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http://fer3.com/arc/m2.aspx/Fuller-Cylindrical-Slide-Rules-Morris-nov-2013-g25471 | 1,656,222,745,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103037089.4/warc/CC-MAIN-20220626040948-20220626070948-00358.warc.gz | 18,745,530 | 5,964 | NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
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Fuller Cylindrical Slide Rules
Date: 2013 Nov 7, 14:32 -0500
Hello Francis
What trigonometric scales does it have? To what resolution can you obtain, say, the sin(45)? That is, how many decimal digits are obtained?
Since you obviously have a Fuller, would you mind reducing an observation, showing the intermediate steps for the enjoyment of the crowd? This will give a sense of the instrument in use.
On Nov 7, 2013 5:48 AM, "Francis Upchurch" <francisupchurch@gmail.com> wrote:
I've been following this fascinating string with interest. Cannot add much to the wisdom already shared, but Lu also asked about slide rules? I find the cylindrical Bygrave and Fuller, with very long spiral scales are usually accurate to 1-2' for sight reduction. the Bygrave is very quick, the Fuller,using the sine/cos formula takes twice as long, so I tend to use the Bygrave.The Fuller dates from early 1900s but I've never found evidence of use in navigation.Chichester famously used a Bygrave in his 1931 solo flight across the Tasman sea.Interestingly, he taught astronav to the RAF during the war and used the Air Almanac, never mentioning the Bygrave, which was clearly never standard RAF issue.However,the top "Pathfinder" navigator AVM Bennett apparently used one until the end of the war in preference to the Air Almanac. I find it much quicker and more fun than tables.I use the Fuller to clear my lunars, great fun!(but I generally check on Frank's site later.)
I notice Frank briefly mentioned Martelli's tables? I had never heard of them, but by amazing coincidence have just been reading the book by one of my heroes Frank Pidgeon, Islander 1922 circumnavigation. On page 12 he recommends the Martelli tables as his favoured method to reduce his time sights. However, by page 17, he says that going below to do the maths made him sea sick, so from then on, stayed on deck and guessed a rough LAN time for longitude from his noon meridean sight! and so on , round the world!
Can send details of slide rules on request. Best wishes, Francis Upchurch
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Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd) | 709 | 3,119 | {"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-2022-27 | latest | en | 0.947857 |
https://www.slideserve.com/harris/geometry-grab-your-clicker-and-get-ready-for-the-warm-up | 1,547,889,358,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583662863.53/warc/CC-MAIN-20190119074836-20190119100836-00629.warc.gz | 940,015,728 | 14,838 | 1 / 16
# Geometry Grab your clicker and get ready for the warm-up - PowerPoint PPT Presentation
Geometry Grab your clicker and get ready for the warm-up. The distance from a point to a line can be called the “ ” distance. P arallel Vertical Perpendicular Circumcenter Bisector. A point on a perpendicular bisector is from the two endpoints of the bisected segment. Equidistant
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Presentation Transcript
The distance from a point to a line can be called the “ ” distance
• Parallel
• Vertical
• Perpendicular
• Circumcenter
• Bisector
A point on a perpendicular bisector is from the two endpoints of the bisected segment
• Equidistant
• Perpendicular
• Corresponding
• Centroid
• Midpoint
• Angles
• Vertices
• Right Angles
• Sides
• Incenters
The point of concurrency for the perpendicular bisectors of a triangle is called the
• Incenter
• Orthocenter
• Midpoint
• Circumcenter
• Centroid
• Midsegment
The point of concurrency for the angular bisectors of a triangle is called the
• Incenter
• Orthocenter
• Midpoint
• Circumcenter
• Centroid
• Midsegment
• Circumcenter
• Angle
• Perpendicular
• Centroid
• Side
• Midpoint
• Orthocenter
• Incenter
• Orthocenter
• Midpoint
• Circumcenter
• Centroid
• Midsegment
An altitude goes from a vertex and is to the opposite side
• Circumcenter
• Angle
• Perpendicular
• Centroid
• Side
• Midpoint
• Orthocenter
• Incenter
• Orthocenter
• Midpoint
• Circumcenter
• Centroid
• Midsegment
The circumcenter of a triangle is equidistant from the
• Vertices
• Incenter
• Centroid
• Perpendicular
• Sides
The incenterof a triangle is equidistant from the
• Vertices
• Incenter
• Centroid
• Perpendicular
• Sides
The Pythagorean Theorem for this right triangle would state:
• a2 + b2 = c2
• f2 + g2 + h2 = 180
• f2 + g2 = h2
• h2 + g2 = f
• g2 + h2 = 90
• g2 + h2 = f2
• g2 – h2 = f2
Given C is the centroidand that CZ = 3, determine CJ
• 9
• 3
• 6
• 1.5
• 4.5
• Not possible
• None of the above
Given C is the centroidand that YI = 15, determine YC
• 9
• 12
• 3
• 6
• 1.5
• 4.5
• 7.5
• 8
• Not possible
• None of the above | 797 | 2,621 | {"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-2019-04 | latest | en | 0.768958 |
https://www.gradesaver.com/textbooks/math/calculus/calculus-8th-edition/appendix-b-coordinate-geometry-and-lines-b-exercises-page-a15/35 | 1,539,706,520,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583510853.25/warc/CC-MAIN-20181016155643-20181016181143-00434.warc.gz | 939,863,561 | 12,141 | ## Calculus 8th Edition
Published by Cengage
# Appendix B - Coordinate Geometry and Lines - B Exercises - Page A15: 35
#### Answer
$y= \frac52x + \frac12$
#### Work Step by Step
We are told to find the equation of the line that satisfies the following conditions: Passes through the point (-1,-2), and perpendicular to the line $2x + 5y +8 = 0$ To find the equation of the line we must find the slope then write it in the form:$y =mx + b$ First solve the given equation for $y$: $2x + 5y + 8 = 0$ $5y = -2x - 8$ $y = -\frac{2}{5}x - \frac{8}{5}$ Since the lines are perpendicular the slope is the negative reciprocal, so the slope of our equation is $m = \frac52$ $y - (-2) = \frac52(x-(-1)$ $y = \frac52x + \frac52 - 2$ $y= \frac52x + \frac12$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 278 | 911 | {"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} | 4.46875 | 4 | CC-MAIN-2018-43 | longest | en | 0.860923 |
https://book.pythontips.com/en/latest/set_-_data_structure.html | 1,623,727,009,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487616657.20/warc/CC-MAIN-20210615022806-20210615052806-00343.warc.gz | 160,695,015 | 4,921 | # 5. `set` Data StructureΒΆ
`set` is a really useful data structure. `sets` behave mostly like lists with the distinction that they can not contain duplicate values. It is really useful in a lot of cases. For instance you might want to check whether there are duplicates in a list or not. You have two options. The first one involves using a `for` loop. Something like this:
```some_list = ['a', 'b', 'c', 'b', 'd', 'm', 'n', 'n']
duplicates = []
for value in some_list:
if some_list.count(value) > 1:
if value not in duplicates:
duplicates.append(value)
print(duplicates)
# Output: ['b', 'n']
```
But there is a simpler and more elegant solution involving `sets`. You can simply do something like this:
```some_list = ['a', 'b', 'c', 'b', 'd', 'm', 'n', 'n']
duplicates = set([x for x in some_list if some_list.count(x) > 1])
print(duplicates)
# Output: set(['b', 'n'])
```
Sets also have a few other methods. Below are some of them.
Intersection
You can intersect two sets. For instance:
```valid = set(['yellow', 'red', 'blue', 'green', 'black'])
input_set = set(['red', 'brown'])
print(input_set.intersection(valid))
# Output: set(['red'])
```
Difference
You can find the invalid values in the above example using the difference method. For example:
```valid = set(['yellow', 'red', 'blue', 'green', 'black'])
input_set = set(['red', 'brown'])
print(input_set.difference(valid))
# Output: set(['brown'])
```
You can also create sets using the new notation:
```a_set = {'red', 'blue', 'green'}
print(type(a_set))
# Output: <type 'set'>
```
There are a few other methods as well. I would recommend visiting the official documentation and giving it a quick read. | 443 | 1,679 | {"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-2021-25 | longest | en | 0.650096 |
https://www.infinity-cdma.com/p/154741282157317/ | 1,555,963,753,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578582584.59/warc/CC-MAIN-20190422195208-20190422221208-00441.warc.gz | 718,318,038 | 5,252 | ### Series Circuit Diagram
Series Circuit Diagram
## Magnetic Level Gauge Working Principle Animation
Specifying Components. Typically the true battery type and bulb kind would be specified in a part list that accompanies the circuit diagram. More info about the battery and bulb type might also be contained in the circuit as text. As an example, the battery might be specified as a 12.8V 90Ah Lithium battery, plus even a 9V PM9 battery. The light bulb might be defined as a 12V 5W incandescent bulb, or 9V 0.5W flashlight bulb.
Following a four section introduction, the very first tutorial at the electronics class indicates the circuit design of a simple LED and resistor circuit and also the way to build it upon breadboard.
Parallel Circuit Example In the circuit below, two light bulbs are connected in parallel to a battery power supply. It can be noted that the best terminals of both light bulbs are all connected together and into the positive terminal of battery. We understand this because the three terminals or link points have a node where they intersect.
The following are overall circuit design principles.
• Wires or lines from circuit diagrams are often vertical or horizontal. Sometimes a diagonal line might be used which is put in 45 degrees.
• Component symbols at a circuit diagram are often placed vertically or horizontally. On very rare occasions a component could be put in 45 degrees, but just for an excellent reason.
• Circuit diagrams are drawn as simply and neatly as possible. This usually means that the physical execution of the circuit might seem different to the circuit diagram, however they are exactly the same.
• Lines connecting parts can be considered insulated wires in most circumstances, with just the ends of the wires being bare conductors for electric connection.
• Three lines intersecting at a point using a node in the intersection usually means that the 3 wires are electrically connected. This link could be thought of as three coated wires bared at the point of junction and soldered together.
• Two wires that cross each other with a node in the junction of the crossing point usually means the wires are electrically connected.
• Physical Circuit. The physical circuit to the circuit diagram may look something like the image below, though a more practical physical circuit could have a light bulb holder and clamps that connect with the battery terminals. A light bulb holder could need screw terminals to attach the wires to, and a socket to twist the light bulb in to. Battery clamps would allow the cables to readily be attached between the battery and light bulb holder.
Series Circuit Example. No nodes are necessary in this circuit to show the bulbs connecting to each other and into the battery because single wires are connecting straight to each other. Nodes are just placed if a few more wires are all connected.
This articles demonstrates how to read circuit diagrams for beginners in electronics. A drawing of an electrical or electrical circuit is also known as a circuit structure, but may also be called a schematic diagram, or only schematic.
Because there might be more than one battery or light bulb in a circuit, reference designators will typically always end with a number, e.g. BAT1 and L1 as shown in the circuit below. Another light bulb in the circuit could then possess the reference designator L2.
A component list can now refer to those components by reference designator. A node is a filled circle or dot. When three or more lines touch each other or mix each other and a node is placed at the junction, this signifies the lines or wires being electrically connected at the point.
Circuit or schematic diagrams contain symbols representing bodily elements and lines representing wires or electric conductors. So as to learn how to read a circuit diagram, it's critical to understand what the design symbol of a part looks like. It is also crucial to understand how the components are linked together in the circuit.
The base terminals of the bulbs are all linked to each other and into the negative terminal of the battery life, because the next node indicates that these connections.
Each electronic or electric element is represented by a symbol as can be observed in this simple circuit arrangement. Lines used to join the symbols signify conductors or wires. Each symbol represents a physiological component that may appear as follows.
Fundamental components for this tutorial include a LED, resistor and battery life that can all be found from the newcomer's component reference.
If wires or lines cross each other and there's absolutely not any node, as shown in the base of the above image, the cables aren't electrically connected. In this case the cables are crossing each other without joining, like two insulated wires put one on top of the other.
Possibly the easiest circuit that may be drawn is one which you might have seen in a college science class: a battery attached to a light bulb as shown below.
Component References. Components in a circuit should always have testimonials, also referred to as reference designators, used to recognize the components in the circuit. This allows the components to easily be referenced in text or a component list.
The easiest method for beginners to keep on learning how to read circuit diagrams would be to adhere to along with the path and establish the circuits from each tutorial.
When beginning to learn to read digital circuit diagrams, it's crucial to learn exactly what the schematic symbol looks like to get various electronic components. Adhering to the course explains how to read basic digital circuit diagrams while building the circuits on digital breadboard. The class contains a list of basic electronic elements with their schematic symbols in which novices can learn what the physical components and their symbols look like. | 1,129 | 5,907 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2019-18 | latest | en | 0.940111 |
http://julia-programming-language.2336112.n4.nabble.com/How-to-implement-a-tree-structure-with-vector-data-in-JULIA-td43420.html | 1,505,977,170,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818687702.11/warc/CC-MAIN-20170921063415-20170921083415-00261.warc.gz | 177,906,651 | 10,004 | # How to implement a tree structure with vector data in JULIA ?
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## How to implement a tree structure with vector data in JULIA ?
Hello,
I need to implement a tree in Julia with depth of l=3. Initially the root node has a vector of m=10000 random values (k=rand(m)).Then this vector is divided into k=10 partitions where each node child has a vector of n=1000 values. Finally the leafs are connected to a given child node. each partition (child node) has 10 leafs where each leaf has a vector of g= 100 values. Since each child node has a vector of 1000 values.this latter is shared with its leafs 100 values for each leaf. so the structure of the tree is as follows: level 0 root node : vector of 10000 values level 1 10 child node each one of 1000 values level 2 10 leafs for each child node of 100 values (that means we have in total we have 100 leafs ) Thank you for helps
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## Re: How to implement a tree structure with vector data in JULIA ?
greetings ...
do you intend for all values at each level of the tree to be integers from [1, 10000] ?
and are random draws meant to be performed without replacement ?
thanks.
On Wednesday, June 29, 2016 at 2:32:54 AM UTC-7, Ahmed Mazari wrote:
Hello,
I need to implement a tree in Julia with depth of l=3. Initially the root node has a vector of m=10000 random values (k=rand(m)).Then this vector is divided into k=10 partitions where each node child has a vector of n=1000 values. Finally the leafs are connected to a given child node. each partition (child node) has 10 leafs where each leaf has a vector of g= 100 values. Since each child node has a vector of 1000 values.this latter is shared with its leafs 100 values for each leaf. so the structure of the tree is as follows: level 0 root node : vector of 10000 values level 1 10 child node each one of 1000 values level 2 10 leafs for each child node of 100 values (that means we have in total we have 100 leafs ) Thank you for helps
--
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## Re: How to implement a tree structure with vector data in JULIA ?
Thank you for responding cdm.
Here is the developed discussion about it
On Friday, July 1, 2016 at 5:06:29 AM UTC+2, cdm wrote:
greetings ...
do you intend for all values at each level of the tree to be integers from [1, 10000] ?
and are random draws meant to be performed without replacement ?
thanks.
On Wednesday, June 29, 2016 at 2:32:54 AM UTC-7, Ahmed Mazari wrote:
Hello,
I need to implement a tree in Julia with depth of l=3. Initially the root node has a vector of m=10000 random values (k=rand(m)).Then this vector is divided into k=10 partitions where each node child has a vector of n=1000 values. Finally the leafs are connected to a given child node. each partition (child node) has 10 leafs where each leaf has a vector of g= 100 values. Since each child node has a vector of 1000 values.this latter is shared with its leafs 100 values for each leaf. so the structure of the tree is as follows: level 0 root node : vector of 10000 values level 1 10 child node each one of 1000 values level 2 10 leafs for each child node of 100 values (that means we have in total we have 100 leafs ) Thank you for helps
--
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## Re: How to implement a tree structure with vector data in JULIA ?
In reply to this post by c.d. mclean
On Friday, July 1, 2016 at 5:06:29 AM UTC+2, cdm wrote:
greetings ...
do you intend for all values at each level of the tree to be integers from [1, 10000] ?
and are random draws meant to be performed without replacement ?
thanks.
On Wednesday, June 29, 2016 at 2:32:54 AM UTC-7, Ahmed Mazari wrote:
Hello,
I need to implement a tree in Julia with depth of l=3. Initially the root node has a vector of m=10000 random values (k=rand(m)).Then this vector is divided into k=10 partitions where each node child has a vector of n=1000 values. Finally the leafs are connected to a given child node. each partition (child node) has 10 leafs where each leaf has a vector of g= 100 values. Since each child node has a vector of 1000 values.this latter is shared with its leafs 100 values for each leaf. so the structure of the tree is as follows: level 0 root node : vector of 10000 values level 1 10 child node each one of 1000 values level 2 10 leafs for each child node of 100 values (that means we have in total we have 100 leafs ) Thank you for helps
--
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## Re: How to implement a tree structure with vector data in JULIA ?
On Fri, Jul 1, 2016 at 10:43 AM, Ahmed Mazari wrote:
On Friday, July 1, 2016 at 5:06:29 AM UTC+2, cdm wrote:
greetings ...
do you intend for all values at each level of the tree to be integers from [1, 10000] ?
and are random draws meant to be performed without replacement ?
thanks.
On Wednesday, June 29, 2016 at 2:32:54 AM UTC-7, Ahmed Mazari wrote:
Hello,
I need to implement a tree in Julia with depth of l=3. Initially the root node has a vector of m=10000 random values (k=rand(m)).Then this vector is divided into k=10 partitions where each node child has a vector of n=1000 values. Finally the leafs are connected to a given child node. each partition (child node) has 10 leafs where each leaf has a vector of g= 100 values. Since each child node has a vector of 1000 values.this latter is shared with its leafs 100 values for each leaf. so the structure of the tree is as follows: level 0 root node : vector of 10000 values level 1 10 child node each one of 1000 values level 2 10 leafs for each child node of 100 values (that means we have in total we have 100 leafs ) Thank you for helps
--
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For more options, visit https://groups.google.com/d/optout. | 1,850 | 7,528 | {"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} | 3.03125 | 3 | CC-MAIN-2017-39 | longest | en | 0.890726 |
https://algebra-class-ecourse.com/question/write-25-8-as-whole-or-mied-number-in-simplest-form-and-write-32-7-as-whole-or-mied-number-in-si-11553234-92/ | 1,632,183,261,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057119.85/warc/CC-MAIN-20210920221430-20210921011430-00469.warc.gz | 140,905,439 | 12,695 | ## write 25/8 as whole or mixed number in simplest form and write 32/7 as whole or mixed number in simplest form 31/4 as whole or mixed number
Question
write 25/8 as whole or mixed number in simplest form and write 32/7 as whole or mixed number in simplest form 31/4 as whole or mixed number in simplest form
0
25/8= 3 1/8 32/7= 4 4/7 31/4= 7 3/4
Step-by-step explanation:
Divide the numerator(25, 32, 31) by the denominator (8,7,4) .
Write down the whole number answer.
Then write down any remainder above the denominator.
2. 6 1/4 for 25/8
4 4/7 for 32/7
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Squares And Square Roots Worksheet PDF
Published at Wednesday, January 06th 2021. by in Multiplication Worksheets.
The alphabet song: This remains a lovely way to practice the alphabet. Sing it slowly and sing it often. If you have a large alphabet chart and point out to each letter while you sing, it will be of great value. You can give all children letter cards in order (alphabet flashcards); they can hold up each letter as it is sung. Show a magazine or picture book to children. Ask them to identify all instances of the given letter in any page. Hand out letter cards to all children. Call out a letter. The child with that card has to come in front of the class and display the letter. Divide the class into two groups. Give one group letter cards. Give other group various objects. The first group will hold up a letter. The second group should hold up an object that starts with that letter.
Remember that with the so many worksheets available, choose one that is best suited for a certain lesson. Plan ahead what type of worksheet to use for a given day, depending on what you plan to teach. There are many free worksheets available, especially online, but still the best worksheet is one that you personally draft. This way, you are able to match the level of difficulty of the activity in accordance to the performance level of your own students. It is not bad to reuse worksheets for another batch of students, but once in a while it is also better to vary the activities you give to kids. Worksheets can be made for fun if it is attuned to the current interests of kids. The kids will respond better to activities close to their own interests.
Simple Multiplication Word Problems
Most kindergartens are expected to have a basic understanding of their letters and numbers. They do not need to be reading books when they start the first day of school but being able to recognize the letters of the alphabet and basic numbers is important. Children should also know how to write most of their letters and numbers and be able to recite them. Whether or not your child went to preschool, you can reinforce these skills at home with kindergarten games for kids online. There are a variety of sites that work on these important skills, as well as provide printable worksheets to allow your child even more practice without the use of a computer.
By the age of three, your child is ready to move onto mathematics worksheets. This does not mean that you should stop playing counting and number games with your child; it just adds another tool to your toolbox. Worksheets help to bring some structure into a child has education using a systematic teaching method, particularly important with math, which follows a natural progression. Learning about numbers includes recognizing written numbers as well as the quantity those numbers represent. Mathematics worksheets should provide a variety of fun activities that teach your child both numbers and quantity. Look for a variety of different ways to present the same concepts. This aids understanding and prevents boredom. Color-by-Numbers pictures are a fun way to learn about numbers and colors too.
With the new school year starting soon, many parents will be concerned about school readiness and looking for ways to help their children prepare for big school. While there are many preschool worksheets available, some are more useful than others in terms of versatility. There is a lot more to school readiness that just knowing the alphabet and counting to ten. Academically, parents can use preschool worksheets to help teach their children some of the basic skills they will need for kindergarten and school. This will include counting to ten, recognizing shapes and colors, being able to hold a pencil or crayon properly, and coloring in without scribbling.
This sounds like an awful lot, does not it! A good set of preschool worksheets should cover all of this, and more. In the preschool years, repetition is the key to learning, but you should look for worksheets that teach the same skills in a variety of ways. This not only prevents boredom setting in, but also reinforces the concepts by encouraging understanding as well. The importance of reading to your child cannot be emphasized enough, and you should encourage them to read as much as possible too.
Many early reading books use pictures to replace new or difficult words. If your child can recognize a red apple, they will be able to read a sentence with a picture of a red apple in it. Recognizing certain objects by their color as well as their shape helps your child learn how to read. Other than making sure your socks match, we use color in ways that we, as adults, are often not aware of. Obviously there are traffic lights that require us to know our colors, and road signs are differentiated by their color too. Reading a map, even on a GPS, relies on color recognition to identify certain features. Color also influences the way we behave, our moods, and how we react to other people.
Recent Post | 1,015 | 5,174 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2021-49 | latest | en | 0.933897 |
https://rd.springer.com/chapter/10.1007/978-3-642-12165-4_25 | 1,571,153,852,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986659097.10/warc/CC-MAIN-20191015131723-20191015155223-00228.warc.gz | 602,155,084 | 18,518 | # Certifying Algorithms for the Path Cover and Related Problems on Interval Graphs
• Ruo-Wei Hung
• Maw-Shang Chang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6017)
## Abstract
A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves the answer has no compromised by a bug in the implementation. A Hamiltonian cycle in a graph is a simple cycle in which each vertex of the graph appears exactly once. The Hamiltonian cycle problem is to test whether a graph has a Hamiltonian cycle. A path cover of a graph is a family of vertex-disjoint paths that covers all vertices of the graph. The path cover problem is to find a path cover of a graph with minimum cardinality. The scattering number of a noncomplete connected graph G = (V,E) is defined by s(G) = max {ω(G − S) − |S|: S ⊆ V and $$\omega(G-S)\geqslant 1\}$$, in which ω(G − S) denotes the number of components of the graph G − S. The scattering number problem is to determine the scattering number of a graph. A recognition problem of graphs is to decide whether a given input graph has a certain property. To the best of our knowledge, most published certifying algorithms are to solve the recognition problems for special classes of graphs. This paper presents O(n)-time certifying algorithms for the above three problems, including Hamiltonian cycle problem, path cover problem, and scattering number problem, on interval graphs given a set of n intervals with endpoints sorted. The certificates provided by our algorithms can be authenticated in O(n) time.
## Keywords
Certifying algorithm path cover Hamiltonian cycle scattering number interval graph
## References
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Arikati, S.R., Rangan, C.: Pandu: Linear Algorithm for Optimal Path Cover Problem on Interval Graphs. Inform. Process. Lett. 35, 149–153 (1990)
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Ascheuer, N.: Hamiltonian Path Problems in the On-Line Optimization of Flexible Manufacturing Systems. Technique Report TR 96-3, Konrad-Zuse-Zentrum für Informationstechnik, Berlin (1996)Google Scholar
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Chu, F.P.M.: A Simple Linear Time Certifying LBFS-Based Algorithm for Recognizing Trivially Perfect Graphs and their Complements. Inform. Process. Lett. 107, 7–12 (2008)
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Chvátal, V.: Tough Graphs and Hamiltonian Circuits. Discrete Math. 5, 215–228 (1973)
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Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)
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Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Annals of Discrete Mathematics 57 (2004)Google Scholar
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Heggernes, P., Kratsch, D.: Linear-Time Certifying Algorithms for Recognizing Split Graphs and Related Graph Classes. Nordic J. Comput. 14, 87–108 (2007)
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Hell, P., Huang, J.: Certifying LexBFS Recognition Algorithms for Proper Interval Graphs and Proper Interval Bigraphs. SIAM J. Discrete Math. 18, 554–570 (2005)
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Jung, H.A.: On a Class of Posets and the Corresponding Comparability Graphs. J. Combin. Theory Ser. B 24, 125–133 (1978)
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Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.P.: Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), pp. 158–167 (2003)Google Scholar
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Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.P.: Certifying Algorithms for Recognizing Interval Graphs and Permutation graphs. SIAM J. Comput. 36, 326–353 (2006)
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Manacher, G.K., Mankus, T.A., Smith, C.J.: An Optimum Θ(nlogn) Algorithm for Finding a Canonical Hamiltonian Path and a Canonical Hamiltonian Circuit in a Set of Intervals. Inform. Process. Lett. 35, 205–211 (1990)
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Ntafos, S.C., Louis Hakimi, S.: On Path Cover Problems in Digraphs and Applications to Program Testing. IEEE Trans. Software Engrg. 5, 520–529 (1979)
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Pinter, S., Wolfstahl, Y.: On Mapping Processes to Processors. Internat. J. Parallel Programming 16, 1–15 (1987)
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Shih, W.K., Chern, T.C., Hsu, W.L.: An O(n 2logn) Time Algorithm for the Hamiltonian Cycle Problem on Circular-Arc Graphs. SIAM J. Comput. 21, 1026–1046 (1992)
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Waterman, M.S., Griggs, J.R.: Interval Graphs and Maps of DNA. Bull. Math. Biol. 48, 189–195 (1986) | 1,418 | 4,952 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2019-43 | latest | en | 0.880418 |
http://xahlee.blogspot.com/2010/12/whats-function-whats-operator.html | 1,508,344,509,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187823016.53/warc/CC-MAIN-20171018161655-20171018181655-00812.warc.gz | 623,843,071 | 29,398 | # What's Function, What's Operator?
Xah Lee, 2010-12-14
Typically, we understand what “function” and “operator” mean, but average programer or mathematician may have a hard time explaining them. Here, we clarify a bit on the meaning of the word “function” and “operator”, their context, their relation.
## Function Is a Mathematical Concept
Function you probably understand. A function takes inputs, and produces a unique value/output for the given inputs. The inputs are called “parameters”. A specific set of input are called “arguments”. The number of parameters of a function is called the function's “arity”. So, for example, the function “sin” has arity 1. A constant, such as 35, Ï€, can be considered as functions of no parameter, so they are functions of arity 0. A function of 2 parameters, such as 「define f(x,y) := x+y」, are arity 2.
Function is a mathematical concept. Viewed in another way, it's a map from one space (aka set) to another. You can read Wikipedia for detail here: Function (mathematics).
A operator, is less of a mathematical concept, but more of a concept of notation, i.e.syntax. A “operator” is a symbol (or symbols) that are written to indicate operations. For example, we write 「1+2」, the “+” is a operator, and the “1” and “2” are its “operands”. Mathematically, operator is a function that acts on its operands. The operands are the arguments of the function.
### Binary Operators
Typically, operators takes 2 arguments, the left and right of the symbol. e.g. 「2×3」, 「3/4」, 「2^3」, union ∩, intersection ∪.
### Unary Operators
But there are also 1-argument operators. For example the minus sign 「-3」, and the logical not 「¬」 sign, the factorial 「3!」, square root 「√3」.
### Multi-symbol Operators
Operators can also involve other forms with more symbols. For example, the absolute sign 「|-3|」, floor 「⌊3.8⌋」 uses a bracket, summation ∑ takes 4 arguments, a expression, a variable, and start and end values. The anti-derivative (aka indefinite integral) ∫ takes 2 arguments, a expression and a variable. In traditional notation, integration as operand involves 2 symbols, ∫ and â…†. For example, we have 「∫ sin(x) â…†x 」.
### Implicit Operators
Operator can be a bit complicated. For example 「-3」 can be interpreted in several ways. We can think of the minus sign as unary operator acting on the argument 「3」. So, mathematically, it is a function of 1 arity that returns the addictive inverse of the element 3. Or, we can interprete it as one single entity, a element denoted 「-3」. When we write 「3-2」, the ways to interprete it gets a bit more complex. One way to think of it as a notation shorthand for 「3 + (-2)」. The 「-2」 part can be thought of as before. Another way is to think of 「-」 as a binary operator on 3 and 2, but this seemingly simple interpretation is a bit complex. Because, what is math definition of the minus binary function? I'm not sure how it can be defined in terms of algebra without ultimately thinking of it as additon of 2 elements, one being a addictive inverse. The other way is to think of it as a real line, moving the first argument to the left by a distance of the second argument. Of course ultimately these are equivalent, but i can't think of a simple, direct, interpretation that can serve as a math foundation. Also, this is directly related to how does one interprete division, such as 「3/2」.
The multiplication operator also gets complicated. For example, when we write 「3 x」, it usually means 「3*x」. The space acts as implicit multiplication sign, but otherwise the space char has no significance and only make things easier to read.
### Operator Stickiness
There's also the concept of “operator stickiness” (aka “operator precendence”) at work that makes expressions with operators more concise. When we write「3△4▲5」, how do you know it's 「(3△4)▲5」 or 「3△(4▲5)」? The concept of operator stickiness is needed to resolve that. Otherwise, you'll need to always write 「3+(4*5)」 instead of the simpler 「3+4*5」. But this again, also introduced more complexity. When you have a expression of tens of different operators, it becomes a problem of remembering the stickiness grammar for each operator. (in practice, you just resort to use explicit priority indicator by parens. Forgetting Operator Precedence is a frequent source of code error in programing. And in written math for human communication, it is prone to miscommunication.)
## Operator is tied to Notation
Because the concept of “operator” more has to do with syntax and notation, and when considering traditional math notation of writing in “2-dimensions”, also the fact that traditional math notation has a lot ambiguities, it gets a bit complicated and not as imprecise as we like. (See: The Problems of Traditional Math Notation)
Mathematically, operator and function are the same thing.
Math function, when written down, usually takes the form e.g. 「sin(x)」, 「f(x,y)」, where the things inside the paren are its parameter/arguments.
Operators are useful because writing everything out in full function notation gets very cumbersome and hard to read. For example, we write 「3+4*5」 instead of 「plus(3,times(4,5))」 or 「+(3,*(4,5))」.
Here's a example of traditional notation using operators, versus traditional full functional notation.
```-b+√(b^2-4 a c)/(2 a)
```
If you don't allow space as implicit multiplication sign, then you have:
```-b+√((b^2)-4*a*c)/(2*a)
```
If you don't allow the implicit operator precedence, then you have:
```(-b)+(√((b^2)-(4*a*c))/(2*a))
```
Finally, writing it out in the traditional function 「f(x)」 form, you have:
```/(+(-(b),√(+(^(b,2),-(*(4,a,c))))),*(2,a))
```
If you prefer words than symbols, as traditionally practiced when writing out functions, you have:
```divide(add(minus(b),sqrt(add(power(b,2),minus(times(4,a,c))))),times(2,a))
```
The notation using operators is much concise, readible, but at the cost of relatively complex lexical grammar. The full functional notation is precise, grammatically simple, but difficult to read.
In math context, it's best to think of functions instead of operator, and sometimes also use a uniform function notation, where all arguments are explicitly indicated in one uniform way.
Here's what Wikipedia has to say about operators: Operation (mathematics). Quote:
An operation ω is a function of the form ω : X1 × … × Xk → Y. The sets Xj are called the domains of the operation, the set Y is called the codomain of the operation, and the fixed non-negative integer k (the number of arguments) is called the type or arity of the operation.
Note that it doesn't really speaks of “operators”, but speaks of “operations”, and flatly defines operation as a function.
## Traditional Function Notation 「sin(x)」 Isn't Perfect
Note that, even the functional notation such as 「sin(x)」, isn't perfect.
### Problem of Functions Returning Functions
Normally, with full function notation, you'd expect the operation clearly corresponds to the nesting structure. For example, our example before:
```divide(add(minus(b),sqrt(add(power(b,2),minus(times(4,a,c))))),times(2,a))
```
But there's a problem when a function returns a function. For example, the derivative takes a function and returns a function. We might write:
```derivative(f)
```
Now, if we want to evaluate the result at 3, then we might write:
```derivative(f)(3)
```
You can see that the notation no longer nests. The operator precedence issue is back. Now, you need a symbol precedence to make it clear.
One solution to this is the lisp language's syntax. In lisp syntax, everything is written inside a paren. The first element is the function name, the rest is its arguments. So, 「sin(x)」 would be written as 「(sin,x)」. (comma is used for separator) Our derivative example would then be:
```((derivative,f),3)
```
In this way, the syntax remains a pure nested form, and provides the utmost precision.
Our formula example in fully nested syntax be:
```(/,(+,(-,b),(√,(+,(^,b,2),(-,(*,4,a,c))))),(*,2,a))
```
We could change the comma separator to space. So, it would look like this:
```(/ (+ (- b) (√ (+ (^ b 2) (- (* 4 a c))))) (* 2 a))
```
(Note: lisp language syntax is not regular. Many of its syntax does not have the form 「(a b c ...)」. See: Fundamental Problems of Lisp.)
## Syntax Design for Computer Languages
### Mixing Operator Syntax with Full Function Notation Syntax
In most computer language, they allow both the operator and full function syntax. For example, you can write 「(sin(x))^2+3」. (almost all languages do this; e.g. C, C++, C#, Java, Pascal, Perl, Python, Ruby, Bash, PowerShell, Haskell, OCmal. The only exception is lisps.) This way is normal, and most flexible. Because, not all functions have a associated operator symbol. And, writing everything in nested brackets is not readible and hard to write too. The question is, is it possible to design a syntax, that has very simple lexical grammar, is regular, and easy to read and write?
Though, almost all computer languages does not have a regular syntax, in fact, non of any major computer lang has a syntax specification. The closest one that has a somewhat regular and simple syntax grammar is Mathematica. See: The Concepts and Confusions of Prefix, Infix, Postfix and Fully Nested NotationsMath Notations, Computer Languages, and the “Form” in Formalism.
So, if we were to design a computer language, with a syntax that has a simple grammar, what would it be like?
The following are half written, still work in progress
### Mathematica Example
Here's a explanation of one approach. (much based on syntax of Mathematica)
Start with a fully nested syntax. So, everything is in a fully nested functional notation, like this: 「(a b c ...)」.
For some function names or builtin names, we give them a operator symbol. For example, say we have a function named plus 「(plus,2,3)」. Now, suppose we assign the s
### Unique Semantics for Each Symbol
Note first that the char paren is used for 2 purposes. (1) as a operation priority grouping indicator. (2) as delimiter for function's arguments.
So, if the context is designing a consistent math notaton or computer language syntax, this we need to fix. One way, is by insisting that each symbol used only has one unique purpose, and not be dependent on adjacent symbols. So, we might insist that, function parameter delimiters should use the square bracket. Like this 「sin[x]」. (this is what Mathematica does) | 2,564 | 10,466 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.46875 | 4 | CC-MAIN-2017-43 | latest | en | 0.873195 |
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Teach your students to find equivalent fractions on a metric number line. | 745 | 3,554 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2020-45 | latest | en | 0.714076 |
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Useless Backstory:
I was trying to guess how many jellybeans were in a jar. If the jar was a glass cube or a glass box, I would just count width × length × height. With a cylinder however, I figure I could still use this method, but just minus the ratio of circle in square. So I became curious to see if the ratios were the same when reversed.
Take a circle, any radius. Now grow a square inside of it, until the four corners of the square touch the perimeters of the circle.
Will the area of the square always hold the same ratio to the area of the circle? If yes, what is that ratio?
Now vice versa
Take a square, any radius. Now grow a circle inside of it, until the circle perimeter touches each side of the square.
Will the area of the circle always hold the same ratio to the area of the square? If yes, what is that ratio?
The circle of radius R in the square of side C is such :
$2 R = C$
Area of the circle $\pi R^2$ , of the square $C^2$ , and the ratio of circle on square is :
and the ratio is : $\pi \frac{R^2}{C^2} = \pi \frac{R^2}{4 R^2} = \frac{\pi}{4}$
If the area of the square is $100 cm^2$ , the circle will have an area of $\frac{\pi}{4} 100 cm^2 \approx 78.54 cm^2$
The square of side C in the circle of radius R is such :
$C^2 = R^2 + R^2$ similarly the ratio is : $\pi \frac{R^2}{C^2} = \pi \frac{R^2}{2 R^2} = \frac{\pi}{2}$
If the area of the square is $100 cm^2$ , the circle will have an area of $\frac{\pi}{2} 100 cm^2 \approx 157,08 cm^2$
• By "rayon" I think you mean "radius".
– user856
Aug 19, 2016 at 4:52
• Keep in mind, the same basic principle applies, but the ratios change in 3 dimensions. Look up "Packing Fraction" for more detail on these concepts. Sep 14, 2018 at 15:52 | 547 | 1,839 | {"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} | 4.53125 | 5 | CC-MAIN-2024-22 | latest | en | 0.909129 |
https://lavelle.chem.ucla.edu/forum/search.php?author_id=12752&sr=posts | 1,569,011,595,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514574077.39/warc/CC-MAIN-20190920200607-20190920222607-00341.warc.gz | 544,708,227 | 15,403 | ## Search found 42 matches
Thu Jun 14, 2018 2:13 am
Forum: Properties & Structures of Inorganic & Organic Acids
Topic: French Toast 28
Replies: 3
Views: 215
### Re: French Toast 28
HI has a larger atomic radius and therefore a longer and weaker bond, making it weaker, and a stronger acid bc it can dissociate easily
Thu Jun 14, 2018 12:56 am
Forum: Calculating pH or pOH for Strong & Weak Acids & Bases
Topic: strong/weak acids (from review worksheet)
Replies: 1
Views: 190
### strong/weak acids (from review worksheet)
Hi,
Could someone please explain the answer to this question from the review worksheet to me
Wed Jun 13, 2018 1:13 am
Forum: Shape, Structure, Coordination Number, Ligands
Topic: 17.37
Replies: 1
Views: 122
### 17.37
How do you do this question? how do you use table 17.4 to answer it?
Wed Jun 13, 2018 1:11 am
Forum: Shape, Structure, Coordination Number, Ligands
Topic: 17.29
Replies: 1
Views: 119
### 17.29
how do you find the oxidation number of the metal?
Wed Jun 13, 2018 1:05 am
Forum: Shape, Structure, Coordination Number, Ligands
Topic: Homework Problem 17.33.)
Replies: 4
Views: 228
### Re: Homework Problem 17.33.)
what is the relation btwn charge and number of binding sites? i thought the no. of binding sites had to do wiht the number of lone pairs
Wed Jun 13, 2018 1:03 am
Forum: Shape, Structure, Coordination Number, Ligands
Topic: ethylenediaminetetraacetato (edta)
Replies: 6
Views: 225
### Re: ethylenediaminetetraacetato (edta)
do we need to memorize the formula for edta?
Wed Jun 13, 2018 12:56 am
Forum: Shape, Structure, Coordination Number, Ligands
Topic: Ligands and Lone Pairs
Replies: 2
Views: 93
### Re: Ligands and Lone Pairs
in the ligand co32-, why is it that only 2 pairs of electrons are considered binding sites when there are actually 8 lone pairS?
Wed Jun 13, 2018 12:53 am
Forum: Shape, Structure, Coordination Number, Ligands
Topic: HW 17.33
Replies: 6
Views: 265
### Re: HW 17.33
can't co32- technically have 8 binding sites since two of the oxygen atoms have 3 pairs of electrons and one has 2 pairs of electrons?
Tue Jun 05, 2018 7:22 pm
Forum: Hybridization
Topic: BF3
Replies: 1
Views: 92
### Re: BF3
I think that's correct but I believe it forms a pi bond (not positive though)
Tue Jun 05, 2018 7:20 pm
Forum: Determining Molecular Shape (VSEPR)
Topic: 4.109
Replies: 1
Views: 68
### Re: 4.109
look at the number of regions of electron density around the central atom you are concerned with, ignoring the rest of the compound. (for ex: if there are lone pairs of electrons on parts of the compound that aren't the central atom, it doesn't matter)
Tue Jun 05, 2018 7:16 pm
Forum: Determining Molecular Shape (VSEPR)
Topic: 4.27
Replies: 2
Views: 91
### Re: 4.27
by the symmetry of the overall molecule (after drawing the lewis structure w/ vsepr in mind)
Mon May 28, 2018 11:33 pm
Forum: Bond Lengths & Energies
Topic: Highest Ionization Energy
Replies: 2
Views: 178
### Re: Highest Ionization Energy
ionization energy increases from left to right and decreases down a group. if the question changes the cation, the molecule with the cation with a higher ionization energy has a greater ionization energy difference. if the question changes the anion, the molecule with the anion with a lower ionizati...
Mon May 28, 2018 11:23 pm
Forum: Bond Lengths & Energies
Topic: HW question 4.1
Replies: 5
Views: 227
### Re: HW question 4.1
if there was no lone pair the bond angle would be 180 degrees. due to the repulsion of the lone pair, the bond angle is reduced from this number
Mon May 28, 2018 11:22 pm
Forum: Determining Molecular Shape (VSEPR)
Topic: 4.1
Replies: 5
Views: 163
### 4.1
in 1b, how come the molecule can have lone pairs? i thought it couldn't
Mon May 14, 2018 8:17 pm
Forum: Ionic & Covalent Bonds
Topic: 3.23 (meaning of oxidation)
Replies: 7
Views: 261
### Re: 3.23 (meaning of oxidation)
but since chlorine needs to gain an electron shouldn't its oxidation state be -1
Mon May 14, 2018 8:14 pm
Forum: Coordinate Covalent Bonds
Topic: format
Replies: 1
Views: 280
### format
what's the correct format for drawing a coordinate bond? In highschool I remember drawing a line with an arrow; is there any specific notation?
Mon May 14, 2018 8:13 pm
Forum: Formal Charge and Oxidation Numbers
Topic: formal charge
Replies: 11
Views: 413
### formal charge
I wasn't able to attend lecture last class and am unsure about how to calculate formal charge. Is it just the number of electrons to add (resulting in a negative charge) or number of electrons to remove (resulting in a positive charge)
Wed May 09, 2018 11:33 am
Forum: Bohr Frequency Condition, H-Atom , Atomic Spectroscopy
Topic: q16
Replies: 2
Views: 148
### Re: q16
sorry forgot to specify! chapter 1
Wed May 09, 2018 2:07 am
Forum: Heisenberg Indeterminacy (Uncertainty) Equation
Topic: equation
Replies: 2
Views: 127
### equation
in the answer key, it says the uncertainty eq is ∆p*∆x=1/2*h
i thought it was ∆p*∆x>=h/4pi
i'm getting different answers to those in the answer key and am confused as to the method of solving such questions (like 1.43 for example)
Wed May 09, 2018 1:11 am
Forum: Heisenberg Indeterminacy (Uncertainty) Equation
Topic: conceptual q (based on q 1.43)
Replies: 1
Views: 118
### conceptual q (based on q 1.43)
sometimes the uncertainty is not given and only the position is given (like in 1.43). how can we incorporate this into the equation when this is the actual momentum value, not the momentum value multiplied by the uncertainty.
Tue May 08, 2018 11:38 pm
Forum: Heisenberg Indeterminacy (Uncertainty) Equation
Topic: Heisenberg Equation
Replies: 2
Views: 134
### Re: Heisenberg Equation
what do you mean by double the uncertainty? wouldn't you just multiply the uncertainty for momentum for example with the actual value of momentum? also im confused because sometimes the uncertainty is not given and only the position is given (like in 1.43). how can we incorporate this into the equat...
Tue May 08, 2018 5:08 pm
Forum: Trends in The Periodic Table
Topic: electron affinity [ENDORSED]
Replies: 15
Views: 455
### electron affinity[ENDORSED]
does electron affinity measure the energy required to gain an electron or the attraction to an electron? for example an element far right on the periodic table would hav a high nuclear charge, and it would be easy to add an electron. does this mean the electron affinity is high (because the attracti...
Tue May 08, 2018 5:04 pm
Forum: Bohr Frequency Condition, H-Atom , Atomic Spectroscopy
Topic: q16
Replies: 2
Views: 148
### q16
how do you do question 16 when both the initial and final n values are unknown?
Tue May 08, 2018 5:02 pm
Forum: SI Units, Unit Conversions
Topic: units
Replies: 4
Views: 268
### units
for the topics covered in test 2, what units are the equations in terms of? some of them are in kg and such but im not sure which ones
Sun May 06, 2018 8:54 pm
Forum: *Shrodinger Equation
Topic: Shrodinger Equation
Replies: 7
Views: 301
### Re: Shrodinger Equation
what kind of questions related to the equation can we expect to see on the midterm?
Sun May 06, 2018 8:50 pm
Forum: Trends in The Periodic Table
Topic: Difference between Periodic trends [ENDORSED]
Replies: 4
Views: 241
### Re: Difference between Periodic trends[ENDORSED]
electron affinity measures the energy change when an electron is added to an atom, whereas electronegativity refers to the attraction an atom has to an electron. one measures an energy difference and the other is a scale of attraction. they are both related, however, as electron affinity decreases (...
Sun May 06, 2018 8:46 pm
Forum: Lewis Structures
Topic: Electron Configuration
Replies: 6
Views: 219
### Re: Electron Configuration
the first shell (n=0) only has one subshell, so it only has s orbitals. after that the second shell (n=1) has two subshells, and therefore has s and p orbitals. the third shell (n=2) has 3 subshells and therefore has s,p, AND d.
Mon Apr 23, 2018 11:45 pm
Forum: Photoelectric Effect
Topic: increasing frequency/ light intensity
Replies: 5
Views: 251
### Re: increasing frequency/ light intensity
what effect does each have on the electrons emitted?
Mon Apr 23, 2018 9:53 pm
Forum: Heisenberg Indeterminacy (Uncertainty) Equation
Topic: test 2
Replies: 2
Views: 150
### test 2
is this equation coming in test 2?
Mon Apr 23, 2018 9:52 pm
Forum: *Shrodinger Equation
Topic: double derivative [ENDORSED]
Replies: 2
Views: 241
### double derivative[ENDORSED]
In questions will we receive H as a function? Is it always sin/cos?
Mon Apr 23, 2018 9:51 pm
Forum: Photoelectric Effect
Topic: increasing frequency/ light intensity
Replies: 5
Views: 251
### increasing frequency/ light intensity
what does increasing the frequency/ light intensity do? are they the same thing? if not what's the difference?
Sat Apr 21, 2018 11:53 am
Forum: Properties of Light
Topic: test 2
Replies: 18
Views: 543
### test 2
For test 2, will the questions be only numericals or will we have to answer qualitative questions too?
Mon Apr 16, 2018 11:00 pm
Forum: Properties of Light
Topic: Planck's constant
Replies: 1
Views: 74
### Planck's constant
what does planck's constant signify?
Mon Apr 16, 2018 10:59 pm
Forum: Limiting Reactant Calculations
Topic: moles + limiting reactant
Replies: 2
Views: 188
### moles + limiting reactant
Is the limiting reactant the reactant with the number of moles only if the mass is the same? if the mass is different how do you determine the limiting reactant
Mon Apr 16, 2018 10:57 pm
Forum: Bohr Frequency Condition, H-Atom , Atomic Spectroscopy
Topic: Bohr frequency condition
Replies: 1
Views: 79
### Bohr frequency condition
Hi,
I know what the formula is for the Bohr frequency condition, but I'm not sure about what it signifies. What is the condition and what does it apply to?
Tue Apr 10, 2018 1:36 am
Forum: Molarity, Solutions, Dilutions
Topic: G 13 [ENDORSED]
Replies: 1
Views: 81
### G 13[ENDORSED]
I got the concentration of the diluted solution as 0.05M, and so shouldn't the number of mols of the compound when the volume is 0.1L be 0.2? not sure why the answer is 0.01
Mon Apr 09, 2018 9:47 pm
Forum: Significant Figures
Topic: Sig Figs [ENDORSED]
Replies: 2
Views: 126
### Re: Sig Figs[ENDORSED]
I think we will be penalized for incorrect sig figs in the tests after this one though
Mon Apr 09, 2018 8:46 pm
Forum: Accuracy, Precision, Mole, Other Definitions
Topic: Homework Question E9a
Replies: 2
Views: 198
### Re: Homework Question E9a
Since 6.022*10^23 is the number of particles (atoms, molecules, etc) in one mole, and since oxygen is repeated 11 times in the formula, we multiply the number of moles of oxygen by 6.02*10^23 to find the number of atoms in one mole. We multiplt 11 to this number since oxygen is repeated 11 times. I ...
Mon Apr 09, 2018 8:18 pm
Forum: SI Units, Unit Conversions
Topic: Length Units
Replies: 15
Views: 494
### Re: Length Units
I think so
Mon Apr 09, 2018 8:17 pm
Forum: SI Units, Unit Conversions
Topic: Moles mols mol? [ENDORSED]
Replies: 21
Views: 959
### Re: Moles mols mol?[ENDORSED]
Mole is the noun, referring to the concept, and mol is the unit for moles, as far as I remember.
Mon Apr 09, 2018 8:15 pm
Forum: SI Units, Unit Conversions
Topic: Temperature
Replies: 5
Views: 248
### Re: Temperature
there are 3 units because it is easier to use some when dealing with certain temperature scales. On a day to day basis, it is easier to use celsius or farenheit because we are not dealing with large numbers or very positive/negative temperatures for which kelvin might be more suitable.
Mon Apr 09, 2018 7:13 pm
Forum: Student Social/Study Group
Topic: Post All Chemistry Jokes Here
Replies: 7348
Views: 902082
### Re: Post All Chemistry Jokes Here
what kind of dog do chemists have? laboratory retrievers | 3,500 | 11,866 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2019-39 | longest | en | 0.820272 |
https://community.qlik.com/t5/New-to-Qlik-Sense/Calculation-between-two/m-p/27029 | 1,542,396,445,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039743110.55/warc/CC-MAIN-20181116173611-20181116195611-00151.warc.gz | 580,941,061 | 40,195 | New to Qlik Sense
Discussion board where members can get started with Qlik Sense.
