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https://man.linuxreviews.org/man3/dlaqge.f.3.html | 1,720,986,550,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514638.53/warc/CC-MAIN-20240714185510-20240714215510-00722.warc.gz | 338,177,222 | 2,774 | # dlaqge.f
Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index
dlaqge.f
## SYNOPSIS
### Functions/Subroutines
subroutine dlaqge (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED)
DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
## Function/Subroutine Documentation
### subroutine dlaqge (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, character EQUED)
DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
Purpose:
``` DLAQGE equilibrates a general M by N matrix A using the row and
column scaling factors in the vectors R and C.
```
Parameters:
M
``` M is INTEGER
The number of rows of the matrix A. M >= 0.
```
N
``` N is INTEGER
The number of columns of the matrix A. N >= 0.
```
A
``` A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M by N matrix A.
On exit, the equilibrated matrix. See EQUED for the form of
the equilibrated matrix.
```
LDA
``` LDA is INTEGER
The leading dimension of the array A. LDA >= max(M,1).
```
R
``` R is DOUBLE PRECISION array, dimension (M)
The row scale factors for A.
```
C
``` C is DOUBLE PRECISION array, dimension (N)
The column scale factors for A.
```
ROWCND
``` ROWCND is DOUBLE PRECISION
Ratio of the smallest R(i) to the largest R(i).
```
COLCND
``` COLCND is DOUBLE PRECISION
Ratio of the smallest C(i) to the largest C(i).
```
AMAX
``` AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.
```
EQUED
``` EQUED is CHARACTER*1
Specifies the form of equilibration that was done.
= 'N': No equilibration
= 'R': Row equilibration, i.e., A has been premultiplied by
diag(R).
= 'C': Column equilibration, i.e., A has been postmultiplied
by diag(C).
= 'B': Both row and column equilibration, i.e., A has been
replaced by diag(R) * A * diag(C).
```
Internal Parameters:
``` THRESH is a threshold value used to decide if row or column scaling
should be done based on the ratio of the row or column scaling
factors. If ROWCND < THRESH, row scaling is done, and if
COLCND < THRESH, column scaling is done.
LARGE and SMALL are threshold values used to decide if row scaling
should be done based on the absolute size of the largest matrix
element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
```
Author:
Univ. of Tennessee
Univ. of California Berkeley | 734 | 2,630 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2024-30 | latest | en | 0.776298 |
https://www.financeformulas.net/Future-Value-Factor.html | 1,590,583,630,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347394074.44/warc/CC-MAIN-20200527110649-20200527140649-00148.warc.gz | 717,254,548 | 3,730 | Future Value Factor
The formula for the future value factor is used to calculate the future value of an amount per dollar of its present value. The future value factor is generally found on a table which is used to simplify calculations for amounts greater than one dollar (see example below).
The future value factor formula is based on the concept of time value of money. The concept of time value of money is that an amount today is worth more than if that same nominal amount is received at a future date. Any amount received today can be invested and receive earnings, as opposed to waiting to receive the same amount with no earnings. An amount of \$105 to be received a year from now may be okay if the individual wants \$100 today, assuming that the individual can earn 5% otherwise in one year.
Rate Per Period/Number of Periods
It is important when using the formula for the future value factor to match the rate per period with the number of periods. The number of periods should also match how often an investment is compounded. For example, assume that the nominal interest rate is 12% per year compounded monthly. Since this account is compounded monthly, then 1% per month would be used in the formula to calculate the future value factor.
Example of Future Value Factor Formula
Using the prior example of 12% compounded monthly, the future value factor formula for one year would show
where 1%, or .01, is the rate per period and 12 is the number of periods. By solving this equation, the future value factor for 12 periods at 1% per period would be 1.1268.
As previously stated, the future value factor is generally found on a table that is used for quick calculations for amounts greater than one dollar. With this example, assume that an individual is attempting to calculate the value after one year for the amount of \$500 today based on a 12% nominal annual rate compounded monthly. By looking at the future value factor table, the individual would find 1.1268. Since this factor is based on \$1, the factor can then be multiplied by the \$500 to find a future value of \$563.40.
New to Finance? | 446 | 2,126 | {"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-2020-24 | latest | en | 0.945278 |
http://isomorphismes.tumblr.com/tagged/the+continuum | 1,398,379,709,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1398223206770.7/warc/CC-MAIN-20140423032006-00456-ip-10-147-4-33.ec2.internal.warc.gz | 180,926,599 | 43,187 | Posts tagged with the continuum
## One
Counting generates from the programmer’s successor function `++` and the number one. (You might argue that to get out to infinity requires also repetition. Well every category comes with composition by default, which includes composition of ƒ∘ƒ∘ƒ∘….)
But getting to one is nontrivial. Besides the mystical implications of 1, it’s not always easy to draw a boundary around “one thing”. Looking at snow (without the advantage of modern optical science) I couldn’t find “one snow”. Even where it is cut off by a plowed street it’s still from the same snowfall.
And if you got around on skis a lot of your life you wouldn’t care about one snow-flake (a reductive way to define “one” snow), at least not for transport, because one flake amounts to zero ability to travel anywhere. Could we talk about one inch of snow? One hour of snow? One night of snow?
Speaking of the cold, how about temperature? It has no inherent units; all of our human scales pick endpoints and define a continuum in between. That’s the same as in measure theory which gave (along with martingales) at least an illusion of technical respectability to the science of chances. If you use Kolmogorov’s axioms then the difficult (impossible?) questions—what the “likelihood” of a one-shot event (like a US presidential election) actually means or how you could measure it—can be swept under the rug whilst one computes random walks on trees or Gaussian copulæ. Meanwhile the sum-total of everything that could possibly happen `Ω` is called 1.
With water or other liquids as well. Or gases. You can have one grain of powder or grain (granular solids can flow like a fluid) but you can’t have one gas or one water. (Well, again you can with modern science—but with even more moderner science you can’t, because you just find a QCD dynamical field balancing (see video) and anyway none of the “one” things are strictly local.)
And in my more favourite realm, the realm of ideas. I have a really hard time figuring out where I can break off one idea for a blogpost. These paragraphs were a stalactite growth off a blobular self-rant that keeps jackhammering away inside my head on the topic of mathematical modelling and equivalence classes. I’ve been trying to write something called “To equivalence class” and I’ve also been trying to write something called “Statistics for People Who Program Computers” and as I was talking this out to myself, another rant squeezed out between my fingers and I knew if I dropped the other two I could pull One off it could be sculpted into a readable microtract. Leaving “To Equivalence Class”, like so many of the harder-to-write things, in the refrigerator—to marinate or to mould, I don’t know which.
But notice that I couldn’t fully disconnect this one from other shared-or-not-shared referents. (Shared being English language and maybe a lot of unspoken assumptions we both hold. Unshared being my own personal jargon—some of which I’ve tried to share in this space—and rants that continually obsess me such as the fallaciousness of probabilistic statements and of certain economic debates.) This is why I like writing on the Web: I can plug in a picture from Wikipedia or point back to somewhere else I’ve talked on the other tangent so I don’t ride off on the connecting track and end up away from where I tried to head.
The difficulty of drawing a firm boundary of "one" to begin the process of counting may be an inverse of the "full" paradox or it may be that certain things (like liquid) don’t lend themselves to counting in an obvious way—in jargon, they don’t map nicely onto the natural numbers (the simplest kind of number). If that’s a motivation to move from discrete things to continuous when necessary, then I feel a similar motivation to move from Euclidean to Hausdorff, or from line to poset. Not that the simpler things don’t deserve as well a place at the table.
