred as it stops at row 69, and I will put my hand up as I didn't mention that rows 70.71,72 etc will be populated as the days & weeks go forward. I Tried to edit your formula for columns E and K to read \$E7:\$E, \$K7:\$K. but this indicated an error (Value). Is there a workaround to this problem? as I will be building on this sheet for at least 3 years. All other elemnts are working fine.
O7: SUMPRODUCT((\$E\$7:\$E\$70>=DATEVALUE("1"&N\$22&\$N\$6))*(\$E\$7:\$E\$70<=EOMONTH(DATEVALUE(1&N\$22&\$N\$6),0))*\$K\$7:\$K\$70)
#### bosco_yip
##### Excel Ninja
Or, try this 1 formula solution instead of 3 formulas, the result is same as Hui's and which also consider your data increment problem.
In O7, copied down :
=IF(N7="","",SUMIFS(K:K,K:K,IF(LEFT(N7)="P",">0",IF(LEFT(N7)="L","<0","<>")),E:E,">="&LOOKUP(9^9,0+(N\$7:N7&N\$6)),E:E,"<="&EOMONTH(LOOKUP(9^9,0+(N\$7:N7&N\$6)),0)))
Regards
Bosco
#### Attachments
• 25.1 KB Views: 11
Last edited:
#### derek davis
##### New Member
Thanks to Hui and Bosco for your views, they were diverse but aceived almost the same result. I appreciate your time to assist me.
Thank you.
#### Peter Bartholomew
##### Well-Known Member
With dynamic ranges for the data and numbers for the months
{= SUMIFS( totals,
totals, {"<>";">0";"<0"},
dates, ">"&DATE(yyyy,mm,0),
dates, "<"&DATE(yyyy,mm+1,1) )} | 928 | 2,696 | {"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} | 3.125 | 3 | CC-MAIN-2019-35 | latest | en | 0.869146 |
http://www.coderanch.com/t/488689/java/java/Convert-minutes-Hours-minutes | 1,467,250,432,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783397865.91/warc/CC-MAIN-20160624154957-00007-ip-10-164-35-72.ec2.internal.warc.gz | 457,461,280 | 10,723 | Win a copy of Mesos in Action this week in the Cloud/Virtualizaton forum!
# Convert minutes to Hours and minutes
Andraz Poje
Ranch Hand
Posts: 32
Hi. I have this code. This code gives me difference in minutes between two date objects.
How do I convert minutes to Hours and minutes?
I tried this:
I get possible loss of precision.... Hm...
Greg Charles
Sheriff
Posts: 2985
12
The problem is the Math.floor() call. You don't need it. It's meant to cut off the fractional part of a floating point number, but you're feeding it a long (integer).
Joanne Neal
Rancher
Posts: 3742
16
As far as the compiler is concerned, floor returns a double, so by assigning it to a long you are losing the decimal part of the value. In this case it doesn't actually matter because that is what you actually want. You need to tell the compiler that you know this is going to happen and you don't care. To do this, you put an explicit cast in.
Edit - as Greg and Henry pointed out, there is a better way to do this. You should use that and just look on this post as an explanation of the compiler error.
Henry Wong
author
Marshal
Posts: 21122
78
You don't need to call floor(), as by default, long operations automatically round down. The floor() method is for floating point, which is probably where the compiler is complaining.
[EDIT: too slow... ]
Henry
Andraz Poje
Ranch Hand
Posts: 32
Greg Charles wrote:That looks right to me. Loss of precision is something you worry about with floating point arithmetic. With integers, you are either wrong or right.
By the way, you don't need Math.floor. Integer division will always truncate off the fractional part.
I understand. But what can I do to skip possible loss of precision error messages?
Andraz Poje
Ranch Hand
Posts: 32
Henry Wong wrote:You don't need to call floor(), as by default, long operations automatically round down. The floor() method is for floating point, which is probably where the compiler is complaining.
[EDIT: too slow... ]
Henry
I casted it... Resolved. Thanks.
Greg Charles
Sheriff
Posts: 2985
12
Sorry, I posted, then realized the when you said you got "possible loss of precision", you actually meant that was a compiler warning. I tried to quickly amend my response, only to find there had been a flurry of activity around it.
If it's not clear already, just do away with the Math.floor() call. You don't need it. As Joanne pointed out, the "loss" that the compiler complains about is converting a double returned by Math.floor() to a long (integer) without a cast. However, you have no reason to stray into the world of floating point arithmetic at all. Your integer division minute / 60 in math may yield a number with fractions, but in the computer will yield an integer with the fractional part throw away. Sorry for the confusion! | 660 | 2,812 | {"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-2016-26 | latest | en | 0.933611 |
http://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-3-review-page-272/13 | 1,524,395,051,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945584.75/warc/CC-MAIN-20180422100104-20180422120104-00497.warc.gz | 427,583,933 | 14,185 | ## Algebra: A Combined Approach (4th Edition)
To graph the given linear equation, look for three points that belong to the line. To find three points on the line, assign a value to one variable and then solve for the value of the other variable. When x = 0: $x-y=1 \\0-y=1 \\-y=1 \\y=1(-1) \\y=-1$ The point is $(0, -1)$. When y = 0: $x-y=1 \\x-0=1 \\x=1$ The point is $(1, 0)$. When y = 2: $x-y=1 \\x-2=1 \\x=1+2 \\x=3$ The point is $(3, 2)$. Plot the three points and connect them using a straight line. (refer to the attached image in the answer part above) | 191 | 561 | {"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} | 4.03125 | 4 | CC-MAIN-2018-17 | latest | en | 0.761213 |
http://math.stackexchange.com/questions/224983/find-formula-for-frac2-ln33-frac4-ln49-frac6-ln527-frac8/224984 | 1,464,092,596,000,000,000 | text/html | crawl-data/CC-MAIN-2016-22/segments/1464049270555.40/warc/CC-MAIN-20160524002110-00223-ip-10-185-217-139.ec2.internal.warc.gz | 185,649,179 | 17,002 | # Find formula for ${-\frac{2\ln3}{3} , \frac{4\ln4}{9} ,\frac{6\ln5}{27},\frac{8\ln6}{81} ,…}$
The question is to find a general formula for the nth term, $a_n$, of the sequence: $${-\frac{2\ln3}{3} , \frac{4\ln4}{9} ,\frac{6\ln5}{27}, \frac{8\ln6}{81} ,\frac{10\ln7}{243},...}$$
Here is what I got, but when I plugged in a few terms, it did not work out right. I got the formula to be: $$a_n = (-1)^n \frac{2\ln(2+1)\cdot 2^{(n-1)}} {3^n}$$
-
One quick comment, my question is about to find the formula of a sequence, not the sum of the series – Jaden Q Oct 30 '12 at 5:09
Each term has a form like $\pm \frac{x\ln y}{z}$.
The sign alternates so it is $(-1)^n$.
$x$ is $2, 4, 6, 8, \dots$, so $x$ is $2n$.
$y$ is $3,4,5,\dots$ so $y$ is $n+2$.
$z$ is $3,9,27, 81, \dots$ so $z$ is $3^n$.
Combining all contributions, we get $a_n = (-1)^n \frac{2n \ln(n+2)}{3^n}$.