Contributor III
Calculation between two
Dear All
i want to calculation sum of values from two date columns
Here is my sample data
UserIDCutOffDateTransDateAmount
User013/12/20183/10/201810
User013/12/20183/11/201810
User013/12/20183/12/201810
User013/12/20183/13/201810
User013/12/20183/14/201810
User013/12/20183/15/201810
User013/12/20183/16/201810
User023/15/20183/14/201810
User023/15/20183/15/201810
User023/15/20183/16/201810
i want to get Sum of Amount between Cutoffdate And Max selected Transdate for each UserID
Example:
if no Transdate selected, it mean Max(TransDate) = '3/16/2018'
here my expected result
UserIDSum AmountDescription
User0150Sum of Amount from Cutoffdate of User01 (3/12/2018) to Max(TransDate) ('3/16/2018')
User0220Sum of Amount from Cutoffdate of User02 (3/15/2018) to Max(TransDate) ('3/16/2018')
if selected Transdate ='3/14/2018'
here my expected result
UserIDSum AmountDescription
User0130Sum of Amount from Cutoffdate of User01 (3/12/2018) to Max(TransDate) ('3/14/2018')
User020Because Cutoffdate > Max(TransDate)
but i am not sure how to write expression correctly.
Any help would be appreciated.
An Pham
3 Replies
Highlighted
MVP
Re: Calculation between two
Hi An, check this: Set analysis by field in other table
To resume: Create a flag in script and use the flag in set analysis
Updated solution without changing the model: SUM({<AccountIndexKey={"=TradeDate>=CutOffDate"} >}Amount)
Contributor
Re: Calculation between two
Hi,
may be like below,
=aggr( sum({<TranDate={">=\$(p(=date(min(CutOffDate))))<=\$(Date(Max(TranDate))) "}>}Amount),UserId)
Contributor II
Re: Calculation between two
Hi Pham,
Please find the attached application. | 549 | 1,796 | {"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} | 3.109375 | 3 | CC-MAIN-2018-47 | latest | en | 0.763027 |
https://www.airmilescalculator.com/distance/tyn-to-zha/ | 1,621,086,024,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991370.50/warc/CC-MAIN-20210515131024-20210515161024-00495.warc.gz | 651,351,980 | 44,661 | # Distance between Taiyuan (TYN) and Zhanjiang (ZHA)
Flight distance from Taiyuan to Zhanjiang (Taiyuan Wusu International Airport – Zhanjiang Airport) is 1147 miles / 1846 kilometers / 997 nautical miles. Estimated flight time is 2 hours 40 minutes.
Driving distance from Taiyuan (TYN) to Zhanjiang (ZHA) is 1359 miles / 2187 kilometers and travel time by car is about 23 hours 28 minutes.
## Map of flight path and driving directions from Taiyuan to Zhanjiang.
Shortest flight path between Taiyuan Wusu International Airport (TYN) and Zhanjiang Airport (ZHA).
## How far is Zhanjiang from Taiyuan?
There are several ways to calculate distances between Taiyuan and Zhanjiang. Here are two common methods:
Vincenty's formula (applied above)
• 1146.795 miles
• 1845.587 kilometers
• 996.537 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth’s surface, using an ellipsoidal model of the earth.
Haversine formula
• 1150.307 miles
• 1851.240 kilometers
• 999.589 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## Airport information
A Taiyuan Wusu International Airport
City: Taiyuan
Country: China
IATA Code: TYN
ICAO Code: ZBYN
Coordinates: 37°44′48″N, 112°37′40″E
B Zhanjiang Airport
City: Zhanjiang
Country: China
IATA Code: ZHA
ICAO Code: ZGZJ
Coordinates: 21°12′51″N, 110°21′28″E
## Time difference and current local times
The time difference between Taiyuan and Zhanjiang is 2 hours. Zhanjiang is 2 hours behind Taiyuan.
CST
+06
## Carbon dioxide emissions
Estimated CO2 emissions per passenger is 159 kg (351 pounds).
## Frequent Flyer Miles Calculator
Taiyuan (TYN) → Zhanjiang (ZHA).
Distance:
1147
Elite level bonus:
0
Booking class bonus:
0
### In total
Total frequent flyer miles:
1147
Round trip? | 534 | 1,929 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2021-21 | longest | en | 0.817973 |
http://jadnohra-tech.blogspot.com/2008/08/ | 1,563,941,580,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195530385.82/warc/CC-MAIN-20190724041048-20190724063048-00289.warc.gz | 78,100,551 | 25,809 | ## Friday, August 15, 2008
### Case Study: Optimizing a Search Algorithm (for AI assisted Footballer switching in WOF)
Motivation
in WOF, We usually seek perfection. In the case of AI assisted Footballer control switching, we wanted to do better than other comparable games. This means, when a human player is controlling a footballer, and the ball is shot or passed, control has to switch to the best candidate. This does not mean, the first footballer in the ball's direction! Even the smallest thought effort gives us a long list of cases where this does not work: lobs, balls unreachable because of ball speed and footballer reaction time, target footballer being busy doing other important actions... (even ball deflections from the goal bar are handled 'correctly' by WOF!)
the AI also had to correctly handle multiple human players in the same team and not allow ping- pong switching between them.
Results
a shy video showing the results (partially) can be seen here:
Non Linearity and Searching
Since we are in 3 dimensions, the speed of the ball being non linear, and the position even much less so, the fact that the footballers speeds can be approximated as linear is not of great help.
Therefore, the correct algorithm had to rely on a search. in it's basic unoptimized form, it should calculate the ball's complete trajectory (colliding with static obstacles only), and for each potential footballer, find the portions of the trajectory (and yes they are portions because of ball height changing) when the ball can be intercepted. Then choose among those based on mix of criteria: first to intercept, wait time after arriving to position, effort needed to arrive to position...
As with every search algorithm, it makes lots of sense trying to optimize it, we do not want this single 'basic' task to wreak havoc on the whole game's performance.
Full Ball Trajectory Calculation
The full ball trajectory is very useful, and we use it for many different purposes, that is why, we already had it implemented. It is calculated using exactly the same physics engine used in game, it is therefore very exact. The collisions are only performed with static objects, it does not make sense to include dynamic ones since they are ... dynamic.
Because of our performant physics, collision detection and spatial subdivision, we can afford to calculate the full ball trajectory every time the ball is shot.
The calculation is optimized in 2 ways. The 1st optimization is splitting the calculation among a configurable amount of frames, since we never need the whole trajectory instantaneously, in practice we obtain it fast enough for all of our purposes. The second optimization is the intelligent choice of sampling technique. Instead of some naive sampling, we use an error metric that allows us to have the least number of samples possible, while keeping the quality of the samples so, that one can linearly interpolate the position of the ball based on a sample's start velocity, until the next sample, keeping the error less than the ball's radius.
Search Optimizations
As with all searches, we can do much better than brute force. And since this search will be continuously executed since the footballers move, it better be performant!
One optimization was made by adding functionality to the trajectory calculation phase, allowing it, on the fly, to split the trajectory into multiple sections, depending on the height of the ball (and therefore it's reachability by footballers), allowing 'too high' sections to be completely skipped during the search.
As for the search itself, we used temporal caching, and a number of WOF specific optimizations.
For temporal caching, we hold on to the last found intercept point, and only check for it's validity using it's type (footballer will wait for ball at intercept, ball will wait for footballer at intercept, no intercept, ...) and the amount of time elapsed since the intercept's first analysis time. This means in one case per example, if we found a valid intercept point where the footballer has to wait 0.5 seconds for the ball after arriving to his position, we can, until 0.5 secs pass, 'simply' recheck for the intercept's validity (while keeping an eye on where the footballer is going) and this is much cheaper than starting a new search.
Of course, samples are invalidated as times passes by, thus making the number of samples to search smaller the further the time advances, but this is obvious.
The implementation itself produces (crudely estimated) 2500 lines of source code (excluding headers), split among multiple files in a nicely organized design, that allows reusing it in a clean way for a number of other purposes (like the scripted AI using it to make it's decisions).
Conclusion
when considering searches, make sure they are unavoidable, if you are sure they are, understand why, implement them, optimize, profile and enjoy the hopefully nice results.
## Wednesday, August 13, 2008
### Smoothing Character Collision Response using Quadratic Equations
Motivation
In WOF, we wanted characters to smoothly collide with the world (goal, advertisement banners, other characters, ...) and therefore 'slide' next to obstacles and not get blocked by them.
This might not be a necessity per se, since in a football game, the footballers have no business being outside the pitch, but this would be nice to have to reuse in other games, it was also something I had not done before so I wanted get my hands dirty with a more general solution then just character / character collision where bounding volumes could be used.
I decided to use the real polygon geometry of the obstacles, and not any specially prepared collision proxies, this meant the algorithm needed to handle colliding simultaneously with a number of objects / triangles and still making the best of it and sliding in the correct direction whenever it would be the right thing to do.
Results Video
A video of the nice results can be seen here:
Usual Approach(es)
So as a first step of course, research, this was some time ago, so I will not post any links, you can search yourselves, but mostly people used nicely formed collision volumes such as spheres, capsules, cylinders. the advantages being per example being able to rotate in place without the collision volume changing, and therefore not causing collisions because of rotations.
This is important, because, if a character is moving, as in changing it's position, we know in which direction it moved, and we can therefore use that direction to make the collision response look credible, however for turning, things are a bit more complicated, and your usual collision tests help you by telling you how to translate volumes to resolve the collision, but not how to rotate, except if we search using bisection, which is expensive, and it seems there is no way around it for now.
This is again related to continuous collision detection (CCD), an active research topic, again linear is much easier than angular, and this of course makes sense, and has an explanation, but this is out of our scope right now, but as usual, the net is there for those who want to know more. A first search points to by , who is known for his research in this area. The Bullet physics forums are probably also a good place for this topic, among many others.
Chosen Solution
Now our math library already had collision tests for many primitives, almost all a game would ever need, except capsules. I did not like the idea of using spheres because they would be too big, and we wanted the characters to be able to come very close before colliding. Of course, the spheres could be made smaller, which then has other disadvantages, basically, the sphere did not fit the real volume closely enough for my taste, (there are many collision detection tutorials / papers that discuss fitting properties of collision shapes). At the time, I chose to use Axis Aligned bounding boxes that do not change their volume when the footballers changes directions, additionally, OBB were being used for accelerating collision detection between the ball and the footballer's limbs using the physics engine, this means we have two types of bounding volumes for 2 different purposes.
Capsules would have been an equally good choice, or even a better one. But the 'technique' I used to resolve collision applies to both.
Plan of Attack
So what do we really want to achieve? we want the character to slide along obstacles and not be blocked by them when it makes sense.
When does it make sense? it makes sense when the obstacle does not directly oppose the direction the character is moving. so except if the obstacle directly opposes the movement direction, there is possibility to slide, this is the basic idea. Of course, we have more than one obstacle, and since we want to use the raw polygons of the obstacles, we will have more than 1 triangle per obstacle, additionally in WOF, obstacles can be volumes, so in the end, we will have a number of triangles and volumes to check against, and we will need to find a sliding direction giving the original movement direction and the triangles and volumes.
There is more than one way to solve this, but I will describe the final solution (and I think in WOF's context the best solution) that I came up with.
'Algorithm'
For all triangles and volumes, I used a swept volume collision detection to gather all the contact normals between the moving volume and the world's objects, for triangles I used only the face normals, this prevents the character from getting stuck because of slight penetrations of polygonal objects, as for cases where we really have a collision with a triangle edge, this works as well, assuming all triangles in an object are connected, whenever we have contact with an edge we also have contact with 2 or more triangle faces that meet at that edge, so we can get away with using triangle face normals and no edges (or points) assuming all triangles are connected, this way we happily slide along polygonal objects even if we hit edges because of slight penetrations and we will still be correct when we hit real edges because in that case more than 1 face normal will be taken into account. (some pictures at this point would be nice, but maybe I will do then later and update this post).
So as i said, I gather all contact normals as explained above, then I use quadratic programming to find a direction that satisfies the following constraint: has a non-zero negative dot product with all the gathered normals, or in other words a direction along which we can move freely without penetrating all current contacting obstacles. I take the resulting direction and if it is zero or if it has the same direction as the movement vector (solvedDir dot moveDir > 0), I block the moving object, sending it to where it was at the last step, I use a fixed step approach to physics, thus making this always look ok, otherwise I use the direction obtained from the solution as the new movement direction, optionally projecting the current movement translation onto it (thus reducing the movement speed), the new direction is not used 'after' the current movement is applied, the contacts are gathered during a 'check potential contacts using the current direction', so this means the new direction (translation) is used instead of the original direction.
Luckily, we have a Convex Quadraitc Prorgramming Problem at hand, this means it can be solved in reasonable time, I used the QuadProg++ library, (which uses the Goldfarb-Idnani dual method), but I modified it to optimize it's memory allocation behaviour
There are some more details to take into consideration, because in WOF per example, in some modes (tackling per example), we allow footballers to penetrate each other, so we need filters to specify which triangles / objects to use for collision detection, there are also issues about how to make swept collision detection behave nicely in all problematic cases, all those issues are solved and work well in WOF as one can see in the video, but the point here was using quadratic programming to solve for the 'sliding direction'. As for performance, there were no problems until now, I will spare you the profiling numbers though, they are only relevant for WOF.
## Tuesday, August 12, 2008
### It's all so easy... (Brain stack dump)
For some time now, I have the feeling that all problems seem to carry no difficulty for me.
So I took some time to think about to find out if it's an illusion, a realtiy, or pure naive stupidity.
What I will begin with is not the first idea link in the chain of thoughts that I went through while thinking about this, but I still found it would be good to start with.
Of course, as with all topics, it is important to first define the used terms.
one dictionary definition of 'difficult' is: "not easy to do, understand, or solve". this definition uses the word easy, so this does not really help much, since I am searching for a deeper definition of difficult.
Looking up the definition for easy I get: "not difficult; simple", which is of course, also not helpful, since it uses the word 'difficult'. Instead of looking up simple (to probably find it using 'difficult' or 'easy'), I stop here and decide that the problem is really worth investigating!
So let us finally start: do you think the question 'what is the result of 1 + 1' is a difficult question for a 2 year old? yes? I think no...
I think there is a clear method to tackle any problem, and that there is no such thing as a difficult problem. The method is: identify the problem, search for a known method to solve the problem, if non is found, search for a way to solve the problem.
Pffff you say, we all know that and it does not make any problems less difficult. Sure it does.
Going back to the '1 + 1' question, let us apply our method. 1st "Identify the problem", ok the problem consits or the parts '1' '+' and the answer we are thinking of is '2'. Can we explain to a 1 year old what '1' is? no. so the problem is not difficult at all, we cannot even 'feed' the problem into the 1 year old, who's brain does not have yet any way of internally representing the 1st symbol '1', so the problem is non existent from the point of view of the 1 year old, but not 'difficult'.
Now what about asking the same question to a 6 year old who is good at math. easy u say? I disagree as well. when we ask what is '1 + 1' we get the answer '2' yes, but if we ask why ... we are stuck. the 6 year old did not solve the problem, he just looked up the answer in his memory, or counted on his fingers, but I do not consider the problem solved. To really solve the problem let us ask ourselves why does 1 + 1 = 2. Stupid question? not at all, 1 + 1 could be 10 like we see printed on popular nerd T-shirts, this would be the case if we are talking binary. 1 + 1 could also be 0, this would be if we are asking how many apples is 1 orange + 1 banana. So again, using our method, we 1st have to identify the problem. what does 1 + 1 actually mean, before we know that, it is useless to start solving. so, painful but necessary, what is '1' ? 1 could be anything, but abstracted it is a number, this is still not enough, what is a number? ... it is also a number using the decimal system, not binary, not hexadecimal. so 1 is one unit of 'anything', and also very important when we say 1+1 we do not many 1 of anything + 1 of anything, no, we mean 1 of anything + 1 of the same anything. of course we also have to define + (for which I do not have a clear definition without using a concrete 'something' like 1+1 oranges is having 1 unit of orange in some container and then adding on more unit of orange into the same container). And all of this is useless is we do not define what 2, 3, 4, 5, 6, 7, 8, 9, 10, (which I also do not find easy to explain in abstract terms without using oranges) and a method to count in decimal. Only after all this can we say that we have identified the problem. After having the problem identified, and by using the definition of how the decimal system works, and what it's symbols and their combinatorial representations mean (99, 1054), we find that 1+1 is basically by definition, 2. So the problem is not 'difficult' in itself, there is a clear method for solving it.
Now what if we try to explain this whole definition to a 15 year old, for 1 whole year, and that person still does not understand it? that's interesting point to think about. It means that people are like Computers, they have processors with capacity and speed, the processors are analogue but they are still processors, they are flexible and can grow and change, but they are still processors, and so I think that when a problem's definition is above the capacity of the brain that is supposed to 'solve' it, it is useless to talk about problem difficulty, the problem simply can't even be 'fed' into the brain.
There is also the case where that 15 year old would understand the problem, but needs 5 seconds to come with an answer, instead of 1 second, this would simply mean the capacity to accept the definition is there, but the processing speed is slow.
It still doesn't me the problem is 'difficult', not even relatively.
(Speaking about processors, here are some very cool mechanical ones)
Now after identifying the problem, our 2nd step says 'search for a known method to solve the problem', this could be using a method that we already know ourselves (saved in the brain), or doing research to find that people already found solutions to our problem or similar ones.
This would be per example the case when asking 'write a skeletal animation library' to someone who just started to learn '3D graphics', after identifying the problem, he would do some research and find that other people have done this countless times and written about it, he would then use his research to write the library. Does this mean the problem is 'difficult' for a 3D beginner ? again, no, we would be tempted to say that it is difficult for the beginner and easy for an experienced 3D Graphics Software engineer, but no, there is no 'difficulty' involved here, there is simply search time envolved that the experienced engineer need not do, but did at some point in the past, again it is not 'difficult'.
Another example is asking 'write a very robust game physics engine', is this difficult? again, I say no, because of the same reasons, defining what is exactly meant by a physics engine is, and what makes it robust, could fill a several papers, to someone who has never written a physics engine or used one, a lot of time would be needed working on step 1, does this mean that the step is difficult ? no, it simply needs, time, additionally, if that someone has no math experience, more papers would be added, and there are also many topics that would also justify a good amount of papers until reaching the end of the 1st step, but we are still following a clear recursive method, there is no magic nor difficuly envoled, it just takes time depending on the brain speed, assuming the capacity is there. after that would come step 2 also consuming lots of time, and if robust means more robust than the best current engines, we would finally come to step 3, if there are no known solution to the 'very robust' problem for problematic cases like huge world dimensions, very fast movements and rotations, huge mass ratios, etc... then we would need to 'search' for solutions, and a search is really a search, it is like an A* or similar in AI, there is no way to circumvent searches when the problems are new, it could also be that the problem is NP hard ( there are many places to read about P=NP problems, one I recommend though is the book "Artificial Intelligence, A Modern Approach, Stuart J. Russell, Peter Norvig"). Simplfied, NP hard means that until now, nobody managed to prove that we can do anything better than 'searching' to find a solution for such problems.
Searching would be done by using all known heursitics, and theoretical information, and trying plausible solutions until one is found or not found, finding out there is no solution is also a solution. Some robustness problems are per example very easy to solve if we use much better data types, like huge 512 bit floating or fixed point numbers instead of our usual floats or doubles, but then we hit the limits of our current technological limits (speed and memory of our current computers) and the real time constraints a game physics engine must satisfy, but all this still does not mean the problem is difficult, there is an obvious way to solve it, the solution might end up with a search that has no time bounds, or with a conclusion that the problem is not solvable given the constraints, but this does not mean 'difficult'. What is important though is finding out that sometimes, a search is needed, and that is of course the case for all 'new' problems, which are usually generated by solutions to old problems, or requiring improvements, and this is how the beautiful train of technology evolution rolls by, taking all of us enthusiasts on a nice ride.
Being the brain dump it is, there is no conclusion for this post, this topic still needs more thinking, and maybe after a few more related posts, a structured conclusion will come out.
## Monday, August 11, 2008
### quote "Cargo Cult Methodology: How Agile Can Go Terribly, Terribly Wrong"
whenever an article contains something to this:
"All of us team members were survivors of another much larger project. That project had been done with outsourcing to a CMM Level 5 organization, with great care in the methodology at our end and with careful detailed project management overall. The project consumed tens of millions of dollars and years of overtime. It failed utterly. "
I just HAVE to read it ...
http://www.cio.com/article/print/442264
related: http://www.ddj.com/architect/209600574?cid=http://www.informationweek.com/maindocs/archive.htm
related: http://brucefwebster.com/2008/06/16/anatomy-of-a-runaway-it-project/
which has a very good part about 'documenting the unnecessary just for the sake of it'
"I truly believe that in the past we have been too ambitious in describing process, in adopting too much process, and in documentation. The reality is that even if people write a lot, very few people will ever read it. Thus the trend towards light will sustain. However, it is easy to be light. The trick is to be as light as possible but not lighter. I believe you will find our work on EssUP and EssWork new and fresh. "
related: http://www.ddj.com/architect/209602001?cid=http://www.informationweek.com/maindocs/archive.htm
" what to do when your stakeholders still insist on having a "precise estimate" at the beginning of the project."
## Thursday, August 7, 2008
### mixing php and the c++ preprocessor?
Idea
here I go again, thinking and complaining about the well known limits of c++ meta programming,
the most known complaint candidate being lack of partial template specialization for functions.
Meta-programming seems to me to be very close to web server side scripting a la php per example. Because in the end, this is what the meta in meta-programming means...
generating source code via 'meta' code. well what about using something like a php processor to meta-program c++ files??
Potential
One could do something like #include "Vector.php.hpp?dims=3" this would include a meta programmed header for a 3d vector, one advantage is the the resulting header would be plain c++, it would be possible generate functions that take 3 arguments, like per example
VectorT::VectorT(Type value1, Type value2, Type value3) which is currently impossible with standard meta-programming.
actually the generated class could directly be generated as Vector3 or Vector3D, where ususally
it would be Vector<3>, of course this can be typedef'd and I am a big fan of typedef's they are great for writing fire and forget, self refactoring code. But anyway, it would be possible...
Taking it to the extreme we would probably be able to do something like this:
#include "Vector.php.hpp?class=FunkyVector3D, dims=3"
, and have a resulting class called FunkyVector3D! changing names of classes at will, would that be a maintenance disaster? or simply more responsability?
Issues
Planning will definitely be needed so that things don't get out of control and turn into a cryptic mess.
I suspect though, that without some perprocessor features to help with this, issues will arise (name collisions, linker errors, classes not found...).
Time for bed though, I will think about it some more when I have more time, but this could definitely be a cool experiment.
## Monday, August 4, 2008
### marriage to c++ (also known as 'c++, elegant static arrays' part 2)
Motivation
I received feedback for the 'c++ static arrays' post from numerous friend developers, who are all unfortunately too lazy to post a comment.
Some were scared by the meta-programming heaviness, while others said it's an overkill.
I fed their feedback into my thinking machine and came to the following conclusion: the difference between us is that I am married to c++, while the skeptics have only been dating it, and it makes a big difference even if they have been dating for years.
Analysis
This kind of situation happens whenever you spend a lot of time in a relationship with something or somebody, be it c++ in my case, your car, your flat, your partner, your friend and EVEN your new IPhone! the situation always evolves the same way: in the beginning, you enjoy the new benefits, you only see the cool features, you are happy it works and you are satisfied, but eventually, you start taking all the good things for granted, and start to only see the small annoyances, which transform into big annoyances, because they become all what you see, it is like taking a small coin, and sticking it into your eye, even though it is small, it is all what you see, and it is very painful. I could turn this into a human relationship post, but I will just say it is different because people have feelings, and trying to change others is in many cases egoistic, in other rarer cases the right thing, but in most cases can hurt feelings, but let's close it here and concentrate on c++, which until now, has not developed any feelings.
Allow me to change you...
The 'issues' can be divided into 2 types:
There are the things that I don't like when done the "copy from book/tutorial/demo" way, and this does not mean that the book/tutorial/demo is bad, of course not! but things have to be put in context. You cannot simply take whatever code was there and stick it into a codebase specially if it is large and complex, the culprit here it turns out is the programmer, but a beginner programmer is automatically excused, he is happy enough that things are working and that's fine, I am happy. But I see many experienced programmers, who should know better, and know that they have to write code that has minimal dependencies and needs minimal changes, and that is robust and very good at detecting problems at run time, and not just for the sake of it, or because of some obscure obsession about code elegance, but becuase this is wasted time and money in any term except the short term, I am not happy!
Most such issues can be easily solved however, by using meta-programming per example, and by thinking long term, how long is long term is also an important skill by the way, but let us skip that and move to the second type.
This is the tougher type, with issues that are impossible to solve wihout the help of the compiler, (except when killing performance or causing other big disasters is no problem). In these cases we can just hope and wait for things like c++0x, tr1 and friends to come to the rescue, one example mentioned in the previous post is the 'auto' keyword which allows code to be made less dependent, and mroe change resilient among other benefits.
But unsolved compiler dependent issues remain (themes for future rants), seemingly meaningless to most ... except the married.
## Saturday, August 2, 2008
### c++, elegant static arrays
It can be better
I will show you a nicer way of 'declaring' c++ static arrays that is more elegant, a bit less error prone, and makes life easier when changing the array size or index type.
This is fairly basic, and I have been using it for a long time, but I have never seen any code or tutorial doing it my way.
In any case, its a really microscopic issue that does not deserve so many words, but only needs a nice small example.
The basic Tutorial
this is tutorial code from the 1st search engine hit for 'tutorial c++ static arrays'
PS: when viewed with IE, the source code is not horizontally scrollable, I am too lazy to find out why, sorry, use firefox.
`int my_array[10];my_array[0] = 100;my_array[1] = 100;my_array[2] = 100;my_array[3] = 100;my_array[4] = 100;my_array[5] = 100;my_array[6] = 100;my_array[7] = 100;my_array[8] = 100;my_array[9] = 100;for(int i = 0; i<10;>my_array[i] = 100;`
ok, this was your standard tutorial, from my point of view though, it should be like this.
`template<typename TypeT, size_t LengthT, typename PreferredIndexT = int>struct StaticArray {typedef int EnumType; //this is an int, except if changed in compiler settings when availabletypedef PreferredIndexT PreferredIndex;typedef TypeT Type;enum { Length = LengthT };Type data[Length];inline StaticArray() { //check if Length fits into enum data type numeric_cast<EnumType>(LengthT);}static inline EnumType length() const { return Length; }template<typename OutT, typename InT>static inline OutT numeric_cast(const InT& val) { assert(((InT) (OutT) val) == val); return (OutT) val; }template<typename T>static inline const T& getLength() const { static const T len = numeric_cast<T>(length()); return len; }template<typename T>inline Type& safeEl(const T& i) { assert(i >= 0 && i < Length); return data[i]; }template<typename T>inline const Type& ctSafeEl(const T& i) const { return safeEl(i); }template<typename T>inline Type& el(const T& i) { return data[i]; }template<typename T>inline const Type& ctEl(const T& i) const { return el(i); }template<typename T>inline Type& operator[](const T& i) { return el(i); }template<typename T>inline const Type& operator[](const T& i) const { return ctEl(i); }typedef Type* iterator;inline iterator begin() const { return data; }inline iterator end() const { return data + Length; }};`
usage, with comments explaining some of the benefits:
`{typedef StaticArray<int, 300> Array;Array arr;//we can do away with the typedef//StaticArray<int, 300>arr;//we can sepcify the preferred index type to be used with this array//StaticArray<int, 300,unsigned short> arr;{int i = 0;arr[i++] = 0; //use i++ and save us from typo problems, we also can copy-paste better like thisarr[i++] = 1;arr[i++] = 2;arr[i++] = 3;arr[i++] = 4;arr[i++] = 5;arr[i++] = 6;arr[i++] = 7;arr[i++] = 8;arr.safeEl(9) = 9; //check that we did not go over the array's size}//with arr.length(), we don't need to change this code if the array size changesfor(int i = 0; i < arr.length(); ++i)arr[i] = i;//this will produce an assert if 'char' cannot hold the size of the array, that's good!for(char i = 0; i < arr.getLength<char>(); ++i)arr[i] = i;//only works with typedef declaration//use the 'preferred' indexfor(Array::PreferredIndex i = 0; i < arr.getLength<Array::PreferredIndex>(); ++i)arr[i] = i;//use an stl type iterator, if we ever use an stl container, no code//needs to change//additionally, we do not to worry about index types{Array::Type i = 0;for(Array::iterator it = arr.begin(); it != arr.end(); ++it) {*it = i++;}}//the 'best' version works only with c++0x//using auto allows changing the iterator (or index type if not using iterator)//without needing to change code anywhere else{Array::Type i = 0;for(auto it = arr.begin(); it != arr.end(); ++it) {*it = i++;}}}`
Evolution
Agreed, this might be too heavy for a 'static arrays' tutorial, BUT the problem is most people don't evolve and don't strive to improving their skills, this approach works so they stick to it.
I have seen senior programmers with 10+ years experience still sticking to it, there's definitely nothing wrong with that, but there is a certain general 'attitude' in play here, being the 'non-naive flexible' perfectionist I am, I cannot help but to keep pushing the limits, and this is the latest version to date.
Benefits
One thing to note is that all this fanciness introduces zero overhead, by using inline functions and static/const variables.
Also notice that this really 'decouples' the array declaration from the code using it, making changes to array properties (size, data types, preferred index) automatically propagate through our code with no need to change anything, and whenever changes are needed but cannot be detected at compile time, asserts will come to the rescue and save us many headaches.
I like this because I have a tendency to try to write 'fire and forget' code as much as c++ allows, this means using asserts to warn me whenever there is danger that things might break at run time.
The extremely simple but effective numeric_cast is an example of that, making sure all data types used to store indexes are 'fire and forget' so that I do not to be paranoid, allowing me to make changes with piece of mind knowing that I'll directly get notified when there is danger lurking around the corner, there maybe room for a more detailed explanation here, but I will leave it at that.
Long Term Thinking
In the end, many will probably dismiss this as pointless overkill, in my personal opinion and experience, in the long term it never is. | 7,539 | 33,757 | {"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} | 3.109375 | 3 | CC-MAIN-2019-30 | latest | en | 0.958086 |
https://unitchefs.com/troy-pounds/troy-ounces/1/ | 1,685,849,047,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649439.65/warc/CC-MAIN-20230604025306-20230604055306-00613.warc.gz | 648,601,848 | 6,970 | # 1 Troy Pounds to Troy Ounces
=
1 Troy Pounds =
12
(decimal)
1.2 x 101
(scientific notation)
12
1
(fraction)
Troy Ounces
## Troy Pounds to Troy Ounces Conversion Formula
[X] oz t = 12 × [Y] troy pounds
where [X] is the result in oz t and [Y] is the amount of troy pounds we want to convert
## 1 Troy Pounds to Troy Ounces Conversion breakdown and explanation
1 troy pounds to oz t conversion result above is displayed in three different forms: as a decimal (which could be rounded), in scientific notation (scientific form, standard index form or standard form in the United Kingdom) and as a fraction (exact result). Every display form has its own advantages and in different situations particular form is more convenient than another. For example usage of scientific notation when working with big numbers is recommended due to easier reading and comprehension. Usage of fractions is recommended when more precision is needed.
If we want to calculate how many Troy Ounces is 1 Troy Pound we have to multiply 1 by 12 and divide the product by 1. So for 1 we have: (1 × 12) ÷ 1 = 12 ÷ 1 = 12 Troy Ounces
So finally 1 troy pounds = 12 oz t | 296 | 1,146 | {"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-2023-23 | latest | en | 0.899655 |
https://waterleaf-ai.com/qa/question-how-many-different-7-digit-numbers-are-there-the-sum-of-whose-digits-are-odd.html | 1,606,370,414,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141186761.30/warc/CC-MAIN-20201126055652-20201126085652-00177.warc.gz | 565,814,850 | 9,063 | # Question: How Many Different 7 Digit Numbers Are There The Sum Of Whose Digits Are Odd?
## How many combinations of 50 numbers are there?
All Possible Number Combinations For 5/1-50 Lottery Games Included with Your Order: All Possible 5/50 Number Combinations.
Total Combinations – 2,118,760..
## How many 6 digit number are there in all?
900,000 6There are 900,000 6-digit numbers in all.
## How do you calculate the number of possible combinations?
Remember that combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula nCr = n! / r! * (n – r)!, where n represents the number of items, and r represents the number of items being chosen at a time.
## What is the least 7 digit number?
1000000The smallest 7-digit number is 1000000.
## What is the smallest 7 digit number?
7-digit numbers 10,00,000 (Ten lakh) is the smallest 7-digit number.
## How many unique 6 digit pins are there if repetition of digits is not allowed?
There are one million of them (999999 + 1). If repetition is not allowed (which is probably what you are referring to in your last sentence), you can pick any of ten digits for the first number, any of the nine remaining for the second, and so forth. This is 10 times 9 times 8 times 7 times 6 times 5 or 151,200.
## How many combinations of 5 numbers are there?
120Hence there are 2 choices for the fourth digit and only 1 choice for the fifth digit. Thus you have made 5 × 4 × 3 × 2 1 = 120 choices and there are 120 possible 5 digit numbers made from 1, 2, 3, 4 and 5 if you don’t allow any digit to be repeated. Now consider the possibilities with 13 as the first two digits.
## How many four digit numbers are there in all?
9000 fourFOUR – DIGIT NUMBERS are the numbers that have four digits, i.e. they have ones, tens, hundreds and thousands places. In fact, to find the number of numbers between any two given numbers, we use the same formula. Therefore, there are 9000 four digit numbers in all.
## What is the smallest number of 6 digit?
∴ The smallest 6-digit number = 1,05,689.
## How many combinations are there in a 7 digit number?
Assuming repetition is allowed, you can have 7-digit numbers from 1,000,000 to 9,999,999 which is a total of 9,000,000 7-digit numbers. These are all the possible 7-digit numbers. In general, there are 9 × 10^(n-1) possible n-digit numbers.
## How many numbers in all do we have with 7 digits and 9 digits?
All the digits after first digit can be anything between 0–9, including both. The easy answer to this is to subtract the value of the largest 6-digit number from the largest 7-digit number. 9,999,999 – 999,999 = 9,000,000. Therefore, there are nine million distinct 7-digit integers.
## How do you say 1000000000000000000000000?
A thousand trillions is a quadrillion: 1,000,000,000,000,000. A thousand quadrillions is a quintillion: 1,000,000,000,000,000,000. A thousand quintillions is a sextillion: 1,000,000,000,000,000,000,000.
## Why is a phone number 7 digits?
Telephone engineers created a 7-digit system for “all number calling” to expand their pool of possible number combinations. The first 3 digits would correspond to a certain phone service provider, and the last 4 digits would remain as a personal calling code.
## How many 6 digit numbers contain exactly 4 different digits?
How many 6-digit numbers contain exactly 4 different digits ? My Solution is : There are 6 digits and 4 needs to be unique so either 2 digits can be same or 3 can be same. But there is another solution mentioned which gives the correct answer. = 9*9*8*7*5*13 = 294840 .
## What is a 7 digit number called?
The smallest 7-digit number is 1 followed by 6 zeros. This number is called one million. The largest 7-digit number is 9 followed by another 6 nines. This number is called nine million nine hundred ninety-nine thousand nine hundred ninety-nine.
## What are all the possible combinations of 3 numbers 0 9?
If what you want are all possible three digit numbers with no repetition of the digits then you have 10 choices for the first digit, you have 9 choices for the 2nd digit, and you have 8 choices for the 3rd digit giving you 10x9x8 = 720 in all.
## What is the 8 digit greatest number?
9How many 8-digit numbers are there? The smallest 8-digit number is 1 followed by 7 zeros. This number is called ten million. The largest 8-digit number is 9 followed by another 7 nines.
## What is the formula of nPr?
Definition: nPr(n,r) = n! / (n-r)! The number of different, unordered combinations of r objects from a set of n objects. Definition: nCr(n,r) = nPr(n,r) / r! Returns a random value between 0 and 1.
## What is the smallest 6 digit even number?
“Whar is the smallest six digit even number that can be formed using the digits 0,2 and 9 at most two times only?”
## What is the largest 6 digit even number?
999998ANSWER : The largest 6-digit even number is 999998. | 1,304 | 4,988 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2020-50 | latest | en | 0.885557 |
https://m.jagranjosh.com/articles/cbse-class-9-multiple-choice-questions-practice-paper-set-i-1299827901-1 | 1,537,722,843,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267159561.37/warc/CC-MAIN-20180923153915-20180923174315-00288.warc.gz | 554,490,481 | 32,299 | # CBSE Class 9 Multiple Choice Questions Practice Paper: Set I
Jul 26, 2018 17:16 IST
CBSE Class 9 MCQs Practice Paper: Set I
Here we bring a collection of Multiple Choice Questions (MCQs) based on Class 9 curriculum. These MCQs have been collated in the form of a practice test. All the MCQs have been taken from the Class 9 NCERT books for Mathematics, Science, Social Science and English subjects.
Some salient features of the Class 9 MCQs practice test are:
• Designed by the experienced teachers
• Covers all four important subjects of CBSE class 9, i.e., Maths, Science, Social Science and English
• Includes questions based on all conceptual topics explained in CBSE Class 9
• Best preparation source to crack entrance level exams or scholarship tests
A few questions from Class 9 MCQs Practice Paper: Set I, are:
Q. The point at which the two co – ordinate axes meet is called
(a) The abscissa (b) The ordinate
(c) The origin (d) The quadrant
Q. The zeroes of the polynomial p(x) = x2 – 3x are
(a) 0,0 (b) 0,3
(c) 0,-3 (d) 3,-3
Q. If (x + 2) and (x – 1) are factors of (x3 + 10x2 + mx + n), then
(a) m=5, n=-3 (b) m=7, n=-18
(c) m=17, n=-8 (d) m=23, n=-19
Q. Much of the countryside ……….flooded.
(a) was (b) were
(c) are (d) have been
Q. Who teaches you English?
(a) By whom are you taught English?
(b) Who was taught by you?
(c) Who is taught by you?
(d) By whom were you taught English?
Q. Neither he nor I ……………mistaken.
(a) was (b) us
(c) are (d) can
Q. Which one of the following was the main occupation of the majority of Russia’s people?
(a) Mining (b) Cattle grazing
(c) Agriculture (d) Fishing
Q. When did Parvez Musharaf issue a legal Framework order in Pakistan?
(a) 1999 (b) 2000
(c) 2002 (d) 2004
CBSE Class 9 Mathematics Question Paper 2018-19: Set I
Q. Which of the following is the highest peak in Western Ghats?
(a) Dada Betta (b) Shevroy Hills
(c) Javadi Hills (d) Anai Mudi
Q. Mohit stands on the top of a tower of height h metres and from there he drops a ball. The ball takes T seconds to breach the ground. What is the position of the ball in T/3 seconds?
(a) h/9 metres from the ground
(b) 7h/9 metres from the ground
(c) 8h/9 metres from the ground
(d) None of these
Q. If the displacement of an object is proportional to square of time, then the object moves with
(a) Uniform velocity
(b) Uniform acceleration
(c) Increasing acceleration
(d) Decreasing acceleration
Solving this practice paper will not only help you analyse your knowledge of different subjects studied in CBSE Class 9 but will also help you to improve your speed and accuracy which is the key factor to crack any competitive exam with flying colours.
To get more of such important articles for Class 9 Exam preparations, click here.
DISCLAIMER: JPL and its affiliates shall have no liability for any views, thoughts and comments expressed on this article.
X | 856 | 3,323 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2018-39 | longest | en | 0.864645 |
https://worldbuilding.stackexchange.com/questions/152129/how-long-can-400-people-survive-in-an-underground-facility-if-they-had-to-seal-o | 1,660,549,403,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572161.46/warc/CC-MAIN-20220815054743-20220815084743-00351.warc.gz | 558,519,848 | 63,636 | # How long can 400 people survive in an underground facility if they had to seal off their heat vents?
Assume the surface of the planet is experiencing ice age conditions and the facility was designed to keep the occupants alive for 6 months.
An emergency forces the permanent closure of all Heating, Ventilation, and Air Conditioning (HVAC) vents for immediate survival. Going to the surface isn't an option.
I had read, though I can't find the source at the moment, that any underground habitat requires cooling or the human's body heat will turn the place into an oven.
There seems to be some doubt that the human body will cause the temperature to rise in a closed underground chamber. If I could access this study on thermal engineering I wouldn't have asked because it would have my answer. However, the link proves that in fact, the temperature will rise if there is no venting. Natural thermal convection based on human body heat. https://www.sciencedirect.com/science/article/abs/pii/S1359431118332563?via%3Dihub
As for size of the facility, using the rpg's construction rules, 400 people would fit in a 240,000 square feet building.
• Even been in a cave? Noticed the average temperature underground? The stink of the livestock will kill them first. Aug 2, 2019 at 1:10
• Hello and Welcome to World building Pentallion. I would recommend adding a question back into the body of your... well question. You seemed to have removed it. Your also missing some details like, how big is this facility. How much open air there is. And what are the heat vents doing? (heating the facility, or pumping heat out of the facility). Aug 2, 2019 at 2:05
There is a lot of unknowns in your question and this is one of those questions where the devil is likely in the detail, but the key point is that unless you're VERY deep underground, you don't need heat vents in the first place. Being underground is actually good for your populace as it acts as natural thermal insulation. In point of fact, in a town called Lightning Ridge in Australia (a mining town inland where temperatures can soar) there are some homes that are effectively excavated out of the ground, underground homes if you will, because of the thermal insulation provided. Given that it doesn't often rain out there you can protect your entrance from rain pretty effectively so it works. But, I digress.
The point is, that if you live in a cave that is fairly well insulated, you have a natural heat source with you; body heat. In point of fact, in Stockholm, the heat generated from people in Central Station is redirected to heat office buildings, reducing their heating costs by up to 25%. In an ice age, you probably don't want to vent away any of that heat away at all.
Your bigger problem is in fact oxygen. Your heat vents are going to double as air vents, allowing air to circulate through natural fissures in the rock formation of your underground habitat and back through the vents, allowing for fresh air on a constant basis. Closing those vents is more likely to cause the air to go stale, leading to a buildup of CO2 but at the very least thinner oxygen levels over an extended period.
Personally, if you're going to shut the vents for an extended period, try to get some plants growing down there; I don't know the tech level of your colony but if they have artificial lights I'd be growing as many plants as I can down there to freshen the air and re-use the detritus all those people and animals are going to generate, if you get my meaning.
• The train station article is written by someone who clearly has no understanding of physics. A room 500ftx150ft with 20ft ceilings, to warm to 70degF with an outside temperature of 32degF requires 2.8million BTU (828,000 watts). My sizes are grossly underestimated as well. All the Stockholm station is doing is recycling excess heat from an inefficient system. Humans are contributing to it but in ridiculously low amounts when the temperature is near freezing. Feb 19, 2020 at 20:21
Look at what happens when miners or speleologists get trapped underground with no supplies: lack of oxygen is the main risk for their survival.
Death by starvation happens in weeks.
Death by dehydration happens in days.
Death from lack of oxygen can happen in hours or even minutes, depending on the amount of air contained in the environment when the trapping happens.
The temperature of a closed environment where human metabolism is the only heat source cannot get higher than the body temperature, (as soon as the environmental temperature is higher than the body temperature the energy flow will revert) so the environment is not going to turn into an oven.
• "As soon as the environmental temperature is higher than the body temperature the energy flow will revert": that is exactly the problem. The human body produces waste heat continuuously. If the human body cannot dissipate waste heat it will overheat and die. Aug 2, 2019 at 8:57
• @AlexP, the OP states that "human in a closed environment make it a hoven".
– L.Dutch
Aug 2, 2019 at 8:58
• The human body emits on avg. the energy of a 100 watt light bulb per hour. The people in question won't die of starvation in weeks nor dehydration in hours, so they most certainly will live long enough to die of the heat their bodies generate, which is why mining companies have heat vents and underground facilities vent their heat. They are enclosed, unlike cold caves. Aug 3, 2019 at 8:03
• @Pentallion, nowhere in my answer I am comparing them to people working in operating mines.
– L.Dutch
Aug 3, 2019 at 8:52 | 1,239 | 5,592 | {"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-2022-33 | longest | en | 0.965577 |
http://facetimeforandroidd.com/margin-of/margin-of-error-research-methods.php | 1,547,633,119,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583657151.48/warc/CC-MAIN-20190116093643-20190116115643-00152.warc.gz | 82,279,119 | 5,186 | Home > Margin Of > Margin Of Error Research Methods
# Margin Of Error Research Methods
## Contents
Survey Research Methods Section, American Statistical Association. The standard error of a reported proportion or percentage p measures its accuracy, and is the estimated standard deviation of that percentage. Weighting adjusts for known differences between respondents and nonrespondents, but it can have substantial effects on precision. But a series of polls showing a gradual increase in a candidate’s lead can often be taken as evidence for a real trend, even if the difference between individual surveys is navigate here
Census Bureau. majority of sampling schemes are quota based, meaning that you cannot calculate your margin of error. PoliticsOct 18, 2016 Most Trump, Clinton Backers Say Spouses Share Their Vote Preferences
1615 L Street, NW, Suite 800 Washington, DC 20036 202.419.4300 | Main 202.419.4349 | Fax 202.419.4372 | Let's try an example: We're on the hunt for a new flavor of ice cream to make, and we wanted to know what base it should be made with, chocolate or https://en.wikipedia.org/wiki/Margin_of_error
## Margin Of Error Formula
The tick marks include 45 twice. MY problem is with ‘research' like that constantly on the television (QUALITATIVE Research, like Focus Groups) which can never be used to support any ‘quantitative conclusions whatsoever'. Here are the steps for calculating the margin of error for a sample mean: Find the population standard deviation and the sample size, n. Stokes, Lynne; Tom Belin (2004). "What is a Margin of Error?" (PDF).
In the case of the Newsweek poll, the population of interest is the population of people who will vote. But they are often overstated. Market Research Firms Kano Surveys Explained A Gentle Introduction to Concept Development How and When to Use NPD Data for Your Research Search Subscribe * indicates required Email Address * Margin Of Error In Polls The numerators of these equations are rounded to two decimal places.
Your cache administrator is webmaster. With margin of error, the statistics represented by the survey make sense. A random sample of size 7004100000000000000♠10000 will give a margin of error at the 95% confidence level of 0.98/100, or 0.0098—just under1%. Introductory Statistics (5th ed.).
For safety margins in engineering, see Factor of safety. Margin Of Error Excel Often, however, the distinction is not explicitly made, yet usually is apparent from context. It can be calculated as a multiple of the standard error, with the factor depending of the level of confidence desired; a margin of one standard error gives a 68% confidence Asking Questions: A Practical Guide to Questionnaire Design.
## Margin Of Error Calculator
Members of the American Association for Public Opinion Research’s Transparency Initiative (including Pew Research Center) are required to disclose how their weighting was performed and whether or not the reported margin check over here In R.P. So in this case, the absolute margin of error is 5 people, but the "percent relative" margin of error is 10% (because 5 people are ten percent of 50 people). It's being fixed Andrew Mercer • 1 month ago The answer to your first question is a bit technical, but if two surveys have the same margin of error, the margin Margin Of Error Definition
The margin of error for a particular individual percentage will usually be smaller than the maximum margin of error quoted for the survey. Copyright © 2016 The Pennsylvania State University Privacy and Legal Statements Contact the Department of Statistics Online Programs Home Research Services Employee Feedback Customer Feedback Market Analysis Education Research Medical Research It is a subsidiary of The Pew Charitable Trusts. his comment is here In statistics margin of error makes the most sense for normally distributed data, but can still be a useful parameter otherwise.
Search over 500 articles on psychology, science, and experiments. Margin Of Error Sample Size gives you the standard error. If you encounter a problem downloading a file, please try again from a laptop or desktop.
## It holds that the FPC approaches zero as the sample size (n) approaches the population size (N), which has the effect of eliminating the margin of error entirely.
All Rights Reserved. For n = 50 cones sampled, the sample mean was found to be 10.3 ounces. Since this precept is indeed violated over and over and over again, I wish you'd join me in fighting it. Margin Of Error Confidence Interval Calculator Unless you've measured every single item/person, every number based on a sample is an estimate or a really good guess based on available data. | 971 | 4,690 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2019-04 | latest | en | 0.88514 |
https://gateoverflow.in/177870/algorithm | 1,580,212,041,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251778168.77/warc/CC-MAIN-20200128091916-20200128121916-00409.warc.gz | 453,152,652 | 16,825 | +1 vote
78 views
| 78 views
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nlogn/2
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yes how according to me answer still be nlogn
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exaplain first how you get?
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according to me at each level n comparisons total logn levels so nlogn
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okk got it question is asking minimum number of comparisons that will be n/2 at each level
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yes .....exactly you got it :)
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i think it should be nlogn-n+1
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how nitish ? i go for simple aprroch plz explain
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@Anu sir,
i cant explain it completely here because it require too much working, but can give hint how i did it.
merging two lists we need in worst case (m+n-1) comparsions...
calculating with above fact taken into account, it will give nlogn-n+1 = O(nlogn) comparisons
0
I think question is talking about 2-way merge sort.
At the last level, there will be n/2 comparisons.
At the second last level, there will be n/2 list each conataing 2 elements, worst case comparisons (m+n-1) = 3
there are n/4 list comparisons, each needs 3 comparisons.
total comparisons: 3*n/4
at the third last level, there are n/4 lists each having 8 elements, n/8 pairs for for comparison, worst case number of comparisons = 8+8-1 = 15
at 4th last level, each list contains 16 elements, n/8 total lists, and n/16 pairs for comparisons. worst case comparisons = 16+16-1 = 31
total comparisons =
=n/2 + 3*n/4 + 15*n/8 + 31*n/16 + .... (in worst case)
In question, minimum number of comparisons are asked:
at last level = n/2 comparisons
at second last level = n/2 lists, n/4 pairs, each needs 2 comparisons, total comparisons = (n/4)*2 = (n/2)
Aat third last leevl = n/4 lists, n/8 pairs, best comparisons = 4, total comparisons = (n/8)*4 = n/2
such way, logn terms of (n/2) total cost = (nlogn/2).
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@Manu,
try to take for n=4, with (nlogn / 2) it will give 4 comparisons, but actually it will take 5 comparisons.
0
@nitish
there are two lists each of size 4,
|1|2|3|4| |10|20|30|40|
1,2,3, and 4 will be compared with 10, when either list becomes empty i will copy all the elements of second list. only min(m,n) comparisons are required in the best case.