We thinkers are fairly free to look at things in different ways—to quotient and equivalence-class creatively or at varying scales. And that’s also a truth of mathematical modelling. Even if maths seems one-right-answer from the classroom, the same piece of reality can bear multiple models—some refining each other, some partially overlapping, some mutually disjoint.
## Measure: Sizing up the Continuum
For those not in the know, here’s what mathematicians mean by the word “measurable”:
1. The problem of measure is to assign a ℝ size `≥ 0` to a set. (The points not necessarily contiguous.) In other words, to answer the question:
How big is that?
2. Why is this hard? Well just think about the problem of sizing up a contiguous ℝ subinterval between `0` and `1`.
• It’s obvious that `[.4, .6]` is `.2` long and that
• `[0, .8]` has a length of `.8`.
• I don’t know what the length of `[¼√2, √π/3]` is but … it should be easy enough to figure out.
• But real numbers can go on forever: `.2816209287162381682365...1828361...1984...77280278254...`.
• Most of them (the transcendentals) we don’t even have words or notation for.
• So there are a potentially infinite number of digits in each of these real numbers — which is essentially why the real numbers are so f#cked up — and therefore ∃ an infinitely infinite number of numbers just between 0% and 100%.
Yeah, I said infinitely infinite, and I meant that. More real numbers exist in-between `.999999999999999999999999` and `1` than there are atoms in the universe. There are more real numbers just in that teensy sub-interval than there are integers (and there are integers).
In other words, if you filled a set with all of the things between `.99999999999999999999` and `1`, there would be infinity things inside. And not a nice, tame infinity either. This infinity is an infinity that just snorted a football helmet filled with coke, punched a stripper, and is now running around in the streets wearing her golden sparkly thong and brandishing a chainsaw:
Talking still of that particular infinity: in a set-theoretic continuum sense, ∃ infinite number of points between Barcelona and Vladivostok, but also an infinite number of points between my toe and my nose. Well, now the simple and obvious has become not very clear at all!
So it’s a problem of infinities, a problem of sets, and a problem of the continuum being such an infernal taskmaster that it took until the 20th century for mathematicians to whip-crack the real numbers into shape.
3. If you can define “size” on the `[0,1]` interval, you can define it on the `[−535,19^19]` interval as well, by extension.
If you can’t even define “size” on the `[0,1]` interval — how do you think you’re going to define it on all of ℝ? Punk.
4. A reasonable definition of “size” (measure) should work for non-contiguous subsets of ℝ such as “just the rational numbers” or “all solutions to `cos² x = 0`(they’re not next to each other) as well.
Just another problem to add to the heap.
5. Nevertheless, the monstrosity has more-or-less been tamed. Epsilons, deltas, open sets, Dedekind cuts, Cauchy sequences, well-orderings, and metric spaces had to be invented in order to bazooka the beast into submission, but mostly-satisfactory answers have now been obtained.
It just takes a sequence of 4-5 university-level maths classes to get to those mostly-satisfactory answers.
One is reminded of the hypermathematicians from The Hitchhiker’s Guide to the Galaxy who time-warp themselves through several lives of study before they begin their real work.
For a readable summary of the reasoning & results of Henri Lebesgue's measure theory, I recommend this 4-page PDF by G.H. Meisters. (NB: His weird ∁ symbol means complement.)
That doesn’t cover the measurement of probability spaces, functional spaces, or even more abstract spaces. But I don’t have an equally great reference for those.
Oh, I forgot to say: why does anyone care about measurability? Measure theory is just a highly technical prerequisite to true understanding of a lot of cool subjects — like complexity, signal processing, functional analysis, Wiener processes, dynamical systems, Sobolev spaces, and other interesting and relevant such stuff.
It’s hard to do very much mathematics with those sorts of things if you can’t even say how big they are.
## Nonterminating decimals do not make sense.
The Banach-Tarski paradox proves how f#cked up the real numbers are. Logical peculiarities confuse our intuitions about “length”, “density”, “volume”, etc. within the continuum (ℝ) of nonterminating decimals. Which is why Measure Theory is a graduate-level mathematics course. These peculiarities were noticed around the turn of the 20th century and perhaps never satisfactorily resolved. (Hence I disagree with the use of real numbers in economic theory: they aren’t what you think they are.)
Axiom of Choice → Garbage
The paradox states that if you assumed the axiom of choice (or Zorn’s Lemma or the well-ordering of ℝ or the trichotomy law), then you could take one ball and make two balls out of it. It follows that you could make seven balls or thirty-seven out of just one. That doesn’t sound like real matter (it’s not; it’s the infinitely infinite mathematical continuum).
I can’t think of anything in real life that that does sound like. Conservation-of-mass-type constraints hold in economics (finite budget), probability (∑pᵢ=1), text mining, and in all the phase and state spaces I can think of as well. Generally you don’t make something out of nothing.
If it’s broke, throw it out.
The logical rule-of-inference Modus Tollens says that if A→B and ¬B, then ¬A. For example if leaving the fridge open overnight leads to rotten food, and the food is not rotten, I conclude that the fridge was not open overnight. Let A = Axiom of Choice and B = Banach-Tarski Paradox. Axiom of Choice leads to Banach Tarski paradox; said paradox is false; so why don’t we reject the Axiom of Choice? I have never gotten a satisfactory answer about that. ℝ is still used as a base corpus in dynamical systems, economics, fuzzy logic, finance, fluid dynamics, and as far as I can tell, everywhere.
How does the proof of paradox work?
The proof gives instructions of how to:
1. Partition a solid ball into five unmeasurable disjoint subsets.
2. Move them around (rigidly, without adding mass).
3. Get a new solid ball, whilst leaving the first ball intact.
The internet has several readable, detailed explanations of the above. You’ll end up reading about Fuchsian groups, Henri Lebesgue’s measure, and hyperbolic geometry (& the Poincaré disk) along the way.
Stan Wagon has also written a Mathematica script to display the subsets in a hyperbolic geometry (whence these pictures come). Thanks, Stan! | 2,503 | 10,724 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2014-15 | latest | en | 0.920856 |
http://kr.mathworks.com/help/matlab/ref/factor.html?s_tid=gn_loc_drop&nocookie=true | 1,430,753,867,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1430454576828.73/warc/CC-MAIN-20150501042936-00091-ip-10-235-10-82.ec2.internal.warc.gz | 112,816,137 | 9,246 | Documentation
라이선스가 부여된 사용자만 번역 문서를 볼 수 있습니다. 번역 문서를 보려면 로그인하십시오.
factor
Syntax
• `f = factor(n)` example
Description
example
````f = factor(n)` returns a row vector containing the prime factors of `n`. Vector `f` is of the same data type as `n`.```
Examples
collapse all
Prime Factors of Double Integer Value
`f = factor(200)`
```f = 2 2 2 5 5```
Multiply the elements of `f` to reproduce the input value.
`prod(f)`
```ans = 200```
Prime Factors of Unsigned Integer Value
```n = uint16(138); f = factor(n)```
```f = 2 3 23```
Multiply the elements of `f` to reproduce `n`.
`prod(f)`
```ans = 138```
Input Arguments
collapse all
`n` — Input valuereal, nonnegative integer scalar
Input value, specified as a real, nonnegative integer scalar.
Example: `10`
Example: `int16(64)`
Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | 295 | 913 | {"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-2015-18 | latest | en | 0.357243 |
https://www.livestrong.com/article/444608-how-long-does-it-take-to-lose-a-pant-size/ | 1,721,566,949,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517701.96/warc/CC-MAIN-20240721121510-20240721151510-00710.warc.gz | 756,287,851 | 70,450 | # How Long Does It Take to Lose a Pant Size?