-
thanks! it totally makes more sense to me – Jaden Q Oct 30 '12 at 5:13
Sign changes in alternative terms,so $(-1)^n$
$2,4,6,8\cdots \implies n$ th term is $2n$
If the question meant, $$\frac{\log 3}{3}, \frac{\log 4}{9}, \frac{\log 5}{27},\cdots$$ its $n$th term is $$\frac{\log (n+2)}{3^n}$$
If the question meant, $$\log \frac{3}{3}, \log \frac{4}{9}, \log \frac{5}{27},\cdots$$ its $n$th term is $$\log \frac{(n+2)}{3^n}$$
-
The answer $a_n = (-1)^n \frac{2n \ln(n+2)}{3^n}$ is true if the sequence was:
${-\frac{2\ln3}{3} , \frac{4\ln4}{9} ,-\frac{6\ln5}{27}, \frac{8\ln6}{81} ,-\frac{10\ln7}{243},...}$
- | 649 | 1,495 | {"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} | 4.15625 | 4 | CC-MAIN-2016-22 | latest | en | 0.709929 |
http://docplayer.net/21053581-2006-geometry-form-a-page-1.html | 1,537,717,574,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267159561.37/warc/CC-MAIN-20180923153915-20180923174315-00073.warc.gz | 71,817,558 | 25,218 | # 2006 Geometry Form A Page 1
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## Transcription
1 2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches () 6 inches (E) 7 inches 2. he sum of the measures of all of the non-overlapping angles formed by 7 rays drawn on the same side of a line from the same point of that line is (?) () 1260 () 1080 () 900 () 360 (E) How many degrees are there in an angle that measures one-ninth of its complement? () 810 () 162 () 81 () 80 (E) 9 4. Each interior angle of a regular octagon is: () 120 () 144 () 135 () 140 (E) Which of the following is true if two given triangles are not similar? () their areas cannot be equal () they may be congruent () they are not congruent () their corresponding sides may be proportional (E) their corresponding angles may be equal 7. he points (1,2), (- 4,3) and (7,- 6) are three vertices of a parallelogram. he fourth vertex is: () (12,- 2) () (2,- 11) () (- 11,5) () all of these 8. triangle and a rectangle have equal areas. he base and height of the triangle are 12 and 4, respectively. Find the width of the rectangle if its length is 8. () 3 () 4 () 5 () 6 (E) 7 5. is a rhombus with = 5, and = 6. What is the length of? () 8 () 9 () 10 () 11 (E) rectangle has length x units and width y units. he rectangle has the same perimeter as an equilateral triangle with a side of m units. Find x in terms of m and y. () m + y () 3m - 2y () 1 2 m + y (E) 1 2 () m - y (3m 2y)
2 2006 Geometry Form Page he side of a cube is decreased by 50%. y how much does the volume decrease? () 12.5% () 25% () 50% () 75% (E) 87.5% 15. If a quadrilateral is inscribed in a circle, the opposite angles are: () congruent () complementary (E) supplementary () obtuse () acute 11. If the circumference of a circle is 12π feet, what is the number of square feet in its area? () 6π () 9π () 36π () 81π (E) 144π 12. What is the area of a circle inscribed in a square that has a side length of 8 cm? () 8π cm 2 () 16π cm 2 () 32 π cm 2 () 64π cm 2 (E) 48π cm In circle, minor arc XK is 1 / 3 of the circumference of the circle. If F is not on minor arc XK, what is the measure of inscribed angle XFK? () 60 () 30 () 15 () 120 (E) Find the area of the shaded part of the figure: () 25cm 2 () 50cm 2 () 35cm 2 () (E) circle can be inscribed in: () any triangle () any octagon () any trapezoid () any polygon (E) any parallelogram 17. he area of a trapezoid is 160 square units, one base is 26 units, and the height is 8 units. What is the length of the other base? () 7 () 14 () 56 () 6 (E) 80 / square piece of paper, with one side equal to 12 units, is folded so that the four corners of the square meet in the center of the square. his forms a new square. What is the side measure of the new square? () 5 () 5 3 () 6 2 () 6 (E) he diameter of the front wheel of a tricycle is 8" and the diameter of each rear wheel is 3". How many revolutions has each back wheel made while the front wheel has turned 1440 degrees? () () 4 () () 24 (E) 96
3 2006 Geometry Form Page circular track has a radius of 210 feet. pproximately how many times must a jogger circle the track in order to jog one mile? () 20 () 4 () 35 () 39 (E) he set of points in a plane at a fixed distance from a given point in that plane is: () a line () a circle () an angle () two lines (E) a point 21. he value of Β is: () 3.14 () () () he area of a circle inscribed in an equilateral triangle is 4π. What is the height of the triangle? () 2 () 4 () 6 () 8 (E) he sum of the exterior angles of any polygon will always be what measure? () 180 () 360 () (n 2) 180 () (n + 2) he area of a square 18 ft. on a side is equal to the area of a rectangle with a length of 3 yards. he width of this rectangle is: () 2 ft. () 9 ft. () 18 ft. () 36 ft. (E) 27 ft. 26. he radii of two circles are 3 cm and, respectively. Find the radius of the circle whose area is equal to the sum of the areas of the two given circles. () 8 () 34 () 34 () 34π 27. hree lines lie in one plane. Line m intersects line n which is parallel to line p. How many points are equidistant from all three lines at the same time? () 2 () 1 () 0 () 4 (E) sector of a circle has the same area as an equilateral triangle whose base is 12. What is the area of the sector? () 6 3 () 36 3 () 12 () he number of points on a circle that are equidistant from the endpoints of a given diameter is: () 1 () 2 () 3 () 4 (E) 5
4 2006 Geometry Form Page he radius of a circle is increased by 50%. y how much does the area increase? () 25% () 50% () 100% () 125% (E) 250% 33. Given line Q which goes through the center of a circle with center, whose radius is 4 and P lies on the circle. If P = 4 and Q =4 find the measure of the angle x = πpq. () x < 20 () 20 # x < 30 () 30 # x < 40 () 40 # x < 50 (E) x In the figure, =, =, π = ½ π, and π = 70. How many degrees are there in π? () 55 () 70 () 105 () 110 (E) QRS is a quadrilateral with Q S and QR RS as shown in the figure below. If Q = 70m, SR = 200m, and S = 240 m, how many square meters are there in quadrilateral QRS? S Q 34. wo sides of a triangle are 12 cm and 8 cm, respectively. he altitude to the 12 cm side is 4 cm. Find the altitude to the 8 cm side. () 3 cm () 24 cm () 12 cm () 6 cm (E) 8 / 3 cm 35. Given quadrilateral PQRS inscribed in a circle with side PQ extended beyond Q to point. How many degrees are in πqr if πqps = 110 degrees, & πpsr = 40 degrees? () 30 () 70 () 140 () 40 (E) In the figure below,,, = 8, = 5, = 4. What is the shortest distance from to? R () 2340 () () () (E) () 12 () 13 () 15 () 16 (E) 17
5 2006 Geometry Form Page What is the effect on the volume of a cylinder if the diameter is doubled and the height is cut in half? () the volume remains the same () the volume is doubled () the volume is cut in half () the volume increases by a factor of four 39. point P is selected at random on a semicircle with diameter RS. is the foot of the perpendicular from P to RS. If RS = 6 and R = x, then the length of P in terms of x is: R P S ( ) 6x x ( ) 6x 2x ( ) 3 x ( ) 3 2x ( E) 2x x What is the length of F in this cube that has edges 1 cm long? 40. In the figure below, the large circle has diameter. he two small circles have their centers on and are tangent to each other at the center of the large circle. Find the area of the shaded region, given that = 4. F () 3 () () () 2 O () 16π () 4π () 2π () 1π O
### LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.
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### SHAPE, SPACE AND MEASURES
SHAPE, SPACE AND MEASURES Pupils should be taught to: Use accurately the vocabulary, notation and labelling conventions for lines, angles and shapes; distinguish between conventions, facts, definitions | 8,943 | 34,043 | {"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} | 3.828125 | 4 | CC-MAIN-2018-39 | longest | en | 0.863975 |
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## Learning Opportunities
This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.
## Goal
The 12 year old child has lost his mother and now he wants to meet his mother.Somehow child navigated to his mother but he wanna know exact shortest distance and in order to help him you have to tell him exact shortest distance .each block =10km
Input
map 10*10 first ten lines input string row only consist of '.' means road where child can move,'#'-means wall where he can't move,'M'-position of mother,'C'-position of child.
NOTE-child can't move diagonally.
Output
one line with the shortest ditance which child have to travel in order to reach his mother
Constraints
length of each row will be 10 and consist of only:-
'.'-Road where child can move(empty space)
'#'-wall child can't move
'M'-position of his mother
'C'-position of child
There will always be a solution
Example
Input
..........
M....C....
..........
..........
..........
..........
..........
..........
..........
..........
Output
50km
A higher resolution is required to access the IDE
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Online Participants | 283 | 1,270 | {"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} | 2.78125 | 3 | CC-MAIN-2021-17 | longest | en | 0.929386 |
http://www.studymode.com/essays/Thermal-Physics-Mcq-1143054.html | 1,513,294,284,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948551162.54/warc/CC-MAIN-20171214222204-20171215002204-00440.warc.gz | 441,314,302 | 19,431 | # Thermal Physics Mcq
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• Published : October 15, 2012
Text Preview
IB Thermal Physics MCQ questions ( Higher)
1.Thermal energy is transferred through the glass windows of a house mainly by A.conduction.
C.conduction and convection.
2.The first law of thermodynamics may be expressed in terms of the quantities below. DU, the increase in the internal energy of the system
Q, the energy transferred to the system by heating
W, the work done on the system
Which one of the following is a correct statement of the law? A.W = DU + Q
B.W = −DU − Q
C.W = DU − Q
D.W = −DU + Q
3.A well-insulated container is divided into two equal volumes by a wall. In one half there is an ideal gas and the other is a vacuum as shown below.
The wall is now removed. Which one of the following correctly gives the changes, if any, that take place in the internal energy and entropy of the gas? Internal energy|Entropy|
A.|stays the same|stays the same|
B.|stays the same|increases|
C.|decreases|stays the same|
D.|decreases|increases|
4.Two bodies are brought into thermal contact with each other. No thermal energy transfer takes place between the bodies. It may be deduced therefore, that the bodies must have the same A.specific heat capacity.