0
i am taking about worst case.
I think the formula for the no of comparison should be n/2 + 3*n/4 + 7*n/8 + 15*n/16 + ....
=(2-1)n/2 + (4-1)*n/4 + (8-1)*n/8 + 1(6-1)*n/16.....
=(n-n/2)+(n-n/4)+(n-n/8)+......log n times
=nlogn-(n+n/2+n/4.........)
=nlogn-n+1 is the answer for no of comparisons in worst case but in the given question it is asking about the minimum no of comparisons i.e. in best case for every level it will perform n/2 comparisons logn times.So the answer is nlogn/2.
We have to keep in mind that no of comparisons is not equal to asymptotic time complexity
by Junior (511 points) | 846 | 2,666 | {"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 | 4 | CC-MAIN-2020-05 | latest | en | 0.871895 |
https://freezingblue.com/flashcards/212331/preview/physics-flashcards-units-and-kinematics | 1,709,387,588,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475825.14/warc/CC-MAIN-20240302120344-20240302150344-00592.warc.gz | 262,426,701 | 4,749 | # Physics Flashcards - Units and Kinematics
What are the units (MKS) of each of the following? 1. Length 2. Mass 3. Force 4. Time 5. Work and Energy 6. Power 1. Meter (m) 2. Kilogram (kg) 3. Newton (N) 4. Second (s) 5. Joule (J) 6. Watt (W) Give the prefix and abbreviation for each of the following powers. 1. 109 2. 106 3. 103 4. 10-2 5. 10-3 6. 10-6 7. 10-9 8. 10-12 1. Giga (G or B) 2. Mega (M) 3. Kilo (K) 4. Centi (c) 5. Milli (m) 6. Micro (μ) 7. Nano (n) 8. Pico (p) Put the following the standard scientific notation: 1. 103 2. 123456 3. 103 x 102 4. 0.103 x 10-4 5. (2 x 106)(9 x 102) = 6. 1. 1.03 x 1022. 1.23456 x 105 3. 1.03 x 10 x 104 4. 1.03 x 10-5 5. 1.8 x 109 6. 5 x 10-4 Put the following the standard scientific notation: 1. (6 x 103)2 2. (3 x 102) + (3 x 103) 1. 3.6 x 107 2. 3.3 x 103 Given the following right triangle, state the trigonometric functions: 1. sinθ = 2. cosθ= 3. tanθ= 1. sinθ = 2. cosθ= 3. tanθ= (SOH CAH TOA) What are the sin and cos values for the following angles? 1. 0° 2. 30° 3. 45° 4. 60° 5. 90° 6. 180° What is the difference between a scalar quantity and a vector quantity? A scalar quantity has magnitude but no direction. A vector quantity has magnitude and direction. Are the following scalar or vector quantities? 1. Distance 2. Speed 3. Mass. 4. Displacement 5. Velocity 6. Force. 1. Scalar 2. Scalar 3. Scalar 4. Vector 5. Vector 6. Vector Given the above, what would the following look like? 1. A + B + C Given the above, what would the following look like? 2. A - B + C Given the above, what would the following look like? 3. A - B - C (T/F) The sum of two vectors is the resultant of the vectors. True. A person walks 2 miles north and then turns around and walks 3 miles south. Total time elapsed = 1 hour. 1. Distance (d) = 2. Displacement (Δx) = 3. Average Velocity (⊽) = 4. Average Speed (s) = 1. d = 2 + 3 = 5 miles 2. Δx = 2 miles (N) - 3 miles (S) = 1 mile (S) 3. ⊽ = Δx/Δt = 1 miles/1 hour = 1 mile/hr (S) 4. s - d/Δt = 5 miles/1 hour = 5 miles/hr Average acceleration (à) = a = Δv/Δt For a body under constant acceleration: 1. v = 2. Δx = 3. v2 = 4. ⊽ = 1. v = v0 + at 2. Δx = v0t + = ⊽t = 3. v2 = v02 + 2a(x-x0) 4. ⊽ = Authorawc1990 ID212331 Card SetPhysics Flashcards - Units and Kinematics DescriptionPhysics Flashcards - Units and Kinematics Kaplan MCAT P2-P10 Updated2013-04-09T05:20:48Z Show Answers | 974 | 2,380 | {"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-2024-10 | latest | en | 0.727075 |
https://qprogramming.net/ch7-user-defined-functions.html | 1,620,797,755,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991252.15/warc/CC-MAIN-20210512035557-20210512065557-00129.warc.gz | 502,799,306 | 5,930 | Anyone Can Code.
User Defined Functions
Sammarth Kumar
What is a User Defined Function? Simply put, it is a function created by a user for themselves. Let's see how we can create these.
Creating User Defined Functions
The syntax for creating a function is as follows:
```1 2 3``` ```def (): return ```
Important Rules for User Defined Functions
1. Function names have the same rules as those for naming identifiers
2. Function headers always end with a `:`
3. Indentation very important and only code within the same indentation level of the function will be consiidered to be part of a function.
4. Elements in `()` are known as parameters. Parameters are not always necessary and neither is a return value
To start, lets create a function to add two numbers.
```1 2 3``` ```def addition(a,b): result = a + b print(result) ```
Now that we have created a function, what do we do with it? In order to run the code inside a function, you must call it. To call a function, you have to use the following syntax: ```<function name>(<paramaters, in order>)```
So lets say we want to execute our `addition` function on the numbers 3 and 5. To do so we would call the function as so:
```1 2 3 4 5``` ```def addition(a,b): result = a + b print(result) addition(3,5) ```
Output
```8
```
When you call a function, you tell the interpreter to execute the code inside the function.
Arguements and Parameters
What are parameters? Parameters are those placeholders created in the parentheses of a function header which can be used to store values given by a user while calling a function. Now, what are arguements? Arguements are the values given during a function call, which fill the placeholders created by parameters.
In the example above, the parameters are a and b while the arguements are 3 and 5.
Let's look at another example.
```1 2 3 4 5 6 7``` ```def subtraction(a,b): result = a - b print(result) num1 = 2 num2 = 1 subtraction(num1,num2) ```
Output
```1
```
Here, the parameters are a and b, and the arguements are num1 and num2, whose respective values are 2 and 1. As a result `a` and `num1` correspond to the same value and hence have the same id. Same applies for `b` and `num2`.
There are two special cases we will look at for parameters:
1. Strings as Parameters: Strings can be used as parameters as well. Though make sure that the code inside the function can be applied to strings. For example, if you have two parameters which are meant to contain strings, every statement inside the function must support strings. For example, you won't be able to multiply the parameters.
2. Default Parameters: Default parameters are those parameters whose values have been assigned beforehand in the definition of the function.
```1 2 3 4 5 6``` ```def subtraction(a,b = 2): result = a - b print(result) num1 = 2 subtraction(num1) ```
Output
```0
```
Here, we gave `b` a value of 2 beforehand, soo we only have to give one parameter while calling the function, since one is already given. However, we can override the default parameter and add a second arguement:
```1 2 3 4 5 6``` ```def subtraction(a,b = 2): result = a - b print(result) num1 = 2 subtraction(num1,3) ```
Output
```-1
```
Key Points for Parameters
1. Default parameters must all be at the end. Once the first default parameter is created, all the other parameters to the right of it must be default parameters.
2. You can use expressions, for example `x+5`, in your arguements.The interpreter will evaluate these expressions before calling the function.
3. The arguements must be in the same order as the parameters.
Return Value
To let the function return a value, we use the `return` statement.
This statement returns a value which can be used somewhere else, and can also return a function call, which can be useful for recursion, a topic beyond the syllabus.
Flow of Control
In order to call a function, it must be defined before the function call. If we don't define a function before, we get the following error:
```1 2 3 4``` ```function() def function(): print(2) ```
Output
```Traceback (most recent call last):
File "", line 1, in <module>
NameError: name 'function' is not defined
```
Therefore, you must always define a function before you call it.
That's it for this tutorial! Scroll up and click on Next for the next tutorial! | 1,064 | 4,353 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2021-21 | latest | en | 0.862972 |
https://howkgtolbs.com/convert/46.28-kg-to-lbs | 1,685,447,625,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224645595.10/warc/CC-MAIN-20230530095645-20230530125645-00751.warc.gz | 359,182,383 | 12,210 | # 46.28 kg to lbs - 46.28 kilograms to pounds
Before we go to the practice - that is 46.28 kg how much lbs calculation - we want to tell you some theoretical information about these two units - kilograms and pounds. So we are starting.
How to convert 46.28 kg to lbs? 46.28 kilograms it is equal 102.0299348536 pounds, so 46.28 kg is equal 102.0299348536 lbs.
## 46.28 kgs in pounds
We are going to begin with the kilogram. The kilogram is a unit of mass. It is a base unit in a metric system, that is International System of Units (in abbreviated form SI).
Sometimes the kilogram is written as kilogramme. The symbol of the kilogram is kg.
Firstly the kilogram was defined in 1795. The kilogram was described as the mass of one liter of water. This definition was simply but impractical to use.
Later, in 1889 the kilogram was defined by the International Prototype of the Kilogram (in short form IPK). The IPK was prepared of 90% platinum and 10 % iridium. The International Prototype of the Kilogram was used until 2019, when it was switched by another definition.
Nowadays the definition of the kilogram is build on physical constants, especially Planck constant. Here is the official definition: “The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.”
One kilogram is equal 0.001 tonne. It could be also divided to 100 decagrams and 1000 grams.
## 46.28 kilogram to pounds
You know a little about kilogram, so now we can go to the pound. The pound is also a unit of mass. We want to point out that there are not only one kind of pound. What are we talking about? For example, there are also pound-force. In this article we are going to to focus only on pound-mass.
The pound is in use in the Imperial and United States customary systems of measurements. To be honest, this unit is in use also in other systems. The symbol of the pound is lb or “.
There is no descriptive definition of the international avoirdupois pound. It is defined as exactly 0.45359237 kilograms. One avoirdupois pound is divided into 16 avoirdupois ounces or 7000 grains.
The avoirdupois pound was implemented in the Weights and Measures Act 1963. The definition of this unit was placed in first section of this act: “The yard or the metre shall be the unit of measurement of length and the pound or the kilogram shall be the unit of measurement of mass by reference to which any measurement involving a measurement of length or mass shall be made in the United Kingdom; and- (a) the yard shall be 0.9144 metre exactly; (b) the pound shall be 0.45359237 kilogram exactly.”
### How many lbs is 46.28 kg?
46.28 kilogram is equal to 102.0299348536 pounds. If You want convert kilograms to pounds, multiply the kilogram value by 2.2046226218.
### 46.28 kg in lbs
The most theoretical section is already behind us. In this section we want to tell you how much is 46.28 kg to lbs. Now you learned that 46.28 kg = x lbs. So it is high time to know the answer. Just see:
46.28 kilogram = 102.0299348536 pounds.
That is an accurate result of how much 46.28 kg to pound. You can also round off the result. After rounding off your result will be exactly: 46.28 kg = 101.816 lbs.
You know 46.28 kg is how many lbs, so see how many kg 46.28 lbs: 46.28 pound = 0.45359237 kilograms.
Obviously, this time you may also round off this result. After it your outcome is as following: 46.28 lb = 0.45 kgs.
We also want to show you 46.28 kg to how many pounds and 46.28 pound how many kg results in tables. Have a look:
We are going to begin with a chart for how much is 46.28 kg equal to pound.
### 46.28 Kilograms to Pounds conversion table
Kilograms (kg) Pounds (lb) Pounds (lbs) (rounded off to two decimal places)
46.28 102.0299348536 101.8160
Now see a chart for how many kilograms 46.28 pounds.
Pounds Kilograms Kilograms (rounded off to two decimal places
46.28 0.45359237 0.45
Now you know how many 46.28 kg to lbs and how many kilograms 46.28 pound, so it is time to go to the 46.28 kg to lbs formula.
### 46.28 kg to pounds
To convert 46.28 kg to us lbs you need a formula. We will show you a formula in two different versions. Let’s begin with the first one:
Number of kilograms * 2.20462262 = the 102.0299348536 result in pounds
The first formula give you the most accurate outcome. In some situations even the smallest difference can be significant. So if you want to get a correct result - this version of a formula will be the best for you/option to convert how many pounds are equivalent to 46.28 kilogram.
So move on to the shorer version of a formula, which also enables calculations to know how much 46.28 kilogram in pounds.
The another formula is as following, see:
Amount of kilograms * 2.2 = the outcome in pounds
As you see, this formula is simpler. It can be the best option if you need to make a conversion of 46.28 kilogram to pounds in quick way, for instance, during shopping. You only need to remember that final result will be not so accurate.
Now we want to show you these two formulas in practice. But before we will make a conversion of 46.28 kg to lbs we are going to show you another way to know 46.28 kg to how many lbs without any effort.
### 46.28 kg to lbs converter
An easier way to check what is 46.28 kilogram equal to in pounds is to use 46.28 kg lbs calculator. What is a kg to lb converter?
Calculator is an application. Converter is based on longer formula which we showed you above. Due to 46.28 kg pound calculator you can easily convert 46.28 kg to lbs. Just enter number of kilograms which you want to calculate and click ‘calculate’ button. The result will be shown in a flash.
So try to calculate 46.28 kg into lbs with use of 46.28 kg vs pound converter. We entered 46.28 as an amount of kilograms. Here is the outcome: 46.28 kilogram = 102.0299348536 pounds.
As you see, our 46.28 kg vs lbs calculator is user friendly.
Now let’s move on to our primary issue - how to convert 46.28 kilograms to pounds on your own.
#### 46.28 kg to lbs conversion
We will begin 46.28 kilogram equals to how many pounds conversion with the first version of a formula to get the most correct outcome. A quick reminder of a formula:
Number of kilograms * 2.20462262 = 102.0299348536 the outcome in pounds
So what have you do to learn how many pounds equal to 46.28 kilogram? Just multiply amount of kilograms, this time 46.28, by 2.20462262. It gives 102.0299348536. So 46.28 kilogram is 102.0299348536.
You can also round it off, for instance, to two decimal places. It is 2.20. So 46.28 kilogram = 101.8160 pounds.
It is time for an example from everyday life. Let’s convert 46.28 kg gold in pounds. So 46.28 kg equal to how many lbs? As in the previous example - multiply 46.28 by 2.20462262. It is exactly 102.0299348536. So equivalent of 46.28 kilograms to pounds, if it comes to gold, is 102.0299348536.
In this case you can also round off the result. Here is the result after rounding off, this time to one decimal place - 46.28 kilogram 101.816 pounds.
Now we can move on to examples calculated with short formula.
#### How many 46.28 kg to lbs
Before we show you an example - a quick reminder of shorter formula:
Amount of kilograms * 2.2 = 101.816 the outcome in pounds
So 46.28 kg equal to how much lbs? As in the previous example you have to multiply number of kilogram, this time 46.28, by 2.2. See: 46.28 * 2.2 = 101.816. So 46.28 kilogram is equal 2.2 pounds.
Let’s make another calculation using shorer version of a formula. Now convert something from everyday life, for instance, 46.28 kg to lbs weight of strawberries.
So let’s convert - 46.28 kilogram of strawberries * 2.2 = 101.816 pounds of strawberries. So 46.28 kg to pound mass is exactly 101.816.
If you know how much is 46.28 kilogram weight in pounds and can convert it using two different formulas, we can move on. Now we are going to show you these results in charts.
#### Convert 46.28 kilogram to pounds
We realize that outcomes presented in tables are so much clearer for most of you. It is totally understandable, so we gathered all these results in tables for your convenience. Due to this you can easily compare 46.28 kg equivalent to lbs outcomes.
Let’s begin with a 46.28 kg equals lbs table for the first version of a formula:
Kilograms Pounds Pounds (after rounding off to two decimal places)
46.28 102.0299348536 101.8160
And now look 46.28 kg equal pound table for the second formula:
Kilograms Pounds
46.28 101.816
As you see, after rounding off, if it comes to how much 46.28 kilogram equals pounds, the outcomes are not different. The bigger amount the more considerable difference. Remember it when you need to do bigger amount than 46.28 kilograms pounds conversion.
#### How many kilograms 46.28 pound
Now you know how to calculate 46.28 kilograms how much pounds but we are going to show you something more. Are you interested what it is? What do you say about 46.28 kilogram to pounds and ounces conversion?
We will show you how you can calculate it little by little. Begin. How much is 46.28 kg in lbs and oz?
First thing you need to do is multiply amount of kilograms, this time 46.28, by 2.20462262. So 46.28 * 2.20462262 = 102.0299348536. One kilogram is exactly 2.20462262 pounds.
The integer part is number of pounds. So in this example there are 2 pounds.
To calculate how much 46.28 kilogram is equal to pounds and ounces you have to multiply fraction part by 16. So multiply 20462262 by 16. It gives 327396192 ounces.
So your outcome is exactly 2 pounds and 327396192 ounces. You can also round off ounces, for example, to two places. Then final result is exactly 2 pounds and 33 ounces.
As you can see, conversion 46.28 kilogram in pounds and ounces quite easy.
The last conversion which we are going to show you is calculation of 46.28 foot pounds to kilograms meters. Both foot pounds and kilograms meters are units of work.
To calculate foot pounds to kilogram meters it is needed another formula. Before we show you this formula, have a look:
• 46.28 kilograms meters = 7.23301385 foot pounds,
• 46.28 foot pounds = 0.13825495 kilograms meters.
Now look at a formula:
Number.RandomElement()) of foot pounds * 0.13825495 = the outcome in kilograms meters
So to convert 46.28 foot pounds to kilograms meters you need to multiply 46.28 by 0.13825495. It is equal 0.13825495. So 46.28 foot pounds is exactly 0.13825495 kilogram meters.
You can also round off this result, for instance, to two decimal places. Then 46.28 foot pounds is exactly 0.14 kilogram meters.
We hope that this conversion was as easy as 46.28 kilogram into pounds conversions.
We showed you not only how to do a conversion 46.28 kilogram to metric pounds but also two other conversions - to check how many 46.28 kg in pounds and ounces and how many 46.28 foot pounds to kilograms meters.
We showed you also another way to do 46.28 kilogram how many pounds calculations, it is with use of 46.28 kg en pound calculator. This will be the best option for those of you who do not like converting on your own at all or need to make @baseAmountStr kg how lbs calculations in quicker way.
We hope that now all of you can do 46.28 kilogram equal to how many pounds calculation - on your own or with use of our 46.28 kgs to pounds calculator.
It is time to make your move! Convert 46.28 kilogram mass to pounds in the best way for you.
Do you need to make other than 46.28 kilogram as pounds conversion? For example, for 15 kilograms? Check our other articles! We guarantee that calculations for other numbers of kilograms are so easy as for 46.28 kilogram equal many pounds.
### How much is 46.28 kg in pounds
To quickly sum up this topic, that is how much is 46.28 kg in pounds , we gathered answers to the most frequently asked questions. Here we have for you all you need to know about how much is 46.28 kg equal to lbs and how to convert 46.28 kg to lbs . You can see it down below.
What is the kilogram to pound conversion? To make the kg to lb conversion it is needed to multiply 2 numbers. Let’s see 46.28 kg to pound conversion formula . Have a look:
The number of kilograms * 2.20462262 = the result in pounds
So what is the result of the conversion of 46.28 kilogram to pounds? The accurate answer is 102.0299348536 lbs.
It is also possible to calculate how much 46.28 kilogram is equal to pounds with another, easier version of the equation. Have a look.
The number of kilograms * 2.2 = the result in pounds
So this time, 46.28 kg equal to how much lbs ? The result is 102.0299348536 pounds.
How to convert 46.28 kg to lbs in just a moment? It is possible to use the 46.28 kg to lbs converter , which will do all calculations for you and you will get an exact result .
#### Kilograms [kg]
The kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side.
#### Pounds [lbs]
A pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms. | 3,483 | 13,301 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2023-23 | longest | en | 0.951059 |
https://physics.stackexchange.com/questions/509773/can-you-balance-an-object-if-its-centre-of-mass-lies-outside/509810 | 1,653,811,121,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663048462.97/warc/CC-MAIN-20220529072915-20220529102915-00523.warc.gz | 506,571,044 | 67,358 | # Can you balance an object if its centre of mass lies outside?
Can you balance an object on a point if its centre of mass lies outside? If yes, how?
• take open box for example Oct 23, 2019 at 15:54
• Like a horseshoe? Why couldn't you balance it?
– user234190
Oct 23, 2019 at 15:59
• What do you mean by balance? Hang a horseshoe on a nail, or concentricity like a ring, or total concentricity of a hollow sphere? Oct 23, 2019 at 17:01
• Like a ring, when its centre of mass lies in space. Can we balance the ring on a point on its periphery? Oct 25, 2019 at 10:23
Provided the centre of gravity is directly under or over the point of support it will be balanced.
It is safer if the centre of gravity is below the support. It is unstable otherwise.
Yes but only if the Vector ,originating from the center of gravity of the body in question and having the direction of weight , coincidences with a surface point of the body such that the normal Vector of the surface at the said point is also collinear with weight and in same direction. (If it coincidences at multiple such surface points, it can be balanced by supporting at each of the points)
For the body to be balanced, net moment of force needs to be zero in addition with net force being zero.
Let's assume that the body is balanced by supporting at a point A. Hence normal force exerted by the pivot on the body at point A is exactly equal in magnitude and opposite in direction to that of Weight of the body (mg). But this condition is not sufficient, net moment must also be zero. But we know two equal and opposite forces constitute a non zero couple, unless they are having same line of action.
The reaction at pivot A is in the direction of normal to the surface of the object at that point (assuming frictionless). The weight is acting from the center of mass. Hence to make their line of action same, the condition stated in the beginning of the answer must be satisfied.
Note : Normal to the surface must not only be collinear with weight but also in the same direction because with know normal force is exerted in a direction opposite to the normal vector of a surface and normal force is always greater than zero.
You can balance it but there needs to be something physical connecting the location of the center of mass to the rest of the structure so that the object can be supported at its center of mass. The mass of that something needs to be negligible compared to the mass of the object to the extent that it does not materially alter the location of the center of mass of the object.
Check out the picture of the forks in a cork at the bottom of following link. Note the addition of the toothpick.
http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_CenterMass.xml
Hope this helps.
• You can also see this effect with tight-rope walkers if they have a heavy pole and they hold that pole low enough. Oct 23, 2019 at 18:02
• As mentioned in the question comments, a horseshoe can be balanced without necessarily having anything physically connected to it's center of mass. Oct 23, 2019 at 18:31
• @Time4Tea The OP is talking about the situation where the center of mass falls outside the object. The center of mass of a horseshoe oriented in a vertical plane falls within the horseshoe. But the COM of a horseshoe oriented in a horizontal plane does not. My answer pertains only to the latter. Oct 23, 2019 at 19:00
• Sorry, I don't follow your sentence: "But the COM of a horseshoe oriented in a horizontal plane does not." In what way does it not? The COM always lies within the envelope of the object. Oct 23, 2019 at 19:03
• @Time4Tea I'm not talking about the "envelope" of the object. I'm talking about the COM not being located on the physical object itself. Where would you put your finger on a horseshoe to balance it when oriented in a horizontal plane? Did you look at the two fork example at the bottom of the link I provided? How would you balance the forks if the toothpick wasn't provided? Oct 23, 2019 at 19:14 | 954 | 4,035 | {"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-2022-21 | latest | en | 0.943451 |
https://www.reddit.com/r/cheatatmathhomework/comments/1hfxpn/finding_the_31st_derivative/catxzvd?context=3 | 1,440,938,499,000,000,000 | text/html | crawl-data/CC-MAIN-2015-35/segments/1440644065306.42/warc/CC-MAIN-20150827025425-00133-ip-10-171-96-226.ec2.internal.warc.gz | 925,359,129 | 14,134 | you are viewing a single comment's thread.
[–] 0 points1 point (2 children)
sorry, this has been archived and can no longer be voted on
Short of just sitting there and doing it for a few hours. I have no idea on how to do this problem. Do you just need the answer? Or actually going and the method for it? What class is this for?
[–][S] 0 points1 point (1 child)
sorry, this has been archived and can no longer be voted on
This is a part of a calculus review exercises set I'm doing. I'm looking for a smart way to solve this, possibly avoiding going through all derivatives, which is very time consuming.
The only thing I got right now is this derivation pattern:
f(x) = g(x) * e-x2
f'(x) = e-x2(g'(x) - 2x*g(x))
This pattern ends up exploding in that polynomial found in /u/fattybake 's answer.
[–] 0 points1 point (0 children)
sorry, this has been archived and can no longer be voted on
Gotcha, I was going to link that same thing actually. I just wanted to see if you didn't just want the answer. | 270 | 1,016 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2015-35 | latest | en | 0.974749 |
http://www.myexception.cn/c/239061.html | 1,606,315,295,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141182794.28/warc/CC-MAIN-20201125125427-20201125155427-00425.warc.gz | 148,846,279 | 7,183 | # 请教，c语言中有没有能够直接求 以2为底数的库函数？谢谢
www.MyException.Cn 网友分享于：2013-03-05 浏览：34次
#include "stdio.h "
main()
{
int i=1,mm; /* m: memory size*/
int s, c=0; /* s: quotient，c: module */
printf( "Enter the size of main memory in bytes: ");
scanf( "%d ",&mm);
s = mm/2;
c = mm%2;
while(c==0)
{
s = s/2;
c = s%2;
i++;
}
printf( "The address bits are %d ", i);
}
------解决方案--------------------
log_2(x) = log(x) / log(2)
#include <stdio.h>
#include <math.h>
int main(void)
{
int i;
unsigned int b;
unsigned int *pm;
/* memory size */
unsigned int mm[]={0xFFFFFFFF, 65537, 65536, 65535, 129, 128, 127, 0};
for (pm = mm; 0 != *pm; pm++)
{
b = 0x80000000;
for (i = 32; 0 == ( (*pm -1) & b) ; i--, b > > = 1)
{
;
}
(void) printf( "memory size = %10u,\taddress bits = %2d ", *pm, i);
printf( ", %u\n ", (unsigned int)ceil(log((double)*pm) / log(2) ));
}
return 0;
} | 383 | 925 | {"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-2020-50 | latest | en | 0.296177 |
http://www.math.ucsd.edu/~bprhoades/196f16/ | 1,516,558,598,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890823.81/warc/CC-MAIN-20180121175418-20180121195418-00203.warc.gz | 511,937,436 | 3,575 | Math 196: Student Colloquium
Fall 2016
Coordinator: Brendon Rhoades
Email: bprhoades (at) math.ucsd.edu
Office: 7250 APM
Colloquium Location: B402A APM
Colloquium Time: Tuesdays, 12:00-12:50 pm
Description: This is a weekly colloquium meant to give students a fun and informative introduction to ideas in research mathematics.
Grading: There will be a sign-in sheet at each colloquium. You may miss at most one colloquium to receive credit.
Schedule
9/27/2016: Brendon Rhoades
Title: Shoving boxes into corners
Abstract: A *partition* is a way to shove a collection of square boxes into a corner. We will describe some of the ways in which partitions arise in mathematics.
10/4/2016: Brendon Rhoades
Title: The Schensted correspondence
Abstract: A *standard Young tableau* is a way to put the numbers 1, 2, ... , n in a corner in such a way that we have increase going down columns and across rows. We will describe a relationship between standard Young tableaux and permutations in S_n.
10/11/2016: David Quarfoot
Title: Curiosity Reborn
Abstract: Research mathematics is about asking questions. When's the last time you did? Bring your cell phone or computer, and be prepared to change the way you approach everything in mathematics, and life.
10/18/2016: Jon Novak
Title: Polya's random walk theorem
Abstract: This lecture will be about a remarkable law of nature discovered by George Polya. Consider a particle initially situated at a given point of the d-dimensional integer lattice. Suppose that, at each tick of the clock, the particle jumps to a neighboring lattice site, with equal probability of jumping in any direction. Polya's law states that the particle returns to its initial position with probability one in dimensions d = 1,2, but with probability strictly less than one in all higher dimensions. Thus, a drunk person wandering a city grid will always return to their starting point, but if the drunkard can fly s/he might never come back.
10/25/2016: Todd Kemp
Title: Calculus and the Heat Equation on Matrix Lie Groups
Abstract: In Math 20, we learned how to differentiate and integrate functions defined on Euclidean spaces. There is a much wider world of smooth spaces (manifolds) where a generalization of calculus is possible, but it requires a steep learning curve and a lot of new language to understand. There is a class of manifolds, however, that is both large and interesting, and also retains enough Euclidean-like structure to do calculus almost the same way as in Math 20. These are called Lie groups.
I will discuss (with two or three guiding examples) how to do calculus on Lie groups, which can usually be realized as groups of square matrices. I will then discuss the most important differential equation in the world -- the heat equation -- in the context of matrix Lie groups, and the beautiful interplay between geometry and heat flow. Finally, I'll talk about my research into the heat flow of eigenvalues in matrix Lie groups -- and there'll be a lot of cool pictureses.
11/1/2016: Ioan Bejenaru
Title: Interesting problems in Harmonic Analysis
Abstract: I will introduce some problems in Harmonic Analysis and explain their relations with other fields of Mathematics.
11/8/2016: Rayan Saab
Title: The cocktail party problem
Abstract: I will talk about the problem of separating multiple signals from each other when we only have access to a few linear (or non-linear) combinations of them. An example of this type of problem is at a cocktail party when you are trying to have a conversation with a friend but there are several converations happening around you. Your ears provide you with a superposition of all the voices, and your brain does remarkably well at focusing on your friend's voice and drowning out all the others. We will talk about one computer algorithm (or time permitting, more) that does such a task (reasonably) successfully. Along the way, we will talk about important tools in mathematical signal processing, including the Fourier transform and sparsity.
11/15/2016: Eric Gelphman
Title: Algorithm for numerically computing Green's Theorem with applications to physics and engineering
Abstract: The Hyades Algorithm is an algorithm which I have invented to numerically compute the area of any complicated shape in R^2 using Green's Theorem by means of parametrizing the boundary of the shape using a traversal algorithm. This has many applications to thermodynamics involving the power and efficiency of internal combustion engines.
11/22/2016: TBA
Title: TBA
Abstract: TBA
11/29/2016: Jeff Rabin
Title: The unreasonable effectiveness of mathematics in physics: Differential geometry and general reletivity
Abstract: 2015 was the Centinnial year of Einstein's General Theory of Relativity, and fittingly concluded with the discovery of gravitational waves, which he had predicted. Despite knowing the key physical principles, Einstein was only able to formulate his theory after learning differential geometry from mathematician Marcel Grossmann in 1912. In a sense, General Relativity simply *is* applied differential geometry. This talk will sketch the key ideas of differential geometry and how they apply to Einstein's theory of gravity. The presentation will emphasize ideas and pictures, rather than equations. | 1,167 | 5,296 | {"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} | 2.734375 | 3 | CC-MAIN-2018-05 | latest | en | 0.875592 |
https://socratic.org/questions/which-polynomial-represents-the-sum-8x-2-5x-3-5x-6-2x-5-4x-2-2x | 1,653,019,610,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662531352.50/warc/CC-MAIN-20220520030533-20220520060533-00486.warc.gz | 595,571,770 | 5,926 | # Which polynomial represents the sum: (8x^2+5x+3)+(-5x^6=2x^5-4x^2-2x)?
Dec 26, 2016
I take it the $=$ in the second parts was meant as a $+$ (forgot the shift-button?)
#### Explanation:
First we lose the brackets (no sign change because of the $+$ between them), then we order by power:
$= - 5 {x}^{6} + 2 {x}^{5} + 8 {x}^{2} - 4 {x}^{2} + 5 x - 2 x + 3$
$= - 5 {x}^{6} + 2 {x}^{5} + \left(8 - 4\right) {x}^{2} + \left(5 - 2\right) x + 3$
$= - 5 {x}^{6} + 2 {x}^{5} + 4 {x}^{2} + 3 x + 3$ | 234 | 496 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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} | 4.3125 | 4 | CC-MAIN-2022-21 | latest | en | 0.778023 |
https://www.scientificlib.com/en/Mathematics/LX/Algebra.html | 1,679,772,276,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945372.38/warc/CC-MAIN-20230325191930-20230325221930-00316.warc.gz | 1,097,292,906 | 14,643 | .
Algebra (from Arabic al-jebr meaning "reunion of broken parts"[1]) is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols[2]; it is a unifying thread of almost all of mathematics.[3] As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Near East, by such mathematicians as Omar Khayyam (1048–1131).[4][5]
Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.[6] For example, in x + 2 = 5 the letter x is unknown, but the law of inverses can be used to discover its value: x=3. In E=mc^2, the letters E and m are variables, and the letter c is a constant. Algebra gives methods for solving equations and expressing formulas that are much easier (for those who know how to use them) than the older method of writing everything out in words.
The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology.
A mathematician who does research in algebra is called an algebraist.
Etymology
The word algebra comes from the Arabic language (الجبر al-jabr "restoration") from the title of the book Ilm al-jabr wa'l-muḳābala by al-Khwarizmi. The word entered the English language during Late Middle English from either Spanish, Italian, or Medieval Latin. Algebra originally referred to a surgical procedure, and still is used in that sense in Spanish, while the mathematical meaning was a later development.[7]
Different meanings of "algebra"
The word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.
As a single word without article, "algebra" names a broad part of mathematics.
As a single word with article or in plural, "algebra" denotes a specific mathematical structure. Examples include those in ring theory and algebra over a field. More generally, in universal algebra, it can refer to any structure.
With a qualifier, there is the same distinction:
Without article, it means a part of algebra, such as linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).
With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra.
Frequently both meanings exist for the same qualifier, as in the sentence: Commutative algebra is the study of commutative rings, which are commutative algebras over the integers.
Algebra as a branch of mathematics
Algebra began with computations similar to those of arithmetic, with letters standing for numbers.[6] This allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic equation
ax^2+bx+c=0,
a, b, c can be any numbers whatsoever (except that a cannot be 0), and the quadratic formula can be used to quickly and easily find the value of the unknown quantity x.
As it developed, algebra was extended to other non-numerical objects, such as vectors, matrices, and polynomials. Then the structural properties of these non-numerical objects were abstracted to define algebraic structures such as groups, rings, and fields.
Before the 16th century, mathematics was divided into only two subfields, arithmetic and geometry. Even though some methods, which had been developed much earlier, may be considered nowadays as algebra, the emergence of algebra and, soon thereafter, of infinitesimal calculus as subfields of mathematics only dates from 16th or 17th century. From the second half of 19th century on, many new fields of mathematics appeared, most of which made use of both arithmetic and geometry, and almost all of which used algebra.
Today, algebra has grown until it includes many branches of mathematics, as can be seen in the Mathematics Subject Classification[8] where none of the first level areas (two digit entries) is called algebra. Today algebra includes section 08-General algebraic systems, 12-Field theory and polynomials, 13-Commutative algebra, 15-Linear and multilinear algebra; matrix theory, 16-Associative rings and algebras, 17-Nonassociative rings and algebras, 18-Category theory; homological algebra, 19-K-theory and 20-Group theory. Algebra is also used extensively in 11-Number theory and 14-Algebraic geometry.
History
Main articles: History of algebra and Timeline of algebra
The start of algebra as an area of mathematics may be dated to the end of 16th century, with François Viète's work. Until the 19th century, algebra consisted essentially of the theory of equations. In the following, "Prehistory of algebra" is about the results of the theory of equations that precede the emergence of algebra as an area of mathematics.
Early history of algebra
A page from Al-Khwārizmī's al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala
The roots of algebra can be traced to the ancient Babylonians,[9] who developed an advanced arithmetical system with which they were able to do calculations in an algorithmic fashion. The Babylonians developed formulas to calculate solutions for problems typically solved today by using linear equations, quadratic equations, and indeterminate linear equations. By contrast, most Egyptians of this era, as well as Greek and Chinese mathematics in the 1st millennium BC, usually solved such equations by geometric methods, such as those described in the Rhind Mathematical Papyrus, Euclid's Elements, and The Nine Chapters on the Mathematical Art. The geometric work of the Greeks, typified in the Elements, provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations, although this would not be realized until mathematics developed in medieval Islam.[10]
By the time of Plato, Greek mathematics had undergone a drastic change. The Greeks created a geometric algebra where terms were represented by sides of geometric objects, usually lines, that had letters associated with them.[6] Diophantus (3rd century AD) was an Alexandrian Greek mathematician and the author of a series of books called Arithmetica. These texts deal with solving algebraic equations,[11] and have led, in number theory to the modern notion of Diophantine equation.
Earlier traditions discussed above had a direct influence on Muhammad ibn Mūsā al-Khwārizmī (c. 780–850). He later wrote The Compendious Book on Calculation by Completion and Balancing, which established algebra as a mathematical discipline that is independent of geometry and arithmetic.[12]
The Hellenistic mathematicians Hero of Alexandria and Diophantus[13] as well as Indian mathematicians such as Brahmagupta continued the traditions of Egypt and Babylon, though Diophantus' Arithmetica and Brahmagupta's Brahmasphutasiddhanta are on a higher level.[14] For example, the first complete arithmetic solution (including zero and negative solutions) to quadratic equations was described by Brahmagupta in his book Brahmasphutasiddhanta. Later, Arabic and Muslim mathematicians developed algebraic methods to a much higher degree of sophistication. Although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Al-Khwarizmi contribution was fundamental. He solved linear and quadratic equations without algebraic symbolism, negative numbers or zero, thus he has to distinguish several types of equations.[15]
In the context where algebra is identified with the theory of equations, the Greek mathematician Diophantus has traditionally been known as the "father of algebra" but in more recent times there is much debate over whether al-Khwarizmi, who founded the discipline of al-jabr, deserves that title instead.[16] Those who support Diophantus point to the fact that the algebra found in Al-Jabr is slightly more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[17] Those who support Al-Khwarizmi point to the fact that he introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which the term al-jabr originally referred to,[18] and that he gave an exhaustive explanation of solving quadratic equations,[19] supported by geometric proofs, while treating algebra as an independent discipline in its own right.[20] His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study". He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems".[21]
The Persian mathematician Omar Khayyam is credited with identifying the foundations of algebraic geometry and found the general geometric solution of the cubic equation. Another Persian mathematician, Sharaf al-Dīn al-Tūsī, found algebraic and numerical solutions to various cases of cubic equations.[22] He also developed the concept of a function.[23] The Indian mathematicians Mahavira and Bhaskara II, the Persian mathematician Al-Karaji,[24] and the Chinese mathematician Zhu Shijie, solved various cases of cubic, quartic, quintic and higher-order polynomial equations using numerical methods. In the 13th century, the solution of a cubic equation by Fibonacci is representative of the beginning of a revival in European algebra. As the Islamic world was declining, the European world was ascending. And it is here that algebra was further developed.
History of algebra
Italian mathematician Girolamo Cardano published the solutions to the cubic and quartic equations in his 1545 book Ars magna.
François Viète's work on new algebra at the close of the 16th century was an important step towards modern algebra. In 1637, René Descartes published La Géométrie, inventing analytic geometry and introducing modern algebraic notation. Another key event in the further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century. The idea of a determinant was developed by Japanese mathematician Kowa Seki in the 17th century, followed independently by Gottfried Leibniz ten years later, for the purpose of solving systems of simultaneous linear equations using matrices. Gabriel Cramer also did some work on matrices and determinants in the 18th century. Permutations were studied by Joseph-Louis Lagrange in his 1770 paper Réflexions sur la résolution algébrique des équations devoted to solutions of algebraic equations, in which he introduced Lagrange resolvents. Paolo Ruffini was the first person to develop the theory of permutation groups, and like his predecessors, also in the context of solving algebraic equations.
Abstract algebra was developed in the 19th century, deriving from the interest in solving equations, initially focusing on what is now called Galois theory, and on constructibility issues.[25] George Peacock was the founder of axiomatic thinking in arithmetic and algebra. Augustus De Morgan discovered relation algebra in his Syllabus of a Proposed System of Logic. Josiah Willard Gibbs developed an algebra of vectors in three-dimensional space, and Arthur Cayley developed an algebra of matrices (this is a noncommutative algebra).[26]
Areas of mathematics with the word algebra in their name
Some areas of mathematics that fall under the classification abstract algebra have the word algebra in their name; linear algebra is one example. Others do not: group theory, ring theory, and field theory are examples. In this section, we list some areas of mathematics with the word "algebra" in the name.
• Elementary algebra, the part of algebra that is usually taught in elementary courses of mathematics.
• Abstract algebra, in which algebraic structures such as groups, rings and fields are axiomatically defined and investigated.
• Linear algebra, in which the specific properties of linear equations, vector spaces and matrices are studied.
• Commutative algebra, the study of commutative rings.
• Computer algebra, the implementation of algebraic methods as algorithms and computer programs.
• Homological algebra, the study of algebraic structures that are fundamental to study topological spaces.
• Universal algebra, in which properties common to all algebraic structures are studied.
• Algebraic number theory, in which the properties of numbers are studied from an algebraic point of view.
• Algebraic geometry, a branch of geometry, in its primitive form specifying curves and surfaces as solutions of polynomial equations.
• Algebraic combinatorics, in which algebraic methods are used to study combinatorial questions.
Many mathematical structures are called algebras:
• Algebra over a field or more generally algebra over a ring.
Many classes of algebras over a field or over a ring have a specific name:
• Associative algebra
• Non-associative algebra
• Lie algebra
• Hopf algebra
• C*-algebra
• Symmetric algebra
• Exterior algebra
• Tensor algebra
• In measure theory,
• Sigma-algebra
• Algebra over a set
• In category theory
• F-algebra and F-coalgebra
• T-algebra
• In logic,
• Relational algebra: a set of finitary relations that is closed under certain operators.
• Boolean algebra, a structure abstracting the computation with the truth values false and true. The structures also have the same name.
• Heyting algebra
Elementary algebra
Main article: Elementary algebra
Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often represented by symbols called variables (such as a, n, x, y or z). This is useful because:
It allows the general formulation of arithmetical laws (such as a + b = b + a for all a and b), and thus is the first step to a systematic exploration of the properties of the real number system.
It allows the reference to "unknown" numbers, the formulation of equations and the study of how to solve these. (For instance, "Find a number x such that 3x + 1 = 10" or going a bit further "Find a number x such that ax + b = c". This step leads to the conclusion that it is not the nature of the specific numbers that allows us to solve it, but that of the operations involved.)
It allows the formulation of functional relationships. (For instance, "If you sell x tickets, then your profit will be 3x − 10 dollars, or f(x) = 3x − 10, where f is the function, and x is the number to which the function is applied".)
Polynomials
The graph of a polynomial function of degree 3.
Main article: Polynomial
A polynomial is an expression that is the sum of a finite number of non-zero terms, each term consisting of the product of a constant and a finite number of variables raised to whole number powers. For example, x2 + 2x − 3 is a polynomial in the single variable x. A polynomial expression is an expression that may be rewritten as a polynomial, by using commutativity, associativity and distributivity of addition and multiplication. For example, (x − 1)(x + 3) is a polynomial expression, that, properly speaking, is not a polynomial. A polynomial function is a function that is defined by a polynomial, or, equivalently, by a polynomial expression. The two preceding examples define the same polynomial function.
Two important and related problems in algebra are the factorization of polynomials, that is, expressing a given polynomial as a product of other polynomials that can not be factored any further, and the computation of polynomial greatest common divisors. The example polynomial above can be factored as (x − 1)(x + 3). A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.
Education
See also: Mathematics education
It has been suggested that elementary algebra should be taught as young as eleven years old,[27] though in recent years it is more common for public lessons to begin at the eighth grade level (≈ 13 y.o. ±) in the United States.[28]
Since 1997, Virginia Tech and some other universities have begun using a personalized model of teaching algebra that combines instant feedback from specialized computer software with one-on-one and small group tutoring, which has reduced costs and increased student achievement.[29]
Abstract algebra
Main articles: Abstract algebra and Algebraic structure
Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts. Here are listed fundamental concepts in abstract algebra.
Sets: Rather than just considering the different types of numbers, abstract algebra deals with the more general concept of sets: a collection of all objects (called elements) selected by property specific for the set. All collections of the familiar types of numbers are sets. Other examples of sets include the set of all two-by-two matrices, the set of all second-degree polynomials (ax2 + bx + c), the set of all two dimensional vectors in the plane, and the various finite groups such as the cyclic groups, which are the groups of integers modulo n. Set theory is a branch of logic and not technically a branch of algebra.
Binary operations: The notion of addition (+) is abstracted to give a binary operation, ∗ say. The notion of binary operation is meaningless without the set on which the operation is defined. For two elements a and b in a set S, a ∗ b is another element in the set; this condition is called closure. Addition (+), subtraction (-), multiplication (×), and division (÷) can be binary operations when defined on different sets, as are addition and multiplication of matrices, vectors, and polynomials.
Identity elements: The numbers zero and one are abstracted to give the notion of an identity element for an operation. Zero is the identity element for addition and one is the identity element for multiplication. For a general binary operator ∗ the identity element e must satisfy a ∗ e = a and e ∗ a = a. This holds for addition as a + 0 = a and 0 + a = a and multiplication a × 1 = a and 1 × a = a. Not all sets and operator combinations have an identity element; for example, the set of positive natural numbers (1, 2, 3, ...) has no identity element for addition.
Inverse elements: The negative numbers give rise to the concept of inverse elements. For addition, the inverse of a is written −a, and for multiplication the inverse is written a−1. A general two-sided inverse element a−1 satisfies the property that a ∗ a−1 = 1 and a−1 ∗ a = 1 .
Associativity: Addition of integers has a property called associativity. That is, the grouping of the numbers to be added does not affect the sum. For example: (2 + 3) + 4 = 2 + (3 + 4). In general, this becomes (a ∗ b) ∗ c = a ∗ (b ∗ c). This property is shared by most binary operations, but not subtraction or division or octonion multiplication.
Commutativity: Addition and multiplication of real numbers are both commutative. That is, the order of the numbers does not affect the result. For example: 2 + 3 = 3 + 2. In general, this becomes a ∗ b = b ∗ a. This property does not hold for all binary operations. For example, matrix multiplication and quaternion multiplication are both non-commutative.
Groups
Main article: Group (mathematics)
See also: Group theory and Examples of groups
Combining the above concepts gives one of the most important structures in mathematics: a group. A group is a combination of a set S and a single binary operation ∗, defined in any way you choose, but with the following properties:
An identity element e exists, such that for every member a of S, e ∗ a and a ∗ e are both identical to a.
Every element has an inverse: for every member a of S, there exists a member a−1 such that a ∗ a−1 and a−1 ∗ a are both identical to the identity element.
The operation is associative: if a, b and c are members of S, then (a ∗ b) ∗ c is identical to a ∗ (b ∗ c).
If a group is also commutative—that is, for any two members a and b of S, a ∗ b is identical to b ∗ a—then the group is said to be abelian.
For example, the set of integers under the operation of addition is a group. In this group, the identity element is 0 and the inverse of any element a is its negation, −a. The associativity requirement is met, because for any integers a, b and c, (a + b) + c = a + (b + c)
The nonzero rational numbers form a group under multiplication. Here, the identity element is 1, since 1 × a = a × 1 = a for any rational number a. The inverse of a is 1/a, since a × 1/a = 1.
The integers under the multiplication operation, however, do not form a group. This is because, in general, the multiplicative inverse of an integer is not an integer. For example, 4 is an integer, but its multiplicative inverse is ¼, which is not an integer.
The theory of groups is studied in group theory. A major result in this theory is the classification of finite simple groups, mostly published between about 1955 and 1983, which separates the finite simple groups into roughly 30 basic types.
Semigroups, quasigroups, and monoids are structures similar to groups, but more general. They comprise a set and a closed binary operation, but do not necessarily satisfy the other conditions. A semigroup has an associative binary operation, but might not have an identity element. A monoid is a semigroup which does have an identity but might not have an inverse for every element. A quasigroup satisfies a requirement that any element can be turned into any other by either a unique left-multiplication or right-multiplication; however the binary operation might not be associative.
All groups are monoids, and all monoids are semigroups.
Set Operation Closed Natural numbers N Integers Z Rational numbers Q (also real R and complex C numbers) Integers modulo 3: Z3 = {0, 1, 2} + × (w/o zero) + × (w/o zero) + − × (w/o zero) ÷ (w/o zero) + × (w/o zero) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Identity 0 1 0 1 0 N/A 1 N/A 0 1 Inverse N/A N/A −a N/A −a N/A 1/a N/A 0, 2, 1, respectively N/A, 1, 2, respectively Associative Yes Yes Yes Yes Yes No Yes No Yes Yes Commutative Yes Yes Yes Yes Yes No Yes No Yes Yes Structure monoid monoid abelian group monoid abelian group quasigroup abelian group quasigroup abelian group abelian group (Z2)
Rings and fields
Main articles: Ring (mathematics) and Field (mathematics)
See also: Ring theory, Glossary of ring theory, Field theory (mathematics) and Glossary of field theory
Groups just have one binary operation. To fully explain the behaviour of the different types of numbers, structures with two operators need to be studied. The most important of these are rings, and fields.
A ring has two binary operations (+) and (×), with × distributive over +. Under the first operator (+) it forms an abelian group. Under the second operator (×) it is associative, but it does not need to have identity, or inverse, so division is not required. The additive (+) identity element is written as 0 and the additive inverse of a is written as −a.
Distributivity generalises the distributive law for numbers. For the integers (a + b) × c = a × c + b × c and c × (a + b) = c × a + c × b, and × is said to be distributive over +.
The integers are an example of a ring. The integers have additional properties which make it an integral domain.
A field is a ring with the additional property that all the elements excluding 0 form an abelian group under ×. The multiplicative (×) identity is written as 1 and the multiplicative inverse of a is written as a−1.
The rational numbers, the real numbers and the complex numbers are all examples of fields.
See also
Portal icon Algebra portal
Outline of algebra
Outline of linear algebra
Algebra tile
Notes
"algebra". Online Etymology Dictionary.
I. N. Herstein, Topics in Algebra, "An algebraic system can be described as a set of objects together with some operations for combining them." p. 1, Ginn and Company, 1964
I. N. Herstein, Topics in Algebra, "...it also serves as the unifying thread which interlaces almost all of mathematics." p. 1, Ginn and Company, 1964
Omar Khayyám
"Omar Khayyam". Encyclopedia Britannica. Retrieved 5 October 2014.
(Boyer 1991, "Europe in the Middle Ages" p. 258) "In the arithmetical theorems in Euclid's Elements VII-IX, numbers had been represented by line segments to which letters had been attached, and the geometric proofs in al-Khwarizmi's Algebra made use of lettered diagrams; but all coefficients in the equations used in the Algebra are specific numbers, whether represented by numerals or written out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions that are so readily available in geometry."
"algebra". Oxford English Dictionary. Oxford University Press.