How long it takes to drop a pants size depends on factors like your starting weight and waist circumference.
Image Credit: coldsnowstorm/iStock/GettyImages
Some people measure their weight loss by how many pounds it takes to drop a jean size. And your rate of weight loss can potentially help gauge how long it will take to lose a pants size, too.
Here's what you need to know about weight loss and its effects on body size to help you estimate a timeline for swapping out your clothing.
Video of the Day
Video of the Day
## How Many Pounds Is a Pant Size?
Unfortunately, no weight loss pant-size calculator is perfectly accurate, which is why there's no clear-cut answer for how much weight to lose to drop a pant size. That's because where you carry weight can depend on your genetics, body type and age, according to Penn Medicine.
What's more, shedding pounds doesn't always immediately translate to a smaller pants size depending on what ratio of body weight you lose. For instance, if someone who weighs 350 pounds loses 10 pounds, they may still wear the same clothing. On the other hand, a 100-pound person who loses 10 pounds may have to get smaller pants.
Similarly, the type of weight you lose can also determine how shedding pounds affects your body size.
For instance, muscle is denser than fat, according to the Cleveland Clinic. Losing fat may thus have a more significant effect on your overall body size than burning muscle (and besides, you want to preserve muscle to support strength and additional calorie burn, per the Cleveland Clinic).
So if you're wondering what weight is a size small or what's a size 10 jeans weight, it can vary from person to person.
Instead, it appears that waist circumference is a more effective correlate to pants size than weight. According to a December 2020 study in Preventive Medicine Reports, the bigger someone's waist circumference, the larger their pant size.
How Many Pounds to Drop a Shirt Size?
Just like there's no one number for how many pounds it takes to lose a pant size, there's no straightforward answer for how much weight loss is needed to lose a size in shirts.
That's because dropping a shirt size also depends on factors like your starting weight and body type.
## How Long Does It Take to Drop a Pants Size?
Because clothing sizes don't always correlate to specific weights, there's no straightforward timeframe for how long it will take you to downsize pants. | 518 | 2,498 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2024-30 | latest | en | 0.942549 |
https://support.office.com/en-us/article/CHOOSE-function-fc5c184f-cb62-4ec7-a46e-38653b98f5bc?CTT=5&origin=HA010342655&CorrelationId=f66acec2-d75e-4345-b680-56c427b8fb64&ui=en-US&rs=en-US&ad=US | 1,438,254,670,000,000,000 | text/html | crawl-data/CC-MAIN-2015-32/segments/1438042987171.38/warc/CC-MAIN-20150728002307-00192-ip-10-236-191-2.ec2.internal.warc.gz | 902,366,668 | 7,896 | CHOOSE function
# CHOOSE function
This article describes the formula syntax and usage of the CHOOSE function in Microsoft Excel.
## Description
Uses index_num to return a value from the list of value arguments. Use CHOOSE to select one of up to 254 values based on the index number. For example, if value1 through value7 are the days of the week, CHOOSE returns one of the days when a number between 1 and 7 is used as index_num.
## Syntax
CHOOSE(index_num, value1, [value2], ...)
The CHOOSE function syntax has the following arguments:
• Index_num Required. Specifies which value argument is selected. Index_num must be a number between 1 and 254, or a formula or reference to a cell containing a number between 1 and 254.
• If index_num is 1, CHOOSE returns value1; if it is 2, CHOOSE returns value2; and so on.
• If index_num is less than 1 or greater than the number of the last value in the list, CHOOSE returns the #VALUE! error value.
• If index_num is a fraction, it is truncated to the lowest integer before being used.
• Value1, value2, ... Value 1 is required, subsequent values are optional. 1 to 254 value arguments from which CHOOSE selects a value or an action to perform based on index_num. The arguments can be numbers, cell references, defined names, formulas, functions, or text.
## Remarks
• If index_num is an array, every value is evaluated when CHOOSE is evaluated.
• The value arguments to CHOOSE can be range references as well as single values.
For example, the formula:
=SUM(CHOOSE(2,A1:A10,B1:B10,C1:C10))
evaluates to:
=SUM(B1:B10)
which then returns a value based on the values in the range B1:B10.
The CHOOSE function is evaluated first, returning the reference B1:B10. The SUM function is then evaluated using B1:B10, the result of the CHOOSE function, as its argument.
## Examples
Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.
Data 1st Nails 2nd Screws 3rd Nuts Finished Bolts Formula Description Result =CHOOSE(2,A2,A3,A4,A5) Value of the second list argument (value of cell A3) 2nd =CHOOSE(4,B2,B3,B4,B5) Value of the fourth list argument (value of cell B5) Bolts =CHOOSE(3,"Wide",115,"world",8) Value of the third list argument world
### Example 2
Data 23 45 12 10 Formula Description (Result) Result =SUM(A2:CHOOSE(2,A3,A4,A5)) Sums the range A2:A4. The CHOOSE function returns A4 as the second part of the range for the SUM function. 80
Applies To: Excel 2010, Excel Starter, Excel 2013, Excel Online, Excel 2016 for Mac, Excel for Mac 2011, Excel 2007
| 719 | 2,726 | {"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-2015-32 | latest | en | 0.772347 |
https://www.coursehero.com/file/5673049/SolutiosnproblemsChp2/ | 1,521,562,072,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647498.68/warc/CC-MAIN-20180320150533-20180320170533-00494.warc.gz | 763,881,584 | 259,197 | {[ promptMessage ]}
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# Solutiosn.problems.Chp2 - Problem 2.1 Amsterdam and New...
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Problem 2.1 Amsterdam and New York Assumptions Values Buy a US dollar in Amsterdam for (€/\$) 0.8200 Which is equivalent, the reciprocal (\$/€) \$1.2195 Buy a euro in NY for (\$/€) \$1.2200 Which is equivalent, the reciprocal (€/\$) 0.8197 In Amsterdam, one can buy a U.S. dollar for €0.8200. In New York, one can buy a euro for \$1.22. What is the foreign exchange rate between the dollar and the euro?
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Problem 2.2 Peso exchange rate change Calculation of Percentage Change in Value Values Initial exchange rate (peso/\$) 3.20 Devalued exchange rate (peso/\$) 5.50 Percentage change in peso value -41.82% (beginning rate - ending rate) / (ending rate) In December 1994 the government of Mexico officially changed the value of the Mexican peso from 3.2 pesos per dollar to 5.5 pesos per dollar. Was this a depreciation, devaluation, appreciation, or revaluation? Explain. Anytime a government sets or resets the value of its currency, it is a managed or fixed exchange rate. If that is the case, any change in its official value must be either a "revaluation" or "devaluation." In this case, a devaluation. This is evident from the fact that it now takes more pesos per U.S. dollar, so its value is less or devalued. In terms of the percentage change calculation, this is indicated by the negative percentage change.
Problem 2.3 Good as gold Gold Standard Assumptions Values What If Price of an ounce of gold in US dollars (\$/oz) \$20.67 \$38.00 Price of an ounce of gold in British pounds (₤/oz) £4.2474 £4.2474 What is the implied \$/₤ exchange rate? \$4.8665 \$8.9466 (dollar price of an ounce / pound price of an ounce) Under the gold standard, the price of an ounce of gold in U.S. dollars was \$20.67, while the price of that same ounce in British pounds was £ 4.2474. What would the exchange rate between the dollar and the pound be if the U.S. dollar price had been \$38.00 per ounce?