B.heat capacity.C.temperature.D.internal energy.
5.An ideal gas expands isothermally, doing 2500 J of external work in the process. The thermal energy absorbed by the gas in this process is A.zero.
B.less than 2500 J.
C.equal to 2500 J.
D.more than 2500 J.
6.Which one of the following correctly describes the changes, if any, of the kinetic energy and the potential energy of the molecules of a liquid as it is boiling? Kinetic energy|Potential energy|
A.|increases|increases|
B.|increases|stays constant|
C.|stays constant|increases|
D.|stays constant|stays constant|
7.The diagram shows the pressure / volume (p/V) diagram for one cycle PQRS of an engine.
In which sections of the cycle is work done on the engine?
A.SP only
B.PQ only
C.SP and PQ only
D.RS and SP only
8.A gas is contained in a cylinder fitted with a piston as shown below.
When the gas is compressed rapidly by the piston its temperature rises because the molecules of the gas A.are squeezed closer together.
B.collide with each other more frequently.
C.collide with the walls of the container more frequently.
D.gain energy from the moving piston.
9.A metal ball at a temperature of 200°C is suspended in an evacuated container. The walls of the container are kept at a constant temperature of 100°C.
Which one of the following statements about the temperature of the ball is correct? A.It will eventually reach absolute zero.
B.It will remain constant at 200°C.
C.It will eventually become 100°C.
D.It will eventually reach a constant temperature between 200°C and 100°C. 10.The diagram below shows energy transfers in a heat pump operating between two reservoirs at temperatures TH and TC (TH > TC). Which of the following gives the correct relationship between W, QC and QH? A.W > QH − QC
B.W < QH − QC
C.W = QH − QC
D.W = QH + QC
11.The specific latent heat of vaporization of a substance is defined as the amount of thermal energy required to A.change a liquid to vapour at constant pressure.
B.change a liquid to vapour at constant temperature.
C.change unit mass of liquid to vapour at constant pressure. D.change unit mass of liquid to vapour at constant temperature. 12.Which one of the following is a correct statement of the second law of thermodynamics? A.When the state of a system changes its entropy increases. B.When the state of a system changes its entropy decreases. C.The total entropy of the universe is increasing with time. D.The total entropy of the universe is decreasing with time. 13.An operating refrigerator with its door open is placed in a thermally insulated room.
The refrigerator operates for a long period of time. Which of the following correctly gives the... | 926 | 3,928 | {"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-2017-51 | longest | en | 0.902026 |
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Make the vector [1 2 3 4 5 6 7 8 9 10]
In MATLAB, you create a vector by enclosing the elements in square brackets like so: x = [1 2 3 4] Commas are optional, s...
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## Integrating Python into MATLAB
We often need to create code using a mixture of languages such as C++, Python and MATLAB. Each language has its own strengths and weaknesses but creating a single program in a mix of languages is typically difficult. MATLAB has had, forever, a MEX interface that allowed C, C++ and Fortran functions to be called from MATLAB, and for a while some limited support to call Python code.
MATLAB R2019a introduced a new mechanism to connect Python code that allows user written Python classes to appear inside MATLAB just like native MATLAB classes. Consider a very simple example:
``````## rectangle.py
class Rectangle:
def __init__(self, x, y, w, h):
self.x = x
self.y = y
self.w = w
self.h = h
def Area(self):
return self.w * self.h``````
We invoke the Python constructor code by
``````>> r = py.rectangle.Rectangle(1, 2, 3, 4)
r =
Python Rectangle with properties:
y: 2
h: 4
x: 1
w: 3
<rectangle.Rectangle instance at 0x177d056c8>``````
and the result is a MATLAB object with properties that reflect the Python class attributes as well as the class methods.
We can invoke the Python code to compute area by
``````>> r.Area
ans =
12``````
We can display or change the class properties (underlying Python class attributes)
``````>> r.x
ans =
1
>> r.w = 4;``````
and as expected the computed area is now different
``````>> r.Area
ans =
16``````
We can similarly construct an instance of a NumPy `ndarray` from a MATLAB vector
``````>> a = py.numpy.array([1 2 3])
a =
Python ndarray:
1 2 3
Use details function to view the properties of the Python object.
Use double function to convert to a MATLAB array.``````
which has a very large number of methods. Conversely, we can create a MATLAB vector from the `NumPy` object by
``````>> double(a)
ans =
1 2 3``````
All of this makes is really easy to exploit existing packages written in Python while keeping the convenience of the interactive MATLAB development process, high-quality graphics, powerful toolboxes and interactive notebooks (called LiveScripts in MATLAB speak). Interestingly all of this works in MATLAB Online as well (the cloud version of MATLAB which runs under Linux on AWS) which means you can share your code to a colleague and have it appear in their MATLAB cloud drive (a bit like shared folders on Dropbox) from where it can be run.
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# Mohit Kumar
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How to construct this matrix without using two for loops?
I was able to figure out the answer to this. The formulation can be written as A = V' * X * V;
7 mois ago | 1
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How to construct this matrix without using two for loops?
Hi, I'm trying to construct a matrix in the following manner: sz=10; V=rand(sz,sz); X=rand(sz,sz); for iter1=1:sz for ...
7 mois ago | 2 answers | 0
### 2
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xlim is not working with the limitmethod option, and how to change its default behaviour?
Hi, I am trying to run xlim('tight') but this gives me an error. According to the documentation it should work. The error is: ...
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Phase Portrait Plotter
Plot the phase portrait for the entered system of differential equations
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How to solve a boundary value problem for a piecewise linear differential equation?
I have two a set of two second order differential equations to which I want to find a periodic solution. The differential equati...
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### 0
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How to check if a user entered input will form a valid function handle?
The user enters a character vector (in the edit text field of Appdesigner). I want to convert it into a function handle. I am do...
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### 1
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How to get mouse coordinates in GUI (AppDesigner) ?
I am using MATLAB App Designer and have inserted axes into the app. When the user clicks a button, I want them to be able to t...
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Why is fimplicit not plotting x^2 = 0 ??
I have a code that takes in an implicit function from the user and then plots it. However, I ran into this odd problem where fim...
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How to find all solutions to a system of two nonlinear equations?
I have a system of two nonlinear equations (f(x,y)=0 and g(x,y)=0) to which I want to find all roots over a region (say x from -...
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How to plot a vector field with coloured arrows?
I'm trying to create a vector field where the colour of the vector represents its magnitude like the one shown in the picture. A...
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How to display Live Editor output in multiple lines?
I have large equations in the output of my code that I want to view. However, in the Live Editor output window it only allows me...
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how to use a excel colum as an input to a function
Hi Giovanna, To change your function so that it works with matrices, all you have to do is replace your multiplication and divi...
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How to solve such a system of nonlinear equations?
Hi, I think this might be a better approach to your problem : img=zeros(320,320); % create a 320x320 zeros matrix to represen...
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How to ensure that dsolve provides a trigonometric solution to a second order differential equation?
Hi, I'm trying to solve the following linear second order equation with dsolve in the symbolic workflow. When I solve it I g...
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How to numerically solve a differential equation with a dirac delta function ?
The differential equation that I want to solve is Upon using ode45 and the dirac function, the dirac function doesn't seem t...
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I'm using MATLAB Live Editor along with the symbolic toolbox. The following expression is not getting simplified. Any fixes? ...
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How to (cleverly) index points in a plot?
I have a for loop which plots a point each iteration. In total there are about 4000+ points to be plotted. From the figure, I w...
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Issue with fsolve tolerance
Turns out function tolerance is compared with norm(fval)^2and the default tolerance was 1e-3. Simply changed it to 1e-10 (in acc...
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Issue with fsolve tolerance
I am using fsolve to solve an overdetermined system of equations using the levenberg marquadt algorithm. It works fine although...
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How to repeat a column several times?
Consider this scenario - a =[1;2.3;3.2;4.5;5.7]; b=[a,a,a,a,a]; Is there a better way to do this?
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Finding Perfect Squares
Given a vector of numbers, return true if one of the numbers is a square of one of the other numbers. Otherwise return false. E...
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Maximum value in a matrix
Find the maximum value in the given matrix. For example, if A = [1 2 3; 4 7 8; 0 9 1]; then the answer is 9.
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Return area of square
Side of square=input=a Area=output=b
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Triangle Numbers
Triangle numbers are the sums of successive integers. So 6 is a triangle number because 6 = 1 + 2 + 3 which can be displa...
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Column Removal
Remove the nth column from input matrix A and return the resulting matrix in output B. So if A = [1 2 3; 4 5 6]; ...
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Pizza!
Given a circular pizza with radius _z_ and thickness _a_, return the pizza's volume. [ _z_ is first input argument.] Non-scor...