"2010 Mathematics Subject Classification". Retrieved 5 October 2014.
Struik, Dirk J. (1987). A Concise History of Mathematics. New York: Dover Publications. ISBN 0-486-60255-9.
Boyer 1991
Cajori, Florian (2010). A History of Elementary Mathematics – With Hints on Methods of Teaching. p. 34. ISBN 1-4460-2221-8.
Roshdi Rashed (November 2009). "Al Khwarizmi: The Beginnings of Algebra". Saqi Books. ISBN 0-86356-430-5
"Diophantus, Father of Algebra". Retrieved 5 October 2014.
"History of Algebra". Retrieved 5 October 2014.
Josef W. Meri (2004). Medieval Islamic Civilization. Psychology Press. p. 31. ISBN 978-0-415-96690-0. Retrieved 25 November 2012.
Boyer, Carl B. (1991). A History of Mathematics (Second ed.). Wiley. pp. 178, 181. ISBN 0-471-54397-7.
Boyer, Carl B. (1991). A History of Mathematics (Second ed.). Wiley. p. 228. ISBN 0-471-54397-7.
(Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation."
(Boyer 1991, "The Arabic Hegemony" p. 230) "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwarizmi's exposition that his readers must have had little difficulty in mastering the solutions."
Gandz and Saloman (1936), The sources of al-Khwarizmi's algebra, Osiris i, p. 263–277: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers".
Rashed, R.; Armstrong, Angela (1994). The Development of Arabic Mathematics. Springer. pp. 11–2. ISBN 0-7923-2565-6. OCLC 29181926
O'Connor, John J.; Robertson, Edmund F., "Sharaf al-Din al-Muzaffar al-Tusi", MacTutor History of Mathematics archive, University of St Andrews.
Victor J. Katz, Bill Barton; Barton, Bill (October 2007). "Stages in the History of Algebra with Implications for Teaching". Educational Studies in Mathematics (Springer Netherlands) 66 (2): 185–201 [192]. doi:10.1007/s10649-006-9023-7
(Boyer 1991, "The Arabic Hegemony" p. 239) "Abu'l Wefa was a capable algebraist as well as a trigonometer. ... His successor al-Karkhi evidently used this translation to become an Arabic disciple of Diophantus – but without Diophantine analysis! ... In particular, to al-Karkhi is attributed the first numerical solution of equations of the form ax2n + bxn = c (only equations with positive roots were considered),"
"The Origins of Abstract Algebra". University of Hawaii Mathematics Department.
"The Collected Mathematical Papers".Cambridge University Press.
"Hull's Algebra" (PDF). New York Times. July 16, 1904. Retrieved September 21, 2012.
Quaid, Libby (September 22, 2008). "Kids misplaced in algebra" (REPORT). Associated Press. Retrieved September 23, 2012.
Hamilton, Reeve (7 September 2012). "THE TEXAS TRIBUNE; U.T.-Arlington Adopts New Way to Tackle Algebra". The New York Times. Retrieved 10 September 2012.
References
Boyer, Carl B. (1991), A History of Mathematics (Second Edition ed.), John Wiley & Sons, Inc., ISBN 0-471-54397-7
Donald R. Hill, Islamic Science and Engineering (Edinburgh University Press, 1994).
Ziauddin Sardar, Jerry Ravetz, and Borin Van Loon, Introducing Mathematics (Totem Books, 1999).
George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics (Penguin Books, 2000).
John J O'Connor and Edmund F Robertson, History Topics: Algebra Index. In MacTutor History of Mathematics archive (University of St Andrews, 2005).
I.N. Herstein: Topics in Algebra. ISBN 0-471-02371-X
R.B.J.T. Allenby: Rings, Fields and Groups. ISBN 0-340-54440-6
L. Euler: Elements of Algebra, ISBN 978-1-899618-73-6
Asimov, Isaac (1961). Realm of Algebra. Houghton Mifflin.
External links
Khan Academy: Conceptual videos and worked examples
Khan Academy: Origins of Algebra, free online micro lectures
Algebrarules.com: An open source resource for learning the fundamentals of Algebra
4000 Years of Algebra, lecture by Robin Wilson, at Gresham College, October 17, 2007 (available for MP3 and MP4 download, as well as a text file).
Algebra entry by Vaughan Pratt in the Stanford Encyclopedia of Philosophy
Retrieved from "http://en.wikipedia.org/"
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## euler function problem
Below is the question and my code. I don't know why its not working need some help
Question
Let S(n,m) = ∑φ(n × i) for 1 ≤ i ≤ m. (φ is Euler's totient function)
You are given that S(510510,10^6 )= 45480596821125120.
Find S(510510,10^11).
Java Code:
```import java.math.BigInteger;
public class TotientSum {
private static final int n = 510510;
private static String calculateSum(){
BigInteger sum = null;
for(BigInteger i= BigInteger.valueOf(10).pow(11);i.compareTo(BigInteger.ONE)>0;i =i.subtract(BigInteger.ONE)){
}
return sum.toString();
}
private static BigInteger totient(BigInteger num) {
int count = 0;
for (BigInteger a = BigInteger.ONE; a.compareTo(num)<0; a=a.add(BigInteger.ONE)) {
if (gcd(num, a) == BigInteger.ONE) {
count++;
}
}
return (BigInteger.valueOf(count));
}
private static BigInteger gcd(BigInteger p, BigInteger q) {
while (q != BigInteger.ZERO) {
BigInteger temp = q;
q = p.mod(q);
p = temp;
}
return p;
}
public static void main(String[] args) {
System.out.println(calculateSum());
}
}```
Last edited by CodeX Pro; 06-16-2013 at 05:25 PM.
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## Re: euler function problem
Try using:
Java Code:
```if (gcd(num, a).equals(BigInteger.ONE)) {
count++;
}```
Java Code:
```if (gcd(num, a) == BigInteger.ONE) {
count++;
}```
Regards,
Jim
3. ## Re: euler function problem
... and a similar construct in line 25.
db
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## Re: euler function problem
Originally Posted by jim829
Try using:
Java Code:
```if (gcd(num, a).equals(BigInteger.ONE)) {
count++;
}```
Java Code:
```if (gcd(num, a) == BigInteger.ONE) {
count++;
}```
Regards,
Jim
Didn't work. Its taking very long to run. Tell me one thing whether I have implemented the functions properly or not. I think its okay.
Will you please to help me with this.
5. ## Re: euler function problem
Get this straight: using == or != to compare object types is just plain wrong. Use equals(...) and !...equals(...).
db
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## Re: euler function problem
Originally Posted by DarrylBurke
Get this straight: using == or != to compare object types is just plain wrong. Use equals(...) and !...equals(...).
db
yes I did didn't work. I would ask you to run this code and see the problem that I am facing
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## Re: euler function problem
Good catch! I didn't see that first time thru. Was getting ready to respond....
Regards,
Jim
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## Re: euler function problem
When I have problems like this I usually put print statements thru out the program to see if they are even close to satisfying my conditionals (among other things). What type of debugging have you done?
Regards,
Jim
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## Re: euler function problem
Originally Posted by jim829
When I have problems like this I usually put print statements thru out the program to see if they are even close to satisfying my conditionals (among other things). What type of debugging have you done?
Regards,
Jim
I have used print statements but they are taking very long to print and this can be understood very well from the maths applied here. So are there better approaches. Also I fear that BigInteger is not big enough to hold the numbers
10. ## Re: euler function problem
Originally Posted by CodeX Pro
I fear that BigInteger is not big enough to hold the numbers
BigIntegers are made as large as necessary to accommodate the results of an operation.
db
11. ## Re: euler function problem
I think you should apply a bit of math instead of trying to solve that bloody thing by brute force; for one thing: phi(n*m) == phi(n)*phi(m)*g/phi(g) where g == gcd(n, m), also 10^11 == 2^11*5^11 ... and phi(2) == 1 and phi(5) == 4
kind regards,
Jos (<--- extremely lazy on a Sunday)
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## Re: euler function problem
Originally Posted by JosAH
I think you should apply a bit of math instead of trying to solve that bloody thing by brute force; for one thing: phi(n*m) == phi(n)*phi(m)*g/phi(g) where g == gcd(n, m), also 10^11 == 2^11*5^11 ... and phi(2) == 1 and phi(5) == 4
kind regards,
Jos (<--- extremely lazy on a Sunday)
Java Code:
```import java.math.BigInteger;
/**
*
* @author CodeX Pro
*/
public class TotientSum {
private static BigInteger n = BigInteger.valueOf(510510);
private static String calculateSum() {
BigInteger sum = BigInteger.ZERO;
for (BigInteger i = BigInteger.ONE; i.compareTo(BigInteger.valueOf(10).pow(11)) < 0; i = i.add(BigInteger.ONE)) {
BigInteger m = (totient(n).multiply(totient(i))).multiply((gcd(n, i).divide(totient(gcd(n, i)))));
//System.out.println(m);
//System.out.println(sum);
}
return sum.toString();
}
private static BigInteger totient(BigInteger num) {
int count = 0;
for (BigInteger a = BigInteger.ONE; a.compareTo(num) < 1; a = a.add(BigInteger.ONE)) {
if (gcd(num, a).equals(BigInteger.ONE)) {
count++;
}
}
return (BigInteger.valueOf(count));
}
private static BigInteger gcd(BigInteger p, BigInteger q) {
while (!q.equals(BigInteger.ZERO)) {
BigInteger temp = q;
q = p.mod(q);
p = temp;
}
return p;
}
public static void main(String[] args) {
System.out.println(calculateSum());
}
}```
Okay I did so I have read it on wiki and used the formula still its not giving the output. Its taking a long time.
What did you meant to say by this "also 10^11 == 2^11*5^11 ... and phi(2) == 1 and phi(5) == 4" , I didn't get this part
Last edited by CodeX Pro; 06-16-2013 at 09:01 PM.
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## Re: euler function problem
Originally Posted by CodeX Pro
I have used print statements but they are taking very long to print and this can be understood very well from the maths applied here. So are there better approaches.
If they're taking to long to print then you are putting them in the wrong place. Try moving them to where they will print. Like inside a loop.
Regards,
Jim
14. ## Re: euler function problem
This message has been deleted by jim829.
ReasonDecided to let Jos explain it
Please don't; I didn't give this problem much thought except for the suggestions in my previous reply. Especially phi(a*b) == phi(a)*phi(b)*gcd(a,b)/phi(gcd(a,b)) should do the trick (just my gut feeling)
kind regards,
Jos
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## Re: euler function problem
Sorry. I started to provide some review on algebra and number theory but I was going down a black hole. And I couldn't tie what you said to an immediate solution at the time. So I didn't want to mislead the OP. And it was midnight here and I was tired.
I enjoy this stuff so I will work on it some. But after putting in some print statements I am uncertain this would finish in my lifetime. Iterating from 1 to 510510 x 10E11 by itself could take a while (I didn't time it). But to successively do that over and over again using the GCD and PHI algorithms just looked like it would take forever.
Regards,
Jim
16. ## Re: euler function problem
I'm too lazy for this puzzle; all I figured out was phi(10^n) == 4*10^(n-1) (all numbers ending with a 1, 3, 7 or 9 are odd and relatively prime to 5) but I fear the untangled mess for the other number ;-) but I don't think BigIntegers are needed; longs will do (<--- lazy guess)
kind regards,
Jos
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## Re: euler function problem
OK, I did the following simple loop with no internal calculations:
Java Code:
```long time = System.nanoTime();
for (long k = 0; k < 510_510_000L; k++) {
}
System.out.printf("%5.2f%n", ((double)System.nanoTime() - time)/1_000_000_000);```
On my machine (which is old) it took 2.09 seconds.
Assuming I understand the problem, the number you are trying to find involves 510_510_000 x 10e8 time consuming iterations. But to just run an empty loop would take:
2 seconds * 10E8 = approx 63 years.
So you need to find a better algorithm.
Regards,
Jim
18. ## Re: euler function problem
Originally Posted by jim829
So you need to find a better algorithm.
Yep, that many calculations are a waste of time; I found a few other things that might help: a simple one: 510510 == 2*3*5*7*11*13*17 (the first seven prime numbers) and a more general one:
let p1, p2, p3 ... be the unique prime divisors of n, then phi(n) == n*(1-1/p1)*(1-1/p2)*(1-1/p3) ...
this little problem is nagging me and a brute force approach as suggested by the OP is a nono ...
kind regards,
Jos
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# Vorland s government is planning a nationwide ban on smoking
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Vorland s government is planning a nationwide ban on smoking [#permalink]
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Updated on: 22 Oct 2017, 20:44
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Question Stats:
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Vorland’s government is planning a nationwide ban on smoking in restaurants. The objection that the ban would reduce restaurants’ revenues is ill founded. Several towns in Vorland enacted restaurant smoking restrictions five years ago. Since then, the amount the government collects in restaurant meal taxes in those towns has increased 34 percent, on average, but only 26 percent elsewhere in Vorland. The amount collected in restaurant meal taxes closely reflects restaurants’ revenues.
Which of the following, if true, most undermines the defense of the government’s plan?
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be correct in the short term.
B. The tax on meals in restaurants is higher than the tax on many other goods and services.
C. Over the last five years, smoking has steadily declined throughout Vorland.
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted.
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions.
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Originally posted by ankit0411 on 15 Sep 2012, 08:22.
Last edited by Mahmud6 on 22 Oct 2017, 20:44, edited 1 time in total.
Formatted
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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15 Sep 2012, 10:33
2
D is the right one.
Conclusion : The objection that the ban would reduce restaurants’ revenues is ill founded. >> Ban would not reduce revenues
Defence: Other towns where restaurants ban smoking show incresed revenue
To undermine the defence, we need to either show that the restuarents where smoking is banned have other resons for increased revenue OR Smoking is still permitted somehow.
Lets look at the answer choices:
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be
correct in the short term. >>> Talks about mean tax. Out of scope.
B. The tax on meals in restaurants is higher than the tax on many other goods and services. >>> Out of scope
C. Over the last five years, smoking has steadily declined throughout Vorland. >>> Out of scope
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted. >>> Smoking is allowed, but under restrictions. Bingo! Answer!
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions. >>> talks about same growth rate of sales taxes. Not adding any value.
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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15 Sep 2012, 11:41
1
piyatiwari wrote:
D is the right one.
Conclusion : The objection that the ban would reduce restaurants’ revenues is ill founded. >> Ban would not reduce revenues
Defence: Other towns where restaurants ban smoking show incresed revenue
To undermine the defence, we need to either show that the restuarents where smoking is banned have other resons for increased revenue OR Smoking is still permitted somehow.
Lets look at the answer choices:
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be
correct in the short term. >>> Talks about mean tax. Out of scope.
B. The tax on meals in restaurants is higher than the tax on many other goods and services. >>> Out of scope
C. Over the last five years, smoking has steadily declined throughout Vorland. >>> Out of scope
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted. >>> Smoking is allowed, but under restrictions. Bingo! Answer!
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions. >>> talks about same growth rate of sales taxes. Not adding any value.
Yea, I think I get it the other way .
Govt thinks that the ban is the reason for increased revenue ( that means smoking does not play any part in the revenue ).
To undermine this we come to D , which says smoking is allowed ( under restrictions) and this might be the cause to lure more customers .
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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10 Mar 2014, 08:33
ankit0411 wrote:
piyatiwari wrote:
D is the right one.
Conclusion : The objection that the ban would reduce restaurants’ revenues is ill founded. >> Ban would not reduce revenues
Defence: Other towns where restaurants ban smoking show incresed revenue
To undermine the defence, we need to either show that the restuarents where smoking is banned have other resons for increased revenue OR Smoking is still permitted somehow.
Lets look at the answer choices:
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be
correct in the short term. >>> Talks about mean tax. Out of scope.
B. The tax on meals in restaurants is higher than the tax on many other goods and services. >>> Out of scope
C. Over the last five years, smoking has steadily declined throughout Vorland. >>> Out of scope
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted. >>> Smoking is allowed, but under restrictions. Bingo! Answer!
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions. >>> talks about same growth rate of sales taxes. Not adding any value.
Yea, I think I get it the other way .
Govt thinks that the ban is the reason for increased revenue ( that means smoking does not play any part in the revenue ).
To undermine this we come to D , which says smoking is allowed ( under restrictions) and this might be the cause to lure more customers .
I am thinking the following way. The passage argues, by giving evidence, against the objection that the plan would decrease restaurant revenues. We are looking for an answer that undermines the argument. A potential answer could state that the revenues in certain town didn't increase due to smoking restrictions.
Answer D - Provides that restaurants can have have separate dining areas, one where smoking is allowed, and one where it's not. This means that these restaurants will attract both smokers and non-smokers, thus increasing the revenues.
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Vorland s government is planning a nationwide ban on smoking [#permalink]
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15 Oct 2014, 01:30
1
Let's try to simplify the question.
Conclusion: Smoking ban did not decrease revenues of restaurants
Support: in towns where smoking is banned, meal taxes are higher
So basically we need to find an answer that weakens the argument
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be correct in the short term.
The argument has nothing to do with opponents, clearly out of scope
B. The tax on meals in restaurants is higher than the tax on many other goods and services.
Out of scope; even if the tax on meals are higher, it does not have any affect on the conclusion
C. Over the last five years, smoking has steadily declined throughout Vorland.
Out of scope
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted.
Correct. Restaurants can still maintain a separate dining area to serve smokers. So if today these restaurants are not allowed to have such separate areas to serve these smokers then revenue will definitely be affected
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions
out of scope, we are not concerned about "sales tax"
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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25 Jul 2016, 14:29
options A,B and C are out of scope options
option E provides information which is not of much importance to the conclusion of the argument
option D is the clear weakener as it exposes the fact that smoking is still permitted somehow and not completely banned as the government intends to do
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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07 Jul 2017, 07:37
In option D it says restaurants can maintain. So it looks like a suggestion not a statement.
Am I getting it wrong ?
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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19 Sep 2017, 04:18
somtsat99 wrote:
In option D it says restaurants can maintain. So it looks like a suggestion not a statement.
Am I getting it wrong ?
Hi somtsat99,
You are not wrong! The question, stated below, says that restaurants have the option to keep smoking. If this is true, then a restaurant with increased, or steady, revenue post-ban could be a result of the restaurant allowing smoking. But just because it is a suggestion doesn't hurt the strength of the answer for this question.
Gov't bans smoking --- restaurant doesn't lose money ----- Gov't says no smoking because the restaurants are fine without it.
How to weaken this? To show that smoking still helped the restaurant make money. This is answer D!
Vorland’s government is planning a nationwide ban on smoking in restaurants. The objection that the ban would reduce restaurants’ revenues is ill founded. Several towns in Vorland enacted restaurant smoking restrictions five years ago. Since then, the amount the government collects in restaurant meal taxes in those towns has increased 34 percent, on average, but only 26 percent elsewhere in Vorland. The amount collected in restaurant meal taxes closely reflects restaurants’ revenues.
Which of the following, if true, most undermines the defense of the government’s plan?
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be
correct in the short term.
B. The tax on meals in restaurants is higher than the tax on many other goods and services.
C. Over the last five years, smoking has steadily declined throughout Vorland.
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted.
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions.
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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07 Feb 2018, 09:48
hello, I did choose D as the correct answer, but I cannot understand how D can connect anything with the premises or the conclusion of the argument. Please help me to understand such gmat method in CR questions.
Thanks.
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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10 Feb 2018, 07:31
Vorland’s government is planning a nationwide ban on smoking in restaurants. The objection that the ban would reduce restaurants’ revenues is ill founded. Several towns in Vorland enacted restaurant smoking restrictions five years ago. Since then, the amount the government collects in restaurant meal taxes in those towns has increased 34 percent, on average, but only 26 percent elsewhere in Vorland. The amount collected in restaurant meal taxes closely reflects restaurants’ revenues. --Highlighted part is the conclusion
Which of the following, if true, most undermines the defense of the government’s plan?
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be correct in the short term.
Argument is about the impact of "smoking" ban on revenues. This choice is out of scope.
B. The tax on meals in restaurants is higher than the tax on many other goods and services.
This will be consistent throughout the country. This doesn't mean that the ban worked or didn't work. Out of scope.
C. Over the last five years, smoking has steadily declined throughout Vorland.
This should strengthen the argument because if the smoking is reducing then the ban should only help the restaurants.
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted.
Correct.
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions.
But the rate at which the tax from banned areas is increasing is higher than the rate from the areas where smoking is not banned. This would actually strengthen the argument.
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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13 Feb 2018, 05:35
Vorland’s government is planning a nationwide ban on smoking in restaurants. The objection that the ban would reduce restaurants’ revenues is ill founded. Several towns in Vorland enacted restaurant smoking restrictions five years ago. Since then, the amount the government collects in restaurant meal taxes in those towns has increased 34 percent, on average, but only 26 percent elsewhere in Vorland. The amount collected in restaurant meal taxes closely reflects restaurants’ revenues.
Which of the following, if true, most undermines the defense of the government’s plan?
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be correct in the short term.
B. The tax on meals in restaurants is higher than the tax on many other goods and services.
C. Over the last five years, smoking has steadily declined throughout Vorland.
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted.
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions.
GMATNinja,
Hello,
What if the government has increased the % of tax collected from restaurants , say the tax % has increased to 10% from 5%, in such case the amount the government collects in restaurant meal taxes in those towns can increase 34 percent, on average, but only 26 percent elsewhere in Vorland. E excludes this possibility and hence, undermines the conclusion.
Where as 'can' in D doesn't guarantee that the restaurants have adopted this measure.
What am I missing?
Thank you
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Vorland s government is planning a nationwide ban on smoking [#permalink]
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15 Feb 2018, 22:12
3
aaba wrote:
hello, I did choose D as the correct answer, but I cannot understand how D can connect anything with the premises or the conclusion of the argument. Please help me to understand such gmat method in CR questions.
Thanks.
Quote:
Vorland’s government is planning a nationwide ban on smoking in restaurants. The objection that the ban would reduce restaurants’ revenues is ill founded. Several towns in Vorland enacted restaurant smoking restrictions five years ago. Since then, the amount the government collects in restaurant meal taxes in those towns has increased 34 percent, on average, but only 26 percent elsewhere in Vorland. The amount collected in restaurant meal taxes closely reflects restaurants’ revenues.
Which of the following, if true, most undermines the defense of the government’s plan?
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be correct in the short term.
B. The tax on meals in restaurants is higher than the tax on many other goods and services.
C. Over the last five years, smoking has steadily declined throughout Vorland.
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted.
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions.
The key is to notice that the government is considering a BAN on smoking in restaurants. To defend the ban, the author of the passage uses evidence from a RESTRICTION on smoking in restaurants. Imposing a ban might be much different than imposing restrictions.
Choice (D) illustrates this point. The restaurants in towns with restrictions were fine because, despite the restrictions, those restaurants could allow customers to smoke in separate dining areas. If those towns had smoking bans instead of smoking restrictions, separate dining areas for smokers would not be allowed and perhaps revenues would decrease.
The author's evidence suggests that revenues might not decrease when smoking restrictions are implemented. But this doesn't necessarily provide any evidence related to the effect of a smoking ban.
If choice (D) is true, then the author's argument falls apart, so (D) is the best answer.
TaN1213 wrote:
GMATNinja,
Hello,
What if the government has increased the % of tax collected from restaurants , say the tax % has increased to 10% from 5%, in such case the amount the government collects in restaurant meal taxes in those towns can increase 34 percent, on average, but only 26 percent elsewhere in Vorland. E excludes this possibility and hence, undermines the conclusion.
Where as 'can' in D doesn't guarantee that the restaurants have adopted this measure.
What am I missing?
Thank you
Choice (E) does not actually tell us whether meal tax rates were increased or decreased. Choice (E) simply tells us that total revenue from SALES taxes (much more general than just meal taxes) did not grow any faster in towns with restrictions. Even if choice (E) is true, revenue from MEAL taxes may have grown faster in towns with restrictions. The restaurants in the towns with restrictions may have done very well, while other kinds of shops did very well in the towns WITHOUT restrictions.
In that case, the total sales taxes may have increased by about the same amount in all towns, even though restaurants in towns with the restrictions did much better than restaurants in other towns. So even if (E) is true, the defense of the plan may not be undermined. Yes, we can think of a situation in which (E) is true and the author's argument is weakened. But without further information, we don't know whether (E) undermines the defense of the plan.
Remember that we are not trying to PROVE that the government's plan will fail. We are only looking for the answer choice that MOST undermines the defense of the plan. We could certainly come up with scenarios in which (D) is true and the plan is not undermined. But (D) undermines the defense of the plan more than any of the other choice, so it is the best answer.
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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23 Apr 2018, 00:49
Pre-thinking: We need to weaken the government plan's defense. in other words, government’s plan will not be much of use. try to find out a loop hole out of it.
A. When the state first imposed a restaurant meal tax, opponents predicted that restaurants’ revenues would decline as a result, a prediction that proved to be correct in the short term. ---- We are looking for ban on smoke not meal tax.
B. The tax on meals in restaurants is higher than the tax on many other goods and services. --- irrelevant
C. Over the last five years, smoking has steadily declined throughout Vorland.---- not helping.
D. In many of the towns that restrict smoking in restaurants, restaurants can maintain separate dining areas where smoking is permitted. --- So this option is saying that suppose government imposes the ban but restaurant open smoking area which is legal. now government’s ban has no effect. this is what we are looking for.
E. Over the last five years, government revenues from sales taxes have grown no faster in the towns with restaurant smoking restrictions than in the towns that have no such restrictions. --- irrelevant
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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23 Apr 2018, 09:25
The second time I solve this question, (I do not remember the argument or the answer), I can do it in 10 seconds by skimming the question. I combine the instinct, meaning, and patterns.
Perhaps, this is the best way to skip questions when time runs out.
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Re: Vorland s government is planning a nationwide ban on smoking [#permalink]
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14 May 2018, 10:28
is this an OG question? Does not seem like it.
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Re: Vorland s government is planning a nationwide ban on smoking &nbs [#permalink] 14 May 2018, 10:28
Display posts from previous: Sort by | 5,988 | 26,985 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2018-47 | latest | en | 0.870426 |
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http://stackoverflow.com/questions/1818376/iphone-accelerometer-works-even-in-flat-surface | 1,405,334,659,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1404776440271.67/warc/CC-MAIN-20140707234040-00063-ip-10-180-212-248.ec2.internal.warc.gz | 113,580,179 | 15,326 | # IPhone accelerometer works even in flat surface
I have an imageView in the view. It moves even if the iphone is still for some time. Why is it so ? Also the image does not respond quickly to the movement of the iphone.
Here is my code written for this:
I have also set the updateInterval and delegate for the accelerometer.
``````#define kVelocityMultiplier 1000;
-(void)accelerometer:(UIAccelerometer *)accelerometer didAccelerate:(UIAcceleration *)acceleration
{
if(currentPoint.x < 0)
{
currentPoint.x=0;
ballXVelocity=0;
}
if(currentPoint.x > 480-sliderWidth)
{
currentPoint.x=480-sliderWidth;
ballXVelocity=0;
}
static NSDate *lastDrawTime;
if(currentPoint.x<=480-sliderWidth&¤tPoint.x>=0)
{
if(lastDrawTime!=nil)
{
NSTimeInterval secondsSinceLastDraw=-([lastDrawTime timeIntervalSinceNow]);
ballXVelocity = ballXVelocity + -acceleration.y*secondsSinceLastDraw;
CGFloat xAcceleration=secondsSinceLastDraw * ballXVelocity * kVelocityMultiplier;
currentPoint = CGPointMake(currentPoint.x + xAcceleration, 266);
}
slider.frame=CGRectMake(currentPoint.x, currentPoint.y, sliderWidth, 10);
}
[lastDrawTime release];
lastDrawTime=[[NSDate alloc]init];
}
``````
Can anyone help me out please ?
-
I notice a couple of things in the code
• The two first if statements to have the position within a certain range should be done just before the slider position is set, otherwise it can happen that the image will be set outside the preferred range.
• `ballXVelocity` is calculated as normalized from the `acceleration.y` value times the delta time. Maybe you should look into multiplying that factor instead of doing the `kVelocityMultiplier` on the next line.
• As the accelerometer is very sensitive and it is hard to make perfect fit on the circuitboard one never get perfect value. Instead one should try to have some calibration stage and perhaps use only a valid range similar the two first if statements.
-
You might consider filtering your values the Apple way.
``````#define kFilteringFactor 0.15
- (void)accelerometer:(UIAccelerometer *)accelerometer didAccelerate:(UIAcceleration *)acceleration {
accelx = acceleration.x * kFilteringFactor + accelx * (1.0 - kFilteringFactor);
accely = acceleration.y * kFilteringFactor + accely * (1.0 - kFilteringFactor);
accelz = acceleration.y * kFilteringFactor + accelz * (1.0 - kFilteringFactor);}
``````
accelx, accely and accelz are UIAccelerometerValues.
Then you can do something like
``````ball.position.x += accelx * ballSpeed * deltaDrawingTime;
``````
The movement should be nicer now.
- | 617 | 2,572 | {"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-2014-23 | latest | en | 0.722803 |
https://testbook.com/question-answer/findrm-frac-d2-cot-1xdx2--5fbb4e87cd391d62958e3ac0 | 1,679,619,479,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945218.30/warc/CC-MAIN-20230323225049-20230324015049-00143.warc.gz | 634,120,559 | 81,727 | # Find $$\rm \frac {d^2 \cot^ {-1}x}{dx^2}$$
1. $$\rm \frac{-2x}{(1+x^2)^2}$$
2. $$\rm \frac{-2}{(1+x^2)^2}$$
3. $$\rm \frac{-1}{(1+x^2)^2}$$
4. $$\rm \frac{2x}{(1+x^2)^2}$$
Option 4 : $$\rm \frac{2x}{(1+x^2)^2}$$
Free
CRPF Head Constable Ministerial 22 Feb 2023 (Shift 1) Memory-Based Test
1.3 Lakh Users
100 Questions 100 Marks 90 Mins
## Detailed Solution
Concept:
Suppose that we have two functions f(x) and g(x) and they are both differentiable.
• Product Rule: $$\frac{{\rm{d}}}{{{\rm{dx}}}}\left[ {{\rm{f}}\left( {\rm{x}} \right){\rm{\;g}}\left( {\rm{x}} \right)} \right] = {\rm{\;f'}}\left( {\rm{x}} \right){\rm{\;g}}\left( {\rm{x}} \right) + {\rm{f}}\left( {\rm{x}} \right){\rm{\;g'}}\left( {\rm{x}} \right)$$
• Division rule: $$\frac{d}{dx}\frac{u}{v}=\frac{v\times u'-u \times v'}{v^2}$$
Formulas:
$$\rm \frac{d \cot^{-1} x}{dx} = \frac{-1}{1+x^2}$$
Calculation:
$$\rm \frac {d^2 \cot^ {-1}x}{dx^2}$$
$$\rm \frac{d}{dx} \times \frac {d\cot^{-1} x}{dx}$$
$$\frac{d}{dx}(\frac{-1}{1+x^2})$$
$$-\:\frac{d}{dx}(\frac{1}{1+x^2})$$
⇒ $$-[\frac{(1+x^2)\times 0-1 \times2x}{(1+x^2)^2}]$$
$$-[\rm \frac{-2x}{(1+x^2)^2}]$$
$$\rm \frac{2x}{(1+x^2)^2}$$ | 565 | 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": 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} | 4.09375 | 4 | CC-MAIN-2023-14 | latest | en | 0.315394 |
http://quant.stackexchange.com/questions/1198/lib-for-arbitrage-free-smoothing-of-implied-volatility-surface?answertab=votes | 1,462,049,272,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860112727.96/warc/CC-MAIN-20160428161512-00209-ip-10-239-7-51.ec2.internal.warc.gz | 233,287,190 | 18,065 | # Lib for Arbitrage-Free Smoothing of Implied Volatility Surface?
I'm looking for an implementation of Arbitrage-Free Smoothing of the Implied Volatility Surface - Matthias R. Fengler.
Does anyone know of any existing libraries that have implemented this paper? Any method is ok (Excel, C++, Matlab, Mathematica, C#, etc).
In fact, any method that implements arbitrage free smoothing of the implied volatility surface is ok (can QuantLib do this?).
-
Arbitrage free smoothing of a local volatility surface is actually quite a difficult feat to accomplish. Its unlikely that this sort of library will be available outside of the big institutions, for some time to come.
-
it is difficult.... and noisy. but totally doable actually. you just need to project onto a parametric set which by construction is arbitrage free (thats one way to do it). but hey his question is answered, no ? – nicolas Jul 16 '11 at 19:45
I know that this question is quite old, but I uploaded a matlab implementation of the method to fileexchange: http://www.mathworks.com/matlabcentral/fileexchange/46253-arbitrage-free-smoothing-of-the-implied-volatility-surface
-
A little off-topic, but arbitrage conditions are locals. and no one cares about local arbitrage (to the extent that it can not be put in practice with reasonable chance).
It's like saying look, you gamma is infinite 1 seconds before expiry : but if your dirac is 1 eur, you'll never make more than that. or, in math speak, time to look if higher order derivatives are not high as well in the region.
All this to say, I'd like to see a non parametric vol surface that actually takes the tradable grid as input. Otherwise it's like talking about angel's sex.
If you know one such lib, I'd like to hear about it.
-
The whole point of specifying "arbitrage free" is to ensure that the vol surface is somewhat stable (i.e. its not offering obvious arb opportunities). You may not be able to profit from an obvious arb, but the CBOE certainly can, and it does. You want a non parametric vol surface that takes a tradable grid as input? Browse to intermarkit.com, and pay them \$7500 for their local volatility surface library. These libraries exist, they are just extremely difficult to get hold of. – Contango May 23 '11 at 10:10
I have no idea what you mean by "you can't but the CBOE can" – nicolas May 28 '11 at 16:24
I think my remark conveys a point, which is that this notion of non arbitrability exists within some boundaries. And it just does not make sense to extend it beyond. – nicolas May 28 '11 at 16:28
I dont mean to convey the idea that local vol arb does not exist. only that each theory has its limit. for the less gifted among you, as a mechanical engineer, I wont use formula for equilibrium when there is a air density which is less than a certain level. then it becomes particle physics. neither would one apply classical mechanics to explain laser. I wont use equilibrium formula for out of equilibrium phenomena. each theory has a domain of definition, and local vol arbitrage too. if your tools cant deal with that you should change your tools, and not the vol surface. – nicolas Jul 16 '11 at 19:41 | 739 | 3,174 | {"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} | 2.734375 | 3 | CC-MAIN-2016-18 | latest | en | 0.936088 |
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# Jupiter-bound space probe captures Earth and Moon
page: 2
32
share:
posted on Sep, 1 2011 @ 02:29 AM
Great thread thanks...it would be great to have a montage of thisscene at ever increasing intervals of distance say evey 100,000miles since the probe left Earth?
posted on Sep, 1 2011 @ 02:46 AM
OK so some above posts got me to thinking, JUNO is just 32.2 light seconds away. It didn't leave earth and head straight out to Jupiter, it's on a sort of orbital trajectory and will head back for a gravity assist boost before it heads to Jupiter, and pick up speed. It's 6 million miles away from earth but really hasn't traveled that far, because it's traveling the same basic direction as the earth, and the earth is traveling faster than JUNO is, so earth is more responsible for creating the distance JUNO is from earth.
Here's a nice video illustrating the JUNO flight path, as you can see it travels much further that the distance to Jupiter.
Juno will cover 2.8 billion kilometers (nearly 1.8 billion miles) during its long, looping voyage. That's 19 times farther than the distance between Earth and the Sun, and 15 times farther than the closest distance between Earth and Jupiter.
(This was all available on a JUNO post I made August 5th, but due to the post not having conspiracy speculations, it was largely ignored here, it was just mission information, boring stuff).
This video here will help explain why JUNO will head back for an earth gravity assist boost in two years.
Incidentally, JUNO will become the fastest manmade spacecraft ever flown.
Jupiter's gravity pulls in Juno faster and faster until the spacecraft reaches a speed over 250,000 kilometers per hour (150,000 miles per hour) — making it the fastest human-made object ever. When it arrives at Jupiter, it slams on the brakes, firing its main engine in reverse. After slowing down, Juno can then enter Jupiter's orbit.
posted on Sep, 1 2011 @ 03:12 AM
I haven't looked into yet how JUNO escaped earth orbit. It took a speed of about 24,500 mph for the Apollo spacecrafts to reach earth escape velocity, and it took them 3 days to reach the moon. The earth is traveling about 66,600 mph around the sun, and covers about 587 million miles a year on its orbit around the sun.
JUNO is going to be drawn to a speed of about 150,000 mph approaching Jupiter, and Jupiter is only traveling at a speed around the sun of about 29,200 mph, so JUNO is going to have to have a lot of power to slow down enough to attain orbit around Jupiter, which will start as a highly elliptical orbit and eventually close in closer to the planet's atmosphere. Lots of maneuvers in orbit will have to take place, I believe using some of the moons of Jupiter for gravity assist as well as its solar power. JUNO is going to be the furthest operating space probe powered by solar panels.
One amazing fact I found is the 2013 earth flyby, JUNO will be within 300 miles to get its final boost, now that's some flying if you ask me.
posted on Sep, 1 2011 @ 03:39 AM
Originally posted by timewalker
"Look again at that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there--on a mote of dust suspended in a sunbeam." ~ Carl Sagan
Minus the sunbeam.
I found this quite humbling indeed. We are infinitesimal on the scale of things.
This image of Earth (on the left) and the moon (on the right) was taken by NASA's Juno spacecraft on Aug. 26, 2011, when the spacecraft was about 6 million miles (9.66 million kilometers) away. It was taken by the spacecraft's onboard camera, JunoCam. The solar-powered Juno spacecraft lifted off from Cape Canaveral Air Force Station in Florida on Aug. 5 to begin a five-year journey to Jupiter. Image credit: NASA/JPL-Caltech
Juno covered the distance from Earth to the moon (about 250,000 miles or 402,000 kilometers) in less than one day's time. It will take the spacecraft another five years and 1,740 million miles (2,800 million kilometers) to complete the journey to Jupiter. The spacecraft will orbit the planet's poles 33 times and use its eight science instruments to probe beneath the gas giant's obscuring cloud cover to learn more about its origins, structure, atmosphere and magnetosphere, and look for a potential solid planetary core.
The solar-powered Juno spacecraft lifted off from Cape Canaveral Air Force Station in Florida at 9:25 a.m. PDT (12:25 p.m. EDT) on Aug. 5 to begin its five-year journey to Jupiter.
Source
edit on 31-8-2011 by timewalker because: (no reason given)
And god created the heaven and the earth
posted on Sep, 1 2011 @ 03:39 AM
Can't help it, but... "That's no moon! It's a space station!"
No seriously, these kind of images indeed make us feel humble. And to imagine that so many people (what is is now? almost 7 billion?) live on that tiny, tiny piece of floating rock! Inspiring!
posted on Sep, 1 2011 @ 07:24 AM
As big as the earth and moon are, its still not enough for humanity! I hope we can start pillaging the resources of other planets soon.
posted on Sep, 1 2011 @ 07:27 AM
edit on 1-9-2011 by mjleonid12 because: better one comment below.
posted on Sep, 1 2011 @ 07:27 AM
Originally posted by Vandalour
I wonder why there is no stars visible in that foto ?
like stars are shown in this foto
Because the photo is a zoom-in (I believe) therefore the stars in the background would become more apart as you zoom in.
posted on Sep, 1 2011 @ 08:05 AM
Originally posted by Illustronic
.
Jupiter's gravity pulls in Juno faster and faster until the spacecraft reaches a speed over 250,000 kilometers per hour (150,000 miles per hour) — making it the fastest human-made object ever. When it arrives at Jupiter, it slams on the brakes, firing its main engine in reverse. After slowing down, Juno can then enter Jupiter's orbit.
Nice post.
Can you explain how the brakes work to slow the the craft from such enormous
speeds. What does the engine have to push against, in the vacuum of space?
posted on Sep, 1 2011 @ 08:08 AM
I saw that this morning checking in with space weather. Article should be titled, "Much Ado About Nothing"
posted on Sep, 1 2011 @ 08:58 AM
Originally posted by pshea38
Originally posted by Illustronic
.
Jupiter's gravity pulls in Juno faster and faster until the spacecraft reaches a speed over 250,000 kilometers per hour (150,000 miles per hour) — making it the fastest human-made object ever. When it arrives at Jupiter, it slams on the brakes, firing its main engine in reverse. After slowing down, Juno can then enter Jupiter's orbit.
Nice post.
Can you explain how the brakes work to slow the the craft from such enormous
speeds. What does the engine have to push against, in the vacuum of space?
It doesn't have to "push against" anything. For every action, there is an equal and opposite reaction; the gas that leaves a spacecraft thruster pushes the craft in the opposite direction simply thanks to Newtonian physics. The gas itself does not need anything in space to "push against."
posted on Sep, 1 2011 @ 09:13 AM
Juno uses a bipropellant Leros-1b main engine that uses hydrazine and nitrogen tetroxide for propulsion and provides a thrust of 645 newtons. It is fixed to the spacecraft body and is used for major burns. The engine bell is enclosed in a debris shield.
Juno utilizes a monopropellant reaction control system (RCS) consisting of twelve jets that are mounted on four rocket engine modules. These thrusters are used for control of the vehicle’s orientation and to perform trajectory correction maneuvers.
And yes, as explained above, equal and opposite reaction, which explains if you were curious, that if you were unprotected floating in space and fart, it would propel you ever so slightly in the opposite direction said fart was directed. But you would have greater gaseous releases if exposed to the vacuum of space I believe would be more forceful than said fart, but that's a whole other topic.
posted on Sep, 1 2011 @ 09:14 AM
Originally posted by Illustronic
I haven't looked into yet how JUNO escaped earth orbit. It took a speed of about 24,500 mph for the Apollo spacecrafts to reach earth escape velocity, and it took them 3 days to reach the moon.
It was boosted out of earth orbit by a Centaur upper stage. In less than 12 hours both Juno and its spent Centaur stage managed to travel about 2/3rds the way to the moon, yet I was still able to track them by regressing the pre-launch trajectory in order to account for the launch delay. Sure enough, there they were, leaving our earth-moon system.
First I looked up at Juno, and now Juno looks back, how cool.
posted on Sep, 1 2011 @ 09:16 AM
I think you might have misunderstood. Importance had nothing to do with it.
To the Mind, no big thing.
To the body, space is really really big.
posted on Sep, 1 2011 @ 09:21 AM
This image of Earth (on the left) and the moon (on the right)
posted on Sep, 1 2011 @ 09:46 AM
Fascinating! Super work. But do you have any idea what speed JUNO reached from the Centaur upper stage boost? I WAS in the understanding that is was supposed to be about 24,000 mph, but I read it is going less than 10,000 mph and I do understand that relative to the earth that is over 20,000 mph and I'm left a bit confused. I understand a bit about gravity assist thrusts and speed isn't constant during those maneuvers, but will 'coast' toward Jupiter after that assist.
I think I read that the New Horizons spacecraft (to Pluto) left earth obit faster than any other space probe, and after a boost from Jupiter should reach a speed of something like 51,000 mph but will reach Pluto at about 31,000 mph. Now realize I'm siting these velocities from memory so I could be way off since I'm not looking up all of the data right now.
posted on Sep, 1 2011 @ 09:48 AM
1 day - 238857 miles = 9952.375
27 days since launch 6m miles = 9959.259
Thats a discrepancy of 693.115740741 mph
I wonder if brain farts would be a propellant? 6.884 mph
posted on Sep, 1 2011 @ 10:00 AM
Me hiring people smarter than me proves Im smarter than them.
I love it. Carry on smart guy's.
posted on Sep, 1 2011 @ 10:31 AM
Originally posted by Illustronic
Fascinating! Super work. But do you have any idea what speed JUNO reached from the Centaur upper stage boost?
I'd have to do some more digging, perhaps sim it myself, to see what the speed was at Centaur booster cutoff, but I can tell you that according to JPL's post-launch data, at the moment of Juno separation minutes later it was traveling at 11.56757 km/sec, which is 25,875.9 mph
posted on Sep, 1 2011 @ 10:34 AM
Sounds right.
People should really visit this great interactive JUNO site. It is believed that Jupiter was the first planet to form after the sun, and finding out more about Jupiter will help us find out more about our very origins.
Mission JUNO | 2,832 | 11,546 | {"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-2018-43 | latest | en | 0.949398 |
https://studylib.net/doc/9707229/answer | 1,606,262,318,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141177607.13/warc/CC-MAIN-20201124224124-20201125014124-00580.warc.gz | 519,922,057 | 12,776 | ```Math A Mania
Review Activity
Algebra
Using
Formulas
Geometry
Statistics
Patterns &
Functions
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
40
40
40
40
40
50
50
50
50
50
10 points
Subtract 4x2 – 2y2 – 8 from
3x2 +2y2 +7.
Question Board
See
10 points
A N S W E R:
2
2
-x +4y
+15
Question Board
20 points
Find: (2x + 3)(x + 5)
Question Board
See
20 points
A N S W E R:
2
2x
+ 13x + 15
Question Board
30 points
Find the product:
x2(4x4 +2x2 +x)
Question Board
See
30 points
A N S W E R:
6
4x
+
4
2x
+
3
x
Question Board
40 points
2
14a bc
Reduce:
3 4
42ab c
Question Board
See
40 points
A N S W E R:
a
2 3
3b c
Question Board
50 points
Simplify:
9x 2x 7 x 5
6
3
4
Question Board
See
50 points
A N S W E R:
23 x 13
12
Question Board
10 points
Find the slope of the line
connecting (2,4) to (-4,-3).
Question Board
See
10 points
A N S W E R:
7
1
1
6
6
Question Board
20 points
Find the sum of the exterior
angles of a pentagon.
Question Board
See
20 points
A N S W E R:
360º
Question Board
30 points
Find the area of a trapezoid
whose bases are 10 and 14 and
whose height is 8.
Question Board
See
30 points
A N S W E R:
96 sq. units
Question Board
40 points
Write the equation of a circle
whose center is at (-4,2) and
Question Board
See
40 points
A N S W E R:
2
2
( x 4) ( y 2) 9
Question Board
50 points
Find the area of a circle whose
circumference is 18 .
Question Board
See
50 points
A N S W E R:
81
Question Board
10 points
The perimeter of a square is
80 inches. What is the area of
the square?
Question Board
See
10 points
A N S W E R:
400 sq. inches
Question Board
20 points
The ratio of the corresponding sides of
two similar triangles is 4:5. What is the
ratio of the corresponding areas?
Question Board
See
20 points
A N S W E R:
16:25
Question Board
30 points
Find the distance between the
points (-4,-5) and (1,-2).
Question Board
See
30 points
A N S W E R:
34
Question Board
40 points
A baseball diamond is a square with
sides of 90 feet. What is the
shortest distance between first and
third base? (Answer to nearest tenth of a foot.)
Question Board
See
40 points
A N S W E R:
127.3 feet
Question Board
50 points
In a cone, if the radius and the
height are doubled, what happens
to the volume of the cone?
Question Board
See
50 points
A N S W E R:
The volume is multiplied by 8.
Question Board
10 points
What is the mean for the data set
24, 26, 28, 30,and 40?
Question Board
See
10 points
A N S W E R:
29.6
Question Board
Math
Test
Scores
20 points
(out of 50 pts)
Stem Leaf
3
4
5
56
0225
000
According to this stem
and leaf plot, how
many test scores are in
the 40’s?
Question Board
See
20 points
A N S W E R:
4
Question Board
30 points
Ducky has grades of 84, 65, and 76 on three
math tests. What grade must he obtain on
the next test to have an average of exactly
80 for the four tests?
Question Board
See
30 points
A N S W E R:
95
Question Board
40 points
In the box and whisker plot shown, the
median score is 80 and the 3rd quartile
score is 90. Using the letters on the plot,
indicate where the 80 and 90 located?
Question Board
See
40 points
A N S W E R:
The 80 is at C.
The 90 is at D.
Question Board
69-76 (2)
77-84 (2)
85-92 (5)
93-100 (3)
50 points
This table shows the scores received by 12
students on a quiz. Students who received at
least an 85% got a sticker. What percent of
Question Board
See
50 points
A N S W E R:
2
66 %
3
Question Board
10 points
Solve for c:
5c - 4 - 2c + 1 = 8c + 2
Question Board
See
10 points
A N S W E R:
c = -1
Question Board
20 points
Solve: 2 - 5x > 3x - 14
Question Board
See
20 points
A N S W E R:
x<2
Question Board
30 points
Write the equation of
a line that is parallel to y = 4x + 6
and has a y-intercept of -5.
Question Board
See
30 points
A N S W E R:
y = 4x - 5
Question Board
40 points
What is the equation of
the axis of symmetry of the graph
y = 3x2 + 12x - 2 ?
Question Board
See
40 points
A N S W E R:
x = -2
Question Board
50 points
Explain why the graph
of the straight line with slope of -2
and y-intercept of -3 passes through
the point (5,-13). | 1,459 | 4,059 | {"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-2020-50 | longest | en | 0.776712 |
www.anniesalphabet.com | 1,558,888,334,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232259316.74/warc/CC-MAIN-20190526145334-20190526171334-00390.warc.gz | 222,908,859 | 2,825 | Spiders
Math
1. Spider web counting boards.
2. Get 4 strawberry baskets, a spinner, plastic spiders, and a piece of poster board. Section
the board into 4 pieces. Cut out 4 circles . . . glue 1 into each section of the board, and put the
spinner in the middle. On two of the sections write "in" and glue a plastic spider in the middle
of the circle. On
the other two sections write "out" and glue the spider next to the circle. Kids spin the spinner
--- if it lands on "in", they can put one spider in their basket...if it lands on "out" they must take
one out. Whoever gets 5 spiders in their basket first wins!!
3.
4.
5.
Science
1. Have your students each take a piece of black construction paper home. Their assignment is
to then spray it with hairspray, and then go hunting for the best-looking web on the street!
Once they have found a real spider web, instruct them to lay the piece of black paper on top if
the web. (It should then attach itself to the paper.) Bring them back to class for a terrific spider
web display! This could even make a great bulletin board for Halloween time or if you are
studying a unit on spiders!
2. Put cooked spaghetti and plastic spiders in the sensory bin
3. Place jars, 2 liter pop bottles, and other see through containers on the table with live spiders
inside with sticks and dirt. Add some bugs and watch the spiders eat them.
4.
5.
6.
7.
8.
9.
10.
Literacy
Art
Food
Get some large marshmellows, pretzel sticks, and eyes. Have them put them together like a
spider. Eat!
Objectives: Children will learn how
valuable spiders can be, what they eat,
where they live, body make-up.