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Problem 2.4 Gold standard Assumptions Values Price of an ounce of gold in US dollars (\$/oz) \$20.67 Price of an ounce of gold in French francs (FF/oz) 310.00 What is the implied French franc/US dollar exchange rate? 15.00 (French franc price of an ounce / US dollar price of an ounce) …. Or if expressed as \$/FF \$0.0667 Before World War I, \$20.67 was needed to buy one ounce of gold. If, at the same time one ounce of gold could be purchased in France for FF310.00, what was the exchange rate between French francs and U.S. dollars?
Problem 2.5 Spot rate -- customer Assumptions Values Spot rate on Mexican peso (pesos/US\$) 10.8000 Your company buys this amount of pesos 180,000.00 What is the cost in US\$? \$16,666.67 (the peso amount divided by the spot exchange rate) Spot transactions are settled in two business days, so in this case, Wednesday. The spot rate for Mexican pesos is Ps10.80/\$. If your company buys Ps180,000 spot from your bank on Monday, how much must your company pay and on what date?
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Problem 2.6 Hong Kong dollar and the Chinese yuan Assumptions Values Original Chinese yuan peg to the dollar, yuan/\$ 8.28 Revalued Chinese yuan to the dollar, yuan/\$ 8.11 Hong Kong dollar peg to the US dollar, HK\$/\$ 7.80 Original HK\$/Yuan cross rate 0.9420 HK\$/Yuan = (HK\$/\$) x (\$/Yuan) New HK\$/Yuan cross rate 0.9618 HK\$/Yuan = (HK\$/\$) x (\$/Yuan) The Hong Kong dollar has long been pegged to the U.S. dollar at HK\$7.80/\$. When
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Solutiosn.problems.Chp2 - Problem 2.1 Amsterdam and New...
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Ask a homework question - tutors are online | 1,127 | 4,187 | {"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} | 3.765625 | 4 | CC-MAIN-2018-13 | latest | en | 0.839105 |
https://forums.aat.org.uk/Forum/discussion/445869/valuation-help | 1,701,480,922,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100309.57/warc/CC-MAIN-20231202010506-20231202040506-00898.warc.gz | 308,234,375 | 20,116 | # Valuation help
Users Awaiting Email Confirmation Posts: 1 New contributor 🐸
Hey everyone, could anyone help me with the following question?
I've got the first part as minus £500 off the inventory, the second i am not sure about. The third i have as plus £350 to the inventory. I don't get any of the answers provided below, so probably got this wrong.
"At the year-end, a business valued its inventory at cost of £106,800.00 However, since the valuation was carried out the following matters have come to light, this means that the original inventory valuation may need to be amended:
One item of inventory is damaged. The item cost £1,000.00, repairs costing £250.00 are necessary to get the item into a saleable condition. The item will then be sold in a 'clearance' sale for £750.00.
One item of inventory which cost the business £500.00 is now obsolete and is to be scrapped.
There are 10 items of inventory, the packaging on which has become damaged. The items cost the business £60.00 each, but they now have to be repackaged; the repackaging will cost £5.00 per item. The items will then be sold at £100.00 each.
Based on the information provided above, indicate which one of the following figures represents the amended inventory valuation:
The answers are £105,750, £107,050, £105,800, £105,300. "
• Registered Posts: 248 Dedicated contributor 🌟 🐵 🌟
I haven't done a question like this for years, should be fun.
I have the damaged inventory as -
Original cost = £1000
Repairs = £250
Total cost = £1250
Net realisable value = £750
Write-off = £1250-£750 = £500
Obsolete inventory -
Write-off to liquidation value = £500
Repackaged inventory -
Original cost = 10 x £60 = £600
Repackaging costs = 10 x £5 = £50
Total cost = £650
Net realisable value = 10 x £100 = £1000
Cost lower than NRV so only an increase of £50 necessary.
Total overall net change £106,800 - £500 -£500 +£50
I don't have one of the answers either.
AAT
Level 2 - 2011
Level 3 - 2012
Level 4 - 2013
ACCA
F4 - Corporate Law - Dec 2015 (passed)
F5 - Performance Management - Dec 2014 (passed)
F6 - Taxation - Dec 2013 (passed)
F7 - Financial Reporting - Jun 2014 (passed)
F8 - Audit & Assurance - Dec 2015 (passed)
F9 - Financial Management - Jun 2015 (passed)
• Registered Posts: 248 Dedicated contributor 🌟 🐵 🌟
£105,800.00
What's the basis for ignoring the damaged packaging?
Is it included in the NRV?
As in... Net realisable value = £1,000 - £50 = £950
AAT
Level 2 - 2011
Level 3 - 2012
Level 4 - 2013
ACCA
F4 - Corporate Law - Dec 2015 (passed)
F5 - Performance Management - Dec 2014 (passed)
F6 - Taxation - Dec 2013 (passed)
F7 - Financial Reporting - Jun 2014 (passed)
F8 - Audit & Assurance - Dec 2015 (passed)
F9 - Financial Management - Jun 2015 (passed)
• Registered Posts: 248 Dedicated contributor 🌟 🐵 🌟
The packaging does not affect inventory.
It would impact the COS, however.
The packaging is part of the inventory surely? The original packaging price would have been included in the original inventory price.
So unless the packaging is part of the selling costs in the NRV calculation (NRV = market price - selling costs), or delivery packaging that forms part of carriage costs, it doesn't make too much sense.
AAT
Level 2 - 2011
Level 3 - 2012
Level 4 - 2013
ACCA
F4 - Corporate Law - Dec 2015 (passed)
F5 - Performance Management - Dec 2014 (passed)
F6 - Taxation - Dec 2013 (passed)
F7 - Financial Reporting - Jun 2014 (passed)
F8 - Audit & Assurance - Dec 2015 (passed)
F9 - Financial Management - Jun 2015 (passed) | 990 | 3,542 | {"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} | 3.203125 | 3 | CC-MAIN-2023-50 | latest | en | 0.953302 |
http://m.hanspub.org/journal/paper/13236 | 1,542,775,645,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039747024.85/warc/CC-MAIN-20181121032129-20181121054129-00268.warc.gz | 211,865,413 | 6,975 | Vol.4 No.2 (March 2014)
# Riemann面——平面上的空间结构Riemann Surface—3-Dimension Construction on a Plane
Riemann面是复变函数课程中的一个很有特色的内容，也是学生学习中的一个难点。本文从代数和几何这两个视度，简单分析了Riemann面的作用。文中的描述，试图简单、直观、易懂，为初学者了解Riemann面，提供点滴直接的帮助。
Riemann surface is a characteristic content in the course of complex variable function, which is also a difficult point in teaching. Our paper, viewing the problem from both algebra and geometry, simply analyses the action of the Riemann surface. The description here is as simple and directive as possible. By this way, we wish that could provide a little help to the beginner.
Top | 190 | 596 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-47 | latest | en | 0.671854 |
https://watchers.news/2011/11/05/a-guide-for-solar-watchers-pt-1/ | 1,660,395,144,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571950.76/warc/CC-MAIN-20220813111851-20220813141851-00789.warc.gz | 536,417,984 | 76,308 | # A Guide for Solar Watchers – Part 1
## A Guide for Solar Watchers pt.1 – Sun basics
For all those who don't quit understand what is happening with our Sun and what is space weather we decided to make A Guide for Solar Watchers. We will start with solar basics – structure, characteristics, solar activity etc. In addition we will present spacecrafts and observatories which task is to observe solar activity. And at the end we will show you how to read solar charts, diagrams and other solar data to make sure you understand what you are reading in our Solar activty posts. So, let's start from the beginning.