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Select every other element of a vector
Write a function which returns every other element of the vector passed in. That is, it returns the all odd-numbered elements, s...
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Determine if input is odd
Given the input n, return true if n is odd or false if n is even.
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https://www.investingzz.com/savings-to-investment-ratio-calculator/ | 1,638,483,485,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362297.22/warc/CC-MAIN-20211202205828-20211202235828-00473.warc.gz | 837,818,369 | 12,878 | # Savings To Investment Ratio Calculator
Filter Type:
### Savings Over Investment Ratio Calculator (SIR Tool
(6 days ago) The Savings to income ratio (SIR) is a metric used to measure the ability of a technology to recover the investment costs through savings achieved from customer utility bill cost reduction. The ratio divides the "savings" by the "investment"; an SIR score above 1 indicates that a household can recover the investment.
https://betterbuildingssolutioncenter.energy.gov/content/savings-over-investment-ratio-calculator-sir-tool
Category: Invest, Saving
### Savings to Investment Ratio Calculator for Renewables
(9 days ago) March 5, 2018. Savings to Investment Ratio Calculator for Renewables. Solar data analysis from the National Renewable Energy Laboratory (NREL) explores the affordability of solar using a “Savings to Investment Ratio” (SIR). This metric captures the ability to recover one’s investment in solar based on the utility bill savings resulting
Category: Invest, Saving
### Savings-Investment Calculator - MyCalculators.com
(7 days ago) Savings / Investment Calculator. then press the button next to the field to calculate. of the period. of the period. is a Withdrawal. Be sure to select the appropriate compounding frequency. To view the schedule, all input fields must contain a value.
https://www.mycalculators.com/ca/savecalcm.html
Category: Invest, Saving
### How to Calculate Savings-to-Investment Ratios …
(7 days ago) A person or business uses the savings-to-investment (SIR) ratio to determine whether the potential savings of a project justifies the initial investment. For example, if a laundromat owner is considering switching to energy-efficient washing machines in his laundromat, the SIR would help him determine whether the
https://budgeting.thenest.com/calculate-savingstoinvestment-ratios-28335.html
### How to Calculate Savings to Investment Ratios Bizfluent
(3 days ago) Divide the total saving over the project's useful life by the cost of the project to obtain the saving-to-investment ratio. For example, if you have to make an investment of \$1,000 for the savings of \$2,500 over five years, the project would have a saving-to-investment ratio of 2.5 (from \$2,500/\$1,000).
https://bizfluent.com/how-8503842-calculate-saving-investment-ratios.html
Category: Invest, Saving
### Savings Goal Calculator Investor.gov
(8 days ago) Test your investing IQ on day trading, mutual funds, margin accounts and more! Veterans: Protect Yourself From Investment Fraud Read our Director’s Take article to stay clear of con artists and their investment scams, and how to invest wisely.
https://www.investor.gov/financial-tools-calculators/calculators/savings-goal-calculator
### Savings vs. Investment Calculator - The Complete
(Just Now) Savings vs. investing calculator showing the difference between saving with monthly compound interest vs. investing with annual compound interest. Stop guessing, start planning.
https://www.completeretirementplanner.com/pages/savings-vs-investment-calculator
Category: Invest, Saving
### Compound Interest Calculator Investor.gov
(3 days ago) Step 3: Interest Rate. Estimated Interest Rate. Your estimated annual interest rate. Interest rate variance range. Range of interest rates (above and below the rate set above) that you desire to see results for.
https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
Category: Investing
### ROI Calculator: Calculate Your Return on Investment Good
(4 days ago) Return on investment (ROI) is presented in percentage terms and is a measurement of the loss or gain that is generated from an investment as a ratio of the total amount that was initially invested. You can use the ROI calculator to compute the ROI in five simple steps:
https://goodcalculators.com/roi-return-on-investment-calculator/
Category: Invest
### Simple Savings to Investment Ratio (SIR) Comparison
(5 days ago) Simple Savings to Investment Ratio (SIR) Comparison Attic Insulation vs. Replacement Window Actual SIR calculations supported by NEAT, MHEA, and other approved audit tools account for the Present Value (PV) of money and fuel escalation rates over the lifetime of the measures to arrive at more accurate savings numbers.
https://www.energy.gov/sites/prod/files/2016/06/f32/Worksheet%20-%20Savings%20to%20Investment%20Ratio.doc
Category: Invest, Saving
### Savings Calculator - SmartAsset
(8 days ago) Use our simple savings calculator to see how quickly your savings will grow. The APY (annual percentage yield, or interest) on your savings account can make a big difference on the future value of your savings. See how the interest earnings on …
https://smartasset.com/checking-account/savings-calculator
Category: Saving
### Savings Rate Calculator: What is Your Savings Rate? - Don
(2 days ago) By following the steps in the calculator, you'll have a normalized rate for both a strict savings rate - that is through your purchases and accumulation of assets - and a regular savings rate, which also includes principal pay-downs of your debt. The calculator will give you results for both gross and net savings.
https://dqydj.com/savings-rate-calculator/
Category: Saving
### Expense Ratio Calculator - For ETFs and Mutual Funds
(5 days ago) Investors pay hundreds of millions of dollars in investment related fees every year. When you calculate the savings on your investments in the expense ratio calculator above, you are looking at relatively small numbers. But consider the impact of higher investment related costs in the entire financial industry…
https://www.begintoinvest.com/expense-ratio-calculator/
Category: Invest, Saving
### Savings Calculator
(4 days ago) Savers can use these free online calculators to figure out how quickly their savings 💵 will grow. In addition to showing the growth of compound interest, this calculator also lets savers account for the impact of income tax on their interest income & adjust the purchasing power of their final savings to account for the impacts of inflation.
https://www.savingscalculator.org/
Category: Saving
### Monthly Deposit Savings Calculator: Calculate Compound
(7 days ago) It can be difficult to put money into savings every month, but it may help you to know what the future value of your deposits will be. This calculator can help you determine the future value of your savings account. First enter your initial investment and the monthly deposit you plan to …
https://www.calculators.org/savings/monthly.php
Category: Invest, Saving
### Savings Rate Calculator How much are you saving
(4 days ago) 25% savings rate: 3 years of work (1-0.25)/0.25. 50% savings rate: 1 year of work (1-0.5)/0.5. 75% savings rate: 1/3 of a year of work (1-0.75)/0.75. During my own financial independence journey my saving rate started at 40% and went as high as 82% some months. That might sound crazy, but it’s easier than you think.
https://millennialmoney.com/calculators/savings-rate-calculator/
Category: Saving
### Savings calculator - MSN Money
(5 days ago) Use our simple, straightforward savings calculator to determine the future value of your savings and see how compound interest can have a dramatic impact.
https://www.msn.com/en-us/money/tools/savingscalculator
Category: Saving
### Savings Calculator Calculate Future Value Old Mutual
(8 days ago) Savings & Investment Calculator Use our savings calculator to work out how much you need to save to reach your goal, how long it will take to save for it and the possible future value of your savings. Save for your goal today. Have a goal in mind? Take a look at some of our great solutions available.
https://www.oldmutual.co.za/personal/tools-and-calculators/savings-calculator/
Category: Invest, Saving
### Savings Calculator With Regular Deposits/Withdrawals
(7 days ago) How to calculate your savings growth. Our simple savings calculator helps you project the growth and future value of your money over time. It uses the compound interest formula, giving options for daily, weekly, monthly, quarterly, half yearly and yearly compounding.If you want to know the compound interval for your savings account or investment, you should be able to …
https://www.thecalculatorsite.com/finance/calculators/savings-calculators.php
Category: Invest, Saving
### SIR - Saving to investment ratio AcronymAttic
(6 days ago) We are also able to measure steady-state efficiency (SSE) and calculate saving-to-investment ratio (SIR). We record the findings and analyze every measurement. DEFINITION: ECIP is a subset of the Defense Agencies Military Construction (MILCON); Projects must have a saving-to-investment ratio greater than.
https://www.acronymattic.com/Saving-to-investment-ratio-(SIR).html
Category: Invest, Saving
### ROI Formula, Calculation, and Examples of Return on Investment
(9 days ago) Return on investment (ROI) is a financial ratio used to calculate the benefit an investor will receive in relation to their investment cost. It is most commonly measured as net income divided by the original capital cost of the investment. The higher the ratio, the greater the benefit earned.
https://corporatefinanceinstitute.com/resources/knowledge/finance/return-on-investment-roi-formula/
Category: Invest
### Budget Calculator
(9 days ago) Detailed free budget calculator to plan personal finances with Debt-to-Income (DTI) ratio and expense breakdown. Also, download our free budget template, learn more about budgeting, experiment with other personal finance calculators, or explore hundreds of calculators covering math, fitness, health, and more.