Working on the number 8 and letters S | 426 | 1,668 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2019-22 | latest | en | 0.896465 |
https://machinelearningknowledge.ai/numpy-random-rand-randn-randint-normal-uniform-binomial-poisson-sample-choice/ | 1,709,384,029,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475825.14/warc/CC-MAIN-20240302120344-20240302150344-00327.warc.gz | 353,342,699 | 67,943 | # Complete Numpy Random Tutorial – Rand, Randn, Randint, Normal, Uniform, Binomial and more
## Numpy Random
In machine learning and data science, at times you would be required to work with randomly generated data. In this post, we will see how we can use different methods of numpy random to generate random integers or a numpy array with random integers. We are going to cover the following –
1) numpy random seed
2) numpy random normal
3) numpy random rand
4) numpy random randn
5) numpy random choice
6) numpy random uniform
7) numpy random binomial
8) numpy random poisson
9) numpy random randint
10) numpy random sample
### Numpy Import
In [1]:
```import numpy as np
```
## 1) np.random.seed
Numpy Random generates pseudo-random numbers, which means that the numbers are not entirely random. They only appear random but there are algorithms involved in it.
If we initialize the initial conditions with a particular seed value, then it will always generate the same random numbers for that seed value. This means numpy random is deterministic for a given seed value.
np.random.seed can be used to set the seed value before generating numpy random arrays or random numbers.
### Syntax
np.random.seed(seed=None)
seed (optional) – The input is int or 1-d array_like.
### Setting the Numpy Seed Value
In [72]:
```np.random.seed(5)
```
## 2) np.random.normal
np.random.normal returns a random numpy array or scalar whose elements are randomly drawn from a normal distribution
### Syntax
np.random.normal(loc=0.0, scale=1.0, size=None)
loc – It represents Mean (“centre”) of the distribution. It is float or array_like of floats
scale – It represents Standard deviation (spread or “width”) of the distribution. It is float or array_like of floats
size (optional) – It represents the shape of the output array. If the given shape is, e.g., (m, n, k), then m n k samples are drawn. If the size is None (default), a single value is returned, if loc and scale are both scalars. Otherwise, np.broadcast(loc, scale).size samples are drawn.
### Example – 1: Creating 1-D Numpy Random Array
In [57]:
```np.random.normal(1,1,2)
```
Out[57]:
`array([ 3.2336465 , -0.40779152])`
### Example – 2: Creating 2-D Numpy Random Array
In [60]:
```np.random.normal(2,1,(3,2))
```
Out[60]:
```array([[1.39441865, 1.28409766],
[2.74850019, 2.03432562],
[1.68098484, 1.94838727]])```
### Example – 3: Creating 3-D Numpy Random Array
In [63]:
```np.random.normal(2,3,(3,2,4))
```
Out[63]:
```array([[[ 2.40038206, -1.60592695, 2.99413407, 3.01597174],
[ 6.24667659, 0.01566748, -2.45512535, 4.55757841]],
[[ 1.98075188, 0.21801424, 4.88015683, 1.08838025],
[ 3.38653395, -0.61127652, 3.29363281, 0.95027105]],
[[-0.12289567, 4.20374089, 7.8723445 , -1.62212758],
[ 7.73655833, 8.64351739, 3.9377977 , 7.42301642]]])```
### Example 4: A Random Python Float
In [64]:
```np.random.normal(2,3)
```
Out[64]:
`4.563562413316882`
## 3) np.random.rand
np.random.rand returns a random numpy array or scalar whose element(s) are drawn randomly from the normal distribution over [0,1). (including 0 but excluding 1)
It returns a single python float if no input parameter is specified.
### Syntax
np.random.rand(d0,d1,d2,.. dn)
d0,d1,d2,.. dn (optional) – It represents the dimension of the required array given as int. It is optional, if not specified, it will return a single python float.
### Example 1: Creating 1-D Numpy Random Array
In [11]:
```np.random.rand(3)
```
Out[11]:
`array([0.7798154 , 0.45685334, 0.89824928])`
### Example 2: Creating 2-D Numpy Random Array
In [19]:
```np.random.rand(5,3)
```
Out[19]:
```array([[0.17963626, 0.46373528, 0.30762711],
[0.27334617, 0.45668808, 0.54813439],
[0.44506229, 0.32059869, 0.92962626],
[0.78297602, 0.20849134, 0.65793903],
[0.66985367, 0.45470811, 0.05023272]])```
### Example 3: Creating 3-D Numpy Random Array
In [16]:
```np.random.rand(3,2,4)
```
Out[16]:
```array([[[0.82564261, 0.99100227, 0.3498416 , 0.25349147],
[0.97474162, 0.8879708 , 0.52644532, 0.48392986]],
[[0.24771917, 0.55511987, 0.64328105, 0.26636461],
[0.83461679, 0.19501868, 0.51199488, 0.75963094]],
[[0.545668 , 0.22256917, 0.51817445, 0.84151684],
[0.80153195, 0.42129928, 0.49337318, 0.8382367 ]]])```
### Example 4: A Random Python Float
In [17]:
```np.random.rand()
```
Out[17]:
`0.5747916494126569`
## 4) np.random.randn
np.random.randn returns a random numpy array or scalar of sample(s), drawn randomly from the standard normal distribution.
It returns a single python float if no input parameter is specified.
### Syntax
np.random.randn(d0,d1,d2,.. dn)
d0,d1,d2,.. dn (optional) – It represents the dimension of the required array given as int. It is optional, if not specified, it will return a single python float.
### Example 1: Creating 1-D Random Array
In [32]:
```np.random.randn(6)
```
Out[32]:
```array([-0.42125684, -0.0421679 , 0.63053175, 0.08204267, -1.08237789,
1.13159155])```
### Example 2: Creating 2-D Numpy Random Array
In [34]:
```np.random.randn(6,4)
```
Out[34]:
```array([[-1.20911446, 0.22615005, 2.74344014, -0.47000636],
[ 2.45453931, -0.36098073, 0.9761115 , 0.21063749],
[ 1.05366423, 0.35103113, -0.16083158, -0.70649343],
[ 0.22107229, 0.17888074, -1.13098505, -0.26359566],
[ 2.29313593, 1.90569166, 0.71343492, 0.85209564],
[ 0.67663365, 0.56029281, 1.11382612, -0.92873211]])```
### Example 3: Creating 3-D Numpy Random Array
In [35]:
```np.random.randn(3,4,2)
```
Out[35]:
```array([[[-0.13509054, 1.31253658],
[ 0.79514661, -0.15733937],
[-0.42428779, 0.07816613],
[ 1.27951041, -1.2528357 ]],
[[-0.49349802, -0.1929593 ],
[-0.51593638, -1.08389571],
[-0.72854643, -0.44708392],
[-0.01845007, 2.02125787]],
[[-1.8826071 , 1.65592025],
[-2.18326764, -0.07711314],
[-2.9275772 , 2.3173623 ],
[ 0.94757097, -0.13646251]]])```
### Example 4: A Random Python Float
In [36]:
```np.random.randn()
```
Out[36]:
`-0.36506602839929475`
## 5) np.random.choice
np.random.choice returns a numpy array or a scalar by drawing random samples from a given 1-D array
### Syntax
np.random.choice(a, size=None, replace=True, p=None)
a – This represents a 1-D array-like (Tuple/Lists) or int. If it is a ndarray, a random sample is generated from its elements. If an int, the random sample is generated as if a were np.arange(a)
size (optional) – This represents the desired output shape. It is either int or tuple of ints If the given shape is, e.g., (m, n, k), then m n k samples are drawn. Default is None, in which case a single value is returned.
replace (optional) – This signifies whether the sample is to be drawn with or without replacement. It is given as boolean.
p – It represents the probabilities associated with each entry in the input ‘a’. It is given as 1-D array-like. If it is not provided, then the sample assumes a uniform distribution over all entries in a.
### Example 1: Generating one Random Sample from List
In [14]:
```np.random.choice([2,4,5,8])
```
Out[14]:
`8`
### Example 2: Generating a Numpy Array of Random Sample from Tuple
In [13]:
```np.random.choice((2,4,5,8), size = (2,3))
```
Out[13]:
```array([[5, 2, 8],
[4, 2, 2]])```
### Example 3: Generating a Numpy Array of Random Sample by passing an int
When we pass an int instead of an array, it treats the input as np.arange(a)
In [20]:
```np.random.choice(4, size = (2,2)) ## 4 is treated as np.arange(4)
```
Out[20]:
```array([[0, 1],
[3, 3]])```
## 6) np.random.uniform
np.random.uniform returns a random numpy array or scalar whose element(s) are drawn randomly from the uniform distribution over [low,high). (including low but excluding high)
### Syntax
np.random.uniform(low=0.0, high=1.0, size=None)
low (optional) – It represents the lower boundary of the output interval. All samples generated are greater than or equal to low. This input is float or array_like of floats. The default value is 0.
high (optional) – It represents the upper boundary of the output interval. All samples generated are less than high. This input is float or array_like of floats. The default value is 1.0.
size (optional) – It represents the output shape. This input is int or tuple of ints. If the given shape is, e.g., (m, n, k), then m n k samples are drawn. If the size is not given, then a single value is returned if low and high are both scalars. Otherwise, np.broadcast(low, high).size samples are drawn.
### Example 1: Generating a Random sample
In [32]:
```np.random.uniform() ## Default inputs
```
Out[32]:
`0.8058568054860041`
In [70]:
```np.random.uniform(low = 2, high = 10)
```
Out[70]:
`8.78205396325222`
### Example 2: Creating a 1-D Random Numpy Array
In [71]:
```np.random.uniform(low = 2, high = 10, size = (3))
```
Out[71]:
`array([6.79454712, 3.03754559, 9.95066636])`
### Example 3: Creating a 2-D Random Numpy Array
In [42]:
```np.random.uniform(low = 2, high = 10, size = (3,4))
```
Out[42]:
```array([[9.86355621, 8.45282899, 3.83705226, 8.13030929],
[7.71767957, 2.05086033, 8.88954274, 4.23133409],
[6.64220628, 3.26866265, 2.71334945, 9.34853175]])```
## 7) np.random.binomial
np.random.binomial returns a random numpy array or scalar whose element(s) are drawn randomly from a binomial distribution
### Syntax
np.random.binomial(n, p, size=None)
n – It represents the parameter of the distribution, >= 0. The input is int or array_like of ints. Floats are valid, but they will be truncated to integers.
p – It represents the parameter of the binomial distribution, >= 0 and <=1. The input is float or array_like of floats.
size – It represents the output shape. The input is int or tuple of ints, optional. If the given shape is, e.g., (m, n, k), then m n k samples are drawn. If the size is not given, a single value is returned if n and p are both scalars. Otherwise, np.broadcast(n, p).size samples are drawn.
### Example 1: Generating a Random Sample
In [75]:
```np.random.binomial(n=52, p=0.7)
```
Out[75]:
`34`
### Example 2: Creating a 1-D Random Numpy Array
In [65]:
```np.random.binomial(n=52, p=0.7, size = (2))
```
Out[65]:
`array([39, 32])`
### Example 3: Creating a 2-D Random Numpy Array
In [73]:
```np.random.binomial(n=52, p=0.7, size = (2,3))
```
Out[73]:
```array([[39, 33, 39],
[32, 37, 36]])```
## 8) np.random.poisson
np.random.poisson returns a random numpy array or scalar whose element(s) are drawn randomly from a poisson distribution
### Syntax
np.random.poisson(lam=1.0, size=None)
lam – It represents the expectation of interval, should be >=0. A sequence of expectation intervals must be broadcastable over the requested size. The input is float or array_like of floats.
*size (optional) – It represents the shape of the output. The input is int or tuple of ints. If the given shape is, e.g., (m, n, k), then m n k samples are drawn. If size is not given, then a single value is returned if lam is a scalar. Otherwise, np.array(lam).size samples are drawn.
### Example 1: Generating a Random Sample
In [74]:
```np.random.poisson(5)
```
Out[74]:
`4`
### Example 2: Creating a 1-D Random Numpy Array
In [79]:
```np.random.poisson(5,size=(4))
```
Out[79]:
`array([2, 3, 1, 7])`
### Example 3: Creating a 2-D Random Numpy Array
In [80]:
```np.random.poisson(5,size=(4,3))
```
Out[80]:
```array([[ 7, 2, 10],
[ 3, 4, 7],
[ 5, 7, 5],
[ 8, 9, 4]])```
## 9) np.random.randint
np.random.randint returns a random numpy array or scalar, whose element(s) is int, drawn randomly from low (inclusive) to the high (exclusive) range.
### Syntax
np.random.randint(low, high=None, size=None, dtype=’l’)
low – It represents the lowest inclusive bound of the distribution from where the sample can be drawn. Unless high=None, in which case this parameter is one above the highest such integer. The input is int
high (optional) – It represents the upper exclusive bound of the distribution from where the sample can be drawn. (see above for behavior if high=None). The input is int.
size (optional) – It represents the shape of the output. The input is int or tuple of ints. If the given shape is, e.g., (m, n, k), then m n k samples are drawn. Default is None, in which case a single value is returned.
dtype (optional) – It represents the required dtype of the result. The default value is ‘np.int’.
### Example 1: Generating a Random Number
In [83]:
```np.random.randint(1,50)
```
Out[83]:
`42`
### Example 2: Creating a 1-D Random Numpy Array
In [93]:
```np.random.randint(1,50, size=(4))
```
Out[93]:
`array([ 4, 24, 4, 32])`
### Example 3: Creating a 2-D Random Numpy Array
In [95]:
```np.random.randint(1,50, size=(4,3))
```
Out[95]:
```array([[48, 8, 1],
[36, 38, 2],
[31, 28, 32],
[30, 7, 8]])```
## 10) np.random.sample
np.random.sample returns a random numpy array or scalar whose element(s) are floats, drawn randomly from the half-open interval [0.0, 1.0) (including 0 and excluding 1)
### Syntax
np.random.sample(size=None)
size (optional) – It represents the shape of the output. The input is int or tuple of ints. If the given shape is, e.g., (m, n, k), then m n k samples are drawn. If no size is given, then a single value is returned.
### Example 1: Generating a Random Sample
In [38]:
```np.random.sample()
```
Out[38]:
`0.4263312607851021`
### Example 2: Creating a 1-D Random Numpy Array
In [67]:
```np.random.sample(2)
```
Out[67]:
`array([0.96748937, 0.74883372])`
### Example 3: Creating a 2-D Random Numpy Array
In [96]:
```np.random.sample((2,4)) ## Two Dimension
```
Out[96]:
```array([[0.52717883, 0.96121114, 0.78901011, 0.49669551],
[0.211141 , 0.60398414, 0.74857581, 0.75586383]])```
• MLK is a knowledge sharing community platform for machine learning enthusiasts, beginners and experts. Let us create a powerful hub together to Make AI Simple for everyone. | 4,469 | 13,818 | {"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-2024-10 | longest | en | 0.669249 |
http://www.gradesaver.com/textbooks/math/precalculus/precalculus-mathematics-for-calculus-7th-edition/chapter-1-section-1-6-complex-numbers-1-6-exercises-page-64/57 | 1,524,367,428,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945484.58/warc/CC-MAIN-20180422022057-20180422042057-00235.warc.gz | 433,132,692 | 14,377 | # Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises: 57
$(3-\sqrt -5)(1+\sqrt -1)=(3+\sqrt 5)+(3-\sqrt 5)i$
#### Work Step by Step
$(3-\sqrt -5)(1+\sqrt -1)=3+3\sqrt -1-\sqrt -5-\sqrt -5\sqrt -1$. However we know that $i=\sqrt -1$ hence $3+3\sqrt -1-\sqrt -5-\sqrt -5\sqrt -1=3+3i-i\sqrt 5-i^{2}\sqrt 5$. We also know that $i^{2}=-1$ hence $3+3i-i\sqrt 5-i^{2}\sqrt 5=3+3i-i\sqrt 5+\sqrt 5$. By grouping the real and the imaginary parts we can write the solution in the form $a+bi$ where $a$ is the real and $b$ is the imaginary as $(3+\sqrt 5)+(3-\sqrt 5)i$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 267 | 730 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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} | 4.21875 | 4 | CC-MAIN-2018-17 | latest | en | 0.751094 |
http://mathhelpforum.com/calculus/15643-chemical-reaction-newtons-cooling-print.html | 1,527,497,396,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794872114.89/warc/CC-MAIN-20180528072218-20180528092218-00034.warc.gz | 176,217,091 | 4,974 | # chemical reaction and newton's cooling
• Jun 5th 2007, 08:32 AM
ggw
chemical reaction and newton's cooling
Thanks Jhevon,
Yeah, the normal body temperature is 37. I just asked my teacher about it.
another two practical problems would have help me a lot. Moving to chemical problem.
1. A compound C is formed when two chemicals A & B are combined. The resulting reaction between the two is such that for each gram of B, 3 grams of A are used. Initially there are 36 grams of A and 18 grams of B. It's observed that 10 grams of the compound C are formed in 15 minutes. Determine the amount of C at any time if the rate of the reaction is proportional to the amounts of A & B remaining. Find the amount after 20 minutes.
2. Another newton's cooling problem.
On Easter, a ham is removed from an oven and placed in a room where the temperature is 70 degree F. A meat thermometer indicates that internal temperature of the ham to be 220 degree F. 30 minutes later, the meat thermometer indicates 200 degree F. How much longer it will take to cool the meat to 100 degree F.
3. Grow and Decay
The wood of an Egyptian sarcophagus (burial case) is found to contain 63% of the Carbon-14 found in a present-day sample. What is the age of the sarcophagus if the half-life of C14 is 5730 years ?
again, thanks Jhevon....I appriciate that.
• Jun 5th 2007, 09:41 AM
Jhevon
Quote:
Originally Posted by ggw
1. A compound C is formed when two chemicals A & B are combined. The resulting reaction between the two is such that for each gram of B, 3 grams of A are used. Initially there are 36 grams of A and 18 grams of B. It's observed that 10 grams of the compound C are formed in 15 minutes. Determine the amount of C at any time if the rate of the reaction is proportional to the amounts of A & B remaining. Find the amount after 20 minutes.
i'll have to think about this problem some more. there's one part of it that is persistent in confusing me. :o
Quote:
2. Another newton's cooling problem.
On Easter, a ham is removed from an oven and placed in a room where the temperature is 70 degree F. A meat thermometer indicates that internal temperature of the ham to be 220 degree F. 30 minutes later, the meat thermometer indicates 200 degree F. How much longer it will take to cool the meat to 100 degree F.
Ok, you know the drill here. we will use the formula:
$\displaystyle T' = -k(T - T_{amb})$
$\displaystyle \Rightarrow T = Ae^{-kt} + T_{amb}$ ...see my previous posts on these types of questions to see how I derived this.
$\displaystyle \Rightarrow T = Ae^{-kt} + 70$
Now $\displaystyle T(0) = 220$
$\displaystyle \Rightarrow 220 = Ae^0 + 70$
$\displaystyle \Rightarrow A = 150$
Also, $\displaystyle T(30) = 200$
$\displaystyle \Rightarrow 200 = 150e^{-30k} + 70$
$\displaystyle \Rightarrow k = \frac {\ln \left( \frac {13}{15} \right)}{-30}$
$\displaystyle \Rightarrow k \approx 0.00477$
So our equaiton is: $\displaystyle T = 150e^{-0.00477t} + 70$
Now just plug in $\displaystyle T = 100$ and solve for $\displaystyle t$
When done, you have to subtract 30 from that value, since the question asked how much LONGER it will take to cool to 100 [after 30 mins].
Quote:
3. Grow and Decay
For growth and decay, we use pretty much one formula. The only difference is, in decay, we use a negative exponent. As a mnemonic, I call this the PERT formula, as in the shampoo Pert, if you remember--that was a great invention, saves a lot of time. Anyway, what does PERT mean? See if you can see the word below:
$\displaystyle P = P_0 e^{rt}$
Notice that the left side of the formula spells PERT. In the above formula, $\displaystyle P$ (a function of time) is the amount of substance after time $\displaystyle t$, $\displaystyle P_0$ is the initial amount of substance, $\displaystyle r$ is the rate of growth, and $\displaystyle t$ is the time elapsed. This is known as the formula for Exponential Growth, and is usually used to predict the growth of bacteria and populations.
For the Exponential Decay formula, we simply make the exponent of $\displaystyle e$ negative. So for exponential decay:
$\displaystyle P = P_0 e^{-rt}$
Note that some books will use different letters for $\displaystyle P$. Other common letters used are $\displaystyle A \mbox{ and } I$.
one more formula you need to know for this topic is:
$\displaystyle r \cdot t_h = \ln 2$
where $\displaystyle r$ is the rate of decay, and $\displaystyle t_h$ is the half-life.
Quote:
The wood of an Egyptian sarcophagus (burial case) is found to contain 63% of the Carbon-14 found in a present-day sample. What is the age of the sarcophagus if the half-life of C14 is 5730 years ?
Now, $\displaystyle r \cdot t_h = \ln 2$
$\displaystyle \Rightarrow r = \frac {\ln 2 }{t_h} = \frac { \ln 2}{5730} \approx 0.000121$
This s a decay problem, so we use the formula:
$\displaystyle A = A_0 e^{-rt}$
So we have: $\displaystyle A = A_0 e^{-0.000121t}$
Now we are not told the amount we have now, or the amount that we started with, so how do we proceed here? Answer: we pick a number. I like to use 1, but any number you pick will work out fine.
So assume we start with a sample containing 1 unit Carbon-14. We now have 63% of that, so now we have 0.63 units of Carbon-14. So we can let $\displaystyle A_0 = 1$, so now we just have to find $\displaystyle t$ such that, $\displaystyle A = 0.63$. Thus, to answer this question, we must solve:
$\displaystyle 0.63 = e^{-0.000121t}$
for $\displaystyle t$.
$\displaystyle t$ will give you the age of the sample
• Jun 5th 2007, 03:06 PM
ggw
the formula for this is dX/dt = k(amount A remaining)(amount B remaining)
for each:
2 parts of A & 3 parts of B are being used.
Original: 36 of A, 18 of B
10 grams are formed in 15 minutes.
X = 10
A = ? , B = ?
dX/dt = k(36 - A)(18 - B)
So 2x/5 for A, B would be 3x/5.
Determined the amount of C at any time if the rate of the reaction is proportional tothe amounts of A & B Remaining. Find the amount after 20 minutes.
• Jun 5th 2007, 03:39 PM
Jhevon
Quote:
Originally Posted by ggw
the formula for this is dX/dt = k(amount A remaining)(amount B remaining)
for each:
2 parts of A & 3 parts of B are being used.
Original: 36 of A, 18 of B
10 grams are formed in 15 minutes.
X = 10
A = ? , B = ?
dX/dt = k(36 - A)(18 - B)
So 2x/5 for A, B would be 3x/5.
Determined the amount of C at any time if the rate of the reaction is proportional tothe amounts of A & B Remaining. Find the amount after 20 minutes.
you're using X here to mean C? i thought it was 3 grams of A uses 1 gram of B to form C.
anyway. let's see if the blind can lead the blind through this. going with the 2 parts A and 3 parts B.
if 10 g of C is formed in 15 mins, 2/3 g is formed in one minute. 2/5 of that is from A, and 3/5 of that is B. So after every minute, we use (2/5)(2/3) = 4/15 g A and (3/5)(2/3) = 2/5 g B.
then, $\displaystyle \frac {dC}{dt} = k \left(36 - \frac {4}{15}t \right) \left(18 - \frac {2}{5} t\right)$
$\displaystyle \Rightarrow \frac {dC}{dt} = k \left( 648 - \frac {96}{5} t + \frac {8}{75} t^2 \right)$
$\displaystyle \Rightarrow dC = k \left( 648 - \frac {96}{5}t + \frac {8}{75} t^2\right) dt$
$\displaystyle \Rightarrow \int dC = k \int \left( 648 - \frac {96}{5}t + \frac {8}{75} t^2 \right) dt$
$\displaystyle \Rightarrow C = k \left(648t - \frac {48}{5} t^2 + \frac {8}{225} t^3\right)$
Now when $\displaystyle t=15$, $\displaystyle C = 10$:
use this to find $\displaystyle k$. then you can use that equation to find $\displaystyle C$ when $\displaystyle t = 20$ | 2,214 | 7,564 | {"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} | 3.390625 | 3 | CC-MAIN-2018-22 | latest | en | 0.957435 |
https://alumniagri.in/task/the-sum-of-2-nos-is-8-and-sum-of-their-reciprocles-is-8-15-17962609 | 1,709,219,119,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474843.87/warc/CC-MAIN-20240229134901-20240229164901-00027.warc.gz | 85,312,172 | 4,693 | # The sum of 2 nos is 8. And sum of their reciprocles is 8/15. Find the nos
0
Hey mate mark me brainliest
Let one number be X. The other number be Y.
GIVEN,
X+Y=8
X=8-Y ---------------(1)
1/X+1/Y=8/15
BY SIMPLIFING 1/X+1/Y=8/15 WE GET,
(X+Y)/XY=8/15
FROM (1) WE GET,
8/8Y-Y2=8/15
Y2-8Y+15=0
(Y - 3)(Y - 5) = 0
Y = 3 or 5
WE KNOW THAT X+Y=8
When Y=5, X=3
When Y = 3, X = 5
Thus, the two numbers are 3 and 5.
1
The two numbers are 5 and 3.
Step-by-step explanation:
Let the two numbers be x and y.
x+y=8------☆
1/x+1/y=8/15
y+x/xy=8/15
15(x+y)=8(xy)
15(8)=8xy(From ☆)
15=xy
xy =15
x=15/y-----♡
From ☆ and ♡
15/y+y=8
(15+y^2)/y=8
15+y^2=8y
y^2-8y+15=0
y^2-3y-5y+15=0(By splitting the middle term)
y(y-3)-5(y-3)=0
(y-3)(y-5)=0
y-3=0; y-5=0
y=3; y=5
x+y=8
x+3=8
x=5
HOPE THIS BRING A SMILE IN YOUR FACE
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Math, 3 months ago | 470 | 1,002 | {"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-2024-10 | latest | en | 0.624752 |
https://crackmytoefl.com/toefl-and-ielts-comparison | 1,702,036,808,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100745.32/warc/CC-MAIN-20231208112926-20231208142926-00032.warc.gz | 215,012,153 | 18,274 | # Toefl And Ielts Comparison
Toefl And Ielts Comparison The definition of the term “defl” is as follows from the definition given in Part I of the book of Sosa, and is used to define the term “efl”. Defl is the concept that a set of words of the form “efl” is defined over the alphabet. It is difficult to define the meaning of “efl”, since the meaning of words of such an alphabet can be found by the mathematical definition. However, if we define “efl,” we can find the meaning of word “efl.” The meaning of “defl,” is that word “defl.” The meaning is that the verb “defl'” is the noun “defl”, meaning “defl”. The meaning for “efl'”, is that the noun “efl'” is “efl’. It is the noun that the verb is used to make the verb “efl’.” The word “def’l” is the verb “dafl’. The verb (dafl) is the verb that is used to say “daf’l’. The definition of the verb is as follows: Thus, the definition of the word “def'” is: And Ielts’ definition is: Do you think Ielts should use to say “defl’l'”? The case of “ef’l” instead of “ef” is not very clear. It is the form of the verb “f’l’. It can be written as “f’lo”. The question about “def”, is not very clean. It can be “def'”, “ef'”, “f’f’l'”, “daflf”, “dlfl’l” and “e’l’l”. What are the reasons that one should use “def'”. What is “ef”, is that Ielts are aware of the fact that Ielks are not “ef’ls” (that is, Ielks). I have not seen the definition of “ef’, nor of “ef”, nor of “f”l”. The meaning of “f’-l’l'” is the other words for those, “f’-le’-l’, “f’-li’l’, “e’-l’-l’, etc. How can Ielts be used to say that Ielk are “efl”? One of the issues with using “ef”l”, is that it is difficult to say the meaning of the words “ef’lf” and “ef’ll’l”.
## Take My Accounting Class For Me
However, it is quite easy to say that “ef'”l’l is “ef-l’l’. If Ielks were used to say what they can do, I would have to say “ef’ly” (that’s, Ielk = Ielk). This may seem complicated, but the meaning for “f’-s’l”, “e-s’-l’, and “ef’-l”-l”, are the same, “f-s’-s’-l’-s-s-s”. I have seen the definition for “ef’-s'” in Chapter 3 of the book “The Book of Sosa”. If this were how I would have been able to say “f’-ld-l’-l’-lf’-ll’-l’-r’-l’-o’-r’-r’-o’-ld’-l’-w’-k’-l’-t’-h’-w’-r-l’-r’. I would have thought of “ef’-ll-l’-w-‘-‘-‘-”-‘-‘-‘–‘. I have shown in this chapter how to say “fi’-ld-f’-ld’-f’-ld”-f’-l’-f’-s’-f’-k’-f’-f’–f’–l’-k’–o’-r-u’. I think that the meanings of “ef”-s’-l’–l’-r-o’-l’-y’-w’-c’-s’-i’-r’-f’-i’-h’-f’-w’-f’-r’-w’-n’-h’-n’-r’-s’-s-o’-t’-iToefl And Ielts Comparison, in a New Republic “The New Republic does not define how it is to be called a democracy.” – Douglas Adams, The New Republic (1864) The New Republic is a democratic republic, in which Americans are elected by the people as citizens. We are in a democracy, and if we are not, we are not elected by the voters. Our nation is a democracy, in which every citizen is now elected by their representatives of the people. It is a democracy in which there is no party elected for partisan gain, but instead—as with so many other democratic systems—the people are elected to serve as citizens. Its very nature is to be regarded as a democracy, but that is not the case. We have a democratic republic in which every person, no matter how small, is elected by the representatives of the People. A democracy is a democratic self-governing nation, a nation which is governed by a government, and whose election is a matter of government. The Constitution is a constitutional document, and if the Constitution is not written, no individual shall be entitled to pass it. The Constitution, therefore, is not a document, but a document that describes the Constitution. This is why we follow the principles of the Constitution, which are not a document that is written, but a constitution that is written. In the Constitution, it is the constitutional law that governs the government (and, we believe, the Constitution is the Constitution. It must be stated that the Constitution is a Constitution for the government, and not for the people).
## We Do Your Accounting Class Reviews
As we have said, In a democracy, no individual is entitled to vote, nor to participate in the election of a majority of the people in the Electoral College. It is the election of the people, not of the people itself. It is their right to participate in it. It is that which we have called the right to vote, and which we call the right to participate. We call this the right to choose. In the United States, we have the right to elect the people for the people, as they choose, by the people, and not by the party that elected them. It is our right to vote on behalf of the people as they choose. (This is why there is the right to support the United States to elect the United States Congress, as they elect the people by the people.) In other countries, we have a right to elect people for the government. There is the right of the people to elect the government, as they have chosen. It is not the right to be elected by the citizens. It is what we have called a democracy, a democracy in a matter of the people’s choosing. When I think of democracy, I think that we have not the right (or the right to do the right thing) to choose our way of thinking about the government. We have the right for the people to choose our political party. We have the right (nor are we the right to put the wrong thing there) to choose the government. We have our right to elect a president, as we elect the people. We have democracy in a democracy. It is democracy in a democratic government. (The Constitution means that democracy is a constitutional system.) We are not in a democracy that has no party elected.
## Pay Someone To Do My Course
It is in a democracy in the UnitedToefl And Ielts Comparison The other day I changed my mind about my Elts comparison. I thought there was actually a difference in the way I would compare it. I looked at my friend and didn’t see any difference in my Elts. I could see that the data was a lot better and not at all different than the other data. I was just fine with the Elts. At the time I don’t know if I was telling you this, but I can’t help but think that you can compare the Elts yourself. So what is your Elts comparison? The Elts are very similar to each other for me. go to this web-site a quick summary of my Elts: The amount of data I have is almost identical (I don’ts take up more space), and the Elts are much faster (I don’t spend more time waiting for the data to arrive). I was able to compare my Elts with my friends, people I don‘t like. see it here you can compare Elts with your friends, and your friend’s Elts. Here’s the difference: Look at the Elts as a percentage of how much data I have. In terms of the data, I don“t know what I want to do with my data. I want to make the data less expensive, but I don”t know what the data will do. That leaves me with one question – because after all, I don’t know what the Elts would do. (Not saying I don’t need to know, but I do know that my friend and Ielts do, so I don‖t have to know what those data would do.) What do you think is the Elts comparison is most important for me? Let me start by saying that the data I have for my Elts is not the same as the data I had for my friends. With the Elts, it doesn‘t matter if you have a friend or not – and you don‘ts have friends, you don“ts have friends. (The Elts and friends are the same) Can you see that the E of the data you have is the same as what you have for my data? That is because I want to compare my friends to my friends. I don„t want to compare them to my friends or my friends to one another. The data that I have for Elts is a lot better than the data I can just compare.
What are the Elts comparisons of the Elts? I don“m wondering if you are thinking the Elts in the same way as I am. Of course, I can‘t tell you this. But it seems counter-intuitive. You can compare your friends to friends, and the Elths are similar. But you can also compare your friends on the Elts to friends. That makes sense. (You can compare a friend to a friend in several ways, but you can“t see the Elths) As I have said, my friend and Elths are the same, and I don�“t want to change the Elths, but I want those
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How to protect my personal information and ensure its confidentiality when interacting with a TOEFL | 2,370 | 8,812 | {"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} | 2.65625 | 3 | CC-MAIN-2023-50 | latest | en | 0.959188 |
http://dml.cz/manakin/handle/10338.dmlcz/133957 | 1,386,583,033,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163955638/warc/CC-MAIN-20131204133235-00029-ip-10-33-133-15.ec2.internal.warc.gz | 53,356,343 | 4,804 | Article
Full entry | PDF (0.3 MB)
Keywords:
strong distance; strong eccentricity; strong center; strong periphery
Summary:
For a nonempty set $S$ of vertices in a strong digraph $D$, the strong distance $d(S)$ is the minimum size of a strong subdigraph of $D$ containing the vertices of $S$. If $S$ contains $k$ vertices, then $d(S)$ is referred to as the $k$-strong distance of $S$. For an integer $k \ge 2$ and a vertex $v$ of a strong digraph $D$, the $k$-strong eccentricity $\mathop {\mathrm se}_k(v)$ of $v$ is the maximum $k$-strong distance $d(S)$ among all sets $S$ of $k$ vertices in $D$ containing $v$. The minimum $k$-strong eccentricity among the vertices of $D$ is its $k$-strong radius $\mathop {\mathrm srad}_k D$ and the maximum $k$-strong eccentricity is its $k$-strong diameter $_k D$. The $k$-strong center ($k$-strong periphery) of $D$ is the subdigraph of $D$ induced by those vertices of $k$-strong eccentricity $\mathop {\mathrm srad}_k(D)$ ($_k (D)$). It is shown that, for each integer $k \ge 2$, every oriented graph is the $k$-strong center of some strong oriented graph. A strong oriented graph $D$ is called strongly $k$-self-centered if $D$ is its own $k$-strong center. For every integer $r \ge 6$, there exist infinitely many strongly 3-self-centered oriented graphs of 3-strong radius $r$. The problem of determining those oriented graphs that are $k$-strong peripheries of strong oriented graphs is studied.
References:
[1] F. Buckley, Z. Miller, P. J. Slater: On graphs containing a given graph as center. J. Graph Theory 5 (1981), 427–434. MR 0635706
[2] G. Chartrand, D. Erwin, M. Raines, P. Zhang: Strong distance in strong digraphs. J. Combin. Math. Combin. Comput. 31 (1999), 33–44. MR 1726945
[3] G. Chartrand, D. Erwin, M. Raines, P. Zhang: On strong distance in strong oriented graphs. Congr. Numer. 141 (1999), 49–63. MR 1744211
[4] G. Chartrand, L. Lesniak: Graphs $\&$ Digraphs, third edition. Chapman $\&$ Hall, New York, 1996. MR 1408678
[5] G. Chartrand, O. R. Oellermann, S. Tian, H. B. Zou: Steiner distance in graphs. Čas. Pěst. Mat. 114 (1989), 399–410. MR 1027236
Partner of | 700 | 2,133 | {"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} | 2.578125 | 3 | CC-MAIN-2013-48 | latest | en | 0.740922 |
https://web2.0calc.com/questions/geometry-question_137 | 1,611,745,151,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704821381.83/warc/CC-MAIN-20210127090152-20210127120152-00126.warc.gz | 641,701,954 | 5,473 | +0
geometry question
0
85
1
Help me find the value of x!
Sep 19, 2020
#1
+10840
+1
Help me find the value of x!
Hello Guest!
\(180^{\circ}-147^{\circ}+x+180^{\circ}-4x=180^{\circ}\\ 3x=180^{\circ}-147^{\circ}\)
\(x=11^{\circ}\)
!
Sep 20, 2020 | 109 | 253 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2021-04 | latest | en | 0.534889 |
https://nrich.maths.org/public/leg.php?code=-25&cl=4&cldcmpid=310 | 1,568,852,862,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573385.29/warc/CC-MAIN-20190918234431-20190919020431-00534.warc.gz | 601,197,858 | 6,589 | Search by Topic
Resources tagged with Number theory similar to Shape and Territory:
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Broad Topics > Numbers and the Number System > Number theory
Diophantine N-tuples
Age 14 to 16 Challenge Level:
Can you explain why a sequence of operations always gives you perfect squares?
An Introduction to Number Theory
Age 16 to 18
An introduction to some beautiful results of Number Theory
Sums of Squares and Sums of Cubes
Age 16 to 18
An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.
Pythagorean Golden Means
Age 16 to 18 Challenge Level:
Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is the Golden Ratio.
Modulus Arithmetic and a Solution to Differences
Age 16 to 18
Peter Zimmerman, a Year 13 student at Mill Hill County High School in Barnet, London wrote this account of modulus arithmetic.
Euler's Squares
Age 14 to 16 Challenge Level:
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
Always Perfect
Age 14 to 16 Challenge Level:
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
There's a Limit
Age 14 to 18 Challenge Level:
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
Never Prime
Age 14 to 16 Challenge Level:
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
More Sums of Squares
Age 16 to 18
Tom writes about expressing numbers as the sums of three squares.
Ordered Sums
Age 14 to 16 Challenge Level:
Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .
Number Rules - OK
Age 14 to 16 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
The Public Key
Age 16 to 18 Challenge Level:
Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.
About Pythagorean Golden Means
Age 16 to 18
What is the relationship between the arithmetic, geometric and harmonic means of two numbers, the sides of a right angled triangle and the Golden Ratio?
2^n -n Numbers
Age 16 to 18
Yatir from Israel wrote this article on numbers that can be written as $2^n-n$ where n is a positive integer.
A Little Light Thinking
Age 14 to 16 Challenge Level:
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Really Mr. Bond
Age 14 to 16 Challenge Level:
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
Data Chunks
Age 14 to 16 Challenge Level:
Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .
Mod 7
Age 16 to 18 Challenge Level:
Find the remainder when 3^{2001} is divided by 7.
Novemberish
Age 14 to 16 Challenge Level:
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100. | 956 | 3,843 | {"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} | 3.6875 | 4 | CC-MAIN-2019-39 | latest | en | 0.869191 |
https://123dok.com/document/q02x15gy-persepsi-mahasiswa-akuntansi-akuntansi-mengenai-penyusunan-keuangan-repository.html | 1,620,339,479,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988763.83/warc/CC-MAIN-20210506205251-20210506235251-00491.warc.gz | 103,080,508 | 23,516 | # Persepsi Mahasiswa Akuntansi Dan Non Akuntansi Mengenai Etika Penyusunan Laporan Keuangan - Unika Repository
21
## Teks penuh
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
### Reliabilitas Dan Validitas
(10)
(11)
Item-Total Statistics
### Uji Oneway ANOVA
(12)
Post-Hoc Test Variabel Misstate
Akuntansi ekonomi non akuntansi
.855 .432 .121 -.17 1.88
Bonferroni Akuntansi ekonomi non akuntansi
(13)
ANOVA COST-BENEFIT
akuntansi ekonomi non akuntansi
-.687* .280 .040 -1.35 -.02
Bonferroni akuntansi ekonomi non akuntansi
-.687* .280 .046 -1.37 -.01
(14)
ANOVA RESPONSIBILITY
akuntansi ekonomi non
akuntansi .423 .292 .319 -.27 1.11
Bonferroni akuntansi ekonomi non
(15)
### Deskriptif Statistik
Descriptive Statistics
N Minimum Maximum Sum Mean Std. Deviation
TOTem 145 1 5 467 3.22 1.017
TOTmist 145 9 20 2261 15.59 2.139
TOTdisc 145 5 15 1754 12.10 1.435
TOTcb 145 2 10 822 5.67 1.414
TOTresp 145 4 10 1075 7.41 1.493
Valid N (listwise) 145
### Compare Means Total Jawaban Responden Per Variabel
RESPONDEN TOTem TOTmist TOTdisc TOTcb TOTresp
akuntansi Mean 3.19 16.17 11.98 5.15 7.92
N 52 52 52 52 52
ekonomi non akuntansi Mean 3.36 15.32 12.05 5.84 7.50
N 44 44 44 44 44
non ekonomi Mean 3.12 15.22 12.27 6.06 6.80
N 49 49 49 49 49
Total Mean 3.22 15.59 12.10 5.67 7.41
(16)
(17)
COMPARE MEANS NILAI
NILAI totEM totMIST totDISC totCB totRES
A Mean 3.45 14.82 11.55 5.36 7.73
N 11 11 11 11 11
Std. Deviation .934 2.676 2.252 1.502 1.555
AB Mean 3.36 17.41 11.95 4.95 8.32
N 22 22 22 22 22
Std. Deviation 1.002 1.532 1.253 1.290 1.129
B Mean 3.08 15.69 12.38 5.15 7.69
N 13 13 13 13 13
Std. Deviation 1.038 1.932 1.805 1.214 2.097
BC Mean 2.40 15.20 12.00 5.60 7.00
N 5 5 5 5 5
Std. Deviation .894 2.775 1.225 1.817 2.345
C Mean 2.00 15.00 12.00 5.00 9.00
N 1 1 1 1 1
Std. Deviation . . . . .
Total Mean 3.19 16.17 11.98 5.15 7.92
N 52 52 52 52 52
(18)
(19)
(20)
(21)
Memperbarui...
## Referensi
Memperbarui...
Related subjects : | 926 | 1,995 | {"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-2021-21 | latest | en | 0.135932 |
https://number.academy/1006381 | 1,685,802,590,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649293.44/warc/CC-MAIN-20230603133129-20230603163129-00655.warc.gz | 468,147,118 | 12,250 | # Number 1006381
Number 1,006,381 spell 🔊, write in words: one million, six thousand, three hundred and eighty-one, approximately 1.0 million. Ordinal number 1006381st is said 🔊 and write: one million, six thousand, three hundred and eighty-first. The meaning of the number 1006381 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 1006381. What is 1006381 in computer science, numerology, codes and images, writing and naming in other languages
## What is 1,006,381 in other units
The decimal (Arabic) number 1006381 converted to a Roman number is (M)(V)MCCCLXXXI. Roman and decimal number conversions.
#### Weight conversion
1006381 kilograms (kg) = 2218667.6 pounds (lbs)
1006381 pounds (lbs) = 456491.4 kilograms (kg)
#### Length conversion
1006381 kilometers (km) equals to 625336 miles (mi).
1006381 miles (mi) equals to 1619614 kilometers (km).
1006381 meters (m) equals to 3301735 feet (ft).
1006381 feet (ft) equals 306749 meters (m).
1006381 centimeters (cm) equals to 396213.0 inches (in).
1006381 inches (in) equals to 2556207.7 centimeters (cm).
#### Temperature conversion
1006381° Fahrenheit (°F) equals to 559082.8° Celsius (°C)
1006381° Celsius (°C) equals to 1811517.8° Fahrenheit (°F)
#### Time conversion
(hours, minutes, seconds, days, weeks)
1006381 seconds equals to 1 week, 4 days, 15 hours, 33 minutes, 1 second
1006381 minutes equals to 2 years, 3 weeks, 5 days, 21 hours, 1 minute
### Codes and images of the number 1006381
Number 1006381 morse code: .---- ----- ----- -.... ...-- ---.. .----
Sign language for number 1006381:
Number 1006381 in braille:
QR code Bar code, type 39
Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ...
## Mathematics of no. 1006381
### Multiplications
#### Multiplication table of 1006381
1006381 multiplied by two equals 2012762 (1006381 x 2 = 2012762).
1006381 multiplied by three equals 3019143 (1006381 x 3 = 3019143).
1006381 multiplied by four equals 4025524 (1006381 x 4 = 4025524).
1006381 multiplied by five equals 5031905 (1006381 x 5 = 5031905).
1006381 multiplied by six equals 6038286 (1006381 x 6 = 6038286).
1006381 multiplied by seven equals 7044667 (1006381 x 7 = 7044667).
1006381 multiplied by eight equals 8051048 (1006381 x 8 = 8051048).
1006381 multiplied by nine equals 9057429 (1006381 x 9 = 9057429).
show multiplications by 6, 7, 8, 9 ...
### Fractions: decimal fraction and common fraction
#### Fraction table of 1006381
Half of 1006381 is 503190,5 (1006381 / 2 = 503190,5 = 503190 1/2).
One third of 1006381 is 335460,3333 (1006381 / 3 = 335460,3333 = 335460 1/3).
One quarter of 1006381 is 251595,25 (1006381 / 4 = 251595,25 = 251595 1/4).
One fifth of 1006381 is 201276,2 (1006381 / 5 = 201276,2 = 201276 1/5).
One sixth of 1006381 is 167730,1667 (1006381 / 6 = 167730,1667 = 167730 1/6).
One seventh of 1006381 is 143768,7143 (1006381 / 7 = 143768,7143 = 143768 5/7).
One eighth of 1006381 is 125797,625 (1006381 / 8 = 125797,625 = 125797 5/8).
One ninth of 1006381 is 111820,1111 (1006381 / 9 = 111820,1111 = 111820 1/9).
show fractions by 6, 7, 8, 9 ...
### Calculator
1006381
#### Is Prime?
The number 1006381 is not a prime number. The closest prime numbers are 1006367, 1006391.
#### Factorization and factors (dividers)
The prime factors of 1006381 are 79 * 12739
The factors of 1006381 are 1, 79, 12739, 1006381.
Total factors 4.
Sum of factors 1019200 (12819).
#### Powers
The second power of 10063812 is 1.012.802.717.161.
The third power of 10063813 is 1.019.265.411.299.204.352.
#### Roots
The square root √1006381 is 1003,185427.
The cube root of 31006381 is 100,212249.
#### Logarithms
The natural logarithm of No. ln 1006381 = loge 1006381 = 13,821871.
The logarithm to base 10 of No. log10 1006381 = 6,002762.
The Napierian logarithm of No. log1/e 1006381 = -13,821871.
### Trigonometric functions
The cosine of 1006381 is -0,997705.
The sine of 1006381 is -0,067705.
The tangent of 1006381 is 0,06786.
### Properties of the number 1006381
Is a Fibonacci number: No
Is a Bell number: No
Is a palindromic number: No
Is a pentagonal number: No
Is a perfect number: No
## Number 1006381 in Computer Science
Code typeCode value
1006381 Number of bytes982.8KB
Unix timeUnix time 1006381 is equal to Monday Jan. 12, 1970, 3:33:01 p.m. GMT
IPv4, IPv6Number 1006381 internet address in dotted format v4 0.15.91.45, v6 ::f:5b2d
1006381 Decimal = 11110101101100101101 Binary
1006381 Decimal = 1220010111101 Ternary
1006381 Decimal = 3655455 Octal
1006381 Decimal = F5B2D Hexadecimal (0xf5b2d hex)
1006381 BASE64MTAwNjM4MQ==
1006381 MD59bf712278832ac6e002556be71cb4c1a
1006381 SHA1998388cf968fe0dffe871c7d75436594ee5f3f3d
1006381 SHA2560bc0e2ab1d6df53ffd7898c9f0c83a816c535d26784d002b03a588bce7d643cf
1006381 SHA3846e1de23f6c27c29f520b2868f7957fefd4169cede72a43f68274c08c2422cf7ea45d4641fe3efab0627ea363c20b21c1
More SHA codes related to the number 1006381 ...
If you know something interesting about the 1006381 number that you did not find on this page, do not hesitate to write us here.
## Numerology 1006381
### Character frequency in the number 1006381
Character (importance) frequency for numerology.
Character: Frequency: 1 2 0 2 6 1 3 1 8 1
### Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 1006381, the numbers 1+0+0+6+3+8+1 = 1+9 = 1+0 = 1 are added and the meaning of the number 1 is sought.
## № 1,006,381 in other languages
How to say or write the number one million, six thousand, three hundred and eighty-one in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 1.006.381) un millón seis mil trescientos ochenta y uno German: 🔊 (Nummer 1.006.381) eine Million sechstausenddreihunderteinundachtzig French: 🔊 (nombre 1 006 381) un million six mille trois cent quatre-vingt-un Portuguese: 🔊 (número 1 006 381) um milhão e seis mil, trezentos e oitenta e um Hindi: 🔊 (संख्या 1 006 381) दस लाख, छः हज़ार, तीन सौ, इक्यासी Chinese: 🔊 (数 1 006 381) 一百万六千三百八十一 Arabian: 🔊 (عدد 1,006,381) واحد مليون و ستة آلاف و ثلاثمائةواحد و ثمانون Czech: 🔊 (číslo 1 006 381) milion šest tisíc třista osmdesát jedna Korean: 🔊 (번호 1,006,381) 백만 육천삼백팔십일 Dutch: 🔊 (nummer 1 006 381) een miljoen zesduizenddriehonderdeenentachtig Japanese: 🔊 (数 1,006,381) 百万六千三百八十一 Indonesian: 🔊 (jumlah 1.006.381) satu juta enam ribu tiga ratus delapan puluh satu Italian: 🔊 (numero 1 006 381) un milione e seimilatrecentottantuno Norwegian: 🔊 (nummer 1 006 381) en million, seks tusen, tre hundre og åtti-en Polish: 🔊 (liczba 1 006 381) milion sześć tysięcy trzysta osiemdziesiąt jeden Russian: 🔊 (номер 1 006 381) один миллион шесть тысяч триста восемьдесят один Turkish: 🔊 (numara 1,006,381) birmilyonaltıbinüçyüzseksenbir Thai: 🔊 (จำนวน 1 006 381) หนึ่งล้านหกพันสามร้อยแปดสิบเอ็ด Ukrainian: 🔊 (номер 1 006 381) один мільйон шість тисяч триста вісімдесят один Vietnamese: 🔊 (con số 1.006.381) một triệu sáu nghìn ba trăm tám mươi mốt Other languages ...