Our solar system is composed of the Sun and all things which orbit around it: the planets, asteroids, and comets.
Mass: 1.99 x 10^30 kg (333 000 times the mass of the Earth).
Luminosity (rate of energy radiation): 3.86 x 10^26 W.
Mean density: 1400 kg/m3 (1.4 times that of water).
The Sun is 150 million kilometers (93 million miles) away from the Earth (this distance varies slightly throughout the year, because the Earth's orbit is an ellipse and not a perfect circle) and this distance we measure in AU (Astronomical units. It would take 8 minutes and 19 seconds from Sun to Earth by speed of light.
Crude diagram of Sun shining light on Earth with distance marked. Sunlight takes about 8 minutes, 19 seconds to reach the Earth (based on the average distance).
1 AU = about 149,597,870.7 kilometres (92,955,807.3 mi)= 8.317 light minutes
1 light-year ≈ 63,241 AU
The Sun is a star – with a diameter of about 1.4 million kilometers (860,000 miles) it would take 110 Earths strung together to be as long as the diameter of the Sun. The Sun is mostly made up of hydrogen (about 92.1% of the number of atoms, 75% of the mass) and helium can also be found in the Sun (7.8% of the number of atoms and 25% of the mass). The other 0.1% is made up of heavier elements, mainly carbon, nitrogen, oxygen, neon, magnesium, silicon and iron. Its mass (about 2×1030 kilograms, 330,000 times that of Earth) accounts for about 99.86% of the total mass of the Solar System.
Stars like the Sun shine for nine to ten billion years. The Sun is about 4.5 billion years old, judging by the age of moon rocks. Based on this information, current astrophysical theory predicts that the Sun will become a red giant in about five billion (5,000,000,000) years.
Earth compared to Sun and solar flare
The Sun is neither a solid nor a gas but is actually plasma. This plasma is tenuous and gaseous near the surface, but gets denser down towards the Sun's fusion core. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields. As the Sun consists of a plasma and is not solid, it rotates faster at its equator than at its poles. This behavior is known as differential rotation, and is caused by convection in the Sun and the movement of mass, due to steep temperature gradients from the core outwards.
4 minute overview video of the Sun
## STRUCTURE OF THE SUN
The Sun can be divided into six layers. From the center out, the layers of the Sun are as follows: the solar interior composed of the core (which occupies the innermost quarter or so of the Sun's radius), the radiative zone, and the the convective zone, then there is the visible surface known as the photosphere, the chromosphere, and finally the outermost layer, the corona.
(Source: SOHO)
The energy produced through fusion in the Sun's core powers the Sun and produces all of the heat and light that we receive here on Earth. The process by which energy escapes from the Sun is very complex. Since we can't see inside the Sun, most of what astronomers know about this subject comes from combining theoretical models of the Sun's interior with observational facts such as the Sun's mass, surface temperature, and luminosity (total amount of energy output from the surface).
All of the energy that we detect as light and heat originates from nuclear reactions deep inside the Sun's high-temperature "core." This core extends about one quarter of the way from the center of Sun (where the temperature is around 15.7 million kelvin (K), or 28 million degrees Fahrenheit) to its surface, which is only 5778 K or 5505 °C.
This diagram shows a cross-section of a solar-type star. (Source: High Energy Astrophysics Science Archive Research Center, NASA Goddard Space Flight Center)
In its core, the Sun fuses 620 million metric tons of hydrogen each second. Once regarded by astronomers as a small and relatively insignificant star, the Sun is now thought to be brighter than about 85% of the stars in the Milky Way galaxy, most of which are red dwarfs.
## SOLAR CYCLES, SUN's MAGNETIC FIELD
The Sun has a complicated and changing magnetic field, which forms things like sunspots and active regions. The magnetic field sometimes changes explosively, spitting out clouds of plasma and energetic particles into space and sometimes even towards Earth. The solar magnetic field changes on an 11 year cycle. Every solar cycle, the number of sunspots, flares, and solar storms increases to a peak, which is known as the solar maximum. Then, after a few years of high activity, the Sun will ramp down to a few years of low activity, known as the solar minimum. This pattern is called the "sunspot cycle", the "solar cycle", or the "activity cycle".
Solar Cycle 24
The Sun's magnetic field leads to many effects that are collectively called solar activity, including sunspots on the surface of the Sun, solar flares, and variations in solar wind that carry material through the Solar System. Effects of solar activity on Earth include auroras at moderate to high latitudes, and the disruption of radio communications and electric power. Solar activity is thought to have played a large role in the formation and evolution of the Solar System. Solar activity changes the structure of Earth's outer atmosphere.
The solar magnetic field extends well beyond the Sun itself. The magnetized solar wind plasma carries Sun's magnetic field into the space forming what is called the interplanetary magnetic field.
## SUNSPOTS
Sunspots are regions of intense magnetic activity where convection is inhibited by strong magnetic fields, reducing energy transport from the hot interior to the surface. The magnetic field causes strong heating in the corona, forming active regions that are the source of intense solar flares and coronal mass ejections. Sunspots expand and contract as they move across the surface of the Sun and can be as large as 80,000 kilometers (50,000 mi) in diameter, making the larger ones visible from Earth without the aid of a telescope. They may also travel at relative speeds ("proper motions") of a few hundred m/s when they first emerge onto the solar photosphere.
Seen in a close-up, sunspots have a distinctive appearance as seen in this solar telescope photo; the surrounding surface contains small, irregular bright areas called granules which are the upwelled part of numerous local convection currents that carry hot Hydrogen gas to the photosphere (Earth shown for scale). (Source: RST Cosmology)
When a magnetic field line arcs away from the Sun's surface as a coronal loop, plasma is drawn along by the magnetic field, forming a chromospheric prominence/filament. When the loop reconnects to another part of the Sun's magnetic field, field lines from different regions are broken and joined together with field lines from other regions. (This is thought to occur between field lines in the loop and those that surround and extend into space). This reconnection generates an immense electric currents that flow to try and oppose the magnetic change. This releases colossal amounts of energy
(the electrical resistance of the plasma heats it up by dissipating the electric current) resulting in flares, coronal loops, prominences/filaments and coronal mass ejections.
## SOLAR WIND
The Sun's hot corona continuously expands in space creating the solar wind, a stream of charged particles that extends to the heliopause at roughly 100 astronomical units. The bubble in the interstellar medium formed by the solar wind, the heliosphere, is the largest continuous structure in the Solar System. Solar wind mostly consists of electrons and protons with energies usually between 1.5 and 10 keV. The stream of particles varies in temperature and speed over time. These particles can escape the Sun's gravity because of their high kinetic energy and the high temperature of the corona.
The solar wind creates the heliosphere, a vast bubble in the interstellar medium that surrounds the Solar System. Other phenomena include geomagnetic storms that can knock out power grids on Earth, the aurora (northern and southern lights), and the plasma tails of comets that always point away from the Sun.
## SOLAR FLARES
Solar flares are massive explosions in the Sun's atmosphere that brighten in a few minutes and then fade over the course of about an hour. They involve all layers of the atmosphere (photosphere, chromosphere and corona). A typical flare ejects plasma at speeds close to the speed of light. Flares emit a burst of electromagnetic radiation, in the forms of visible light, radio waves and gamma waves. At the site of reconnection, it is though that a helix of unconnected magnetic field lines radiates from the Sun, carrying plasma with it in a coronal mass ejection.