https://www.calculator.net/budget-calculator.html
Category: Finance
### What does the acronym SIR mean? – Home Energy
(5 days ago) It is the ratio of the savings generated by the weatherization project to the cost of the project. SIR is calculated by dividing the sum of a project’s discounted savings by its investment costs. For a project to be cost effective, weatherization programs generally require the SIR to be greater than 1.
https://home-energy.extension.org/what-does-the-acronym-sir-mean/
Category: Invest, Saving
### Retirement Calculator
(3 days ago) Free calculators that help with retirement planning, taking inflation, social security, life expectancy, and many more factors into account. They can estimate how much to save, how much is withdrawable, and how long savings can last in retirement. Also explore many more calculators covering retirement, finance, math, fitness, health, and numerous other topics.
https://www.calculator.net/retirement-calculator.html
Category: Finance, Saving
### 10 CFR § 436.21 - Savings-to-investment ratio. CFR US
(6 days ago) The numerator of the ratio is the present value of net savings in energy or water and non-fuel or non-water operation and maintenance costs attributable to the proposed energy or water conservation measure. The denominator of the ratio is the present value of the net increase in investment and replacement costs less salvage value attributable
https://www.law.cornell.edu/cfr/text/10/436.21
Category: Invest, Saving
### Savings Calculator - MoneySense
(4 days ago) Your current savings (if any): Expected interest rate (annual, %): i. Take note that annual rate of return or interest rates could vary. (As reference, the average interest rates of Singapore Savings Bonds generally range between 1.5% and 2.5%.) Amount to save each month: 0 …
https://www.moneysense.gov.sg/financial-tools/savings-calculator
Category: Saving
### Investment Calculator: ULIP Calculator & Savings
(6 days ago) The working of investment calculators and savings calculators is based on various factors, one of which is the expected rate of returns. While several investment calculators are available online, you need to pick the right one based on the instrument chosen to know how to calculate return on investment.
https://www.maxlifeinsurance.com/investment-plans/investment-plan-calculator
Category: Invest, Saving
### How To Calculate Your Savings Rate - ChooseFI
(Just Now) Based on these assumptions, a savings rate of 5% will result in 66 years until you have enough money to reach FI. On the other hand, a 25% savings rate shrinks that time to 32 years. A 50% savings rate shortens the time to 17 years. And 75% savings rate slashes your time until FI to just seven years. Listen: How To Calculate Your Savings Rate
https://www.choosefi.com/how-to-calculate-your-savings-rate/
Category: Saving
### Personal Finance Ratios: Savings-to-Income, Debt-to-Income
(6 days ago) Savings include the current value of one’s investments, such as a 401(k), IRAs, brokerage accounts, investment real estate, and the value of any private business interests. The home is excluded as an investment. Debt comprises all debt, including mortgage, student loans, car, and consumer debt.Savings rate refers to the percentage of pre-tax income an investor is …
https://www.mymoneyblog.com/personal-finance-ratios-savings-to-income-debt-to-income-and-savings-rate-to-income.html
Category: Invest, Real estate, Business, Saving
### Investing Vs. Saving: Which Should You Do, When, And How
(8 days ago) Pros of saving. There are plenty of benefits to saving rather than investing. First, the dollar amount you save in a savings account won’t decrease over time as long as you don’t make withdrawals. This is important because some goals need to happen regardless of whether investment prices are up or down.
https://www.moneyunder30.com/investing-vs-saving
Category: Invest, Saving
### Expense Ratio Calculator - Expense Ratio for ETF & Mutual Fund
(6 days ago) Online Calculators > Financial Calculators > Expense Ratio Calculator Expense Ratio Calculator. Expense Ratio Calculator to calculate yearly returns and expense ratio for your ETF or mutual fund investments. It has options to include yearly contributions and expense ratio or fund fees for your investment.
https://online-calculator.org/finance/expense-ratio-calculator.php
Category: Invest
### Mutual Fund Calculator: Find What Fees Will Cost You
(7 days ago) How to use the mutual fund calculator. Enter an initial investment amount. Next, enter an annual contribution if you plan (as experts advise) to make regular new investments. Many mutual funds
https://www.nerdwallet.com/article/investing/mutual-fund-calculator
Category: Invest
### Profitability Index Calculator Good Calculators
(9 days ago) Home » Sales and Investments Calculators » Profitability Index Calculator Profitability Index Calculator The Profitability Index (PI) or profit investment ratio (PIR) is a widely used measure for evaluating viability and profitability of an investment project.
https://goodcalculators.com/profitability-index-calculator/
Category: Invest
### What is the Savings-to-Investment Ratio (SIR)? - Colorado
(7 days ago) What is the Savings-to-Investment Ratio (SIR)? The SIR tells all stakeholders whether a project will be cash-flow-positive. It is calculated by dividing the projected energy cost savings over the finance term by the total installed cost of the project, including the …
https://copace.com/faq/what-is-the-savings-to-investment-ratio-sir/
Category: Invest, Finance, Saving
### Health Savings Account (HSA) Calculator - HSA Bank
(Just Now) Note: The HSA Savings Calculator should only be used as a guide to measure hypothetical HSA tax savings and growth. Amount of money you will pay into your HSA for the year. This includes any contributions received from employers. In 2020, maximum contributions are: \$3,550 single; \$7,100 family. In 2021, maximum contributions are: \$3,600 single
https://www.hsabank.com/hsabank/learning-center/hsa-savings-calculator
Category: Saving
### Real Estate Calculator For Analyzing Investment Property
(1 days ago) The reality is your investment property profits are driven by the math behind the deal, which can be complicated. There are a lot of numbers and ratios to consider. This investment property calculator makes the math easy so you can focus on negotiating and operating your property portfolio, rather than analyzing it.
https://financialmentor.com/calculator/real-estate-calculator
Category: Invest
### Financial Planning Calculators - Groww Calculate Your
(8 days ago) Take your Investment strategy to the next level using Groww's online Financial planning Calculators for different investment methods. Choose the best investment option & achieve your financial goals.
https://groww.in/calculators
Category: Invest
### Investment vs savings Top 4 Useful Differences (With
(5 days ago) On the other hand, when savings are made within banks, the interest amount is taxed when it crosses a certain amount. Inflation and rate of return. Investment has the ability to combat with the inflation rate. Instruments like Bonds, debentures can only give a marginally higher return than inflation.
https://www.educba.com/investment-vs-savings/
Category: Invest, Bank, Saving
### Free Savings Calculator for Excel - Vertex42.com
(9 days ago) CAGR Formula - Explains how to calculate annual growth rate for an investment. Retirement Savings Calculator - www.vertex42.com - Similar to the simple savings calculator, but specifically related to retirement (graphed by age) and less flexibility in making deposits. Savings Bond Calculator at treasurydirect.gov - Includes the effect of
https://www.vertex42.com/Calculators/savings-interest-calculator.html
Category: Invest, Saving
### Discount Calculator Percentage Discount Calculator
(1 days ago) Our calculator even works with fractions of percentages. If you see an item with an original price of \$24.99, and the discount is 17.5 percent, you can plug all of those numbers into our calculator and easily find out that the new price is \$20.62 with a discount of \$4.37.
https://www.calculatorpro.com/calculator/discount-calculator/
Category: Investing
### Free Online Calculators Calculators CalculatorPro.com
(Just Now) Financial Calculators. Our free online financial calculators can do everything from help you to calculate your net worth to calculate the debt to equity ratio of a business or individual to even help you to calculate the cost of your mortgage points. Make your financial decisions with facts. Get hard and fast concrete numbers for every
https://www.calculatorpro.com/
### Evaluate the Economics of Energy Efficiency Projects
(9 days ago) This calculator uses the prevailing price/earnings ratio to estimate the market value of increased earnings that can result from increased energy efficiency. It uses corporate data you enter to calculate your company's potential financial returns. Who It’s Designed For: Publicly- and privately-held companies. Use the Financial Value Calculator.
https://www.energystar.gov/buildings/save_energy_commercial_buildings/economics_efficiency_projects
Category: Investing
### Investment Fees Calculator – Ativa Interactive Corp.
(5 days ago) Investment Fees Calculator Calculatrice français . Share this Facebook Google+ Twitter Pinterest LinkedIn StumbleUpon Reddit Email. Tale of Two RRSPs Calculator. Planning Toolkit 10 Changes. Search for: FreshPlan Online Featured Calculators. Magic of Compounding.
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### How To Calculate Your Debt-to-Income Ratio
(Just Now) Calculate Your Debt-to-Income Ratio. To find out what your debt-to-income ratio is, use a debt-to-income ratio calculator or simply …
https://www.msn.com/en-us/money/personalfinance/economy-explained-how-to-calculate-your-debt-to-income-ratio/ar-BB1ddnvL
Category: Investing
Filter Type: | 4,384 | 19,832 | {"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-2021-49 | latest | en | 0.829126 |
https://forum.allaboutcircuits.com/threads/wheatstone-bridge.14508/ | 1,563,874,194,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195529175.83/warc/CC-MAIN-20190723085031-20190723111031-00106.warc.gz | 392,853,964 | 20,297 | # Wheatstone bridge
Discussion in 'Homework Help' started by hitmen, Sep 22, 2008.