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http://gmatclub.com/forum/do-you-agree-or-disagree-to-what-extent-do-you-agree-or-111128.html#p895201 | 1,481,346,295,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542939.6/warc/CC-MAIN-20161202170902-00070-ip-10-31-129-80.ec2.internal.warc.gz | 113,984,547 | 45,766 | Do you agree or disagree / To what extent do you agree or .. : TOEFL
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Do you agree or disagree / To what extent do you agree or ..
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Manager
Joined: 14 Mar 2011
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Do you agree or disagree / To what extent do you agree or .. [#permalink]
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19 Mar 2011, 06:44
Dear all,
I want to ask you about 2 similar kinds of TOEFL essays.
The first one is "Do you agree or disagree with the statement". The second one is "To what extent do you agree or disagree with the statement". What is the difference between them?
Thank you.
Current Student
Joined: 12 Apr 2010
Posts: 459
Location: Spain
Schools: Chicago (Booth) - Class of 2013
GMAT 1: 740 Q50 V40
WE: Information Technology (Investment Banking)
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Re: Do you agree or disagree / To what extent do you agree or .. [#permalink]
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28 Mar 2011, 23:21
I would give the same answer for both questions
Re: Do you agree or disagree / To what extent do you agree or .. [#permalink] 28 Mar 2011, 23:21
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https://kr.mathworks.com/matlabcentral/cody/problems/207-hackathon-impossible/solutions/290811 | 1,604,098,648,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107911792.65/warc/CC-MAIN-20201030212708-20201031002708-00323.warc.gz | 316,365,489 | 17,092 | Cody
# Problem 207. hackathon impossible
Solution 290811
Submitted on 27 Jul 2013 by Claudio Gelmi
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% rand(1,12345); assert(isequal(randi(10000),hackathon3))
[Warning: Function /users/msssystem2/assert.m has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In hackathon3 at 2 In verifyCode>evaluateCode at 227 In verifyCode at 40 In fevalJSON at 14]
2 Pass
%% assert(isequal(randi(10000),hackathon3))
[Warning: Function /users/msssystem2/assert.m has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In hackathon3 at 2 In verifyCode>evaluateCode at 227 In verifyCode at 40 In fevalJSON at 14]
3 Pass
%% assert(isequal(randi(10000),hackathon3))
[Warning: Function /users/msssystem2/assert.m has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In hackathon3 at 2 In verifyCode>evaluateCode at 227 In verifyCode at 40 In fevalJSON at 14]
4 Pass
%% assert(isequal(randi(10000),hackathon3))
[Warning: Function /users/msssystem2/assert.m has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In hackathon3 at 2 In verifyCode>evaluateCode at 227 In verifyCode at 40 In fevalJSON at 14]
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https://brainmass.com/economics/utility/marginal-utility-5582 | 1,490,640,856,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218189495.77/warc/CC-MAIN-20170322212949-00466-ip-10-233-31-227.ec2.internal.warc.gz | 783,056,946 | 18,231 | Share
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# marginal utility
1. simple dispensing machines offer opportunites for consumers to take numerous copies for the price of 1 copy. why do consumers usually take only one copy?
2. the price of a seasonal pass to six flags great adventure is not much more than a weekly pass. why is this a reasonable pricing policy?
3. Tim eats only burgers and tacos. in equilibrium, his marginal utility of burgers is 20 and his marginal utility of tacos is 10. The price of burgers is \$4. what is the price of a taco?
====
#### Solution Preview
1: marginal utility is decreasing. In this case from the second copy marginal utility is negative, so that taking only one copy maximize ...
#### Solution Summary
A marginal utility case is demonstrated.
\$2.19 | 167 | 774 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2017-13 | latest | en | 0.927813 |
https://x-engineer.org/graduate-engineering/mechatronics/mechanisms/what-is-efficiency/ | 1,597,256,974,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738913.60/warc/CC-MAIN-20200812171125-20200812201125-00549.warc.gz | 892,004,961 | 13,165 | # What is efficiency ?
Efficiency has multiple definitions, all of them valid. We can define efficiency as:
• the ability to avoid wasting energy when performing a particular work
• the ratio between the useful work performed by a device and the total energy consumed as input
Let’s suppose we have a system which receives a power as input and outputs another power. The efficiency is the ratio between the output and input power.
Image: Efficiency of a system
The symbol used to define efficiency is the Greek letter eta (η):
$\begin{split} \bbox[#FFFF9D]{\eta=\frac{P_{out}}{P_{in}}} \end{split}$
If we want to express the efficiency as percentage the mathematical expression becomes:
$\eta = \frac{P_{out}}{P_{in}} \cdot 100 [\%]$
For example if we take an electric motor which receives a 1000 W power from a battery and outputs 900 W at the rotor, what is the efficiency of the motor?
$\eta_{mot} = \frac{900}{1000} \cdot 100 = 90 \%$
Where are the remaining 100 W gone? Why aren’t they available at the motor output (rotor)?
The answer is simple. Since the rotor is mounted on some bearings, there is an amount of friction in the bearings. The friction absorbs a part of the input power and transforms it into heat. Also there are some winding losses in the motor itself. The friction losses together with the winding losses reduces the output power of the motor.
$P_{out} = P_{in} – P_{loss}$
If we divide the above expression to input power we get:
$\begin{equation*} \begin{split} \frac{P_{out}}{P_{in}} &= \frac{P_{in}}{P_{in}} – \frac{P_{loss}}{P_{in}}\\ \eta &= 1 – \frac{P_{loss}}{P_{in}}\\ \end{split} \end{equation*}$
If we know the input power of a system and its efficiency, we can easily calculate the output power as:
$\begin{split} \bbox[#FFFF9D]{P_{out} = \eta \cdot P_{in}} \end{split}$
Now we are going to work on a example which will highlight the impact of efficiency on the output of an actuation system. Also we will see how to use efficiency for the calculation of output power.
Suppose we have an electro-mechanical actuation system composed by:
• a battery
• an electric motor
• a worm gear
• a spur gear
Image: Electro-mechanical actuation system
By knowing the voltage and electrical current of the battery and the efficiency of motor, worm gear and spur gear, we can calculate the output power at the spur gear.
Physical variable Symbol Value Unit Battery voltage $U_{bat}$ 12 V Battery current $I_{bat}$ 10 A Motor efficiency $\eta_{mot}$ 95 % Worm gear efficiency $\eta_{worm}$ 70 % Spur gear efficiency $\eta_{spur}$ 98 %
For a better understanding of the input and output power for each component, we can describe the above actuation system with block diagrams:
Image: Electro-mechanical actuation system block diagram
First we calculate the input power, the battery power:
$P_{bat} = U_{bat} \cdot I_{bat} = 12 \cdot 10 = 120 W$
Next we calculate the motor output power:
$P_{mot} = \eta_{mot} \cdot P_{bat} = 0.95 \cdot 120 = 114 W$
Next we calculate the worm gear output power:
$P_{worm}=\eta_{worm} \cdot P_{mot} = 0.70 \cdot 114 = 79.8 W$
Finally we calculate the spur gear output power:
$P_{spur} = \eta_{spur} \cdot P_{worm} = 0.98 \cdot 79.8 = 78.204 W$
By knowing the input power and the output power we can calculate the overall efficiency of the system:
$\eta = \frac{P_{out}}{P_{in}} = \frac{P_{spur}}{P_{bat}} = \frac{78.204}{120}=0.6517 = 65.17 \%$
The overall system efficiency can be also calculated by multiplying together all the efficiency of the components:
$\eta = \eta_{mot} \cdot \eta_{worm} \cdot \eta_{spur} = 0.95 \cdot 0.70 \cdot 0.98 = 0.6517 = 65.17 \%$
We can calculate the power losses by subtracting the output power from the input power:
$P_{loss} = P_{in} – P_{out} = P_{bat} – P_{spur} = 120 – 78.204 = 41.796 W$
With the power losses we can recalculate the overall efficiency as:
$\eta = 1 – \frac{P_{loss}}{P_{in}} = 1 – \frac{41.796}{120} = 1 – 0.3483 = 0.6517 = 65.17 \%$
With this exercise should be pretty obvious how the efficiency is calculated and it’s impact on the power output of a system.
For any questions or observations regarding this tutorial please use the comment form below.
Don’t forget to Like, Share and Subscribe! | 1,186 | 4,252 | {"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} | 4.28125 | 4 | CC-MAIN-2020-34 | latest | en | 0.849445 |
http://webwork.maa.org/viewvc/npl/trunk/NationalProblemLibrary/ASU-topics/setTrigIdentities/srw7_3_53.pg?revision=305&view=markup&pathrev=2584 | 1,369,478,687,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368705936437/warc/CC-MAIN-20130516120536-00004-ip-10-60-113-184.ec2.internal.warc.gz | 285,835,452 | 2,745 | [npl] / trunk / NationalProblemLibrary / ASU-topics / setTrigIdentities / srw7_3_53.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww
# View of /trunk/NationalProblemLibrary/ASU-topics/setTrigIdentities/srw7_3_53.pg
Thu Jun 29 18:44:08 2006 UTC (6 years, 10 months ago) by jj
File size: 1185 byte(s)
Fixed tags.
1 ##DESCRIPTION
2 ## Precalculus, Trigonometric Identities
3 ##ENDDESCRIPTION
4
5 ## KEYWORDS('precalculus','trigonometry','identities')
6 ## Tagged by skm9b
7
8 ## DBsubject('Trigonometry')
9 ## DBchapter('Analytic Trigonometry')
10 ## DBsection('Trigonometric Identities')
11 ## Date('')
12 ## Author('')
13 ## Institution('ASU')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT(); # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 0; 32 33$a = random(2,9,1);
34
35 TEXT(EV2(<<EOT));
36 Use the formula for lowering the powers to simplify the expression:
37 $BR 38 (a) If $$\cos^2 a x - \sin^2 a x = \cos (f(x))$$, then 39$BR
40 $$f(x) =$$ \{ans_rule(10)\};
41 $BR 42 (b) If $$\cos^4 a x - \sin^4 a x = \cos (g(x))$$, then 43$BR
44 $$g(x) =$$ \{ans_rule(10)\}.
45 $BR 46$BBOLD
47 Hint: $EBOLD For part (b), use $$a^4-b^4=(a^2-b^2)(a^2+b^2)$$! 48 49$BR
50 EOT
51
52 $ans1= "2*$a*x";
53 $ans2= "2*$a*x";
54
55 ANS(fun_cmp($ans1)); 56 ANS(fun_cmp($ans2));
57
58 ENDDOCUMENT(); # This should be the last executable line in the problem. | 577 | 1,629 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2013-20 | latest | en | 0.395129 |
https://maths2art.com.sg/2017/02/12/math-education/?replytocom=2051 | 1,638,459,236,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362230.18/warc/CC-MAIN-20211202145130-20211202175130-00456.warc.gz | 453,254,442 | 57,171 | I have been pondering why Maths is one of the most hated subjects among the kids as well as adults. Why is it that the mere thought of it makes a few of them uneasy? What can be done to reduce this Math anxiety? To understand the origin of the adverse reactions towards Math and to get a deeper insight into Math anxiety, I read the book “Mind over Math” by Dr. Stanley Kogelman & Dr. Joseph Warren. The authors quote,
“Many people remember their first negative experiences with Math with such clarity and emotion that it seems as if it were just yesterday, even if it really was twenty, thirty or even fifty years ago.”
The book claims that Math anxiety is an emotional inhibition, not an intellectual one and one can overcome it. I agree. Let’s take a look into it together.
## Where are we going wrong with Maths?
Unfortunately, in most of the cases, maths concepts and methods have been presented in a ready-made form. The history of the mathematical ideas and the lives of mathematicians are rarely discussed while teaching Maths . Maths is looked upon as some eternal truth, as if it has always been there, not something that was discovered and developed. Math has been portrayed as a subject which is to be accepted, not understood.
When we teach our children with this mindset, we convert this beautiful, creative and flexible subject into a boring & rigid one in our children’s memories.
## What can we do to correct it?
What can we do to convert this uninteresting and inflexible looking subject into its original form – that is creative, flexible & beautiful?
We need to give them some background of the concepts and we need to help them in visualizing these concepts rather just accepting them. It is our duty to create a plot where they can see how these mathematical ideas were developed by people like us.
We need to help our children in building their own concept ladder rather than taking the stairs created by someone else.
Maths concepts are not isolated. They are very well connected to each other. When a student is unable to see this connection, he loses interest in the subject.
## Let me explain my point using one example – Area & Volume.
When my students are clear with the concept of Area, I do not pass them the formula for Volume directly. I give them some time to think about the connection between Area & Volume. In case they are unable to find any connection, I give them a clue to think about a ‘paper’ and a ‘book’. I believe in giving minimum clues.
A paper represents Area. When we start stacking papers, it gets converted into a book. This is like multiplication, which is repetitive addition.
So, the book (Volume) is nothing but the repetitive addition of pages (Area).
Volume = Area X Height
This 10 – 15 mins time invested in visualizing a new concept (volume) based on the previously known concepts (area and multiplication) pays a huge return in terms of learning. Once the visuals are clear, they develop genuine interest in solving the problems and they get the taste of ‘Joy of Learning’.
## Moral of the Story
There is no best way to do Maths.
It is such a flexible subject that it offers us many ways to solve the same problem. And, we should promote this flexibility by giving our students freedom to solve it in their own way. There is no need of uniquely created/crafted tricks for different problems. Flexibility comes with the visual understanding of concepts and the connection between various concepts.
Forget Maths, let’s think about Movies – How do you feel when you watch a movie where the scenes are not well connected? When a movie can be so boring in the absence of well connected scenes, think about a child’s situation who is doing Maths without any clarity about these concept connections.
We need well connected visual explanations to take away Math anxiety. I use such visual examples during my sessions. I will try to publish some of these visuals as time permits. In the meantime, get creative and try to make your own visual examples for helping your children in visualizing this beautiful subject. You can message us anytime in case you need an idea for the same. It will be a pleasure for Maths2Art to be a part of such creative Maths initiative.
Let’s make Maths Simple & Visual together !
## 11 thoughts on “Math is not to be accepted. It is to be understood.”
1. Priya Asthana says:
I am glad that you liked it.
Every complex concept is nothing but a combination of various simple concepts. So, if you have crystal clear understanding of simple concepts then no topic will be complex for you.
Feel free to reach out in case you are not clear with any specific concept.
Like
1. Such a beautiful read. Brought me back to the memory lanes, the days of starting to get exposed to the world of science and Maths.
Like
2. Amit Patel says:
So inspiring!
Like | 1,002 | 4,858 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2021-49 | latest | en | 0.98242 |
http://mymathforum.com/geometry/344728-equation-line.html | 1,550,697,004,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247496694.82/warc/CC-MAIN-20190220210649-20190220232649-00170.warc.gz | 192,372,467 | 9,682 | My Math Forum Equation of a line
Geometry Geometry Math Forum
August 22nd, 2018, 03:37 AM #1 Member Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 Equation of a line Help!!! I need a mathematician to solve this... The line 5x+Ky-15=0 is perpendicular to the line 2x+5y-3=0,find the value of K. Last edited by Harmeed; August 22nd, 2018 at 03:40 AM. Reason: to erase
August 22nd, 2018, 04:35 AM #2
Senior Member
Joined: May 2016
From: USA
Posts: 1,306
Thanks: 549
Quote:
Originally Posted by Harmeed Help!!! I need a mathematician to solve this... The line 5x+Ky-15=0 is perpendicular to the line 2x+5y-3=0,find the value of K.
A few questions.
The slope of line A has a slope of m. Line B is perpendicular to line A. What is the slope of line B? The answer to that question should be in your text or lecture notes, but you may not have seen its relevance.
Its relevance is this: if you determine the slope of 2x + 5y - 3 = 0, you can then find the slope of 5x + ky - 15 = 0. And then you can find k.
So what is the slope of 2x + 5y - 3 = 0?
August 22nd, 2018, 09:02 AM #3 Member Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 The slope of 5x+Ky-15=0 is -5/k and 2x+5y-3=0 is -2/5...Help me guy how are my going to find constant k Thanks from o2jam
August 22nd, 2018, 09:12 AM #4 Senior Member Joined: Sep 2015 From: USA Posts: 2,312 Thanks: 1224 the product of the slopes of two perpendicular lines is -1
August 24th, 2018, 04:53 PM #5
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Originally Posted by Harmeed The slope of 5x+Ky-15=0 is -5/k and 2x+5y-3=0 is -2/5...Help me guy how are my going to find constant k
the opposite reciprocal of -2/5x is 5/2x, so the first equation's slope has to equal this value, and the only way to do that is by letting k be 2 and then dividing 5x by 2 to get 5/2x once you first rewrite the equations in slope-intercept form. Please correct me if i'm wrong I would like to know the correct solution.
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Contact - Home - Forums - Cryptocurrency Forum - Top | 797 | 2,436 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2019-09 | longest | en | 0.93669 |
http://reference.wolfram.com/legacy/language/v11/ref/RadialityCentrality.html | 1,508,364,968,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187823153.58/warc/CC-MAIN-20171018214541-20171018234541-00795.warc.gz | 276,553,813 | 9,472 | # Wolfram Language & System 11.0 (2016)|Legacy Documentation
This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL
gives a list of radiality centralities for the vertices in the graph g.
gives a list of in-centralities for a directed graph g.
gives a list of out-centralities for a directed graph g.
uses rules vw to specify the graph g.
## DetailsDetails
• Radiality in-centralities are also known as integration centralities.
• RadialityCentrality will give high centralities to vertices that are a short distance to every other vertex in its reachable neighborhood compared to its diameter.
• Radiality out-centrality for a vertex is computed using the out component for the vertex and is given by , where is the distance from to in , is the diameter of , and the sum is over the vertices in .
• Radiality in-centrality for a vertex is computed using the in component for the vertex and is given by , where is the distance from to in , is the diameter of , and the sum is over the vertices in .
• The radiality centrality for an isolated vertex is taken to be zero.
• RadialityCentrality works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.
## ExamplesExamplesopen allclose all
### Basic Examples (2)Basic Examples (2)
In[1]:=
In[2]:=
Out[2]=
Highlight:
In[3]:=
Out[3]=
Rank vertices. Highest-ranked vertices are at a short distance to all reachable vertices compared to the highest distance in the graph:
In[1]:=
In[2]:=
Out[2]= | 371 | 1,547 | {"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-2017-43 | latest | en | 0.903264 |
https://www.doorsteptutor.com/Exams/KVPY/Stream-SB-SX/Physics/Questions/Topic-Ray-Optics-15/Part-2.html | 1,503,309,391,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886107744.5/warc/CC-MAIN-20170821080132-20170821100132-00274.warc.gz | 889,668,705 | 19,506 | # Ray Optics (KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Physics): Questions 4 - 7 of 13
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## Question number: 4
» Ray Optics » Snell's Law
Appeared in Year: 2011
MCQ▾
### Question
A material is embedded between two glass plates. Refractive index n of the material varies with thickness as shown below. The maximum incident angle (in degrees) on the material for which beam will pass through the material is –
### Choices
Choice (4) Response
a.
60.0
b.
53.1
c.
43.5
d.
32.3
## Question number: 5
» Ray Optics » Spherical Mirror
Appeared in Year: 2013
MCQ▾
### Question
A ray of light incident on a glass sphere suffers total internal reflection before emerging out exactly parallel to the incident ray. The angle of incidence was –
### Choices
Choice (4) Response
a.
300
b.
750
c.
600
d.
450
## Question number: 6
» Ray Optics » Snell's Law
Appeared in Year: 2012
MCQ▾
### Question
On a bright sunny day a diver with height h stands at the bottom of a lake of depth H. Looking upward, he can see objects outside the lake in a circular region of radius r. Beyond this circle he sees the images of objects lying on the floor of the lake. If refractive index of water is, then the value of r is,
### Choices
Choice (4) Response
a.
b.
c.
d.
## Question number: 7
» Ray Optics » Reflection and Refraction of Light
Appeared in Year: 2014
MCQ▾
### Question
Monochromatic light passes through a prism. Compared to that in air, inside the prism the light’s
### Choices
Choice (4) Response
a.
wavelength and frequency are different, but speed remains same.
b.
speed and wavelength are different but frequency remains same.
c.
speed, wavelength and frequency are all different.
d.
speed and frequency are different but wavelength remains same.
f Page | 528 | 2,049 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2017-34 | longest | en | 0.827176 |
https://forum.allaboutcircuits.com/threads/can-anyone-help-me-find-ideal-component-values-for-this-audio-cable-tester-xlr-midi-trs.147153/ | 1,628,200,448,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046157039.99/warc/CC-MAIN-20210805193327-20210805223327-00377.warc.gz | 271,957,561 | 20,391 | # Can Anyone Help Me Find Ideal Component Values For This Audio Cable Tester? - XLR/MIDI/TRS
#### Jimmyjam
Joined Mar 28, 2018
2
Hi, Everybody. Can Someone help me calculate Component values in a simple continuity tester for audio cables that must consist of 3 resistors, 3 LEDs(red,yellow,green), 2 TRS 1/4” Stereo jacks (l&r), 2 TRS 1/4” Mono jacks(l&r), 2 TRS 1/8” Jacks(l&r), 2 XLR (m&f) jacks, 2 MIDI (m&f), and a battery power cell?
Like this plot image:
#### MrChips
Joined Oct 2, 2009
23,966
You are missing a vital piece of information: the voltage of the battery.
Once you know the voltage V of the battery, you can calculate the value if each resistor using Ohm's Law.
For example, if you wish the LED to be lit with 10mA,
R = (V - 2) / 0.01
= ( V - 2) x 100
approximately | 251 | 792 | {"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-2021-31 | latest | en | 0.755379 |
https://math.stackexchange.com/questions/2937606/how-to-determine-the-step-size-using-eulers-method | 1,643,112,263,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304810.95/warc/CC-MAIN-20220125100035-20220125130035-00380.warc.gz | 429,590,545 | 34,364 | # How to determine the step size using Euler's Method?
Consider the initial value problem $$x' = x+e^{-x}$$ , $$x(0)= 0$$. This problem can’t be solved analytically.
Using the Euler method, compute $$x$$ at $$t = 1$$, correct to three decimal places. How small does the stepsize need to be to obtain the desired accuracy? (Give the order of magnitude, not the exact number.
I am not sure how to go about this, I was thinking guess and check but figured that would take too long. Is there a method for determining the stepsize given these conditions?
Any help or intuition would be greatly appreciated.
• Oct 1 '18 at 5:38
Consider a Taylor series expansion with the Lagrange remainder $$x(t+d) = x(t) + x'(t)d + \frac{x''(c)}{2}d^2,$$ where $$t \leq c \leq t+d$$. The Euler's method is basically a truncation of this expansion, so the error at each step is bound by the remainder term. Now $$x'' = \frac{df}{dx}x' = \frac{df}{dx}f(x) = (x + e^{-x})(1 - e^{-x}) < (x+1)x$$ So each step may introduce an error $$\delta = \frac{(x(c) + 1)\cdot x(c)}{2}d^2$$. To estimate it we need some bounds on $$x$$. Note that if $$y' = y + 1,\ y(0) = 0$$, then $$x < y$$, and there is an analytic solution $$y(t) = e^t - 1$$. So per step $$\delta = \frac{(x(c) + 1)\cdot x(c)}{2}d^2 < \frac{(y(c) + 1)\cdot y(c)}{2}d^2 < \frac{(y(1) + 1)\cdot y(1)}{2}d^2 = \frac{(e + 1)\cdot e}{2}d^2$$ Altogether there are $$N = 1/d$$ steps, and the full error is $$N\delta < \frac{(e + 1)\cdot e}{2}d \approx 5.054 \ d$$ You need $$5.054\ d < 0.001$$, so $$d < 0.0002$$ is enough. There might be a tighter estimate if you choose $$y(t)$$ more ingeniously.
UPDATE As LutzL poined out in his comment, we can take $$y(t) = \sqrt 2\tan\frac{t}{\sqrt{2}}$$. Then $$y(1) \approx 1.208$$ and $$N\delta < \frac{(y(1) + 1)\cdot y(1)}{2}d \approx 1.334\ d$$ which gives for the desired precision: $$d < 0.0007$$
• You could better estimate $1-e^{-x}\le\min(1,x)\le 1$ for $x\ge 0$. -- Numerical experiments give the factor for the error as even smaller at about $0.282$ with a maximum value $x(1)=1.153638..$. Oct 1 '18 at 7:30
• To get a tighter analytical solution use $e^{-x}\le 1-x+\frac12x^2$ for $x\ge 0$. This gives $x(t)\le y(t)=\sqrt2\tan(t/\sqrt2)$ with $y(1)=1.20846..$ Oct 1 '18 at 7:40 | 809 | 2,265 | {"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": 22, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2022-05 | latest | en | 0.786036 |
https://reason.town/conditional-independence-machine-learning/ | 1,674,876,998,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499470.19/warc/CC-MAIN-20230128023233-20230128053233-00084.warc.gz | 499,924,517 | 27,804 | # What is Conditional Independence in Machine Learning?
Conditional independence is a key concept in machine learning that is often misunderstood. This blog post will explain what conditional independence is and why it is important.
Checkout this video:
## What is conditional independence?
Conditional independence is a statistical property that describes the relationship between two or more random variables. Specifically, it means that the probability of one event occurring is not affected by the occurrence or non-occurrence of another event. In other words, the events are independent of each other.
Conditional independence is an important concept in machine learning because it allows us to build models that are more efficient and accurate. If two variables are independent of each other, then we can learn about one without having to worry about the other. This can be a major advantage when we’re working with large datasets.
There are a few different ways to test for conditional independence. The most common method is called the chi-squared test. This method assesses whether two variables are independent by looking at how often they occur together in a dataset. If the variables are truly independent, then we would expect them to occur together roughly half the time. If they occur together less than half the time, then we would conclude that they are dependent on each other.
The chi-squared test is just one way to test for conditional independence. There are also methods that rely on information theory and Bayesian inference. These methods can be more accurate than the chi-squared test, but they are also more computationally intensive.
## What is machine learning?
In machine learning, we use mathematical models to find patterns in data so that we can make predictions about new, unseen data. This process is similar to the way humans learn from past experiences to form predictions about the future. Machine learning is a growing area of computer science with many real-world applications.
Conditional independence is a fundamental concept in machine learning. It is based on the idea that if we know something about a certain event, this information can help us make better predictions about other events. For example, if we know that it is sunny outside, this information can help us predict that the temperature will be warm. However, if we do not know anything about the weather, our prediction would be less accurate.
In machine learning, we often use probability theory to represent our knowledge about an event. This allows us to calculate the likelihood of an event happening, given some information. For example, if we know that it is sunny outside and we have a data set of historical temperatures, we can use this information to calculate the probability of it being warm today. If this probability is high, then we can be confident in our prediction. However, if the probability is low, then we know that our prediction is less reliable.
The concept of conditional independence can be applied to many different areas of machine learning, such as classification and regression tasks. It is also a key ingredient in many popular machine learning algorithms, such as belief propagation and support vector machines.
## What are the applications of conditional independence in machine learning?
In machine learning, conditional independence is a statistical property that is often exploit to make better predictions. When two random variables are conditionally independent, it means that the value of one variable does not give any information about the value of the other variable given some other third variable. Mathematically, this is represented as:
P(x|y,z) = P(x|z)
This property can be used in many ways in machine learning. For example, it can be used to select features for training a model or to design more efficient algorithms. It can also be used to make better predictions by taking into account the dependencies between different variables.
## What are the benefits of using conditional independence in machine learning?
In machine learning, conditional independence is often used to make the learning process more efficient. By assuming that certain variables are independent of each other, the number of possible combinations that the algorithm has to consider is reduced, which can lead to faster and more accurate results.
There are several different ways to measure conditional independence, but one of the most popular is mutual information. This metric quantifies the amount of information that two variables share with each other. If two variables are completely independent, they will have zero mutual information. On the other hand, if they are completely dependent on each other, their mutual information will be maximized.
Mutual information can be used to detect relationships between variables that may not be immediately apparent. For example, two variables may appear to be unrelated when considering only their marginal distributions. However, if we take into account their joint distribution, we may find that there is actually a significant relationship between them. This type of relationship is known as a hidden relationship.
Conditional independence can also be used to improve the accuracy of predictive models. By making certain assumptions about the data, the number of free parameters in the model can be reduced, which can lead to more accurate predictions.
Overall, conditional independence is a powerful tool that can be used to improve the efficiency and accuracy of machine learning algorithms.
## What are the challenges of using conditional independence in machine learning?
There are a few challenges that come with using conditional independence in machine learning. First, it can be difficult to determine whether or not two variables are actually independent. This can be especially tricky when dealing with large data sets. Second, even if two variables are independent, that doesn’t necessarily mean that they will be useful for predictive purposes. In other words, just because two variables are independent doesn’t mean that they will provide any information that can help us better understand the data set as a whole.
## How can conditional independence be used in machine learning?
In machine learning, we often want to find structure in data in order to make predictions. One way to do this is to look for conditional independence relationships. That is, we want to find variables that are independent given some other variable. For example, imagine we have data on people’s heights and weights. We might want to know if height and weight are conditionally independent given gender. If they are, then we can make better predictions by using both height and weight when we know the person’s gender.
However, it’s not always easy to find conditional independence relationships in data. In some cases, the relationships may be hidden by other factors. For example, imagine that we have data on people’s heights and weights, but also on their diets. If diet affects both height and weight, then it will be hard to tell if height and weight are really independent given diet.
Fortunately, there are some machine learning methods that can help us find conditional independence relationships in data, even when there are other confounding factors. These methods include mutual information estimation and minimum description length methods.
## What are the limitations of using conditional independence in machine learning?
Conditional independence is a concept that is often used in machine learning. It essentially states that two variables are independent given a third variable. For example, you might say that two variables are conditionally independent given a third variable if the two variables are independent when the third variable is present. However, if the third variable is not present, then the two variables might not be independent.
There are some limitations to using conditional independence in machine learning. First, it can be difficult to determine whether or not two variables are actually independent given a third variable. Second, even if two variables are conditionally independent given a third variable, they might not be independent in general. That is, they might be dependent when the third variable is not present. Finally, conditional independence can only be used for linear models; it cannot be used for nonlinear models.
## What are the future prospects of using conditional independence in machine learning?
Despite the fact that machine learning is still in its infancy, there has been a lot of progress made in the field in recent years. One area of particular interest is conditional independence. This is a powerful tool that can be used to improve the accuracy of predictions made by machine learning algorithms.
There are a number of different ways to achieve conditional independence. One popular method is to use independent components analysis (ICA). This approach involves decomposing the data into a set of independent sub-sets. Another common method is to use feature selection. This involves selecting a subset of features that are most relevant to the task at hand.
Feature selection can be used in conjunction with ICA to further improve accuracy. It is also possible to use kernels methods to obtain conditional independence. This approach involves transforming the data into a high-dimensional space where it becomes easier to find structure in the data.
The future prospects for using conditional independence in machine learning are very promising. There are a number of different ways to achieve it, and it can be used to improve the accuracy of predictions made by machine learning algorithms.
## What are the best practices for using conditional independence in machine learning?
There is no one-size-fits-all answer to this question, as the best practices for using conditional independence in machine learning will vary depending on the specific application. However, some general tips that may be helpful include:
-Using conditional independence to simplify the learning problem by reducing the number of variables that need to be considered. | 1,830 | 10,234 | {"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-2023-06 | longest | en | 0.959945 |
http://mathhelpforum.com/differential-geometry/202961-1-n-1-1-a.html | 1,481,390,771,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698543316.16/warc/CC-MAIN-20161202170903-00120-ip-10-31-129-80.ec2.internal.warc.gz | 177,967,450 | 10,084 | Thread: -1^n = 1 or -1
1. (-1)^n = 1 or -1
Okay, this might be a little bit stupid question...
I'm studying ross elementary analysis.
And I'm trying to get some skills in writing formal proofs, instead of intuitive ideas.
I want to proof that the sequence (-1)^n = 1 or -1.
But how do I give a real proof for this ?
2. Re: -1^n = 1 or -1
Originally Posted by kasper90
Okay, this might be a little bit stupid question...
I'm studying ross elementary analysis.
And I'm trying to get some skills in writing formal proofs, instead of intuitive ideas.
I want to proof that the sequence -1^n = 1 or -1.
But how do I give a real proof for this ?
-1^n = -1, since you need to do the exponentiation before the negation.
3. Re: (-1)^n = 1 or -1
I actually meant to say (-1)^n.
sorry for that
4. Re: -1^n = 1 or -1
(-1)^n = 1 if n is even, and (-1)^n = -1 if n is odd.
5. Re: -1^n = 1 or -1
Okay, but how do I prove that ?
6. Re: -1^n = 1 or -1
Originally Posted by kasper90
Okay, but how do I prove that ?
If $n$ is even, $n=2k$ then $(-1)^n=(-1)^{2k}=[(-1)^{2}]^k=[1]^k=1$.
If $n$ is odd, $n=2k+1$ then (WHAT?)
7. Re: -1^n = 1 or -1
Okay, I'll try:
If n is even,
than ∃k∈N : n = 2k,
than (-1)^n = (-1)^2k=[(-1)^2]^k = 1^k
If n is uneven,
than ∃k∈N : n=2k-1,
than (-1)^n = (-1)^[2k-1] = -1^k,
Induction (prove that 1^k =1)
1^1
if 1^k = 1, than 1^(k+1)=1^k * 1 = 1^k = 1
By induction, 1^k =1 for all natural numbers.
8. Re: -1^n = 1 or -1
Plato posted his post just before I did,
but I think I got the idea, right ?
Is this a valid proof ?
9. Re: -1^n = 1 or -1
Originally Posted by kasper90
Plato posted his post just before I did,
but I think I got the idea, right ? Is this a valid proof ?
You have proved that $(-1)^{2k}=1$ so use it.
$(-1)^{2k+1}=(-1)^{2k}(-1)^{1}=(1)(-1)=-1$. | 684 | 1,795 | {"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": 7, "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-2016-50 | longest | en | 0.846652 |
http://mathhelpforum.com/pre-calculus/95446-quadratics.html | 1,526,909,068,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864186.38/warc/CC-MAIN-20180521122245-20180521142245-00517.warc.gz | 199,264,331 | 9,867 | how do i find the minimum value or maximum value of function
x^2-12x+9?
2. Originally Posted by Rose Wanjohi
how do i find the minimum value or maximum value of function
x^2-12x+9?
Rewrite it in vertex form:
$\displaystyle y = a(x - h)^2 + k$.
If the leading coefficient is positive, then the vertex (h, k) is the minimum point; if the leading coefficient is negative, then the vertex (h, k) is the maximum point.
So, we complete the square to rewrite the equation in vertex form:
$\displaystyle x^2-12x+9$
\displaystyle \begin{aligned} &= x^2 - 12x \;{\color{red}+\;36}\;+ 9\; {\color{red}-\;36} \\ &= (x - 6)^2 - 27 \end{aligned}
The leading coefficient was positive (a = 1), so the point (6, -27) is the minimum of the parabola.
01
3. Originally Posted by Rose Wanjohi
how do i find the minimum value or maximum value of function
x^2-12x+9?
Hello: The formula for the minimum or the
the maximum point by the function f(x) = a x 2 +bx +c is :
(-b/2a; f(-b/2a))
In this exercice : a =1 , b= -12 c =9
I'have : (-(-12)/2 ,f(6))
f(6) = 36-12(6)+9=-27 Conclusion : A ( 6 , -27 ) | 366 | 1,081 | {"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} | 4.21875 | 4 | CC-MAIN-2018-22 | latest | en | 0.679443 |
https://www.hackmath.net/en/example/161?tag_id=33 | 1,503,290,043,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886107490.42/warc/CC-MAIN-20170821041654-20170821061654-00655.warc.gz | 901,605,031 | 8,139 | # Orchard
5 trees in 3 lines grows in the orchard. How many trees are in the orchard?
Result
x = 15
#### Solution:
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
Showing 1 comment:
Math student
I which you guys let us type math problems
## Next similar examples:
1. Forestry workers
In the forest is employed 63 laborers planting trees in nurseries. For 11 hour work day would end job in 43 days. After 14 days, 22 laborers go forth. How many days is needed to complete a planting trees in nurseries by others, if they will work 15 hours
2. Chocolate
Charlie bought 7 same chocolates for 14 Eur. How many euros he pay for 27 chocolates?
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Gross wage was 1113 USD including 16% bonus. How many USD were bonuses?
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A cyclist passes 88 km in 4 hours. How many kilometers he pass in 8 hours?
7. Hands
The clock shows 12 hours. After how many minutes will agle between hour and minute hand 80°? Consider the continuous movement of both hands hours.
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9. Quotient 3
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10. Brick
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11. Root
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12. Store
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13. Diophantus
We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life. Diophantus's youth l
14. Motion
If you go at speed 6.6 km/h, you come to the station 51 minutes after leaving train. If you go by bike to the station at speed 30 km/h, you come to the station 45 minutes before its departure. How far is the train station?
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In stock are three kinds of branded coffee prices: I. kind......5.3 USD/kg II. kind......11.6 USD/kg III. kind.....5.8 USD/kg Mixing these three species in the ratio 2:8:3 create a mixture. What will be the price of 800 grams of this mixture? | 727 | 2,694 | {"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-2017-34 | longest | en | 0.952549 |
https://www.coursehero.com/file/6692381/Lecture-13-regression-2/ | 1,498,297,056,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320243.11/warc/CC-MAIN-20170624082900-20170624102900-00700.warc.gz | 867,292,560 | 25,233 | Lecture 13_regression 2
# Lecture 13_regression 2 - Experimental growth tannin Unit 1...
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Unformatted text preview: Experimental growth tannin Unit 1 12 2 10 1 3 8 2 4 11 3 5 6 4 6 7 5 7 2 6 8 3 Effects of food quality (% tannin content) on caterpillar growth y = a – b x Sum of Square: SSY Sum of square: SSX Y X Calculate total variance for XY growth Mean growth Y 12 6.9 10 6.9 8 6.9 11 6.9 6 6.9 7 6.9 2 6.9 3 6.9 3 6.9 Deviation from the mean 5.1 3.1 1.1 4.1-0.9 0.1-4.9-3.9-3.9 Sum of products-73 ( Sum of Square: SSXY ) Y (Y – Y) (X – X)-4-3-2-1 1 2 3 4-20.44-9.33-2.22-4.11 0.11-9.78-11.67-15.56 (Y – Y)(X – X) Sum of Square for Y: SSY= 108.89 Sum of square for X: SSX= 60.00 Sum of products for XY: SSXY=-73.00 Slope (b)= SSXY SSX = = -1.22 Estimate Sum Square for regression SSR = b * SSXY = -1.22X(-73) =88.82-73.00 60.00 Growth=11.76-1.22 tannin Variance partition Sum of Square (SSY) = Total variance Residual SS Regression SS Total SS: SSY Analysis of Variance Table Response: growth Df Sum Sq Mean Sq F value tannin 1 88.817 88.817 30.974 Residuals 7 20.072 2.867 P=0.000846 (Coefficient of determination: R 2 ) Y X r 2 = Regression SS Total SS How strong the relationship? Y X √r 2 = r Pearson correlation coefficient How strong the relationship? x Simple linear correlation and regression De pe nde nt va ria b le Y Inde pe nde nt va ria b le X Line a r de pe nde nc e o f Y o n X re g re s s io n No line a r de pe nde nc e b e twe e n Y a nd X c o rre la tio n Regression in R >dta<-read.csv("C:\\Documents and Settings\\bwyp\\Desktop\\regression.csv") > colnames(dta) [1] "growth" "tannin" > mod<-lm(growth~tannin, data=dta) > summary(mod) Regression in R...
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## This note was uploaded on 01/12/2012 for the course ENVIRONMET 340 taught by Professor Dr.pan during the Winter '11 term at Portland State.
### Page1 / 34
Lecture 13_regression 2 - Experimental growth tannin Unit 1...
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Ask a homework question - tutors are online | 898 | 2,830 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2017-26 | longest | en | 0.767465 |
https://byjusexamprep.com/gate-ce/for-a-quick-soil-the-critical-gradient-is | 1,708,875,777,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474617.27/warc/CC-MAIN-20240225135334-20240225165334-00565.warc.gz | 155,110,924 | 28,138 | # For a Quick Soil, the Critical Gradient is
By BYJU'S Exam Prep
Updated on: September 25th, 2023
A coarse-grained soil has a voids ratio 0.75, and specific gravity as 2.75. For a quick soil, the critical gradient is-
1. 0.25
2. 0.50
3. 0.75
4. 1.00
## For a quick soil, having void ratio 0.75 and specific gravity as 2.75, the critical gradient is 1.00
Solution
Given, e=0.75
G=2.75
We know that for a quick soil, the critical gradient is given by,
ic G-1/1+e = (1-n)(G-1)
ic 2.65-1/1+0.75 1.65/1.75=1.00
☛ Related Questions:
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https://www.cnblogs.com/ws-fqk/p/4658142.html | 1,623,516,800,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487586239.2/warc/CC-MAIN-20210612162957-20210612192957-00081.warc.gz | 664,509,222 | 7,620 | # [Usaco2008 Feb][BZOJ1609] Eating Together麻烦的聚餐
## 1609: [Usaco2008 Feb]Eating Together麻烦的聚餐
Time Limit: 10 Sec Memory Limit: 64 MB
Submit: 1093 Solved: 655
[Submit][Status][Discuss]
## Sample Input
5
1
3
2
1
1
NlogN求最长不上升和不下降子序列，取最大值与N作差即可。8Ms水过。
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<set>
#include<map>
#include<vector>
#include<queue>
using namespace std;
{
char c=getchar();
int a=0;
while (c<'0'||c>'9') c=getchar();
while (c>='0'&&c<='9')
{
a=a*10+c-'0';
c=getchar();
}
return a;
}
int n,d[30001],top,stack[30001],la,lb;
int main()
{
for (int i=1;i<=n;i++) d[i]=read();
top=0;
stack[0]=-1;
for (int i=1;i<=n;i++)
{
if (d[i]>=stack[top]) stack[++top]=d[i];
else
{
int l=1,r=top;
while (l<=r)
{
int mid=(l+r)>>1;
if (d[i]>=stack[mid]) l=mid+1; else r=mid-1;
}
stack[l]=d[i];
}
}
la=n-top;
top=0;
stack[0]=10000007;
for (int i=1;i<=n;i++)
{
if (d[i]<=stack[top]) stack[++top]=d[i];
else
{
int l=1,r=top;
while (l<=r)
{
int mid=(l+r)>>1;
if (d[i]<=stack[mid]) l=mid+1; else r=mid-1;
}
stack[l]=d[i];
}
}
lb=n-top;
printf("%d",min(la,lb));
return 0;
}
posted @ 2015-07-19 08:52 ws_fqk 阅读(203) 评论(0编辑 收藏 举报 | 507 | 1,199 | {"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} | 2.703125 | 3 | CC-MAIN-2021-25 | latest | en | 0.144504 |
https://testbook.com/question-answer/how-many-pairs-of-letters-are-there-in-the-word-l--5f5a10e8d5af066229e8c7bb | 1,638,759,788,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363229.84/warc/CC-MAIN-20211206012231-20211206042231-00500.warc.gz | 584,963,656 | 40,838 | # How many pairs of letters are there in the word “KILOGRAM” each of which has as many letters between them in the word (in the forward direction) as they have between them in the English alphabetical order?
1. Three
2. Zero
3. One
4. Five
5. Two
## Answer (Detailed Solution Below)
Option 2 : Zero
Free
Syllogism (Clear Your Basics)
75408
10 Questions 10 Marks 10 Mins
## Detailed Solution
The alphabets are positioned in the following order:
The word can be represented as follows:
In forward direction: 0
Thus, there are zero pair of letters in the word “KILOGRAM” as according to the English alphabetical series.
Hence, zero is the correct answer. | 166 | 660 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2021-49 | latest | en | 0.94748 |
http://www.estima.com/forum/viewtopic.php?p=3060 | 1,369,121,235,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368699776315/warc/CC-MAIN-20130516102256-00038-ip-10-60-113-184.ec2.internal.warc.gz | 462,829,189 | 10,672 | Evaluating density forecasts
Econometrics questions and discussions
Evaluating density forecasts
If I generate a sequence of rolling one-step ahead point forecasts it is straightforward to evaluate these via:
(a) Graphical Analysis: Theil’s Prediction Realization Diagram.
(b) Standard Loss Measures: there are plenty.
(c) Sign test.
But how do I evaluate the point forecasts from the view of density forecasts ?
Initial research into this suggests by the examining distributional and autocorrelation properties of probability integral transformations.
Can you provide an example on how to proceed for evaluation ?
Thanks!
ac_1
Posts: 56
Joined: Thu Apr 15, 2010 6:30 am
Location: Surrey, England, UK
Re: Evaluating density forecasts
I've pasted below a link to a starting point (by James Mitchell and Kenneth Wallis) on the literature on density evaluation. You are right that PITS are a key measure. But tests based on the normalized transforms can have better power (a result from a paper by Berkowitz). At this point, my sense is that most econometricians view the log predictive score as the best overall indicator of the calibration/accuracy of density forecasts.
http://www.niesr.ac.uk/pdf/DP320.pdf
Todd Clark
Economic Research Dept.
Federal Reserve Bank of Cleveland
tclark
Posts: 35
Joined: Wed Nov 08, 2006 4:20 pm
Re: Evaluating density forecasts
Thanks for the link to the paper Todd - I'll start to read - then get back for ideas on implementation.
I'm not certain if evaluating forecasts from this view is covered in the existing RATS reference manual/users guide
ac_1
Posts: 56
Joined: Thu Apr 15, 2010 6:30 am
Location: Surrey, England, UK
Re: Evaluating density forecasts
Todd,
I have had a quick read of the Mitchell and Wallis (2010) paper and, without delving into details, an initial surmise/overview is (this is so others can see what is involved re Mitchell and Wallis (2010) ):
Idea
Generate p(t) and z(t) values, if p(t) and z(t) appear-like a random sample from U[0,1] or N[0,1] respectively, the forecasts are said to be ‘well-calibrated’.
Transform the outcomes into p(t) and z(t) as:
A.
Probability Integral Transformations (PITS): p(t) = F(t)(x(t)) ~ IID U[0,1]
where F(.) is the density forecast distribution, x(t) is the observed outcome.
p(t) is a cumulative density function corresponding to the density F(t)(x(t)) evaluated at x(t) i.e. the forecast probability of observing an outcome no greater than that actually realised.
In otherwords, given outcomes x(t), t=1,....,n, forecasts from a certain model can be evaluated by computing PITS w.r.t. forecast density F(t), as
p(t) = integral from (–infinity) to x(t) of F(t)(u) du and testing whether p(t) ~ IID U[0,1].
Diebold, Gunther and Tay (1998) provide a rationale and proof of the IID U[0,1] result.
B.
z(t)=invnormal(p(t)) ~ IID N[0,1]
z(t) values can be viewed as the standardized value of the outcome x(t).
Also, z(t) = (point forecast error / forecast standard deviation), given that the mean of the density forecast is taken as the point forecast.
z(t) has certain advantages over p(t) in the sense that:
• there are more tests available for normality.
• it is easier to test for independence/autocorrelation under normality than uniformity.
• the normal likelihood can be used to construct LR tests.
Given the shortcomings of Gneiting, Balabdaouri and Raftery (2007), Mitchell and Wallis (2010) provide a more realistic example (including a time dimension in their simulated data) in which several competing forecasts distinguish the ‘ideal’ forecast from its competitors, whilst emphasising augmenting the present ‘complete calibration’ evaluation techniques by an assessment of sharpness. Their statistical framework is akin to the recipe:
So a recipe for density forecast evaluation:
(a) Graphical:
• Visual inspection of p(t) & z(t) histograms, with comparison to U[0,1] or N[0,1], respectively.
• [ I have also seen plots of p(t) against a 45 degree line – the theoretical uniform distribution, with 95% confidence intervals from the critical values of KS statistics.
• Indeed in a recent paper of yours you have p(t) histograms shown as decile counts of the PITs transforms – how was this done? ]
(b) Formal Goodness-of-Fits tests:
• Pearson chi-squared on p(t) values.
• Kolmorgorov-Smirnov (KS) - for equality of distributions (around their means).
• Anderson-Darling - modification of KS test (but around the tails of distributions).
• Doornik & Hansen (2008) - for normality, on z(t) values only.
(c) Independence/autocorrelation tests (to test for departure from the IID hypothesis):
• For p(t) – LB test.
• For z(t) - parametric test of Berkowitz (2001).
(d) Scoring rules, Distance measures and Sharpness:
• -logScore.
• KLIC (Kullback-Leibler information criterion) or distance measure, similar to mean error/bias in point forecast evaluation.
Please correct any of the above overview. I have not yet absorbed all details, especially for the latter part of (c) and all of (d).
So, for a sequence of one-step ahead forecasts, how do I generate the p(t) and z(t) values in RATS? That’ll get me started!
In the recipe above I am able to achieve: (a) up to the LB test in (c).
Thereafter, I need your help with the remaining tests: the independence test for z(t), the scoring rule, and KLIC.
ac_1
Posts: 56
Joined: Thu Apr 15, 2010 6:30 am
Location: Surrey, England, UK
Re: Evaluating density forecasts
Using a sample of N draws of forecasts (obtained by Bayesian Markov Chain Monte Carlo simulation), I computed the PIT as follows:
sstats(mean) 1 N (forecast{0}<=actual(t))>>pit
where *forecast* is a series from 1 to N with a projection for period t, actual(t) is the actual value of the variable in period t, and the result, the PIT, is stored in PIT. Once you have a time series of PITS, you can use DENSITY and SCATTER commands for a histogram. I used more of a brute force approach to getting the exact decile counts.
From the PIT time series, I computed the normalized error with
set statser stpt endpt = %invnormal(pit)
where pit is a time series.
Todd Clark
Economic Research Dept.
Federal Reserve Bank of Cleveland
tclark
Posts: 35
Joined: Wed Nov 08, 2006 4:20 pm
Re: Evaluating density forecasts
Okay,
sstats(mean) 1 N (forecast{0}<=actual(t))>>pit
calculates a single PIT value (from a sample of N draws of the forecast & actual), as the mean of the number of times the forecast is less than or equal to the actual.
I need to generate an entire time series of PIT values. In otherwords, I need assistance with the Bayesian MCMC, or another (simpler) way to generate PIT values as a time series.
ac_1
Posts: 56
Joined: Thu Apr 15, 2010 6:30 am
Location: Surrey, England, UK
Re: Evaluating density forecasts
So, given the actual and forecasts, I know that this is NOT correct, but something like the following will generate a sample of PITS (called gibbs).
Please assist, so that I am able to generate a viable series of PITS.