Example of solar flare
Flares occur in active regions around sunspots, where intense magnetic fields penetrate the photosphere to link the corona to the solar interior. Flares are powered by the sudden (timescales of minutes to tens of minutes) release of magnetic energy stored in the corona. The same energy releases may produce coronal mass ejections (CME), although the relation between CMEs and flares is still not well established.
X-rays and UV radiation emitted by solar flares can affect Earth's ionosphere and disrupt long-range radio communications. Direct radio emission at decimetric wavelengths may disturb operation of radars and other devices operating at these frequencies.
Active region 10486, already under close scrutiny by several instruments on SOHO and other satellites, as well as numerous ground observatories, started up a spectacular two-part show in the morning on Tuesday 28 October 2003. An X 17.2 flare, the second largest flare observed by SOHO, was setting off a strong high energy proton event and a fast-moving Coronal Mass Ejection, hitting Earth early on Wednesday 29 October. (Source: SOHO)
Solar flares are classified as A, B, C, M or X according to the peak flux (in watts per square meter, W/m2) of 100 to 800 picometer X-rays near Earth, as measured on the GOES spacecraft. Each class has a peak flux ten times greater than the preceding one, with X class flares having a peak flux of order 10−4 W/m2. Within a class there is a linear scale from 1 to 9, so an X2 flare is twice as powerful as an X1 flare, and is four times more powerful than an M5 flare. The more powerful M and X class flares are often associated with a variety of effects on the near-Earth space environment.
Solar flares strongly influence the local space weather in the vicinity of the Earth. They can produce streams of highly energetic particles in the solar wind, known as a solar proton event, or "coronal mass ejection" (CME). These particles can impact the Earth's magnetosphere and present radiation hazards to spacecraft, astronauts and cosmonauts.
## CORONAL MASS EJECTION (CME)
A coronal mass ejection (CME) is a massive burst of solar wind, other light isotope plasma, and magnetic fields rising above the solar corona or being released into space.
Coronal mass ejections are often associated with other forms of solar activity, most notably solar flares. Most ejections originate from active regions on Sun's surface, such as groupings of sunspots associated with frequent flares. Near solar maximum the Sun produces about 3 CMEs every day, whereas near solar minimum there is about 1 CME every 5 days.
Normal Condition: Earth’s magnetic field deflects the charged particles streaming out from the Sun
The ejected material is a plasma consisting primarily of electrons and protons, but may contain small quantities of heavier elements such as helium, oxygen, and even iron. It is associated with enormous changes and disturbances in the coronal magnetic field.
When the ejection is directed towards the Earth and reaches it as an interplanetary CME (ICME), the shock wave of the traveling mass of Solar Energetic Particles causes a geomagnetic storm that may disrupt the Earth's magnetosphere, compressing it on the day side and extending the night-side magnetic tail. When the magnetosphere reconnects on the nightside, it releases power on the order of terawatt scale, which is directed back toward the Earth's upper atmosphere.
Earth directed coronal mass ejection
This process can cause particularly strong auroras in large regions around Earth's magnetic poles. These are also known as the Northern Lights (aurora borealis) in the northern hemisphere, and the Southern Lights (aurora australis) in the southern hemisphere. Coronal mass ejections, along with solar flares of other origin, can disrupt radio transmissions and cause damage to satellites and electrical transmission line facilities, resulting in potentially massive and long-lasting power outages.
Solar particles interact with Earth's magnetosphere.
Humans in space or at high altitudes, for example, in airplanes, risk exposure to intense radiation. Short-term damage may include skin irritation with potential increased risk of developing skin cancer, but it's likely that any affected individuals would recover from any such exposure.
## GEOMAGNETIC STORM
A geomagnetic storm is a temporary disturbance of the Earth's magnetosphere caused by a disturbance in the interplanetary medium. A geomagnetic storm is caused by a solar wind shock wave and/or cloud of magnetic field which interacts with the Earth's magnetic field. The increase in the solar wind pressure initially compresses the magnetosphere and the solar wind magnetic field will interact with the Earth’s magnetic field and transfer an increased amount of energy into the magnetosphere. Both interactions cause an increase in movement of plasma through the magnetosphere (driven by increased electric fields inside the magnetosphere) and an increase in electric current in the magnetosphere and ionosphere.
(Source: NASA)
During the main phase of a geomagnetic storm, electric current in the magnetosphere create magnetic force which pushes out the boundary between the magnetosphere and the solar wind. The disturbance in the interplanetary medium which drives the geomagnetic storm may be due to a solar coronal mass ejection (CME) or a high speed stream (CIR) of the solar wind originating from a region of weak magnetic field on the Sun’s surface. The frequency of geomagnetic storms increases and decreases with the sunspot cycle. CME driven storms are more common during the maximum of the solar cycle and CIR driven storms are more common during the minimum of the solar cycle.
Aurora Borealis or Northern Light (Credit: KaseyJoan)
### EFFECTS OF GEOMAGNETIC STORMS
Intense solar flares release very-high-energy particles that can cause radiation poisoning to humans (and mammals in general) in the same way as low-energy radiation from nuclear blasts.
Earth's atmosphere and magnetosphere allow adequate protection at ground level, but astronauts in space are subject to potentially lethal doses of radiation. The penetration of high-energy particles into living cells can cause chromosome damage, cancer, and a host of other health problems. Large doses can be fatal immediately.
Solar protons with energies greater than 30 MeV are particularly hazardous. In October 1989, the Sun produced enough energetic particles that, if an astronaut were to have been standing on the Moon at the time, wearing only a space suit and caught out in the brunt of the storm, he would probably have died; the expected dose would be about 7000 rem. Note that astronauts who had time to gain safety in a shelter beneath moon soil would have absorbed only slight amounts of radiation. The cosmonauts on the Mir station were subjected to daily doses of about twice the yearly dose on the ground, and during the solar storm at the end of 1989 they absorbed their full-year radiation dose limit in just a few hours.
Geomagnetic Storms – the effects of Space Weather on Modern Technology (Source: SpaceWeather.gc.ca)
Solar proton events can also produce elevated radiation aboard aircraft flying at high altitudes. Although these risks are small, monitoring of solar proton events by satellite instrumentation allows the occasional exposure to be monitored and evaluated, and eventually the flight paths and altitudes adjusted in order to lower the absorbed dose of the flight crews.
The K-index quantifies disturbances in the horizontal component of earth's magnetic field with an integer in the range 0-9 with 1 being calm and 5 or more indicating a geomagnetic storm. It is derived from the maximum fluctuations of horizontal components observed on a magnetometer during a three-hour interval.
So, this image bellow is the summary of terms we defined above:
A composite diagram of Solar structure (made with photos courtesy of SOHO/NASA and a Pov-Ray representation of the interior structure). The labels are as follows: C: core; CME: coronal mass ejection; Co: corona; CoSt: coronal streamers; CS: chromosphere; CZ: convective zone; F: filament; Fl: flare; G: granules; P: plages (bright spots); Pr: prominence; RZ: radiative zone; SG: supergranules; Sp: sprites; SS: sunspots; SW: solar wind.
(Compiled material from SOHO, Wikipedia, Cronodon)
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• New features and apps suggestions | 4,008 | 18,705 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2022-33 | longest | en | 0.920714 |
http://mathhelpforum.com/differential-geometry/23013-tetrahedron-unit-sphere.html | 1,553,109,212,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202450.86/warc/CC-MAIN-20190320190324-20190320212324-00208.warc.gz | 141,638,834 | 11,393 | # Thread: Tetrahedron in a unit sphere
1. ## Tetrahedron in a unit sphere
Hi everyone, i'm in need of help with a certain aspect of my project, hopefully someone has some suggestions:
Im doing a mesh morphing program for two arbitrary genus0 meshes, i'm using the method of Marc Alexa for implementation.