Not open for further replies.
1. ### hitmen Thread Starter Active Member
Sep 21, 2008
159
0
I have a qn about the wheatstone bridge. If the two ends are parallel, then where does the voltage flow? Is it in a forever loop?
Also can anyone provide me with a link on how to calculate the pd across each resistor. I know how to simplify the circuit blindly. However, I do not know how to calculate their respective pdf.
Thanks for helping.
Last edited: Sep 24, 2008
2. ### mik3 Senior Member
Feb 4, 2008
4,846
70
The voltage does not flow, the one that flows is the current through the resistors due to the applied voltage.
By two ends you mean the two branches of series resistors?
The power dissipation for a resistor equals:
P=V*I=(V^2)/R=(I^2)*R
where
P=power dissipation
V=voltage across the resistor
I=current through the resistor
R=resistance of the resistor
You can choose on of the three above equations!
3. ### studiot AAC Fanatic!
Nov 9, 2007
5,003
522
The whole point of a wheatstone bridge is that there is no current through the detector.
This occurs because the potential (voltage) is the same at both nodes connected to it.
So the signal, ac or dc, is applied across two of the four corners (nodes) and the output (equals zero) is taken across the other two.
This configuration is called a bridge circuit in general terms. In general terms each of four sides has an impedance or an active element.
Specifically for a wheatstone bridge there are only resistors, and the signal is dc.
Thus if the signal is applied across (r1+r3) in parallel with (r2+r4) and the detector is across the junction of (r1,r3) and the junction of (r2,r4):
the voltage at the junction of r1 and r3 equals the voltage at the junction of r2 and r4
This voltage = Vin x r1/(r1+r3) but it also equals Vin x r2/(r2+r4)
This is the condition for balance.
4. ### hitmen Thread Starter Active Member
Sep 21, 2008
159
0
I guess i should upload a sample of the question I dont understand. The example has 2 parts, both of which I do not understand. Firstly, In which direction does the current from the 156V flow? Also, how do I know which resistor is in parallel or series with another.
I will gladly appreciate anyone explaining the concepts.
The circuit looks like a very complicated Wheatstone bridge.
In part 2 of the question, my lecturer gives only 2 loop equation. Isnt a three one needed for current flowing through the source?
Also, is there a better way of uploading 1 PAGE from a PDF instead of cutting and pasting the image onto paint?
File size:
60.6 KB
Views:
120
File size:
56.2 KB
Views:
111
5. ### silvrstring Active Member
Mar 27, 2008
159
0
hitmen,
You do need to use two equations because you have two variables----I1 and I2. Two loops, two equations. You don't need a 3rd eq for the source. It is accounted for in the loop equations.
Your first equation is off. It should read (I1 - I2)*4 + (I1)*2 + (I1)*4 - 52 = 0
Your second equation (loop) will be (I2 - I1)*4 + 52 + (I2)*4 + (I2)*4 = 0.
Simplify them and solve for each loop current, then you can find your E(th) accross those two 4ohms resistors closest to the R(L).
For part c), the maximum power transfer theorem proves that the greatest amt of power transferable to R(L) will happen when R(L) is equal to R(th). So I think you need to find the R(th) before you can go further. You will need to do a delta-wye conversion so they will be in a more workable form. Then you will easily be able to determine the R(th).
If there is an easier way, let me know. But this will work.
6. ### hitmen Thread Starter Active Member
Sep 21, 2008
159
0
I dont understand part of of how the Rth is obtained. The answers were provided by the professor.
You said that the third loop linking to the source is "taken care of". how is that so?
7. ### The Electrician AAC Fanatic!
Oct 9, 2007
2,701
490
Replace the 156 volt source with a short; connect a 1 volt source to the A-B terminals. Solve for the current drawn from the 1 volt source.
I think if you choose carefully, 2 loops will be enough.
Last edited: Oct 7, 2008
8. ### kai88 New Member
Jan 26, 2010
10
0
Since,Output voltage = Vin x r1/(r1+r3) but it also equals Vin x r2/(r2+r4),
So if i change the Input voltage(due to instability) ,will it affect output voltage(Indicator)?
I juz wan to know whether wheatstone bridge is power-source dependent or power source independent(like ratiometer type)?
9. ### kai88 New Member
Jan 26, 2010
10
0
So if i change the Input voltage(due to instability) ,will it affect output voltage(Indicator)?
I juz wan to know whether wheatstone bridge is power-source dependent or power source independent(like ratiometer type)?
10. ### beenthere Retired Moderator
Apr 20, 2004
15,808
295
You are hijacking an old thread, and have another thread open on this subject elsewhere. | 1,315 | 4,935 | {"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} | 3.78125 | 4 | CC-MAIN-2019-30 | latest | en | 0.935541 |
https://community.qlik.com/t5/App-Development/Adding-two-values-with-respect-to-date-conditions-at-backed/td-p/1738764 | 1,628,154,414,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046155458.35/warc/CC-MAIN-20210805063730-20210805093730-00489.warc.gz | 202,400,110 | 54,238 | # App Development
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Creator II
## Adding two values with respect to date conditions at backed script
Hello everyone,
I am trying to achieve the below:-
If("Calendar Year" <= Year(today()), Actual) + if("Calendar Year" >=year(today()), RB) as Hours
Is this correct to calculate the dimension at backend.
I want to create a dimension "Hours" using this conditon
Hours = “actual” hours when Year < Today + “RB” hours when Year >= Today
Pleas help
Labels (3)
• ### @sunny_talwar
2 Solutions
Accepted Solutions
Assuming that you have all column in same table then try below in script You can then use the hour as a dimension
If("Calendar Year" <= Year(today()), Actual, RB) as Hours
MVP
Not entirely sure, but may be this
``````RangeSum(
If("Calendar Year" < Year(Today()), Actual),
If("Calendar Year" > Year(Today()), RB)
) as Hours,``````
But what happens when Calendar year = Year(Today())? Right now both you are if statements don't include that condition. You might want to change one of the if statement logic to include =, either >= or <= depending on the value needed for current year
9 Replies
Master II
can you share a sample data and if possible the expected output ?
Regards,
Taoufiq ZARRA
"Please LIKE posts and "Accept as Solution" if the provided solution is helpful "
(you can mark up to 3 "solutions") 😉
You an create a Flag in script and then you can use it to create the measure
if("Calendar Year" <= Year(today()), 1,2) as Year_Flag
FROM Source;
then you can use below measure in chart
=sum({<Year_Flag={1}>}Actual)+sum({<Year_Flag={2}>}RB)
Creator II
Author
Actual,
If("Calendar Year" < Year(today()), Actual) + if("Calendar Year" > year(today()), RB) as Hours,
CB,
"CB - Unit",
RB
From....
Creator II
Author
Mnay thanks Kush for your response.
But i have to create a dimension as "Hours" using this calculation at the backend. Could you please help me on that.
Many thanks again
Assuming that you have all column in same table then try below in script You can then use the hour as a dimension
If("Calendar Year" <= Year(today()), Actual, RB) as Hours
Creator II
Author
Hello Kush , i wish to achieve this:
Hours = “actual” hours when Yearmonth < Today + “RB” hours when Yearmonth >= Today
We have to add them at the backend and display them as "Hours" in dimension.
Thanks
Creator II
Author
Can anyone please help on this as it is very critical for me and i tried everything but not working.
It's really not clear what you are trying to do. did you check my last response?
MVP
Not entirely sure, but may be this
``````RangeSum(
If("Calendar Year" < Year(Today()), Actual),
If("Calendar Year" > Year(Today()), RB)
) as Hours,``````
But what happens when Calendar year = Year(Today())? Right now both you are if statements don't include that condition. You might want to change one of the if statement logic to include =, either >= or <= depending on the value needed for current year
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# Complex arithmetic resources
Show me all resources applicable to
### 3GP Mobile Phone (8)
Adding and Subtracting Complex Numbers
This mobile phone video explains how complex numbers can be added or subtracted. There is an accompanying leaflet. Sigma resource Unit 4. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.
Division of complex numbers
This mobile phone video explains how to divide complex numbers. Sigma resource Unit 7. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.
Imaginary numbers and quadratic equations
This mobile phone video shows how the imaginary number i can be used in the solution of some quadratic equations. Sigma resource Unit 2. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.
Motivating the study of complex numbers
This mobile phone download introduces complex numbers by explaining how it is useful to be able to formally write down the square root of a negative number. Sigma resource Unit 1. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.