Code: Select all
`* Bayesian MCMC*compute nburn =100compute ndraws=1000*dec series gibbsset gibbs 1 ndraws = 0.0*do draw=-nburn,ndraws* sstats(mean) 1 draw (forecast{0}<=actual(t))>>pit* if draw<=0 next* compute gibbs(draw)=pit*end do draw*prin / gibbs*`
ac_1
Posts: 56
Joined: Thu Apr 15, 2010 6:30 am
Location: Surrey, England, UK
Re: Evaluating density forecasts
What you need to do is loop over time to generate posterior distributions of forecasts, as opposed to looping over draws. For example, at period 2000:Q1, generate 10k draws of a forecast for period 2000:Q2. Then apply sstats (to a series of the 10k draws) as I suggested to get the PIT value for the forecast in period 2000:Q2. Then move to period 2000:Q2, generate 10k draws of a forecast for period 2000:Q3, and apply sstats (to a series of the 10k draws) as I suggested to get the PIT value for the forecast in period 2000:Q3. Etc.
Todd Clark
Economic Research Dept.
Federal Reserve Bank of Cleveland
tclark
Posts: 35
Joined: Wed Nov 08, 2006 4:20 pm
Re: Evaluating density forecasts
Still not getting values for PITS!
An example - this is a VAR from the Canmodel.prg example from RATS.
I am generating one-step ahead forecasts (that's okay) but having issues with the 10K draws for the PITS - I get "NA's" when I display the PITS.
Code: Select all
`*open data oecdsample.ratcalendar(q) 1981data(format=rats) 1981:1 2006:4 can3mthpcp canexpgdpchs canexpgdpds canm1s canusxsr usaexpgdpch*set logcangdp = log(canexpgdpchs)set logcandefl = log(canexpgdpds)set logcanm1 = log(canm1s)set logusagdp = log(usaexpgdpch)set logexrate = log(canusxsr)*system(model=canmodel)variables logcangdp logcandefl logcanm1 logexrate can3mthpcp logusagdplags 1 to 2det constantend(system)*compute width = 70compute ibegin = 1999:12compute iend = 2006:4*do iend = ibegin,iend estimate(noprint) iend-width+1 iend do draw = 1, 10000 forecast(model=canmodel,results=fcasts,from=iend+1,to=iend+1,noprint) sstats(mean) 1 draw (fcasts(1)<=logcangdp(t))>>pit end do draw disp pitend do iend*prin / fcasts(1) fcasts(2) fcasts(3) fcasts(4) fcasts(5)`
ac_1
Posts: 56
Joined: Thu Apr 15, 2010 6:30 am
Location: Surrey, England, UK
Re: Evaluating density forecasts
The SSTATS should be **outside** the do draw loop, and you need to store each forecast draw in a series with observations 1 to 10,000, and apply SSTATS once to the entire set of 10,000 draws to get the PIT in each period t.
Todd Clark
Economic Research Dept.
Federal Reserve Bank of Cleveland
tclark
Posts: 35
Joined: Wed Nov 08, 2006 4:20 pm
Re: Evaluating density forecasts
Have made alterations – I still get “NA’s” when displaying PITS!
Code: Select all
`*declare vector[series] fdrawS(10000)*do iend = ibegin,iend estimate(noprint) iend-width+1 iend clear fdrawS(10000) do draw = 1,10000 forecast(model=canmodel,results=fcasts,from=iend+1,to=iend+1,noprint) set fdrawS(draw) = fcasts(1) end do draw sstats(mean) 1 10000 (fdrawS(draw)<=logcangdp(t))>>pit disp pitend do iend`
ac_1
Posts: 56
Joined: Thu Apr 15, 2010 6:30 am
Location: Surrey, England, UK
Re: Evaluating density forecasts
Just to be clear, Todd's not an employee of Estima, so it's not his responsibility to fix or correct anyone's code. He may offer further suggestions, but he's already gone well above and beyond the call of duty as a fellow RATS user on this one.
We'll take a look at the good and see if we can offer any suggestions.
Thanks,
Tom Maycock
Estima
moderator
Posts: 306
Joined: Thu Oct 19, 2006 4:33 pm
Re: Evaluating density forecasts
Looks like you have several coding issues here, and one theoretical issue.
First, the coding issues:
1) do iend = ibegin,iend
You don't want the same variable as the loop index variable and to specify the end of the loop. Try something like:
compute last = 2006:4
do iend = ibegin,last
2) You only need 10,000 draws for each period. So just make fdrawS a series with 10,000 elements, not a vector of 10,000 series.
3) Inside the "draw" loop, store the current forecast value (entry "iend+1" of the FCASTS series) into entry "draws" of the fdraws series. Here's one way to do that:
set fdrawS draw draw = fcasts(1)(iend+1)
4) It doesn't make sense to refer to entry "draw" on the SSTATS outside of the DO loop (since "draw" will just be equal to the last value from the loop). Also, you need to refer to a specific entry of LOGCANGDP, not not entry "t" (which would run from 1 through 10000). So, with that in mind and with fdrawS being a single series not an array of series, instead of:
sstats(mean) 1 10000 (fdrawS(draw)<=logcangdp(t))>>pit
I think you want:
sstats(mean) 1 10000 (fdrawS<=logcangdp(iend+1))>>pit
With the addition of the use of a variable for the number of draws, these changes give you this:
Code: Select all
`compute ndraws=10000set fdrawS 1 ndraws = %nacompute last = ibegin+2do iend = ibegin,last estimate(noprint) iend-width+1 iend clear fdrawS do draw = 1,ndraws forecast(model=canmodel,results=fcasts,from=iend+1,to=iend+1,noprint) set fdrawS draw draw = fcasts(1)(iend+1) end do draw sstats(mean) 1 ndraws (fdrawS<=logcangdp(iend+1))>>pit disp pitend do iend`
Which brings us to the theoretical problem: As written, you're just computing actual forecasts, producing the exact same forecasts for each draw, rather than doing any sort of simulation (such as the MCMC simulation Todd mentioned). So, this doesn't really produce any result. You would need to incorporate some simulation method into this for it to actual do anything. Not having read the papers, I assume they spell out a recommended approach?
Regards,
Tom Maycock
moderator
Posts: 306
Joined: Thu Oct 19, 2006 4:33 pm
Re: Evaluating density forecasts
Thanks for the reply Tom, I appreciate your response and pointing out the errors in the code.
What I initially wanted when starting this thread was a worked example within RATS of how to proceed for evaluation of density forecasts given a set of out-of-sample point forecasts, (I have seen this type of evaluation in various papers, but not in any standard textbook), hence the post by Todd of the Mitchell and Wallis (2010) paper.
Although it’s not a necessity, density forecast evaluation is another way to evaluate the forecasts from a model. Albeit, in my view, loss measures and sign/direction tests say more about the quality of a model than if it’s a “model that is well calibrated”.
I, as am sure others reading this thread are interested in density forecast evaluation within RATS.
As far as I can tell density forecast evaluation is not covered in the RATS reference manual/users guide. Hence, it would be of practical use and fair to have an example of this type of evaluation. Thanks.
ac_1
Posts: 56
Joined: Thu Apr 15, 2010 6:30 am
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Quandaries & Queries
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Topic: cubic mile
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The volume of Lake Utah 2015-01-29 From Hannan:Lake Utah has a surface area of 3,846 square miles and an average depth of 10.5 feet. In cubic miles, how much water does it hold? How would you approach this question? Where would you start?Answered by Robert Dawson and Penny Nom. A one cubic mile lake 2009-01-09 From dye:how many liters are in a one cubic mile lakeAnswered by Robert Dawson. A cubic mile of water 2008-08-03 From Fred:[QQ] HOW MUCH WATER IS THERE IN A CUBIC MILE?Answered by Stephen La Rocque. Cubic furlongs 2004-01-11 From A student:1 mile=8 furlongs, how many cubic furlongs in a cubic mile?Answered by Penny Nom. How many cubic feet are in a cubic mile? 2002-08-30 From William:How many cubic feet are in a cubic mile?Answered by Penny Nom.
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about math central :: site map :: links :: notre site français | 296 | 1,091 | {"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-2020-24 | longest | en | 0.886944 |
https://www.uen.org/lessonplan/view/103 | 1,713,061,068,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816863.40/warc/CC-MAIN-20240414002233-20240414032233-00730.warc.gz | 964,957,769 | 13,032 | # Caloric Burning Activities
#### Main Core Tie
Strand 5: NUTRITION (N) Standard 4.N.3:
#### Time Frame
1 class periods of 60 minutes each
Individual
#### Life Skills
Thinking & Reasoning
BONNIE CROOK
### Summary
Students will use problem solving, decision making and basic math skills to calculate calories used during different activities.
### Materials
• Energy Expenditure Chart for each student
• pencil for each student
• calculators
### Student Prior Knowledge
Students need to be able to multiply and add using their calculator
### Instructional Procedures
Begin by defining the term, "calorie" (a unit of heat/energy available in foods and used for basic living as well as participation in activities).
1. Hand out the Energy Expenditure Chart to each student.
2. Tell the class they are going to make a plan of how to burn 1,000 calories in one day, using at least eight different activities from the chart.
3. Students will need to figure out the activity, duration of activity, and the calories burned.
4. At the end of the worksheet they will add up all of their Calories.
5. Inform students that if the total calories don't add up to exactly 1,000, they will need to go back and adjust their activity or duration of activity.
6. Possible prompts:
What did you noticed about the calories burned in the various activities?
If a person burns more calories through increased activity, what might happen? (They'll need to eat more calories, their weight may change, etc.)
7. Collect their worksheets for assessment.
### Strategies for Diverse Learners
Pair special needs learners with students who can provide assistance.
### Extensions
Have the class write down all of their activities for a day and calculate the total calories burned.
### Assessment Plan
#### Attachments
Each student will turn in a worksheet.
### Bibliography
Exercise Physiology - Authors William D. McArddle, Frank I. Katch, Victor L. Katch - pages 804 - 811
### Rubrics
Created: 07/08/2002
Updated: 01/15/2020
47449
/> | 461 | 2,035 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-18 | latest | en | 0.900529 |
https://www.portablesolarexpert.com/how-long-will-a-24v-200ah-battery-last/ | 1,695,562,464,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506646.94/warc/CC-MAIN-20230924123403-20230924153403-00342.warc.gz | 1,046,641,206 | 32,632 | # How Long Will a 24V 200ah Battery Last?
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There are a growing number of solar power users who prefer 24 volt batteries because they contain twice the energy of a 12V of the same capacity. But how long will a 24V 200ah battery last? Is it better than a 12V battery and worth the price? Before you buy one, you should know how much load it can carry and for how long.
A 24V 200ah battery contains 4800 watts, so the duration will depend on how many watts are drawn per hour. If the system is connected to a 350 watt hour load, the battery will last about 12 hours before it is drained.
### Calculate How Many Hours a 24V 200ah Will Last
Calculating the runtime for a 24V 200ah battery is similar to a 12V battery. The runtime is determined by the watts or amps per hours drawn from the battery and its depth discharge.
To determine the battery runtime, use the following formula:
200 ah (amp hours) x 24V = 4800 watts
4800 watts / watts used per hour = battery life
Suppose you want to run a 50 inch TV, a 12V fridge, a few lights and a small fan. The total load is 500 watts per hour. Divide battery watts by watt hour:
4800 / 500 = 9.6
A 24V 200ah battery like the ExpertPower AGM can run a 500W load for 9.6 hours before it runs out. If you connect this system to a 24V solar panel the runtime will be even longer. Why? Because the solar panel can keep the battery fully charged even as you run appliances off it.
As you probably noticed this runtime assumes the battery will be drained completely. You can do that with a lithium system, but for lead acid batteries the depth of discharge should be 50%.
If you recharge at 50% the usable battery capacity is reduced to half. Instead of 4800 watts there is 2400 watts available for load. You can still run the 500W load we mentioned, but it will be for 4 to 5 hours only. If you recharge at 70%, 30% etc., adjust the numbers accordingly.
These numbers are not exact because of the way batteries work. When more watts or amps are consumed per hour, the faster the battery gets discharged. The fewer amps or watts used, the slower the discharge rate.
### Amps Drawn and Battery Capacity Explained
Another way to find out how long a battery lasts is to calculate the amps drawn per hour. A 200ah battery literally means 200 amp hours, or the battery will last one hour if you pull 200 amps.
However, Peukert’s Law states that the higher the discharge rate, the faster usable capacity goes down. In other words, the more amps are drawn the faster the battery gets depleted. There is no exact formula to determine the rate, only estimates.
So if the load is 100 amps an hour, the battery can theoretically last for two hours, but due to Peukert’s Law it will be less than that. The lower the amps drawn the longer the battery life. Drawing 50 amps an hour means the battery could last around 4 hours or near to it.
Your battery documentation includes details on its specific runtime so you should check it. Also keep in mind that these estimates assume the battery will be fully drained. Reduce the run times if only half the battery capacity will be used.
If you have the Ampere Time 12V Lithium you can do a 90% or 100% discharge, but otherwise you should not let the percentage drop below 50. If you need the full 200ah capacity, get a lithium 200ah or a 400ah lead battery.
Whether you compute the power load in watts or amps, one thing is certain. You should never overestimate how long the battery will last. It is always better to underestimate the runtime and have more capacity available.
### What Can a 24V 200ah Battery Run?
A 24V 200ah battery can run TVs, coffee machines, blenders, laptops, fans, lights, power tools, a mini fridge, microwave and other appliances. With literally thousands of watts at your disposal, the battery can run a wide range of electronics.
If the battery will be used to full capacity, it can:
• Run a 60 inch TV for 25-30 hours
• Run a ceiling fan for 72 hours
• Power a clothes dryer for 2 to 3 hours
• Use a corded drill for 1 and half hours
• Power a deep freezer for 45-50 hours
• Run an espresso machine for 2 hours
A lot of these tools and appliances are not run continuously. A blender uses 400 watts an hour, but you only use it for a few minutes at a time. Same thing with a drill and other power tools, so a 200ah battery can last for days on end.
The appliances and tools above are just examples. You can combine various items and run them on the battery for hours or days.. The duration will depend not only on the load but also how much of the capacity will be used.
A 200ah battery is large enough to take during camping. If you have an RV you can use it to charge other appliances. If you have a solar powered jeep you can connect it to a solar panel and run even more devices for longer stretches.
No matter what battery type or size, avoid using it to the maximum capacity. Calculate the amp or watt load and if the total is at 4800 watts / 200ah or near it, reduce the load or get a larger battery. Inverters, charge controllers and solar panels should never be used at their maximum capacity. The same applies for the batteries.
### How Many Solar Panels to Charge a 24V 200ah Battery?
By hooking up a battery to solar panels, you can run an appliance on both and conserve battery life. Instead of using it all day, let the solar panels charge the system so you have full power available when the sun sets.
It takes 4 x 300 watt or 3 x 350 watt solar panels to recharge a 200ah battery. If you are using a 24V battery, the panels must also be at least 24V. A 12V system cannot charge a 24V battery because the PV voltage has to be higher.
If the solar panel and battery voltage are both 24V you can use a PWM charge controller. If the solar panel is 48V, use an MPPT charge controller. A PMW controller will just drop the panel voltage down to the battery and waste its power. With an MPPT, it will run the panel at 48V and adjust the current going into the battery. for the best results.
#### Sample Calculations
A 300 watt solar panel is good for up to 1500 watts a day with 5 sun hours in perfect condition. With three of these the power output can reach 4500 watts, which is not enough to fully charge the battery. If the battery is only 50% discharged then it is enough.
200ah = 4800 watts
4800 watts / 2 = 2400 watts
To fill up a fully discharged battery however you need 4 x 300W or 3 x 350W solar panels. With three 350 watt panels you have 5250 watts in 5 sun hours. Even assuming for energy losses, imperfect weather etc. there should be enough power here to produce the 4800 watts needed by the battery.
We chose 5 hours in this example, but yours might be different. During summer your area might receive up to 7 hours of sunlight. With that much sun you can use 3 x 300W solar panels (300 watts x 6 hours = 1800 watts x 3 = 5400 watts).
the reverse is also true. You might need more solar panels if the sky is overcast. In this case you should charge the battery at home before leaving or use more solar panels. If you plan ahead a lot of these potential issues will be resolved.
### Conclusion
A lot of the calculations involving batteries and solar panels are not exact because of how solar power works. But using the tips given above you can get a pretty good estimate of how long you can use a 24V 200ah battery. | 1,783 | 7,484 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2023-40 | longest | en | 0.915927 |
https://www.geeksforgeeks.org/relation-between-mass-number-and-atomic-number/?type=article&id=646069 | 1,685,484,640,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224646144.69/warc/CC-MAIN-20230530194919-20230530224919-00569.warc.gz | 814,843,688 | 35,278 | Get the best out of our app
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# Relation Between Mass Number and Atomic Number
Atoms are the fundamental building blocks of matter, and they may combine in a variety of ways to produce various substances. You must be aware that all atoms are made up of electrons, protons, and neutrons. But did you know that the presence of these subatomic particles may explain an element’s properties? In this post, we will look in-depth at the Atomic Mass and Atomic Number, as well as their significance. In this article, we will discuss the relation between the mass number and the atomic number. Before that, let’s understand what is the mass number and atomic number?
### Atomic Number
It is the number of protons in an atom. Protons are known to exist in an atom’s nucleus. The atomic number of an atom is determined by the number of protons in the atom. As a result, we may define an atomic number as:
The atomic number of an element is the number of protons in one atom. An element’s atomic number equals the number of protons in one atom of the element is termed as Atomic Number.
The atomic number of sodium, for example, is 11, since one atom of this element has 11 protons. A carbon atom, for example, has six protons, giving it an atomic number of sixes, whereas a hydrogen atom has just one proton in its nucleus. As a result, hydrogen has an atomic number of ones. The letter Z represents an element’s atomic number.
• All atoms of the same element have the same number of protons and hence the same atomic number.
• The amount of protons in the nuclei of various elements varies.
• The atomic number of two elements cannot be the same.
• Because each element has a unique atomic number, the atomic number may be used to identify it.
For example, if the atomic number is 6, it indicates that the element is carbon. There is no other element with an atomic number of 6. Thus, the atomic number differentiates one element’s atoms from the atoms of another element. Because different elements have distinct atomic numbers, their atoms differ. The number of protons in a typical atom is equal to the number of electrons. As a result, we may state-
Atomic number of an element = Number of electrons in one neutral atom
Only a neutral atom has an equal number of protons and electrons; an element’s atomic number is equal to the number of electrons in the neutral atom, not the ion. An ion, on the other hand, is formed by either removing or adding electrons to a conventional atom, and therefore contains either fewer or more electrons than protons. Chemical processes solely involve the electrons of atoms, not their protons. The number of electrons can change throughout a chemical reaction, while the amount of protons does not. As a result, the atomic number of an element does not change throughout a chemical reaction and stays constant.
### Mass Number
Protons, neutrons, and electrons make up an atom. Because electrons have a tiny mass in comparison to protons and neutrons, the mass of an atom is determined solely by protons and neutrons. The mass number of an element is the total number of protons and neutrons contained in one atom.
The mass number is equal to the sum of the number of protons and neutrons or,
Mass number = Number of protons + Number of neutrons
One atom of sodium, for example, contains 12 neutrons and 11 protons, therefore the mass number of sodium is 11+12=23. Similarly, because a carbon atom contains 6 protons and 6 neutrons, its mass number is 6+6=12.
A hydrogen atom has one proton but no neutrons. As a result, the mass number of hydrogen is only one. The letter A represents an element’s mass number. Because the mass of the sodium atom is 23, we may state that A=23 for sodium.
### Notation of the Atomic Number and Mass Number
If the element is X, then the atomic number Z and mass number A are written in chemical notation as-
### Relationship Between Mass Number and Atomic Number
The Relationship Between Mass Number and Atomic Number is stated as:
Mass Number = No. of protons + No. of neutrons
We know,
Atomic Number = No. of protons
Therefore, we can say
Mass Number = Atomic Number + No. of electrons
Symbolically this can be represented by
A = Z + n
where A = Mass number, Z = Atomic number and n= no. of neutrons.
### Sample Problems
Problem 1: The mass no. of chlorine atom is 35 and the atomic no. is 17. Find the number of neutrons present in the chlorine atom.
Solution:
Mass No. (A) = 35
Atomic No (Z) =17
We know
Mass No = Atomic No+ no. of neutrons present
n = Mass no – Atomic no
n= 35-17
n = 18
Therefore, the no. of neutrons present in the chlorine atom is 18.
Problem 2: The number of electrons presents in the calcium atom is 20 and the no. of neutrons present is 20. Find the atomic no. and the mass no of the calcium atom.
Solution:
We know, an atom is electrically neutral. Thus, the no. of electrons present in an atom is equal to the no. of protons present in the atom.
So, the no. protons present in the atom = 20.
We know, that the Atomic no. of an atom of an element = no. of protons present.
Thus, atomic no. = 20
The mass no = Atomic no + No. of neutrons
Mass no = 20+20
Mass no = 40
Problem 3: The atomic nucleus of an atom has a mass number of 23 and has 12 neutrons inside its nucleus. Calculate its atomic number.
Solution:
Mass Number = 23
No. of neutrons =12
Mass no = No. of protons + No. of neutrons
No. of protons = Mass no. – No. of neutrons
No. of protons = 23-12
No. of protons = 11
We know
Atomic no of an element = No. of protons present in the element = 11
Atomic No. of the element = 11
Problem 4: Two elements A and B have no. of neutrons have 20 and 13 and no. of protons have 18 and 20. Which will have more mass number?
Solution:
For element A:
No. of neutrons = 20
No. of protons=18
Mass no. of element A = 20+18
=38
For element B:
No. of neutrons = 13
No. of protons = 20
Mass no. of element B = 13+20
= 33
Therefore, the Element B has more mass no. than element A.
Problem 5: It is said that the Atomic no. of an Element M is 12 and the no. of electrons present in the element is 13”. Is it a valid statement?
Solution:
No, it is not a valid statement. This is because an atom of an element is electrically neutral , thus the atomic no. of an element ( No. of protons ) should be equal to the no. of electrons present inside an atom. But here, it is said that the Atomic no ( or no. of protons) = 12 and no. of electrons is 13. Thus, they are not equal and the statement is invalid.
My Personal Notes arrow_drop_up
Related Tutorials | 1,634 | 6,645 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2023-23 | latest | en | 0.875417 |
https://blog.drewolson.org/elixirs-secret-weapon/ | 1,713,809,521,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818337.62/warc/CC-MAIN-20240422175900-20240422205900-00243.warc.gz | 116,966,996 | 6,808 | I recently began using a new(ish) feature of Elixir that completely transformed the way I build programs. I’m talking about the special form `with`. It can feel unfamiliar at first, but it is extremely powerful and flexible. This article will explain how `with` works and how it can be used to make your code more robust to errors. First, though, let’s look at the problem `with` is trying to solve.
# Tagged Tuples#
The Elixir community has borrowed an idiom from the Erlang community called tagged tuples. Using this approach, our functions will return a tuple where the first value is an atom describing the “type” of the result. A common pattern is returning `{:ok, value}` for a successful response and `{:error, some_error}` for an error response.
``````defmodule Math do
def divide(_, b) when b == 0, do: {:error, "divide by zero"}
def divide(a, b), do: {:ok, a / b}
end
case Math.divide(1, 2) do
{:ok, result} -> "success: #{result}"
{:error, error} -> "error: #{error}"
end
# => "success: 0.5"
``````
This is nice for a few reasons. First, it allows us to treat errors as values. We know that our function will always return even when provided semantically invalid data. Second, we can use pattern matching to act explicitly on both the success and failure case.
This patterns starts to break down when we want to perform multiple, dependent actions that can all fail. Suppose, for example, that we’d like to divide two numbers and, if successful, divide the result by a third number.
``````case Math.divide(1, 2) do
{:ok, result} ->
case Math.divide(result, 4) do
{:ok, result} -> "success: #{result}"
{:error, error} -> "error: #{error}"
end
{:error, error} -> "error: #{error}"
end
# => "success: 0.125"
``````
This works, sure, but it’s becoming challenging to read. You can easily imagine the mess this becomes with an arbitrarily long list of dependent operations.
What should we do? We want to continue using this pattern because it is safe and explicit but it feels ugly and unreadable with real-world examples. The answer, of course, is to use `with`.
# Using `with`#
The `with` special form allows you to define a set of operations to perform and associated patterns to match their results against. Each operation can use bindings from the pattern match of the previous operations. If any of the matches fail, the entire `with` form stops and that non-matching result is returned. Let’s explore by rewriting the above example using `with`.
``````with {:ok, a} <- Math.divide(1, 2),
{:ok, b} <- Math.divide(a, 4) do
"success: #{b}"
end
# => "success: 0.125"
``````
Let’s walk through the execution. First, we call `Math.divide(1, 2)`. The result is `{:ok, 0.5}`. The `with` form checks to see if this matches the pattern on the lefthand side of `<-`. It does, so the variable `a` is bound to `0.5` and execution continues. On the second line, we run `Math.divide(0.5, 4)` (because `a` is now bound to `0.5`). This returns `{:ok, 0.125}`. We check if it matches the pattern on the lefthand side of its `<-`. It does, so `b` is bound to `0.125`. There are no more operations to perform, so the body of the `do` block is executed. This `do` block can use any of the bindings from the `with` operations above. It uses `b` to return the string `"success: 0.125"`.
Now, let’s try walking through an error case.
``````with {:ok, a} <- Math.divide(1, 0),
{:ok, b} <- Math.divide(a, 4) do
"success: #{b}"
end
# => {:error, "divide by zero"}
``````
First, we call `Math.divide(1, 0)`. The result is `{:error, "divide by zero"}`. We check to see if this matches the patter on the left of `<-`. It doesn’t! As soon as this mismatch occurs, the `with` form immediately stops executing further operations and returns the result that did not match. Therefore, the return value of the form is `{:error, "divide by zero"}`.
# Better Error Handling#
We’re already in a better spot by using `with` but we can go even further. The `with` form allows us to describe an `else` clause that handles any non-matching values rather than simply returning them. Let’s add one.
``````with {:ok, a} <- Math.divide(1, 0),
{:ok, b} <- Math.divide(a, 4) do
"success: #{b}"
else
{:error, error} -> "error: #{error}"
end
# => "error: divide by zero"
``````
Now, when the first operation returns `{:error, "divide by zero"}` and it doesn’t match the pattern, the value is passed to the `else` block. Next, we check each clause of the `else` block in order (in this example there is only one clause). The first clause matches `{:error, "divide by zero"}`, so the string `"divide by zero"` is bound to `error`. Finally, the body of that clause is executed with the bindings from the match. It returns the string `"error: divide by zero"`.
# More#
The `with` form allows even more flexibility, including guard clauses in each of the operations. For more examples see the docs. | 1,298 | 4,877 | {"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} | 2.703125 | 3 | CC-MAIN-2024-18 | latest | en | 0.858883 |
https://documen.tv/question/10-points-an-airplane-takes-four-hours-to-travel-a-distance-of-2800-miles-with-the-wind-the-retu-19737616-39/ | 1,638,176,105,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358702.43/warc/CC-MAIN-20211129074202-20211129104202-00448.warc.gz | 280,138,645 | 15,707 | ## 10 POINTS!!! An airplane takes four hours to travel a distance of 2800 miles with the wind. The return trip takes 5 hours agains
Question
10 POINTS!!!
An airplane takes four hours to travel a distance of 2800 miles with the wind. The return trip takes 5 hours against the wind. Find the speed of the plane in still air and the speed of the wind
The speed of the plane is__ mph.
And the speed of the wind is__ mph.
in progress 0
3 months 2021-08-19T05:16:43+00:00 1 Answers 7 views 0
648mph and 72 mph
Step-by-step explanation:
velocity Against wind=2880/5=576Mph
velocity with the wind =2880/4=720mph
let x be speed of plane y be speed of wind
then velocity with winf=720
x+y=720
velocity against the wind=576
x-y=576
using both
2x=1296
x=648mph
and y=72mph | 232 | 779 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2021-49 | latest | en | 0.817075 |
http://mathhelpforum.com/calculus/20356-complicated-problem.html | 1,529,764,961,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267865081.23/warc/CC-MAIN-20180623132619-20180623152619-00293.warc.gz | 210,349,757 | 9,708 | # Thread: Complicated Problem!!
1. ## Complicated Problem!!
if
f(x)=g^2(x)
f'(3)=?
We're doing differentiation now, but I don't know how to solve this.
2. $\displaystyle g^2(x) = [g(x)]^2$ the inner function is $\displaystyle g(x)$ is other is $\displaystyle x^2$.
3. I don't understand....
4. Originally Posted by MiDude
I don't understand....
Neither do we!
You have not told us about $\displaystyle g(x)$!
What is that function? | 128 | 438 | {"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} | 3.046875 | 3 | CC-MAIN-2018-26 | latest | en | 0.920858 |
https://www.gradesaver.com/textbooks/science/physics/CLONE-afaf42be-9820-4186-8d76-e738423175bc/chapter-13-section-13-3-applications-of-simple-harmonic-motion-example-page-238/13-4 | 1,723,087,307,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640719674.40/warc/CC-MAIN-20240808031539-20240808061539-00363.warc.gz | 607,402,337 | 12,173 | ## Essential University Physics: Volume 1 (4th Edition)
We find: $T = \frac{2\pi}{\omega}=2\pi \times \sqrt{\frac{I}{mgL}} = 2\pi \times \sqrt{\frac{\frac{1}{3}m(2L^2)}{mgL}} = 2\pi \times \sqrt{\frac{4L}{3g}}$ Plugging in the values gives an answer of $\fbox{1.6 seconds}.$ | 112 | 275 | {"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} | 3.3125 | 3 | CC-MAIN-2024-33 | latest | en | 0.535408 |
https://www.coursehero.com/file/215546/ex1/ | 1,527,473,544,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794870604.65/warc/CC-MAIN-20180528004814-20180528024814-00204.warc.gz | 720,255,989 | 38,679 | {[ promptMessage ]}
Bookmark it
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# ex1 - u t 2 3 Consider the system shown below with input r...
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ME 451 Examination #1 February 15, 2008
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1. Consider the mechanical system shown below with input f ( t ) and output y ( t ) . f ( t ) y ( t ) M B K (a) [20 pts] Find the transfer function from f ( t ) to y ( t ) . (b) [15 pts] Find the transfer function from f ( t ) to a ( t ) = ¨ y ( t ) . 1
2. Consider the system shown below. r ( t ) y ( t ) u ( t ) F ( s ) G ( s ) H ( s ) + + - (a) [15 pts] Find the transfer function from r ( t ) to y ( t ) . (b) [15 pts] Find the transfer function from r ( t ) to
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Unformatted text preview: u ( t ) . 2 3. Consider the system shown below with input r ( t ) and output y ( t ) . r ( t ) y ( t ) C ( s ) G ( s ) +-(a) [15 pts] Find the step response of the system when C ( s ) = 1 and G ( s ) = 1 /s . (b) [20 pts] Find the step response of the system when C ( s ) = 5 and G ( s ) = 1 / [ s ( s + 2)] . 3...
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### What students are saying
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https://cs.stackexchange.com/questions/112688/undirected-hamcycle-to-hampath-reduction/112689 | 1,603,380,474,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107879673.14/warc/CC-MAIN-20201022141106-20201022171106-00718.warc.gz | 281,125,893 | 32,783 | # UNDIRECTED HAMCYCLE to HAMPATH reduction
I'll define the problems
UHAMPATH
Input: A undirected graph G and 2 nodes, s and t
Question: Is there a hamiltonian path from s to t in G?
UHAMCYCLE
Input: A undirected graph G
Question: Is there a hamiltonian cycle in G?
$$UHAMCYCLE \leq_p UHAMPATH$$
my reduction is as followed $$(G) \to (G', s, t)$$
function(G)
for each e = (u, v) in E(G)
G' = G
add nodes u' and v' to G'
add edges (u', u) and (v, v')
s = u'
t = v'
if there is a hamilton path from s to t:
return (G', s, t)
Basically if there is a hamilton cycle in G then some edge in $$G$$ will form a hamilton path in $$G'$$.
An example to further illustrate the reduction:
Graph G
(a) ---- --(d)
| \ |
| \ |
| \ |
| \ |
| \ |
| \ |
| \| |
(b) ------ (c)
Has a clear Hamilton cycle (a, b, c, d).
If we choose edges (a, d)
Graph G'
(s)--(a) ---- --(d)
| \ |
| \ |
| \ |
| \ |
| \ |
| \ |
| \|
(b) ------ (c)--(t)
Doesn't have a hamilton path from s to t. However if you choose any other edge such as (a, d) then
(s)--(a) ---- --(d)--(t)
| \ |
| \ |
| \ |
| \ |
| \ |
| \ |
| \|
(b) ------ (c)
$$(s \to a \to b \to c \to d \to t)$$. Holds.
I'm confused whether or not I can use this line:
if there is a hamilton path from s to t:
return (G', s, t)
Checking to see if a graph has a hamilton path is NP complete but since we are looking to reduce it to it I think we can? | 517 | 1,553 | {"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": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2020-45 | latest | en | 0.852704 |
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• algebra with pizzazz | 1,325 | 5,759 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2018-09 | latest | en | 0.851143 |
http://www.howtodothings.com/finance-real-estate/how-to-calculate-and-use-gross-rent-multiplier | 1,556,295,627,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578841544.98/warc/CC-MAIN-20190426153423-20190426175423-00132.warc.gz | 238,946,555 | 7,459 | # How To Calculate and Use Gross Rent Multiplier
The realty market is sensitive and capable of yielding either good profits or causing heavy losses to anybody who's involved in it. Any involvement in realty requires that you analyze the market scientifically and have a fair knowledge about it.
There are quite a few ways to evaluate your investment property, some of them are:
• Gross Rent Multiplier (GRM)
• Income Capitalization Rate (Cap rate)
• Cash-on-cash Rate of Return
Of these, the GRM is a simple and quick way to decide whether a property is worth considering as an investment. It is at the most, only a rough and ready estimate and is certainly not the best way to assess your property value. The GRM is an indicator on whether any further analysis and research is needed on your property value. By itself, it is not a robust measurement. GRM finds its place in realty analysis by virtue of being a quick way to decide whether it is worth expending further time and effort in assessing the property for further investments.
What is Gross Rent Multiplier?
It is the ratio of the price of an income producing property to its gross annual income.
How is Gross rent Multiplier calculated?
GRM is calculated by dividing the market value of the property by the gross scheduled income. Gross scheduled income is the maximum amount of annual rental income obtainable from a property (at 100% occupancy).
To illustrate with an example -
A property has a market value of \$475,000 and a gross scheduled income or annual gross income of \$80,000. The GRM for this property would be \$475,000/\$80,000 = 5.93.
Suppose a property is in the market with an asking price of \$840,000 and with an established annual gross income of \$100,000. The GRM of comparable properties, which have recently been dealt in the market, is 6.2. To find out if the property is worth investing in, the reasonable market value for this property can be arrived at.
GRM * Annual income = Market Value
6.2 * \$100,000 = \$620,000
Thus at the asking rate of \$840,000, it may not be a wise decision to invest in this property.
While the decision for investment is being taken, this GRM should only be used to evaluate this property when compared to similar properties. Therefore, a lower GRM presents a more attractive investment prospect than a property with a higher GRM.
In a scenario where the depreciation rate, recurring costs like taxes and insurance, operating expenses are consistent and trivial in relation to the gross income across similar properties, the GRM ratio is a good measure. When GRM is calculated using the effective gross income, i.e. annual potential income less vacancy value, then it becomes a much more reliable indicator.
While the GRM is a convenient tool of measurement because of its simplicity, it is limited in use, as it does not take into account factors like credit loss, vacancy, operating expenses etc. | 623 | 2,933 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2019-18 | latest | en | 0.949991 |
http://stats.stackexchange.com/questions/104528/the-idea-of-making-the-data-have-a-zero-mean | 1,462,006,900,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860111809.10/warc/CC-MAIN-20160428161511-00064-ip-10-239-7-51.ec2.internal.warc.gz | 265,533,083 | 19,290 | The idea of making the data have a zero-mean
I often see people making a dimension/feature of a dataset be of a zero-mean by removing the mean from all the elements. But I never I understood why to do so? What is the effect of doing that as a preprocessing step? Does it improve the classification performance? Does it help to answer something about the dataset? Does it help when doing a visualization to understand the data?
-
This approach is called centering. One of its applications is to turn the regression model's intercept into "predicted y when x is at average," making the intercept a bit more interpretable. – Penguin_Knight Jun 24 '14 at 12:40
Some cases where "centering the data on its mean" (hereafter just "de-meaning") is useful:
1) Visual detection of whether a distribution is "the same" as another distribution, only, it has been shifted on the real line. Making both distributions having zero-mean, makes this visual inspection much more easy. Sometimes, if the mean value differs by much, viewing them on the same chart is impractical. Think of two normal r.v.'s, say a $N(10,4)$ and a $N(100,4)$. The shapes of the density graphs are identical, only their position on the real line differs. Now imagine that you have the graphs of their density functions, but you don't know their variance. De-meaning them will superimpose the one graph over the other.
2) Simplify calculations of higher moments: although adding a constant to a random variable does not change its variance, or its covariance with another random variable, still, if you have a non-zero mean, and you must write out the detailed calculations, you have to write all the terms and show that they cancel out. If the variables are de-meaned, you save a lot of useless calculations.
3) Random variables centered on their mean are the subject matter of the Central Limit Theorem
4) Deviations from the "average value" are in many cases the issue of interest, and whether they tend to be "above or below average", rather than the actual values of the random variables. "Translating" (visually and/or computationally) deviations below the mean as negative values and deviations above the mean as positive values, makes the message clearer and stronger.
When should you center your data & when should you standardize?
Centering data in multiple regression
If you search "centered data" on CV, you will also find other interesting posts.
-
@OP: I think this answer should be accepted. – akshob Nov 28 '15 at 6:15
Also, for practical reasons, it is advantageous to center the data, for example, when training neural networks.
The idea is that to train a neural network one needs to solve a non-convex optimization problem using some gradient based approach. The gradients are calculated by means of backpropagation. Now, these gradients depend on the inputs, and centering the data removes possible bias in the gradients.
Concretely, a non-zero mean is reflected a in large eigenvalue which means that the gradients tend to be bigger in one direction than others (bias) thus slowing the convergence process, eventually leading to worse solutions.
-
To add to what Alecos said, which is very good, centering your data at zero is extremely important when using Bayesian statistics or regularization, since otherwise the data can be correlated with the intercept, which makes regularization not do what you usually want.
Making the data zero mean can diminish many off-diagonal terms of the covariance matrix, so it makes the data more easily interpretable, and the coefficients more directly meaningful, since each coefficient is applying more primarily to that factor, and acting less through correlation with other factors.
- | 785 | 3,723 | {"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} | 3.15625 | 3 | CC-MAIN-2016-18 | longest | en | 0.940141 |
https://www.urionlinejudge.com.br/judge/en/profile/53240?sort=Ranks.created&direction=asc | 1,600,689,874,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400201699.38/warc/CC-MAIN-20200921112601-20200921142601-00687.warc.gz | 1,150,450,087 | 6,382 | # PROFILE
Check out all the problems this user has already solved.
Problem Problem Name Ranking Submission Language Runtime Submission Date
1004 Simple Product 03048º 2187227 C 0.000 5/12/15, 6:34:55 PM
1001 Extremely Basic 04001º 2187116 C 0.000 5/18/15, 6:56:20 PM
1002 Area of a Circle 03280º 2187357 C 0.000 5/18/15, 7:30:49 PM
1003 Simple Sum 03114º 2187375 C 0.000 5/18/15, 7:33:17 PM
1005 Average 1 02664º 2189556 C 0.000 5/19/15, 1:09:30 AM
1006 Average 2 02674º 2189584 C 0.000 5/19/15, 1:12:17 AM
1007 Difference 02621º 2189607 C 0.000 5/19/15, 1:15:01 AM
1008 Salary 02499º 2189732 C 0.000 5/19/15, 1:21:57 AM
1009 Salary with Bonus 02264º 2214748 C 0.000 5/19/15, 5:40:59 PM
1010 Simple Calculate 02248º 2214796 C 0.000 5/22/15, 1:43:11 PM
1011 Sphere 02212º 2214831 C 0.000 5/22/15, 1:47:16 PM
1012 Area 01941º 2214986 C 0.000 5/22/15, 1:57:26 PM
1013 The Greatest 01810º 2215047 C 0.000 5/22/15, 2:11:11 PM
1014 Consumption 01956º 2220708 C 0.000 5/23/15, 2:01:07 AM
1015 Distance Between Two Points 01821º 2220740 C 0.000 5/23/15, 2:06:12 AM
1016 Distance 01639º 2226797 C 0.000 5/24/15, 4:06:27 AM
1017 Fuel Spent 01833º 2226809 C 0.000 5/24/15, 4:12:40 AM
1018 Banknotes 04488º 3784866 C 0.000 5/24/15, 4:24:25 AM
1019 Time Conversion 01659º 2226863 C 0.000 5/24/15, 4:39:36 AM
1020 Age in Days 01664º 2226877 C 0.000 5/24/15, 4:43:32 AM
1035 Selection Test 1 01413º 2226979 C 0.000 5/24/15, 5:37:29 AM
1036 Bhaskara's Formula 05399º 4282292 C 0.000 5/24/15, 5:58:32 AM
1037 Interval 01244º 2227043 C 0.000 5/24/15, 6:06:26 AM
1038 Snack 01392º 2227059 C 0.000 5/24/15, 6:14:01 AM
1168 LED 00217º 2227109 C 0.000 5/24/15, 6:44:52 AM
1040 Average 3 01944º 2909923 C 0.000 5/25/15, 3:55:22 PM
1043 Triangle 01100º 2238145 C 0.000 5/26/15, 2:25:15 AM
1042 Simple Sort 01203º 2238284 C 0.000 5/26/15, 2:41:31 AM
1044 Multiples 01345º 2238317 C 0.000 5/26/15, 2:58:35 AM
1795 Trinomial Triangle 00042º 2278306 C 0.000 6/1/15, 12:03:20 PM
1 of 7 | 997 | 1,958 | {"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} | 2.703125 | 3 | CC-MAIN-2020-40 | latest | en | 0.255193 |
https://www.themaven.net/roamingmillennial/ask/so-i-concocted-a-scenario-where-a-third-party-candidate-won-a-presidential-election-with-only-1-53-6uh2bi3RKkakLc4tE5gxUw | 1,532,008,213,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590901.10/warc/CC-MAIN-20180719125339-20180719145339-00312.warc.gz | 986,876,979 | 43,104 | So I concocted a scenario where a third party candidate won a presidential election with only 1.53% of the popular vote. To do as such I made the following assumptions:
1. Every congressional district in the country is equally populous.
2. Every congressional district has equal voter turnout.
3. Only three candidates appear on the ballot in every state.
4. Every voter votes for the same party for U.S. house as they do for president.
5. Should no candidate receive the necessary 270 electoral votes, and the election is thrown to the U.S. house as laid out in the 12th amendment, then the Republican and third-party congressmen will want to work together to prevent the Democratic candidate from winning.
6. Should assumption 5 be put into effect, the presidential candidate this coalition will throw their weight behind shall be from the party that controls more U.S. house state delegations.
Thoughts?
So the scenario I put forth is not meant to be realistic, it's supposed to represent a logical extreme within the system. I'm well aware that assumption 1 is not actually true, as Montana, which has one congressional district, has almost twice the population of Wyoming, which also has one congressional district. As far as Texas being blue, I was just choosing the largest states for the democratic candidate, not necessarily states they would realistically win. The assumptions I chose were because I needed some ground rules in calculating the smallest percentage a candidate in a three-way race could win with, otherwise I could say something completely ridiculous like only one person bothered to vote in California. The way I made my calculation was as follows. I assumed the third-party candidate won one congressional district by one vote in the twenty least populous states. As there are seven states that only have one congressional district, the third-party would control seven U.S. house state delegations. I also assumed the Democrats controlled the 24 most populous U.S. house state delegations (if you're wondering how they can control the 24 most populous state delegations, but not actually hold all of those states on my electoral college map, the answer is gerrymandering). The next six most populous state delegations would be controlled by the Republicans. The remaining 13 state delegations would have split control (no one party controlling a majority of its seats). Since the third-party would control seven delegations, and the Republicans would control six, they would throw their weight behind the third-party candidate. Including DC, there are 436 congressional districts in the country of which the third party would have won 20 of them by a single vote over the other two candidates. 100/436*20/3 = 1.53%
This is not a logical extreme. It CANNOT happen because in order for a candidate to win each state, they must receive more votes than the other candidates in that state. You would have to have FAR MORE candidates on the ballot than just three (about 10 or so), AND voting would need to be spread out almost evenly between them all.
Um, yes it can happen? In the scenario I put forth above the states and congressional districts won by the third party candidate were won by only one vote. That means each candidate got roughly one-third of the vote, with the third-party candidate with just slightly more. You don't need ten candidates on the ballot for that. In fact, if there were ten candidates on the ballot, the smallest popular vote percentage a candidate could win with would be 0.02%
Actually, it could even be far less than that. In a close race if there's a faithless elector or a third party wins the 2nd congressional district in say Nebraska for example AND neither main party gets 270, the House would pick the next President from the candidates with 1 or more electoral vote.
Right, I forgot to list in my assumptions that I was assuming no faithless electors (because then technically the smallest percentage would be 0%). If you look through the scenario I put forth above, you'll see I already have it going to the House. I made the assumption that every voter in the race voted straight ticket (same party for president and the house). I made the assumption that the third party in the race needed enough support in the house in order for the republicans to throw their weight behind them to get elected, which is why on my map the third party has won several states. As you said, technically, to get considered by the house they only need one electoral vote, but in that situation their party wouldn't have enough support in the house to actually be elected. Also, this point doesn't really apply because I limited the number of candidates in the race to three, but, technically the house doesn't choose from all the candidates that have received at least one electoral votes, they only choose from the top three electoral vote winners.
Fresh Conversations | 995 | 4,924 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2018-30 | latest | en | 0.975699 |
https://www.hackmath.net/en/math-problem/32901 | 1,611,106,516,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703519843.24/warc/CC-MAIN-20210119232006-20210120022006-00188.warc.gz | 802,610,198 | 12,246 | Insert AP member
Insert arithmetic means between 75 and 180.
Correct result:
m = 127.5
Solution:
$m=\frac{75+180}{2}=\frac{255}{2}=127.5$
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://www.r-bloggers.com/2014/10/the-world-we-live-in-2-to-study-or-to-work/ | 1,726,242,180,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651523.40/warc/CC-MAIN-20240913133933-20240913163933-00383.warc.gz | 885,349,930 | 23,098 | Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
I was getting ready for school and about to wear my uniform when I remembered that our principal had told us not to wear uniforms. So I decided to wear my favorite pink dress (Malala Yousafzai)
After reading the diary of a Pakistani schoolgirl and Malala’s history, there is no doubt of being in front of a brave girl. A girl that will fight against monsters who deprive children of their childhood. A girl who knows that one book, one pen, one child and one teacher can change this unfair world. A girl who knew she had won the Nobel Prize of Peace in her chemistry lesson and finished the school time before making her first statement. A girl for whom the prize is just the beginning: a girl that gives us hope. Long live Malala:
To know where to obtain data for this plot, check out this post. This is the code:
```require("sqldf")
require("plyr")
require("stringdist")
population=rename(population, replace = c("Country.or.Area" = "Country"))
education=rename(education, replace = c("Reference.Area" = "Country"))
education=rename(education, replace = c("Time.Period" = "Year"))
childlabour=rename(childlabour, replace = c("Country.or.Area" = "Country"))
population=sqldf("SELECT a.Country, a.Year, a.Value as Pop
FROM population a INNER JOIN (SELECT Country, MAX(Year) AS Year FROM population GROUP BY 1) b
ON (a.Country=b.Country AND a.Year=b.Year)
WHERE (a.Country NOT LIKE '%INCOME%')
AND (a.Country NOT LIKE '%WORLD%')
AND (a.Country NOT LIKE '%developing%')
AND (a.Country NOT LIKE '%OECD%')
AND (a.Country NOT LIKE '%countries%')
AND (a.Country NOT LIKE '%South Asia%')
AND (a.Country NOT LIKE '%Small states%')
AND (a.Country NOT LIKE '%Euro area%')
AND (a.Country NOT LIKE '%European Union%')
AND (a.Country NOT LIKE '%North America%')")
childlabour=sqldf("SELECT * FROM childlabour WHERE Subgroup='Total 5-14 yr'")
education=sqldf("SELECT a.* FROM education a INNER JOIN (SELECT Country, MAX(Year) AS Year FROM education GROUP BY 1) b
ON (a.Country=b.Country AND a.Year=b.Year)")
data=sqldf("SELECT a.Country, a.Pop, b.Value as ChildLabour, c.Observation_Value as Education
FROM
population a INNER JOIN childlabour b
ON (a.Country=b.Country) INNER JOIN education c
ON (a.Country=c.Country)")
require(ggplot2)
require(scales)
opts=theme(
panel.background = element_rect(fill="gray98"),
panel.border = element_rect(colour="black", fill=NA),
axis.line = element_line(size = 0.5, colour = "black"),
axis.ticks = element_line(colour="black"),
panel.grid.major = element_line(colour="gray75", linetype = 2),
panel.grid.minor = element_blank(),
axis.text.y = element_text(colour="gray25", size=15),
axis.text.x = element_text(colour="gray25", size=15),
text = element_text(size=20),
legend.key = element_blank(),
legend.position = "none",
legend.background = element_blank(),
plot.title = element_text(size = 45)
)
ggplot(data, aes(x=ChildLabour/100, y=Education/100, size=log(Pop), label=Country), guide=FALSE)+
geom_point(colour="white", fill="red", shape=21, alpha=.55)+
scale_size_continuous(range=c(2,40))+
scale_x_continuous(limits=c(0,.5), labels = percent)+
scale_y_continuous(limits=c(0,.12), labels = percent)+
labs(title="The World We Live In #2: To Study Or To Work",
x="% of Child Workers between 5-14 years old",
y="Public Expenditure on Education as % of GNI")+
geom_text(data=subset(data, ChildLabour/100>.3 | Education/100>.07| Education/10<.022), size=5.5, colour="gray25", hjust=0, vjust=0)+
geom_text(aes(.2, .0), colour="gray25", hjust=0, label="Countries of the world (Source: United Nations Statistics Division) Size of bubble depending on population", size=5)+
opts
``` | 980 | 3,699 | {"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-2024-38 | latest | en | 0.861864 |
https://e2e.ti.com/support/power-management-group/power-management/f/power-management-forum/1233067/tps62816-q1-comp-fset-pin-design?ReplyFilter=Answers&ReplySortBy=Answers&ReplySortOrder=Descending | 1,716,261,971,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058383.61/warc/CC-MAIN-20240521025434-20240521055434-00783.warc.gz | 186,968,425 | 30,555 | This thread has been locked.