However i am stuck on a certain part which says:
'Choose a random regular tetrahedron with vertices on the unit sphere'.
Ive been searching for a few days now to find out how to construct a regular tetrahedron which fits exactly (more or less) inside a unit sphere.
From what i have read, i need to have a 'circumscribed' tetrahedron', which has the sphere going outside through all the vertices in the tetrahedron.
But i am having great difficulty programming this as i cannot work out how to determine how big the tetrahedron should be so that the vertices are on the surface of the sphere.
Any help or suggestions would be greatly appreciated.
Many Thanks
Dan
2. Look at this page Tetrahedron -- from Wolfram MathWorld
Are you looking for the circumradius?
3. Hi there,
Thanks. I already came across that page however, it was useful for understanding tetrehedron but was hard to think of implementing it. I've actually finished a class now that will generate a regular tetrahedron for a unit sphere, ill post it on here later.
4. For anyone thats interested:
public
class Tetrahedron {
/*
The standard equation for points on a sphere will be used:
x = r * cos(theta) * cos(phi)
y = r * sin(theta) * cos(phi)
z = r * sin(phi)
x^2 + y^2 + z^2 = 1 for the unit sphere
The angle theta goes around the equator 0 to 360 degrees, 0 to 2Pi
The angle phi goes from north pole 90 to -90 degrees, Pi/2 to -Pi/2
Radians = Pi * (angle_in_degrees) / 180
*/
public ArrayList<GL_Vertex> verts = new ArrayList();
public ArrayList<GL_Triangle> tris = new ArrayList();
doublePi = 3.141592653589793238462643383279502884197;
doublephiaa = -19.471220333; /* the phi angle needed for generation */
public Tetrahedron(){
for(int i = 0; i<4; i++)
{
GL_Vertex v =
new GL_Vertex();
}
double r = 1.0; /* any radius in which the polyhedron is inscribed */
double phia = Pi*phiaa/180.0; /* 1 set of three points */
double the120 = Pi*120.0/180.0;
double the = 0.0;
verts.get(0).pos.x = (float) 0.0;
verts.get(0).pos.y = (float) 0.0;
verts.get(0).pos.z = (float) r;
for(int i=1; i<4; i++)
{
verts.get(i).pos.x =(float) (r*Math.cos(the)*Math.cos(phia));
verts.get(i).pos.y =(float) (r*Math.sin(the)*Math.cos(phia));
verts.get(i).pos.z =(float) (r*Math.sin(phia));
the = the+the120;
}
for(int i=0; i<4; i++){
System.
out.println(verts.get(i).toString());
}
GL_Triangle tri0 =
new GL_Triangle(verts.get(0), verts.get(1), verts.get(2));
GL_Triangle tri1 =
new GL_Triangle(verts.get(0), verts.get(2), verts.get(3));
GL_Triangle tri2 =
new GL_Triangle(verts.get(0), verts.get(3), verts.get(1));
GL_Triangle tri3 =
new GL_Triangle(verts.get(1), verts.get(2), verts.get(3));
/* map vertices to 4 faces */
//polygon(0,1,2);
//polygon(0,2,3);
//polygon(0,3,1);
//polygon(1,2,3);
//Length of every edge 1.6329932 */
}
}
Based on algorithm from : Regular Polyhedron Generators | 923 | 3,179 | {"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-2019-13 | latest | en | 0.908193 |
http://www.cubefreak.net/speed/mgls/f2lc_llco.php | 1,519,047,826,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812665.41/warc/CC-MAIN-20180219131951-20180219151951-00102.warc.gz | 437,679,702 | 2,925 | F2L Last Corner + LLCO
These algorithms simultaneously fix the last F2L corner and correct the orientation of the last layer corners without disturbing the orientation of the last layer edges. I started generating these algorithms around US National 2004 in the hope of using the following as an alternative to the Fridrich Method:
Steps Algorithms Moves on avg. (FTM) Step 1: Cross Intuitive 6 Step 2: F2Lx3 Not considered algs 7x3 = 21 Step 3: F2Le+LLEO Intuitive 5.71 Step 4: F2Lc+LLCO 27+15+? x Step 5: PLL 21 11.21 Total 43.92+x
This method is the same as Ryan Heise's up to Step 3, but by fixing the orientation of the corners, it makes the last step PLL, which Fridrich cubers are already familiar with. For this method to have an average of moves less than that of Fridrich (54.43), Step 4 must be done in less than 10.51 moves on average. The advantage of this method is that it cuts the memorization of the numerous OLL algorithms completely and replaces them with easier algorithms.
At this point, I have only memorized a few cases that I use when those pattern come up during normal Fridrich solves. Since most patterns have quick 2-generator solutions, taking advantage of certain cases results in considerably easier solve.
Thanks to Andy Camann for his help with generating these algorithms (10, 14, 16, 22, 26, and 27), and to Ron van Bruchem for his Cube Solver. Algorithms using R and U only can be found: here.
Corner on Top - Facing Front
Code Pattern Algorithm 1 L'U2wRU2R'U2wLURF'L'FR'F'LFB'DBU'B'D'BL'D2LU2L'D2L 2 RUR'U'RU'R'URU'R'U2F'U2FU2F'U'FUF'U'FU 3 ULU'RUL'U'R'U'F'U'B'UFU'BR'D'LDRD'L'DDU'B'D'FDBD'F'LEF'U'FDF'UFU'F' 4 URUR'URUR'U2RU'R'R'FRF'URU'R'U'F'UFU'RU'R'U'RU2R'L'E2LURU'R'L'E2LURU'R'UR'U'R'U'R'URURURU'R'U'R'U'R'U'RURUR 5 U2F2UBU'F2UB'U'RU'R'U2RUR'U'RUR'U'RU'R'U'RU'R'U'F'UFU'F2LFL'F 6 U2R'FRF'URU'R'UF'U'F 7 y'R'U'RURURURU'R'U'R'y'RURURU'R'U'R'U'R'U'RRUR'U'F'U'FUR'FRF'UF'U2FU'F'U'FU'F'U'FU2F'UFUF'UFRUR'U'RU'R'U2RU2R' 8 U'RU'R'U2RUR'U'RU'R'RU'RU'L'UR'U'LU'R'U2RUR' 9 RU'RU2R'U'RU'R2LEF'U'FUwL'U2LU2L' 10 (R U2 R2 U R')(U2 R' U' R U')(R U' R) 11 U'RU'R'U2RU'R'R'U2RUwRU'R'U'wUB2L'B'LB' 12 FR'F'R2U'R'U2F2LFL'FUR2UR'URU2R'UR' 13 U'F'U'FU2F'U'FL'E2URU'R'E2LBE2F'U'FUE2B'U2RU'R'U2RU2R'U'RU2R'U2R'FRF'U'RUR'U2F'U'FR'U'RU'DR'U'RD'R'U'R
Code Pattern Algorithm 14 (R2 U R' U)(R2 U' R2 U R')(U2 R2) 15 F'UFU2R2B'DB'D'B2R2 16 (R U2 R' U2)(R' U' R U' R')(U2 R2 U' R') 17 U'F'UFU'F'U'FUF'U'FRU2R'UR2U2R'U'RU'R2URU'R'UL'B2D'R'DB2L 18 U'RUR'U2RU'R'U2R'U'R'U'R'URURU'RUR'U2RU'R2U'R'U'RURURL'E2LU2RU2R'U2L'E2LF'U'FUBL2DFD'L2B'U2RU2R2U'R'U'RURURU2RU2R'U2R'U'R'U'R'URUR 19 F'U2FUR2B'DB'D'B2R2 20 U'RU'R'U'RU'R'URU2R'RUR'URU'R'URU'R'U'R'U'R'U'R'URUR 21 URUR'URUR'U'RU2R' 22 (R2 U2)(R U' R' U)(R2 U')(R U' R' U R') 23 U'RUR'U'RU2R2U'R'U'R'URURU'RUR'U'RU2R'U2R'U'R'U'RURUR 24 U'RU'R'U'RU'R'URU'R'URU2R' 25 U2RU'R'U2RU2R'U2RU'R'U'F'U'FU2F'U2FU'F'U2F 26 (R U' R' U)(R' U' R U' R')(U2 R2 U' R') 27 (U2 R U R')(U2 R' U' R U' R')(U2 R2 U R')
Corner on Top - Facing Up
Code Pattern Algorithm 28 [R'FRF']x3 29 29m 30 30m 31 31m 32 32m 33 33m 34 34m