Multiplying complex numbers
This mobile phone video explains how complex numbers can be multiplied together. There is an accompanying leaflet. Sigma resource Unit 5. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.
The complex conjugate
This mobile phone video explains what is meant by the complex conjugate of a complex number. Sigma resource Unit 6. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.
The polar form of a complex number
This mobile phone video explains what is meant by the polar form of a complex number. Sigma resource Unit 10. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.
What is a complex number
This mobile phone video explains what is meant by a complex number, and how to find its real and imaginary parts. Sigma resource Unit 3. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by mathcentre.
Website design by Pink Mayhem, Leicester | 509 | 2,638 | {"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-2020-10 | latest | en | 0.85517 |
http://pcp.vub.ac.be/ASC/INFORM_THEOR.html | 1,718,240,323,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861319.37/warc/CC-MAIN-20240612234213-20240613024213-00840.warc.gz | 22,926,606 | 2,305 | PRINCIPIA CYBERNETICA WEB - ©
Parent Node(s):
# INFORMATION THEORY
(or statistical communication theory) a calculus or variation, variability and variance initially developed by Shannon, to separate noise from information carrying signals, now used to trace the flow of information in complex systems, to decompose a system into independent (see independence) or semi-independent sub-systemS, to evaluate the efficiency of communication channels and of various communication codes (see redundancy, noise, equivocation) and to compare information needs with the capacities of existing information processors (see computer, bremermann's limit), etc. The basic quantity this calculus analyses (see analysis) is the total amount of statistical entropy given data contain about an observed system. The calculus provides an algebra for decomposing and thus accounting for this entropy in numerous ways. E.g. the quantity of entropy in an observed system equals the sum of the entropies in all of its separate parts minus that amount of information transmitted within the system. The latter quantity is the amount of entropy in a system not explainable from its parts and an expression of the communication between these parts. This formula is another example of the cybernetic analysis of systems, according to which any whole system is accounted for or defined in terms of a set of components and its organization. The total amount of information transmitted in a quantitative analogue to and hence can be thought of as a measure of a system's structure. Information theory has provided numerous theorems and algebraical identities with which observed systems may be approached, e.g., the law of requisite variety, the TENTH theorem of information theory (Krippendorff)
* Next * Previous * Index * Search * Help
URL= http://cleamc11.vub.ac.be/ASC/INFORM_THEOR.html | 364 | 1,864 | {"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-2024-26 | latest | en | 0.888339 |
https://secondsminutes.com/109292-minutes-in-seconds | 1,685,276,718,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224643784.62/warc/CC-MAIN-20230528114832-20230528144832-00277.warc.gz | 570,704,662 | 6,661 | # 109292 minutes in seconds
## Result
109292 minutes equals 6557520 seconds
## Conversion formula
Multiply the amount of minutes by the conversion factor to get the result in seconds:
109292 min × 60 = 6557520 s
## How to convert 109292 minutes to seconds?
The conversion factor from minutes to seconds is 60, which means that 1 minutes is equal to 60 seconds:
1 min = 60 s
To convert 109292 minutes into seconds we have to multiply 109292 by the conversion factor in order to get the amount from minutes to seconds. We can also form a proportion to calculate the result:
1 min → 60 s
109292 min → T(s)
Solve the above proportion to obtain the time T in seconds:
T(s) = 109292 min × 60 s
T(s) = 6557520 s
The final result is:
109292 min → 6557520 s
We conclude that 109292 minutes is equivalent to 6557520 seconds:
109292 minutes = 6557520 seconds
## Result approximation:
For practical purposes we can round our final result to an approximate numerical value. In this case one hundred nine thousand two hundred ninety-two minutes is approximately six million five hundred fifty-seven thousand five hundred twenty seconds:
109292 minutes ≅ 6557520 seconds
## Conversion table
For quick reference purposes, below is the minutes to seconds conversion table:
minutes (min) seconds (s)
109293 minutes 6557580 seconds
109294 minutes 6557640 seconds
109295 minutes 6557700 seconds
109296 minutes 6557760 seconds
109297 minutes 6557820 seconds
109298 minutes 6557880 seconds
109299 minutes 6557940 seconds
109300 minutes 6558000 seconds
109301 minutes 6558060 seconds
109302 minutes 6558120 seconds
## Units definitions
The units involved in this conversion are minutes and seconds. This is how they are defined:
### Minutes
The minute is a unit of time or of angle. As a unit of time, the minute (symbol: min) is equal to 1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to 1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time. In contrast to the hour, the minute (and the second) does not have a clear historical background. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of "precision" timepieces (mechanical and water clocks). However, no consistent records of the origin for the division as 1⁄60 part of the hour (and the second 1⁄60 of the minute) have ever been found, despite many speculations.
### Seconds
The second (symbol: s) (abbreviated s or sec) is the base unit of time in the International System of Units (SI). It is qualitatively defined as the second division of the hour by sixty, the first division by sixty being the minute. The SI definition of second is "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom". Seconds may be measured using a mechanical, electrical or an atomic clock. SI prefixes are combined with the word second to denote subdivisions of the second, e.g., the millisecond (one thousandth of a second), the microsecond (one millionth of a second), and the nanosecond (one billionth of a second). Though SI prefixes may also be used to form multiples of the second such as kilosecond (one thousand seconds), such units are rarely used in practice. The more common larger non-SI units of time are not formed by powers of ten; instead, the second is multiplied by 60 to form a minute, which is multiplied by 60 to form an hour, which is multiplied by 24 to form a day. The second is also the base unit of time in other systems of measurement: the centimetre–gram–second, metre–kilogram–second, metre–tonne–second, and foot–pound–second systems of units. | 1,034 | 4,321 | {"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} | 4.15625 | 4 | CC-MAIN-2023-23 | latest | en | 0.784602 |
https://stackoverflow.com/questions/4019110/raphael-position/9809761 | 1,721,794,271,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518154.91/warc/CC-MAIN-20240724014956-20240724044956-00239.warc.gz | 470,881,553 | 44,156 | # Raphael Position
How can I get the position of an object in Raphael? I can get the size using getBBox(), but there appears to be no way to get the position?
• The problem may first be a definition of "position" of an object. If you mean the "gravity center" of the object, that must currently be computed by application code as it depends on the kind of object. Right now, it seems there is no library code to get the center of common shapes. For arbitrary shapes, I guess it may need be defined at the application level anyway, and the bounding box allows to compute it. If by position you mean the classical top-left corner position, the bounding box's (x, y) attributes is the result, as @b_dubb mentioned. Commented Jul 25, 2012 at 7:05
getBBox() should give you position as well as x and y properties.
``````var bbox = el.getBBox();
``````
• thanks but it would be great if you could add those tips in the documentation of raphaeljs. Commented Feb 25, 2011 at 9:50
• It is in the Raphael documentation Commented Apr 18, 2012 at 11:19
getBBox() returns an object with 5 properties. they are:
1. x
2. y
3. width
4. height
5. toString()
if you set getBBox( false ) it will return coordinate data for the object's position AFTER a transformation. set it to getBBox( true ) to return coordinates for the object prior to transformation
use like this ...
``````paper.Raphael(10,10,300,300);
circle.paper( 30, 55, 15 );
var circleBBox = circle.getBBox( false );
``````
edit: just downloaded R 2.1 and i believe it has added x2 and y2 to the properties returned by getBBox()
Depending on what kind of shape it is, the documentation seems to say it can be accessed using the `.attr()` function. So, if it's a circle...
``````var x = myCircle.attr('cx'); //cx is the center-x-coordinate of the circle
var y = myCircle.attr('cy'); //same, for y
var r = myCircle.attr('r'); //Radius of circle.
``````
A square would have `attr`s of x, y, width, height. Check the documentation for more info.
• el.getBBox is the correct approach. Please see Dmitry's answer. Commented Oct 27, 2010 at 7:47
you may also access the x and y values this way:
``````var x = myCircle.attrs.x;
var y = myCircle.attrs.y
``````
attributes x, y are those within the set. The issue here is that if the set gets translated somewhere else, the x and y given in by .getBBOx() do not account for the translation.
Raphael.transformPath(path, transform) can help by applying the same transforms that the set has...
to translate that point you can:
``````tp = Raphael.transformPath("M"+x+","+y, set.attr('transform'))
x = tp[0][1]
y = tp[0][2]
`````` | 701 | 2,629 | {"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-2024-30 | latest | en | 0.888569 |
https://www.calculatorbit.com/en/temperature/1-megakelvin-to-decikelvin | 1,679,562,371,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945030.59/warc/CC-MAIN-20230323065609-20230323095609-00021.warc.gz | 777,206,099 | 6,910 | # Convert 1 Megakelvin to Decikelvin
Result:
1 Megakelvin = 10000000 Decikelvin (dK)
Rounded: ( Nearest 4 digits)
1 Megakelvin is 10000000 Decikelvin (dK)
1 Megakelvin is 999726.85C
## megakelvin:
Megakelvin (MK) is a unit of measurement used to describe extremely high temperatures. The prefix "mega" denotes one million, so one megakelvin is equal to one million Kelvin. The Kelvin scale is an absolute temperature scale that is used by scientists to measure extremely high temperatures. The highest temperature ever recorded on Earth is approximately 58 MK, which was achieved during a nuclear test in 1961. Megakelvin is also used to describe the temperatures found in the Sun's core, which are thought to be around 15 MK. While the megakelvin scale is not commonly used in everyday life, it is a valuable tool for scientists who study extremely high temperatures.