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# TPS62816-Q1: COMP/FSET pin design
Part Number: TPS62816-Q1
These three descriptions in the manual are not very clear, please help to interpret them, thank you
1. When working in PWM mode, why should minimum open time and minimum close time be considered when setting frequency through COMP/FSET's resistance to the ground?Is the specification of ton and min referred to the upper tube or the lower tube?
2. As shown in the screenshot below, what does V represent in the formula for calculating the minimum output capacitance?Does it mean the input voltage?
3. What is the internal structure of COMP/FSET pin?In R11002 and a 10 nF capacitor, the PWM frequency at SW end is relatively stable, R11002 and a 100 nF capacitor, the PWM frequency at SW end is in variable frequency mode
• Hi,
Thank you for the inquiry.
I will address your questions as follows:
• 1. When working in PWM mode, why should minimum open time and minimum close time be considered when setting frequency through COMP/FSET's resistance to the ground?Is the specification of ton and min referred to the upper tube or the lower tube?
Referring to screenshot you shared, the min on time in the calculation for fs,max is considering the min on time of the high-side FET. For more information regarding the the minimum on time and its relation to other parameters, please refer to this Application note: "Understanding output voltage limitations of DC/DC buck converters".
Application note: https://www.ti.com/lit/an/slyt293/slyt293.pdf?ts=1685602881812
• 2. As shown in the screenshot below, what does V represent in the formula for calculating the minimum output capacitance?Does it mean the input voltage?
In the formula for minimum output capacitance, V/ Vout is a ratio where V = 1 V. For example in the highlighted equation, if Vout = 1.3 V, minimum output capacitance = 32 uF x (1 V/ 1.3 V) = 24.6 uF.
• 3. What is the internal structure of COMP/FSET pin?In R11002 and a 10 nF capacitor, the PWM frequency at SW end is relatively stable, R11002 and a 100 nF capacitor, the PWM frequency at SW end is in variable frequency mode
The COMP/FSET pin is used for device compensation and frequency set input. For more information regarding its functionality, please refer to section 9.3.2 in the datasheet, titled "COMP/FSET".
Thank you.
Kind Regards,
Rameen
• Hi Rameen,
Thank you for you reply.
I have doubts about the third question
• 3. What is the internal structure of COMP/FSET pin?In R11002 and a 10 nF capacitor, the PWM frequency at SW end is relatively stable, R11002 and a 100 nF capacitor, the PWM frequency at SW end is in variable frequency mode
The COMP/FSET pin is used for device compensation and frequency set input. For more information regarding its functionality, please refer to section 9.3.2 in the datasheet, titled "COMP/FSET".
without any description about,the structure about COMP/FSET pin,As follows
When the ripple is tested, it is found that the ripple regularly increases/decreases, and the frequency is about 32K(both light and heavy load). When the ripple is large, the corresponding frequency of the SW signal changes greatly.
But in pin:MODE/SYNC, I was forced to work in PWM mode, and the output of the chip was not as expected. Please help to analyze it, thank you!
Overshoot, when the ripple is large, the frequencies of adjacent periods are 2.53M and 1.89M, respectively
Undershoot, when the ripple is large, the frequencies of adjacent periods are 1.82M and 1.52M, respectively
• Hi,
Thank you for the inquiry.
When the ripple is tested, it is found that the ripple regularly increases/decreases, and the frequency is about 32K(both light and heavy load). When the ripple is large, the corresponding frequency of the SW signal changes greatly.
I need the complete information to be able to provide proper recommendations.
Could you let me know about the parameters you are using?
What is the COMP setting that you are using in the circuit?
Have you connected the MODE/SYNC to high or low?
Additionally, where are you measuring the output voltage?
Please refer to table 9-1 in the datasheet for the appropriate COMP setting according to the output capacitance used in the circuit.
Moreover, it would also help if I could review your schematic.
Thank you.
Kind Regards,
Rameen
• Hi Rameen,
Thank you for you reply.
What is the COMP setting that you are using in the circuit?
：connect 100k resister to ground,reference the fellowing picture
Have you connected the MODE/SYNC to high or low?
：pull high,connect 4.7k resister to Vin,reference the fellowing picture
Additionally, where are you measuring the output voltage?
：the buck output capacitor,reference the fellowing picture
Please refer to table 9-1 in the datasheet for the appropriate COMP setting according to the output capacitance used in the circuit.
Moreover, it would also help if I could review your schematic.
• Hi,
Thank you for sharing the schematic. I don't see any issues there.
Please refer to table 9-1 in the datasheet for the appropriate COMP setting according to the output capacitance used in the circuit.
Moreover, it would also help if I could review your schematic.
Would it be possible to check the layout as well? Perhaps, I can identify an issue in the layout that may be causing the frequency variations?
Thank you.
Kind Regards,
Rameen
• Hi Rameen,
Thank you for you reply.
layout for you
• Hi,
Thanks for sharing the layout.
Could you explain how the Mode pin (Pin 1) is connected?
Additionally, Could you also provide some background on how the switching frequency was measured? Also, where it was measured? At the switch node?
layout for you
Additionally, I would recommend checking out this video which provides tips on measuring Vout ripple and switching frequency.
https://www.ti.com/video/5779650185001
Thank you.
Kind Regards,
Rameen
• Hi Rameen,
Thank you for you reply.
1.pin 1 trace is for the yellow line
2.test point as bellow,test through Passive probe,at the switch mode, Use the same method to test other BUCK switch frequency
• Hi,
I would suggest to try measuring the frequency directly at the switch node.
There doesn't seem to be an issue in your layout or schematic. So perhaps, it is a matter on how the frequency is measured.
2.test point as bellow,test through Passive probe,at the switch mode, Use the same method to test other BUCK switch frequency
Thank you.
Kind Regards,
Rameen
• Hi
this test point is at the switch node.
Corresponding position in the SCH
• Hi
The frequency vibrate, maybe caused by the buck chip ?
• Hi,
The frequency vibrate, maybe caused by the buck chip ?
Since your schematic was properly configured and the components connected appropriately in the layout, I do not see how the converter could have caused it.
We have not seen any such issue in the converter from our side.
Thank you.
Kind Regards,
Rameen | 1,649 | 7,138 | {"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} | 3.03125 | 3 | CC-MAIN-2024-22 | latest | en | 0.854477 |
https://vintage-kitchen.com/advices/question-how-long-does-prime-rib-take-to-cook/ | 1,723,105,075,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640723918.41/warc/CC-MAIN-20240808062406-20240808092406-00615.warc.gz | 484,857,994 | 16,450 | # Question: How long does prime rib take to cook?
## How long does it take to cook a prime rib at 350 degrees?
For cooking instructions for a boneless rib steak, the basic cook time is medium. A 3- to 4-pound rib steak should cook at 350 degrees Fahrenheit for 23 to 30 minutes per kilogram, for a 4- to 6-pound rib steak, it should cook at 350 degrees Fahrenheit for 18 to 20 minutes per kilogram.
## How long does it take to cook an 8 pound prime rib?
The bones make a natural roaster for meat, so don’t worry if you don’t have one. Cook the steak for 15 minutes, then reduce the oven temperature to 325 degrees. Continue cooking the steak until your meat thermometer reads 120 degrees. It is estimated about 15 minutes of cooking time per kilogram of raw ribs.
## How long do you cook a fully cooked raw rib?
Preparation: Remove from the plastic bag and wrap in aluminum foil. Place in a 300 ° F oven and monitor with a meat thermometer until the desired internal temperature is reached. Recommended indoor temperature: 135 ° F Approximate duration: 2.5-3.5 hours. Cooking time varies based on weight and oven temperature.
## How long does it take to cook a prime rib at 325?
At 325 degrees F, the meat lasts 17-20 minutes per kilogram.
## Can you find a fried rib with bone up or down?
Cooking the ribs Place the steak in a large skillet with the fat side up and the bone side down. Cook for 15 minutes, then reduce the oven temperature to 325 ° F. This allows the heat to fry the steak and trap the juicy flavors inside while the rest of the meat cooks.
## Does the prime rib need to be at room temperature before cooking?
Preparing cold steaks Cooking cold cuts is one of the biggest cooking mistakes, because refrigerated meat has to be exposed to heat for a long time, causing its outer parts to overcook. Start on the right foot, letting the first rib rest for 3 hours at room temperature before frying.
## At what temperature should a prime rib be cooked?
Rule No. 11: Use a thermometer! A thermometer is the only way to guarantee perfectly cooked meat, and a good instant reading (like a thermometer) is best for serving. The goal is 115 to 120 ° F for rare environments (125 to 130 ° F for rest) or 125 to 130 ° F for medium (135 to 140 ° F after rest).
## Should you burn a baking sheet before cooking?
Dry cleaning the prime rib the day before frying means every bite has flavor, and slow frying on a low heat, followed by a spicy bake, will make a delicious medium cook with a thick herb crust.
## Is Prime Rib the same as Ribeye?
The prime rib is also known as stand-up bake. The ribeye cut comes from the same area as the animal’s ribs. The cut comes from the deep-fried rib, also known as the primary rib. To be considered a ribeye, the steak must be cut before cooking.
## How long does it cook in the refrigerator?
After dinner is ready, wrap the remaining raw ribs tightly in plastic wrap and refrigerate or freeze. Ideally, the next day, the rest of the raw ribs can be stored in the refrigerator for five to seven days or in the freezer for up to six months.
## How long can a fried rib keep in the fridge before cooking?
The USDA says that a raw steak should take 3-5 days to refrigerate, and unfortunately a 3-rib steak would take about 3 days to thaw, which means if I put it in tonight, I should take it out. good morning away.
## How do you reheat the prime rib without cooking it further?
Preheat the oven to 250F and add the raw rib slices in a small skillet with a few tablespoons of the broth (water will work too, but it can slightly dilute the flavor of the meat). Cover the pan tightly with aluminum foil and heat it in the oven until the ribs feel like they have heated up, about 10 minutes.
## How long does it take to cook a raw rib at 300 degrees?
Rub the steak with garlic, then season with salt and pepper and place in an open skillet with the fat on top. Boil in a very hot oven (450-475 degrees) for 30 minutes, reduce heat to 300 degrees and cook as follows: Rare – 18-20 minutes per kilogram, Medium – 25 minutes per kilogram, Well done – 30 minutes per kilogram.
## How long do you cook a steak at 325?
Guidelines for frying in the oven.
Cut the meat Oven temperature (preheated) Approximate total cooking time
Frying from the center of the beef tenderloin 325 ° F Medium Rare: 1-1 / 4 to 1-1 / 2 hours
Cake with sponge cake, round sponge cake in the background 325 ° F Medium Rare: 1-1 / 4 to 1-3 / 4 hours
Round steak eyes 325 ° F Medium Rare: 1-1 / 4 to 1-1 / 2 hours
## What is the temperature of the rib in the middle well?
Final raw rib temperature for raw meat is 120-125 ° F, raw meat average 130-135 ° F, and well done 140-145 ° F. | 1,155 | 4,717 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-33 | latest | en | 0.892493 |
https://www.gecode.org/doc/3.7.3/reference/classGecode_1_1IntSet.html | 1,653,054,645,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662532032.9/warc/CC-MAIN-20220520124557-20220520154557-00751.warc.gz | 887,056,317 | 4,796 | Generated on Thu Mar 22 10:39:52 2012 for Gecode by doxygen 1.6.3
# Gecode::IntSet Class Reference [Integer variables, Set variables]
Integer sets. More...
`#include <int.hh>`
List of all members.
## Classes
class MinInc
Sort ranges according to increasing minimum. More...
## Related Functions
(Note that these are not member functions.)
template<class Char , class Traits >
std::basic_ostream< Char,
Traits > &
operator<< (std::basic_ostream< Char, Traits > &os, const IntSet &s)
Print integer set s.
## Predefined value
static const IntSet empty
Empty set.
## Constructors and initialization
IntSet (void)
Initialize as empty set.
IntSet (int n, int m)
Initialize as range with minimum n and maximum m.
IntSet (const int r[], int n)
Initialize with n integers from array r.
IntSet (const int r[][2], int n)
Initialize with n ranges from array r.
template<class I >
IntSet (I &i)
Initialize with range iterator i.
## Range access
int ranges (void) const
Return number of ranges of the specification.
int min (int i) const
Return minimum of range at position i.
int max (int i) const
Return maximum of range at position i.
unsigned int width (int i) const
Return width of range at position i.
## Entire set access
bool in (int n) const
Return whether n is included in the set.
unsigned int size (void) const
Return size (cardinality) of set.
unsigned int width (void) const
Return width of set (distance between maximum and minimum).
int min (void) const
Return minimum of entire set.
int max (void) const
Return maximum of entire set.
## Detailed Description
Integer sets.
Integer sets are the means to specify arbitrary sets of integers to be used as domains for integer variables.
Definition at line 159 of file int.hh.
## Constructor & Destructor Documentation
Gecode::IntSet::IntSet ( void ) ` [inline]`
Initialize as empty set.
Definition at line 47 of file int-set-1.hpp.
Gecode::IntSet::IntSet ( int n, int m ) ` [inline]`
Initialize as range with minimum n and maximum m.
Note that the set is empty if n is larger than m
Definition at line 101 of file int-set-1.hpp.
Gecode::IntSet::IntSet ( const int r[], int n ) ` [inline]`
Initialize with n integers from array r.
Definition at line 96 of file int-set-1.hpp.
Gecode::IntSet::IntSet ( const int r[][2], int n ) ` [inline]`
Initialize with n ranges from array r.
For position i in the array r, the minimum is r[i][0] and the maximum is r[i][1].
Definition at line 91 of file int-set-1.hpp.
template<class I >
Gecode::IntSet::IntSet ( I & i ) ` [inline, explicit]`
Initialize with range iterator i.
Definition at line 86 of file int-set-1.hpp.
## Member Function Documentation
int Gecode::IntSet::ranges ( void ) const` [inline]`
Return number of ranges of the specification.
Definition at line 125 of file int-set-1.hpp.
int Gecode::IntSet::min ( int i ) const` [inline]`
Return minimum of range at position i.
Definition at line 106 of file int-set-1.hpp.
int Gecode::IntSet::max ( int i ) const` [inline]`
Return maximum of range at position i.
Definition at line 112 of file int-set-1.hpp.
unsigned int Gecode::IntSet::width ( int i ) const` [inline]`
Return width of range at position i.
Definition at line 118 of file int-set-1.hpp.
bool Gecode::IntSet::in ( int n ) const` [inline]`
Return whether n is included in the set.
Definition at line 131 of file int-set-1.hpp.
unsigned int Gecode::IntSet::size ( void ) const` [inline]`
Return size (cardinality) of set.
Definition at line 152 of file int-set-1.hpp.
unsigned int Gecode::IntSet::width ( void ) const` [inline]`
Return width of set (distance between maximum and minimum).
Definition at line 158 of file int-set-1.hpp.
int Gecode::IntSet::min ( void ) const` [inline]`
Return minimum of entire set.
Definition at line 140 of file int-set-1.hpp.
int Gecode::IntSet::max ( void ) const` [inline]`
Return maximum of entire set.
Definition at line 146 of file int-set-1.hpp.
## Friends And Related Function Documentation
template<class Char , class Traits >
std::basic_ostream< Char, Traits > & operator<< ( std::basic_ostream< Char, Traits > & os, const IntSet & s ) ` [related]`
Print integer set s.
Definition at line 227 of file int-set-1.hpp.
## Member Data Documentation
const IntSet Gecode::IntSet::empty` [static]`
Empty set.
Definition at line 247 of file int.hh.
The documentation for this class was generated from the following files: | 1,177 | 4,460 | {"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-2022-21 | latest | en | 0.610051 |
http://gmatclub.com/forum/amount-earned-day-28346.html?kudos=1 | 1,467,049,218,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783396100.16/warc/CC-MAIN-20160624154956-00127-ip-10-164-35-72.ec2.internal.warc.gz | 126,623,730 | 42,775 | Find all School-related info fast with the new School-Specific MBA Forum
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# Amount Earned/Day $96$84 $80$70 $48 post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message Intern Joined: 12 Dec 2005 Posts: 9 Location: Singapore Followers: 0 Kudos [?]: 0 [0], given: 0 Amount Earned/Day$96 $84$80 $70$48 [#permalink]
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13 Apr 2006, 16:12
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Amount Earned/Day $96$84 $80$70 $48 No of days 4 7 4 3 2 A Student worked for 20 days. For each of the amounts shown in the first two rows of the table, the second row gives the no of days that the student earned that amount. What is the median amount of money that the student earned per day for the 20 days. a.$96
b. $84 c.$80
d. $70 e.$48
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13 Apr 2006, 16:25
The median is the "middle" number in a set. If the set of numbers is even, then it is the average of the two middle numbers.
Easiest surest way to solve this is honestly to just quickly write out the set:
96,96,96,96,84,84,84,84,84,84,84,80,80,80,80,70,70,70,48,48
The two middle numbers are 84 and 84. Therefore, the answer is B.
There may be an easier way, but this took less than a minute as long as you understand the concept.
Display posts from previous: Sort by | 610 | 2,172 | {"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} | 3.9375 | 4 | CC-MAIN-2016-26 | longest | en | 0.880123 |
https://itpcb.com/a/8293 | 1,620,570,641,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988986.98/warc/CC-MAIN-20210509122756-20210509152756-00138.warc.gz | 350,065,930 | 10,295 | # 数据结构 | 双向链表简单实现及图示
————————————————————————————————————————————
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
``` 1 #include <stdio.h>
2 #include <stdlib.h>
3 #include <string.h>
4 typedef struct Node pNode;
5 struct Node
6 {
7 int data;
8 pNode *prev, *next;
9 };
10 /* 初始化链表，尾插法 */
11 pNode *InitList(pNode **head, int n)
12 {
13 pNode *p, *s;
16 exit(0);
20 int i;
21 for (i = 0; i < n; ++i)
22 {
23 s = (pNode *)malloc(sizeof(pNode));
24 if (s == NULL)
25 exit(0);
26 printf("Input the value of the %dth node:", i + 1);
27 scanf("%d", &s->data);
28 s->next = NULL;
29 p->next = s;
30 s->prev = p;
31 p = s;//p指向尾节点
32 }
33 return p;
34 }
35 /* 遍历打印 */
37 {
38 pNode *p;
41 printf("the list is empty\n");
42 while(p != NULL)
43 {
44 printf("%d ", p->data);
45 p = p->next;
46 }
47 printf("\n");
48 }
49 /* 清空链表 */
51 {
52 pNode *p;
54 {
56 p->next->prev = NULL;
58 free(p);
59 }
60 }
61 /* 查找链表内的某个值 */
63 {
64 int number;
65 printf("Values are about to be deleted:");
66 scanf("%d", &number);
67 pNode *p;
69 while(p != NULL)
70 {
71 if (p->data == number)
72 {
73 return number;
74 }
75 p = p->next;
76 }
77 return 0;
78 }
79 /* 删除链表中某个元素，令p的前驱节点和后驱节点相互指向即可，如果p是尾节点则直接将前驱节点指向NULL*/
80 void DelNumqList(pNode **head, int n)
81 {
82 int i;
83 pNode *p;
85 for (i = 1; i < n; ++i)
86 p = p->next;
87 if(p->next == NULL)
88 {
89 p->prev->next = NULL;
90 free(p);
91 }
92 else
93 {
94 p->next->prev = p->prev;
95 p->prev->next = p->next;
96 free(p);
97 }
98 }
99 int main(int argc, char const *argv[])
100 {
101 int n, element, flag;
103 /***************************************************************/
104 printf("Please input the size of the list:");
105 scanf("%d", &n);
107 printf("%d %d \n", head->next->data, last->data); //打印为第一个元素和最后一个元素
109 /***************************************************************/
111 if (flag > 0 && flag <= n)
112 {
115 }
116 else
117 printf("Element does not exist, cannot be deleted\n");
118 /***************************************************************/ | 876 | 2,654 | {"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} | 3.15625 | 3 | CC-MAIN-2021-21 | latest | en | 0.352403 |
https://www.coursehero.com/file/p27edta/b-still-10-mss-c-less-than-10-mss-d-not-able-to-be-determined-10-Galileo/ | 1,601,339,460,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401617641.86/warc/CC-MAIN-20200928234043-20200929024043-00571.warc.gz | 778,345,787 | 36,469 | b still 10 mss c less than 10 mss d not able to be determined 10 Galileo
B still 10 mss c less than 10 mss d not able to be
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*b) still 10 m/s/s.c) less than 10 m/s/s.d) not able to be determined.10. Galileo discovered that when two balls with different masses are in free fall something remains the same. What remains the same as the balls fall to earth?a) The distance they fall each second is 10 meters.*b) Their velocities are the same. (are constant.)*c) Their speeds are the same. (are constant.)*d) Their accelerations are the same.Question 10 was poorly stated and I accepted any of the three answers b, c, or d.I intended for d) to be the correct answer.2
11. You shoot an arrow straight up at a rate of 70 m/s. When does reach its highest point?12. How high will the arrow, shot up at 70 m/s, be when it reaches its highest point?13. What is the acceleration of the arrow when it is at the top of its flight?14. Who discovered that Aristotle’s physics of motion did not correctly describe observed motion?a) Newtonb) Halleyc) Copernicus*d) Galileo15. What is the unit of weight in the metric system of measure?16, A Mack truck and a Honda Civic traveling at the same speed collide head-on. The impact force is greatest on the a) Hondab) Mack truck*c) ...is the same for both17. A Mack truck and a Honda Civic traveling at the same speed have a head-on collision. The vehicle to undergo the greatest acceleration will be the *a) Hondab) Mack truckc) ...is the same for both3
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• Spring '13
• Wilson | 422 | 1,626 | {"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} | 2.6875 | 3 | CC-MAIN-2020-40 | latest | en | 0.875731 |
https://blog.spp2026.de/page/14/ | 1,721,099,496,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514726.17/warc/CC-MAIN-20240716015512-20240716045512-00549.warc.gz | 115,742,563 | 11,272 | Triangulating real projective n-space
How many vertices do you need to triangulate the real projective n-space? From this blog post of Gil Kalai I learned about a recent preprint (arXiv:2009.02703) by Adiprasito-Avvakumov-Karasev where they construct triangulations with $\exp\big((1/2 + \mathcal{o}(1))\sqrt{n}\log{n}\big)\text{-many}$ vertices, which is the first construction needing subexponentially-many vertices. More information, also about the history of this problem, may … Continue reading "Triangulating real projective n-space"
Resolution of Keller’s conjecture
Keller’s conjecture states that in any tiling of Euclidean space by identical hypercubes there are two cubes that meet face to face. (Consider the 2-dimensional picture on the right taken from Wikipedia. The squares share horizontal edges.) The conjecture is completely solved by now: it is true in dimensions 7 and less, but false in higher dimensions. The last missing part was … Continue reading "Resolution of Keller’s conjecture"
Catastrophe theory
This term I am teaching a course on catastrophe theory for 2nd year students. When you look up this topic on Wikipedia, you will see words like chaos and singularities mentioned, and you will be shown fancy pictures of the seven elementary catastrophes. But when you try to understand what the actual mathematical content of … Continue reading "Catastrophe theory"
Immersions of manifolds into Euclidean space
Recall the well-known result of Whitney that any (compact) smooth $$n$$-manifold admits an immersion into $$\mathbb{R}^{2n-1}$$. Today there was a preprint posted on the arXiv (arXiv:2011.00974) which mentioned in its introduction the following result of Cohen, which strengthens Whitney’s result as follows: Any (compact) smooth $$n$$-manifold admits an immersion into $$\mathbb{R}^{2n-\alpha(n)}$$, where $$\alpha(n)$$ is the … Continue reading "Immersions of manifolds into Euclidean space"
Blockseminar on Dirac operators and scalar curvature
In mid-October we gathered for one week in Bollmannsruh (somewhat west of Berlin) to work our way through the seminal paper Positive scalar curvature and the Dirac operator on complete Riemannian manifolds by Gromov and Lawson. The hotel we stayed in lies directly at the beautiful lake Beetzsee. It was the perfect place to do … Continue reading "Blockseminar on Dirac operators and scalar curvature"
Gehaltsverhandlungen als PostDoc
Gehaltsverhandlungen als PostDoc? Das gibt’s doch nur für Professoren … Das dachte ich mir zumindest bis jetzt und ging davon aus, dass man in Deutschland solange auf E13 (bzw. A13) beschäftigt wird bis man es bis zum Professor bzw. Professorin schafft. Dann aber ließ sich die Universität Münster doch überreden mich auf E14 einzustellen. Wie … Continue reading "Gehaltsverhandlungen als PostDoc"
Seminar on soap bubbles and positive scalar curvature
Together with Rudolf Zeidler I am organizing a reading seminar this winter on generalized soap bubbles and positive scalar curvature. The goal of it is to read the corresponding preprint by Chodosh-Li (arXiv:2008.11888). The two main results we want to understand are the following: No closed aspherical manifold of dimension 4 or 5 admits a … Continue reading "Seminar on soap bubbles and positive scalar curvature"
Nobel Prize for Sir Roger Penrose
Sir Roger Penrose won the Nobel Prize in Physics for the discovery that black hole formation is a robust prediction of the general theory of relativity. I have to admit that I connected him up to now only with aperiodic tilings of the plane (Wikipedia link). If you want to know more about him you … Continue reading "Nobel Prize for Sir Roger Penrose" | 889 | 3,690 | {"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} | 3.109375 | 3 | CC-MAIN-2024-30 | latest | en | 0.853926 |
https://morethingsjapanese.com/why-do-linguists-study-n-grams/ | 1,643,185,061,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304928.27/warc/CC-MAIN-20220126071320-20220126101320-00071.warc.gz | 446,726,410 | 9,948 | Why do linguists study n-grams?
Why do linguists study n-grams?
Generating a list of the most frequent n-grams will help us linguistic phenomena that might go unnoticed when using other tools. Ngrams can identify discourse markers or chunks of language which should be taught/learnt as fixed phrases in leanguage teaching.
What do n-grams tell us?
Basically, an N-gram model predicts the occurrence of a word based on the occurrence of its N – 1 previous words. So here we are answering the question – how far back in the history of a sequence of words should we go to predict the next word?
What is a n-gram language model?
An N-gram model is built by counting how often word sequences occur in corpus text and then estimating the probabilities. An N-gram model is one type of a Language Model ( LM ), which is about finding the probability distribution over word sequences.
What are the stages of NLP?
There are the following five phases of NLP:
• Lexical Analysis and Morphological. The first phase of NLP is the Lexical Analysis.
• Syntactic Analysis (Parsing)
• Semantic Analysis.
• Discourse Integration.
• Pragmatic Analysis.
What is smoothing in NLP?
Smoothing techniques in NLP are used to address scenarios related to determining probability / likelihood estimate of a sequence of words (say, a sentence) occuring together when one or more words individually (unigram) or N-grams such as bigram(wi/wi−1) or trigram (wi/wi−1wi−2) in the given set have never occured in …
What do you mean by n-gram model explain bigram & Unigram in detail?
An n-gram is a sequence. n-gram. of n words: a 2-gram (which we’ll call bigram) is a two-word sequence of words. like “please turn”, “turn your”, or ”your homework”, and a 3-gram (a trigram) is a three-word sequence of words like “please turn your”, or “turn your homework”.
What are the 5 phases of NLP?
The five phases of NLP involve lexical (structure) analysis, parsing, semantic analysis, discourse integration, and pragmatic analysis. Some well-known application areas of NLP are Optical Character Recognition (OCR), Speech Recognition, Machine Translation, and Chatbots.
What does the n gram mean in linguistics?
In the fields of computational linguistics and probability, an n-gram is a contiguous sequence of n items from a given sample of text or speech.
How are n gram models used in speech recognition?
Applications and considerations. n-gram models are widely used in statistical natural language processing. In speech recognition, phonemes and sequences of phonemes are modeled using a n-gram distribution. For parsing, words are modeled such that each n-gram is composed of n words.
What is n gram model?
An n-gram model is a type of probabilistic language model for predicting the next item in such a sequence in the form of a (n − 1)–order Markov model .
What can n-gram search be used for?
n-gram-based searching can also be used for plagiarism detection. Other applications [ edit ] n -grams find use in several areas of computer science, computational linguistics , and applied mathematics. | 692 | 3,082 | {"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} | 2.703125 | 3 | CC-MAIN-2022-05 | latest | en | 0.919253 |
http://herbie.uwplse.org/demo/09f6505e1d506b0b1974919a6240225de3fcc405.4e924be3125566e8e27de69ca0ee25cd0b20a544/graph.html | 1,553,373,293,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912203021.14/warc/CC-MAIN-20190323201804-20190323223804-00378.warc.gz | 92,229,558 | 3,376 | Average Error: 53.0 → 2.4
Time: 30.6s
Precision: 64
Internal Precision: 2368
$\frac{{2}^{\left(\frac{1}{3}\right)}}{{\left(\left(-3\right) \cdot x + \sqrt{4 + 9 \cdot {x}^{2}}\right)}^{\left(\frac{1}{3}\right)}} - \frac{{\left(\left(-3\right) \cdot x + \sqrt{4 + 9 \cdot {x}^{2}}\right)}^{\left(\frac{1}{3}\right)}}{{2}^{\left(\frac{1}{3}\right)}}$
$\begin{array}{l} \mathbf{if}\;x \le -0.6805997101349137:\\ \;\;\;\;\left(\left(\frac{\sqrt[3]{2}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}} + \frac{\frac{\frac{5}{729} \cdot \sqrt[3]{2}}{{x}^{4}}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}\right) + \frac{4}{729} \cdot \frac{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}{\frac{{x}^{4}}{\sqrt[3]{\frac{1}{2}}}}\right) - \left(\left(\left(\frac{\sqrt[3]{2}}{x \cdot x} \cdot \frac{1}{27}\right) \cdot {\left(e^{-\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} + {\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} \cdot \sqrt[3]{\frac{1}{2}}\right) + \frac{1}{27} \cdot \frac{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}{\frac{x \cdot x}{\sqrt[3]{\frac{1}{2}}}}\right)\\ \mathbf{elif}\;x \le 0.6839042917823821:\\ \;\;\;\;\left(x + \frac{1}{3} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{\frac{\frac{1}{27} \cdot \sqrt[3]{2}}{x \cdot x}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}} + \left(\frac{\sqrt[3]{\frac{1}{2}}}{x} \cdot \frac{1}{27}\right) \cdot \frac{{\left(\frac{1}{x}\right)}^{\frac{1}{3}}}{\frac{x}{{\frac{2}{3}}^{\frac{1}{3}}}}\right) - \left(\frac{\frac{\sqrt[3]{2} \cdot \frac{4}{729}}{{x}^{4}}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot {\frac{2}{3}}^{\frac{1}{3}}\right)\right)\right) - \left(\frac{{\left(\frac{1}{x}\right)}^{\frac{1}{3}}}{\frac{{x}^{4}}{{\frac{2}{3}}^{\frac{1}{3}}}} \cdot \left(\frac{5}{729} \cdot \sqrt[3]{\frac{1}{2}}\right) - \frac{\sqrt[3]{2}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}}\right)\\ \end{array}$
# Try it out
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In Out
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# Derivation
1. Split input into 3 regimes
2. ## if x < -0.6805997101349137
1. Initial program 33.1
$\frac{{2}^{\left(\frac{1}{3}\right)}}{{\left(\left(-3\right) \cdot x + \sqrt{4 + 9 \cdot {x}^{2}}\right)}^{\left(\frac{1}{3}\right)}} - \frac{{\left(\left(-3\right) \cdot x + \sqrt{4 + 9 \cdot {x}^{2}}\right)}^{\left(\frac{1}{3}\right)}}{{2}^{\left(\frac{1}{3}\right)}}$
2. Initial simplification33.1
$\leadsto \frac{{2}^{\left(\frac{1}{3}\right)}}{{\left(\sqrt{9 \cdot \left(x \cdot x\right) + 4} - 3 \cdot x\right)}^{\left(\frac{1}{3}\right)}} - \frac{{\left(\sqrt{9 \cdot \left(x \cdot x\right) + 4} - 3 \cdot x\right)}^{\left(\frac{1}{3}\right)}}{{2}^{\left(\frac{1}{3}\right)}}$
3. Taylor expanded around -inf 5.0
$\leadsto \color{blue}{\left({2}^{\frac{1}{3}} \cdot \frac{1}{e^{\frac{1}{3} \cdot \left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}} + \left(\frac{4}{729} \cdot \left(\frac{e^{\frac{1}{3} \cdot \left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}{{x}^{4}} \cdot {\frac{1}{2}}^{\frac{1}{3}}\right) + \frac{5}{729} \cdot \left(\frac{1}{e^{\frac{1}{3} \cdot \left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} \cdot {x}^{4}} \cdot {2}^{\frac{1}{3}}\right)\right)\right) - \left(\frac{1}{27} \cdot \left(\frac{e^{\frac{1}{3} \cdot \left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}{{x}^{2}} \cdot {\frac{1}{2}}^{\frac{1}{3}}\right) + \left(e^{\frac{1}{3} \cdot \left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} \cdot {\frac{1}{2}}^{\frac{1}{3}} + \frac{1}{27} \cdot \left({2}^{\frac{1}{3}} \cdot \frac{1}{e^{\frac{1}{3} \cdot \left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} \cdot {x}^{2}}\right)\right)\right)}$
4. Simplified4.5
$\leadsto \color{blue}{\left(\frac{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}{\frac{{x}^{4}}{\sqrt[3]{\frac{1}{2}}}} \cdot \frac{4}{729} + \left(\frac{\sqrt[3]{2}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}} + \frac{\frac{\sqrt[3]{2} \cdot \frac{5}{729}}{{x}^{4}}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}\right)\right) - \left(\left(\left(\frac{1}{27} \cdot \frac{\sqrt[3]{2}}{x \cdot x}\right) \cdot {\left(e^{-\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} + {\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} \cdot \sqrt[3]{\frac{1}{2}}\right) + \frac{1}{27} \cdot \frac{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}{\frac{x \cdot x}{\sqrt[3]{\frac{1}{2}}}}\right)}$
## if -0.6805997101349137 < x < 0.6839042917823821
1. Initial program 58.6
$\frac{{2}^{\left(\frac{1}{3}\right)}}{{\left(\left(-3\right) \cdot x + \sqrt{4 + 9 \cdot {x}^{2}}\right)}^{\left(\frac{1}{3}\right)}} - \frac{{\left(\left(-3\right) \cdot x + \sqrt{4 + 9 \cdot {x}^{2}}\right)}^{\left(\frac{1}{3}\right)}}{{2}^{\left(\frac{1}{3}\right)}}$
2. Initial simplification58.6
$\leadsto \frac{{2}^{\left(\frac{1}{3}\right)}}{{\left(\sqrt{9 \cdot \left(x \cdot x\right) + 4} - 3 \cdot x\right)}^{\left(\frac{1}{3}\right)}} - \frac{{\left(\sqrt{9 \cdot \left(x \cdot x\right) + 4} - 3 \cdot x\right)}^{\left(\frac{1}{3}\right)}}{{2}^{\left(\frac{1}{3}\right)}}$
3. Taylor expanded around 0 0.2
$\leadsto \color{blue}{\left(\frac{1}{3} \cdot {x}^{5} + x\right) - \frac{1}{3} \cdot {x}^{3}}$
## if 0.6839042917823821 < x
1. Initial program 61.6
$\frac{{2}^{\left(\frac{1}{3}\right)}}{{\left(\left(-3\right) \cdot x + \sqrt{4 + 9 \cdot {x}^{2}}\right)}^{\left(\frac{1}{3}\right)}} - \frac{{\left(\left(-3\right) \cdot x + \sqrt{4 + 9 \cdot {x}^{2}}\right)}^{\left(\frac{1}{3}\right)}}{{2}^{\left(\frac{1}{3}\right)}}$
2. Initial simplification61.6
$\leadsto \frac{{2}^{\left(\frac{1}{3}\right)}}{{\left(\sqrt{9 \cdot \left(x \cdot x\right) + 4} - 3 \cdot x\right)}^{\left(\frac{1}{3}\right)}} - \frac{{\left(\sqrt{9 \cdot \left(x \cdot x\right) + 4} - 3 \cdot x\right)}^{\left(\frac{1}{3}\right)}}{{2}^{\left(\frac{1}{3}\right)}}$
3. Taylor expanded around inf 5.2
$\leadsto \color{blue}{\left({2}^{\frac{1}{3}} \cdot \frac{1}{e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{x}\right) + \log \frac{2}{3}\right)}} + \left(\frac{1}{27} \cdot \left({2}^{\frac{1}{3}} \cdot \frac{1}{{x}^{2} \cdot e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{x}\right) + \log \frac{2}{3}\right)}}\right) + \frac{1}{27} \cdot \left(\frac{e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{x}\right) + \log \frac{2}{3}\right)}}{{x}^{2}} \cdot {\frac{1}{2}}^{\frac{1}{3}}\right)\right)\right) - \left({\frac{1}{2}}^{\frac{1}{3}} \cdot e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{x}\right) + \log \frac{2}{3}\right)} + \left(\frac{4}{729} \cdot \left({2}^{\frac{1}{3}} \cdot \frac{1}{{x}^{4} \cdot e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{x}\right) + \log \frac{2}{3}\right)}}\right) + \frac{5}{729} \cdot \left(\frac{e^{\frac{1}{3} \cdot \left(\log \left(\frac{1}{x}\right) + \log \frac{2}{3}\right)}}{{x}^{4}} \cdot {\frac{1}{2}}^{\frac{1}{3}}\right)\right)\right)}$
4. Simplified4.7
$\leadsto \color{blue}{\left(\left(\frac{\frac{\frac{1}{27} \cdot \sqrt[3]{2}}{x \cdot x}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}} + \left(\frac{1}{27} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{x}\right) \cdot \frac{{\left(\frac{1}{x}\right)}^{\frac{1}{3}}}{\frac{x}{{\frac{2}{3}}^{\frac{1}{3}}}}\right) - \left({\left(\frac{1}{x}\right)}^{\frac{1}{3}} \cdot \left({\frac{2}{3}}^{\frac{1}{3}} \cdot \sqrt[3]{\frac{1}{2}}\right) + \frac{\frac{\frac{4}{729} \cdot \sqrt[3]{2}}{{x}^{4}}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}}\right)\right) - \left(\left(\sqrt[3]{\frac{1}{2}} \cdot \frac{5}{729}\right) \cdot \frac{{\left(\frac{1}{x}\right)}^{\frac{1}{3}}}{\frac{{x}^{4}}{{\frac{2}{3}}^{\frac{1}{3}}}} - \frac{\sqrt[3]{2}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}}\right)}$
3. Recombined 3 regimes into one program.
4. Final simplification2.4
$\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.6805997101349137:\\ \;\;\;\;\left(\left(\frac{\sqrt[3]{2}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}} + \frac{\frac{\frac{5}{729} \cdot \sqrt[3]{2}}{{x}^{4}}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}\right) + \frac{4}{729} \cdot \frac{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}{\frac{{x}^{4}}{\sqrt[3]{\frac{1}{2}}}}\right) - \left(\left(\left(\frac{\sqrt[3]{2}}{x \cdot x} \cdot \frac{1}{27}\right) \cdot {\left(e^{-\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} + {\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)} \cdot \sqrt[3]{\frac{1}{2}}\right) + \frac{1}{27} \cdot \frac{{\left(e^{\frac{1}{3}}\right)}^{\left(\log 6 - \log \left(\frac{-1}{x}\right)\right)}}{\frac{x \cdot x}{\sqrt[3]{\frac{1}{2}}}}\right)\\ \mathbf{elif}\;x \le 0.6839042917823821:\\ \;\;\;\;\left(x + \frac{1}{3} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{\frac{\frac{1}{27} \cdot \sqrt[3]{2}}{x \cdot x}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}} + \left(\frac{\sqrt[3]{\frac{1}{2}}}{x} \cdot \frac{1}{27}\right) \cdot \frac{{\left(\frac{1}{x}\right)}^{\frac{1}{3}}}{\frac{x}{{\frac{2}{3}}^{\frac{1}{3}}}}\right) - \left(\frac{\frac{\sqrt[3]{2} \cdot \frac{4}{729}}{{x}^{4}}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}} + {\left(\frac{1}{x}\right)}^{\frac{1}{3}} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot {\frac{2}{3}}^{\frac{1}{3}}\right)\right)\right) - \left(\frac{{\left(\frac{1}{x}\right)}^{\frac{1}{3}}}{\frac{{x}^{4}}{{\frac{2}{3}}^{\frac{1}{3}}}} \cdot \left(\frac{5}{729} \cdot \sqrt[3]{\frac{1}{2}}\right) - \frac{\sqrt[3]{2}}{{\left(e^{\frac{1}{3}}\right)}^{\left(\log \frac{2}{3} - \log x\right)}}\right)\\ \end{array}$
# Runtime
Time bar (total: 30.6s)Debug log
herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "2^(1/3)/(-3 x + sqrt(4 + 9 x^2))^(1/3) - (-3 x + sqrt(4 + 9 x^2))^(1/3)/2^(1/3)"
(- (/ (pow 2 (/ 1 3)) (pow (+ (* (- 3) x) (sqrt (+ 4 (* 9 (pow x 2))))) (/ 1 3))) (/ (pow (+ (* (- 3) x) (sqrt (+ 4 (* 9 (pow x 2))))) (/ 1 3)) (pow 2 (/ 1 3))))) | 4,822 | 10,726 | {"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} | 2.71875 | 3 | CC-MAIN-2019-13 | latest | en | 0.211593 |
https://www.superteacherworksheets.com/multiplication-arrays.html | 1,726,406,260,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651630.14/warc/CC-MAIN-20240915120545-20240915150545-00873.warc.gz | 939,285,800 | 17,333 | # Multiplication & Division with Arrays
Learn about using arrays for multiplication and division with these printables worksheets, task cards, and activities.
## Multiplication with Arrays:Worksheets
Examine each array illustration. Tell how many rows, how many columns, and how many dots. Then write a multiplication fact for each.
2nd through 4th Grades
On this worksheet, your students will practice using arrays to solve multiplication facts. Count the row and columns to solve.
2nd through 4th Grades
Teach students to draw their own arrays. They are given a multiplication fact with space to draw circles in neat rows and columns.
2nd through 4th Grades
Write a multiplication fact for each array shown.
Here's a table with 100 stars. Numbers 1 through 10 are listed on the x and y axis. Use the L-shaped tool to make an array for any basic multiplication fact.
Cut out the multiplication facts, products, and array illustrations. Glue each in the correct position on the table.
Kids will love making these creative city skylines using graph paper! This activity helps them practice basic multiplication skills using arrays.
2nd through 4th Grades
Draw arrays for any multiplication facts on this template graphic organizer.
## Distributive Property ofMultiplication Using Arrays
This worksheet uses arrays to make it easy for students to understand the distributive property of multiplication.
Here's another worksheet that uses arrays to help students understand the distributive property of multiplication.
## Multiplication with Arrays:Math Games & Task Cards
Cut out the 36 cards in this set. Match the facts, array graphics, and answers/products. You can also use this set to play a memory-match game.
Roll a pair of dice. Draw a rectangular array for each pair of numbers rolled.
2nd through 4th Grades
Each of these 30 task cards has a question related to multiplication with arrays. Use them for classroom scavenger hunts, learning centers, or exit slips. They work great with document cameras too.
2nd through 4th Grades
## Division with Arrays
Answer the questions for each array shown. Then find and solve the division fact.
3rd and 4th Grades
Write the basic division fact shown by each array.
3rd and 4th Grades
## Fact Families(Multiplication & Division)
Students are shown an array. They write the four multiplication and division facts for each.
Basic Multiplication Worksheets
On this page, you'll find a link to hundreds of worksheets and printable games for teaching basic multiplication facts.
## Sample Worksheet Images
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A047485 Numbers that are congruent to {0, 3, 5, 7} mod 8. 1
0, 3, 5, 7, 8, 11, 13, 15, 16, 19, 21, 23, 24, 27, 29, 31, 32, 35, 37, 39, 40, 43, 45, 47, 48, 51, 53, 55, 56, 59, 61, 63, 64, 67, 69, 71, 72, 75, 77, 79, 80, 83, 85, 87, 88, 91, 93, 95, 96, 99, 101, 103, 104, 107, 109, 111, 112, 115, 117, 119, 120, 123, 125 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA From Colin Barker, May 14 2012: (Start) G.f.: x^2*(3+2*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). a(n) = (-5+(-1)^n-i*(-i)^n+i*i^n+8*n)/4 where i=sqrt(-1). (End) From Wesley Ivan Hurt, Jun 04 2016: (Start) a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. a(2k) = A004767(k-1) for n>0, a(2k-1) = A047615(k). (End) E.g.f.: (2 - sin(x) + (4*x - 3)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, Jun 04 2016 MAPLE A047485:=n->(-5+I^(2*n)-I*(-I)^n+I*I^n+8*n)/4: seq(A047485(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016 MATHEMATICA Select[Range[0, 120], MemberQ[{0, 3, 5, 7}, Mod[#, 8]]&] (* Harvey P. Dale, May 20 2011 *) PROG (MAGMA) [n : n in [0..150] | n mod 8 in [0, 3, 5, 7]]; // Wesley Ivan Hurt, Jun 04 2016 CROSSREFS Cf. A004767, A047615. Sequence in context: A190061 A288624 A168162 * A024969 A296233 A276112 Adjacent sequences: A047482 A047483 A047484 * A047486 A047487 A047488 KEYWORD nonn,easy AUTHOR STATUS approved
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Last modified December 3 11:54 EST 2020. Contains 338900 sequences. (Running on oeis4.) | 872 | 2,162 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2020-50 | latest | en | 0.665044 |
https://math.answers.com/Q/How_many_right_angles_in_a_right_trapezoid | 1,696,019,308,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510528.86/warc/CC-MAIN-20230929190403-20230929220403-00559.warc.gz | 407,256,795 | 43,487 | 0
# How many right angles in a right trapezoid?
Updated: 10/25/2022
Wiki User
7y ago
At most two.
Wiki User
6y ago
Earn +20 pts
Q: How many right angles in a right trapezoid?
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Related questions
### How many right angles are in a trapezoid?
A trapezoid can have either none or two right angles.
### How many right angles does trapezoid have?
A trapezoid can have up to two right, 90 degree angles for it still to be classified as a trapezoid.
### What trapezoid has 2 right angles?
A right trapezoid has at least two right angles.
### Does a trapezoid have one or two right angles?
A trapezoid may have two right angles.
0 or 2.
### How many right angels are there in a trapezoid?
A trapezoid may have no right angles, or it may have two adjacent ones.
### Does a trapezoid has 4 right angles?
A shape with 4 right angles would be a square or rectangle. A trapezoid does not have any right angles..
### How many parallel sides and right angles in trapezoid?
There is one pair of parallel sides. A trapezoid can have at most one right angle. Not all trapezoids have right angles.
### How many angles does a trapezoid has?
A trapezoid has four angles.
### How many different angles are in a trapezoid?
There are obtuse, acute, and right angles. It depends on what type.
### How many right angles can a trapezoid have?
A trapezoid can have 2 right angles, 1 acute angle and 1 obtuse angle that all add up to 360 degrees
### How many right acute and obtuse angles does a trapezoid have?
It can have 0 or 2 right angles, 1 or 2 acute or obtuse angles. | 446 | 1,604 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2023-40 | latest | en | 0.891471 |
https://www.greaterwrong.com/posts/fCg3pLZqthXsGznHP/troll-timers/comment/RsESwQihhRS2Gacin | 1,669,959,685,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710898.93/warc/CC-MAIN-20221202050510-20221202080510-00349.warc.gz | 790,238,947 | 4,893 | # Dirichlet-to-Neumann comments on Troll Timers
• Why not use a standard chess clock when you can freely choose to allocate your time as needed, playing easy moves instantly and taking more time when needed ? It’s a bit sad if the important decision that decides the game has to be made on a 5 s clock at move 23 but you get the whole 5 minutes to contemplate your ruined hopeless position at move 25...
Besides real life mostly plays out like a chess game when you can allocate more time to a decision when needed. In fact, deciding which situations call for a longer time to think is a key chess skill and also a key life skill.
• I want to start by saying I’d be delighted to hear people try variations on troll timers and report back how that worked. My confidence here is closer to “how to spice a recipe” than “how to do a math problem” if that makes sense. You’re absolutely right that deciding what situations call for a longer time to think is a key skill, and it’s even a skill that I’m trying to build some foundation for in troll timers.
I think playing on a standard chess clock is going to teach something in the neighborhood of what troll timers are aimed at. Certainly one skill that I value is realizing you can stop, pause, and take some time to actually think. The failure mode that I see a lot and worry that standard chess clocks don’t solve is stopping the thinking process after the first idea or the first failure. To quote HPMoR:
“So figure it out,” Harry said. “I have confidence in you. Not total confidence, but if you can’t do it, tell me that, and I’ll try someone else, or do it myself. If you have a really good idea—for both the ridiculous story, and how to convince Rita Skeeter and her editors to print it—then you can go ahead and do it. But don’t go with something mediocre. If you can’t come up with something awesome, just say so.”
Fred and George exchanged worried glances.
“I can’t think of anything,” said George.
“Neither can I,” said Fred. “Sorry.”
Harry stared at them.
And then Harry began to explain how you went about thinking of things.
It had been known to take longer than two seconds, said Harry.
You never called any question impossible, said Harry, until you had taken an actual clock and thought about it for five minutes, by the motion of the minute hand. Not five minutes metaphorically, five minutes by a physical clock.
On a standard chess clock, taking five whole minutes to study the board and think about where this game might go is usually a poor choice. There’s a feeling one learns to notice inside yourself when you’ve hit diminishing returns and it’s better to put the clock back on your opponent. The intention behind forcing people to spend five minutes, yes the whole five minutes, you don’t get any of that time back by saving it so use all of it, is that it helps learn how to keep thinking. Sometimes the brilliant play is the seventh or eighth idea you came up with. Sometimes it takes a couple of minutes to get rid of your first knee-jerk reaction. If you know you have five minutes, then maybe you play around with taking the first whole minute to close your eyes, calm down, and then look at the board with a fresh mind.
There’s something in the space of letting people choose the turn that they need to take the long timer. Like you said, it’s sad if someone realizes that turn 23 is the crucial moment but doesn’t have the time to think it through. What do you think of Aphyer’s idea of offering a set number of tokens to spend and get longer turns? I tried something like that very early on but I didn’t try reintroducing it once people were a little more comfortable with the fast turns.
• That’s what they do in go and it makes more sense than a fixed pause after 25 moves. Or if you want to really force people to think for 5 minutes you could make it a 5 minutes every 5 moves—then you can use your 5 minutes to really map out your options for the next 5 moves before the next pause. And it may even be a good training for chess players, avoiding to waste time by redoing the same calculations move after move. | 898 | 4,110 | {"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-2022-49 | latest | en | 0.954098 |
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