## decikelvin:
Decikelvin (dK) is a unit of measurement for extremely low temperatures. It is defined as one-tenth of a kelvin, or 0.001 K. The decikelvin is used primarily in scientific research, especially in the fields of cryogenics and astrophysics. Its symbol is dK or sometimes dΚ. When describing extremely low temperatures, it is often more convenient to use smaller units like the decikelvin rather than the kelvin. For example, the temperature ofouter space is typically about 2.7 K, which can be written as 2700 dK. Similarly, the temperature of interstellar gas clouds can be expressed as 10 dK (-263.15 °C). While the decikelvin is not an SI unit, it is recognized by the International Union of Pure and Applied Chemistry (IUPAC).
## Megakelvin to Decikelvin Calculations Table
Now by following above explained formulas we can prepare a Megakelvin to Decikelvin Chart.
Megakelvin (MK) Decikelvin (dK)
1 10000000
2 20000000.00000001
3 30000000.00000001
4 40000000.00000001
5 50000000.00000001
6 60000000.00000001
Nearest 4 digits
## Convert from Megakelvin to other units
Here are some quick links to convert 1 Megakelvin to other temperature units.
## Convert to Megakelvin from other units
Here are some quick links to convert other temperature units to Megakelvin.
## FAQs About Megakelvin and Decikelvin
Converting from one Megakelvin to Decikelvin or Decikelvin to Megakelvin sometimes gets confusing. | 603 | 2,306 | {"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-2023-14 | latest | en | 0.879167 |
https://brainly.in/question/108128 | 1,485,227,390,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560283689.98/warc/CC-MAIN-20170116095123-00512-ip-10-171-10-70.ec2.internal.warc.gz | 793,384,040 | 10,418 | # A plane left 30 min later than the scheduled time and in order to reach the destination 1500km away in time it has to increase the speed by 250km/h from the usual speed. find its usual speed
1
2015-05-09T22:01:56+05:30
### This Is a Certified Answer
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Given ;-
⇒ Time taken by the plane after the scheduled time = 30 min
⇒ Total distance = 1500 km
⇒Increased. speed of aeroplane from the usual speed = 250 km / hr
To find :-
⇒Usual speed of aeroplane = ?
Sol ;-
⇒We dont know the usual speed so let us take usual speed as x.
Usual speed = x
⇒Total distance travelled by aeroplane = 1500 km
Speed of aeroplane -
Speed = Distance / Time = (1500 / x) Hrs { As we dont know time taken so let us take it as x }
⇒ {case - 1 }
⇒Total .Time taken by the aeroplane to travel = ( x - 1/2 ) Hrs
⇒ Distance travelled by aeroplane = 1500 km
Therefore we get the speed as ,
Speed = Distance / Time
= 1500 / (x - 1/2) Hrs [ Case - 2 ]
Total. increased speed by the aeroplane is 250 km / hr .
⇒ Case - 1 - Case - 2 = Increased speed
⇒ [ 1500 / ( x - 1 /2 ] - [ 1500 / x ] = 250
⇒ 1 / ( 2 x² - x ) = 1/6
⇒ 2x² - x = 6
⇒ ( x - 2 ) ( 2 x + 3 ) = 0
Therefore we get x as
⇒ x = 2
So, the usual time taken by aeroplane = 2 hrs
Usual speed = Total distance / Usual time taken
= 1500 / 2
⇒ 7 5 0 km / hr is the answer. | 645 | 2,067 | {"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-2017-04 | latest | en | 0.459279 |
http://poj.org/problem?id=3417 | 1,477,628,491,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988721555.54/warc/CC-MAIN-20161020183841-00041-ip-10-171-6-4.ec2.internal.warc.gz | 199,992,946 | 3,674 | Online JudgeProblem SetAuthorsOnline ContestsUser
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ACM-ICPC亚洲区预选赛(北京赛区)游戏对抗邀请赛正在报名中
Language:
Network
Time Limit: 2000MS Memory Limit: 65536K Total Submissions: 4986 Accepted: 1430
Description
Yixght is a manager of the company called SzqNetwork(SN). Now she's very worried because she has just received a bad news which denotes that DxtNetwork(DN), the SN's business rival, intents to attack the network of SN. More unfortunately, the original network of SN is so weak that we can just treat it as a tree. Formally, there are N nodes in SN's network, N-1 bidirectional channels to connect the nodes, and there always exists a route from any node to another. In order to protect the network from the attack, Yixght builds M new bidirectional channels between some of the nodes.
As the DN's best hacker, you can exactly destory two channels, one in the original network and the other among the M new channels. Now your higher-up wants to know how many ways you can divide the network of SN into at least two parts.
Input
The first line of the input file contains two integers: N (1 ≤ N ≤ 100 000), M (1 ≤ M ≤ 100 000) — the number of the nodes and the number of the new channels.
Following N-1 lines represent the channels in the original network of SN, each pair (a,b) denote that there is a channel between node a and node b.
Following M lines represent the new channels in the network, each pair (a,b) denote that a new channel between node a and node b is added to the network of SN.
Output
Output a single integer — the number of ways to divide the network into at least two parts.
Sample Input
```4 1
1 2
2 3
1 4
3 4
```
Sample Output
`3`
Source
[Submit] [Go Back] [Status] [Discuss] | 492 | 1,892 | {"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-2016-44 | longest | en | 0.905196 |
https://www.daniweb.com/programming/software-development/threads/114677/eliminating-some-random-particle-in-an-animation | 1,540,018,435,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583512592.60/warc/CC-MAIN-20181020055317-20181020080817-00158.warc.gz | 901,446,620 | 11,981 | ## nish88
hi everyone i'm trying to make an animation and at the end i am getting a rectangle by using lots of small rectangle. it is not so attractive.
what i want is that while the animation is being performed, some of the small rectangles that i am using are deleted randomly. so that its does not get the form of a concrete rectangle.
can anyone help me to perform this task.
thank you....
here are my codes:
from Tkinter import *
import array
import time
A=[]
B=[]
C=[]
D=[]
E=[]
F=[]
G=[]
H=[]
I=[]
J=[]
frame=Tkinter.Frame()
frame.pack()
canvas =Tkinter.Canvas(frame,bg = 'white',width=500, height=500)
canvas.pack()
def calculate(a,b):
b1=b
a1=a
e1=a
f1=b
j1=b
i1=a
for j in range(50):
for i in range(10):
B.append(b)
C.append(a1)
E.append(e1)
J.append(j1)
#print len(A)
b=B[i]+4
a1=C[i]-4
e1=E[i]+4
j1=J[i]-4
x1=a+2
y1=b+2
a11=a1+2
b11=b1+2
e11=e1+2
f11=f1+2
i11=i1+2
j11=j1+2
time.sleep(0.3)
canvas.create_rectangle(a,b,x1,y1,fill="red",outline="red")
canvas.create_rectangle(a1,b1,a11,b11,fill="red",outline="red")
canvas.create_rectangle(e1,f1,e11,f11,fill="red",outline="red")
canvas.create_rectangle(i1,j1,i11,j11,fill="red",outline="red")
canvas.update()
a = a+4
b1=b1+4
f1=f1-4
i1=i1-4
A.append(a)
D.append(b1)
F.append(f1)
I.append(i1)
#canvas.create_rectangle(200,300,210,310,fill="black")
def animate():
c=200
b=300
canvas.create_oval(200,300,210,310,fill="violet", outline="violet")
calculate(c,b)
button=Tkinter.Button(frame,fg="blue", text="ANIMATE", activebackground='red',font=('verdana', 10, 'bold'),command=animate).pack(padx =50,side = LEFT)
mainloop()
## jrcagle 77
I watched it for a while and didn't see any rectangles being deleted. But you're right; the algorithm doesn't make a rectangle shape.
So what's the issue, exactly?
Jeff
## nish88
ya you are right the piece of codes for deleting rectangle is not there.
actually i am not able to write the deleting section that why i am asking someone if he or she can help me in doing it....
can anyone?????? | 643 | 2,018 | {"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} | 2.625 | 3 | CC-MAIN-2018-43 | latest | en | 0.69417 |
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