Code Pattern Algorithm 35 35m 36 37 37m 38 39 39m 40 40m 41 41m 42 42m | 1,503 | 3,143 | {"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-2018-09 | latest | en | 0.800193 |
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# Space Math IX
This collection of activities is based on a weekly series of space science mathematics problems distributed during the 2012-2013 school year. They were intended for students looking for additional challenges in the math and physical science... (View More)
# MY NASA DATA: Deep Convective Clouds
Assuming the role of a meteorologist, students will proclaim one month as "Thunderstorm season" for their chosen study area. This decision will be based on analysis of deep convective cloud data downloaded from the Live Access Server. This lesson... (View More)
Audience: Elementary school
Materials Cost: Free
# MY NASA DATA: Graphing S'COOL Data--Temperature, Pressure and Humidity
Accessing, graphing and analyzing data are skills emphasized in this lesson. Using the S'COOL (Students' Cloud Observations On-Line) website, students will download NASA data on cloud cover, temperature, pressure, and relative humidity to generate a... (View More)
Audience: Elementary school, Middle school
Materials Cost: Free
# Space Survey
This is a lesson about society and space exploration. Learners will survey the public about their different opinions about space exploration and the use of robotics in space exploration. Then they will represent and analyze the results. This is... (View More)
# Mars Bingo
This is a classroom bingo-style game about vocabulary and concepts related to Mars and Mars missions. A list of vocabulary words and their definitions is provided. Note: Find the latest information and updates on Mars missions at the NASA Mars... (View More)
# Remote Sensing and Ground Truth Primer
This chapter provides background information to teachers about remote sensing. Topics include the electromagnetic spectrum, sensors and platforms, scale and resolution, geographic information systems, and ground truthing images. The reading is... (View More)
1 | 483 | 2,358 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-34 | longest | en | 0.87448 |
https://metanumbers.com/32825 | 1,686,234,792,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224655027.51/warc/CC-MAIN-20230608135911-20230608165911-00437.warc.gz | 435,976,280 | 7,647 | # 32825 (number)
32,825 (thirty-two thousand eight hundred twenty-five) is an odd five-digits composite number following 32824 and preceding 32826. In scientific notation, it is written as 3.2825 × 104. The sum of its digits is 20. It has a total of 4 prime factors and 12 positive divisors. There are 24,000 positive integers (up to 32825) that are relatively prime to 32825.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 5
• Sum of Digits 20
• Digital Root 2
## Name
Short name 32 thousand 825 thirty-two thousand eight hundred twenty-five
## Notation
Scientific notation 3.2825 × 104 32.825 × 103
## Prime Factorization of 32825
Prime Factorization 52 × 13 × 101
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 6565 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 32,825 is 52 × 13 × 101. Since it has a total of 4 prime factors, 32,825 is a composite number.
## Divisors of 32825
1, 5, 13, 25, 65, 101, 325, 505, 1313, 2525, 6565, 32825
12 divisors
Even divisors 0 12 12 0
Total Divisors Sum of Divisors Aliquot Sum τ(n) 12 Total number of the positive divisors of n σ(n) 44268 Sum of all the positive divisors of n s(n) 11443 Sum of the proper positive divisors of n A(n) 3689 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 181.177 Returns the nth root of the product of n divisors H(n) 8.89808 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 32,825 can be divided by 12 positive divisors (out of which 0 are even, and 12 are odd). The sum of these divisors (counting 32,825) is 44,268, the average is 3,689.
## Other Arithmetic Functions (n = 32825)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 24000 Total number of positive integers not greater than n that are coprime to n λ(n) 300 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3520 Total number of primes less than or equal to n r2(n) 48 The number of ways n can be represented as the sum of 2 squares
There are 24,000 positive integers (less than 32,825) that are coprime with 32,825. And there are approximately 3,520 prime numbers less than or equal to 32,825.
## Divisibility of 32825
m n mod m 2 3 4 5 6 7 8 9 1 2 1 0 5 2 1 2
The number 32,825 is divisible by 5.
• Arithmetic
• Deficient
• Polite
## Base conversion (32825)
Base System Value
2 Binary 1000000000111001
3 Ternary 1200000202
4 Quaternary 20000321
5 Quinary 2022300
6 Senary 411545
8 Octal 100071
10 Decimal 32825
12 Duodecimal 16bb5
20 Vigesimal 4215
36 Base36 pbt
## Basic calculations (n = 32825)
### Multiplication
n×y
n×2 65650 98475 131300 164125
### Division
n÷y
n÷2 16412.5 10941.7 8206.25 6565
### Exponentiation
ny
n2 1077480625 35368301515625 1160964497250390625 38108659622244072265625
### Nth Root
y√n
2√n 181.177 32.0185 13.4602 8.00278
## 32825 as geometric shapes
### Circle
Diameter 65650 206246 3.38501e+09
### Sphere
Volume 1.4815e+14 1.354e+10 206246
### Square
Length = n
Perimeter 131300 1.07748e+09 46421.6
### Cube
Length = n
Surface area 6.46488e+09 3.53683e+13 56854.6
### Equilateral Triangle
Length = n
Perimeter 98475 4.66563e+08 28427.3
### Triangular Pyramid
Length = n
Surface area 1.86625e+09 4.16819e+12 26801.5
## Cryptographic Hash Functions
md5 757ef3cdc6e89291664b0033ac007cfa 5ffe52394fd0556e32042c8ae1a92c4f6dd846fc caa4a423c6594ee207427f0a93c89ed01445104fea64c359b568d18486dcbb20 bf13353062d42b94680c97e85db287cfc88f8e0dcdfa77f9717fd8453f1fab14ff77c298d3487ca3d9fc8e124a120cbafbf1dac0ff61b565ef09b3d94c6d556c 385f7d83da5081c9398d8bd9e78dfa0d8b95d38b | 1,451 | 4,099 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2023-23 | latest | en | 0.806048 |
https://brainly.com/question/361797 | 1,484,638,286,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560279489.14/warc/CC-MAIN-20170116095119-00431-ip-10-171-10-70.ec2.internal.warc.gz | 815,314,089 | 8,709 | # What is 5x+84=10x what is it, what is it, what is it, what is it , what is it , what is it, what is it , what is it , what is it , what is it.
2
by TehZylem
2015-03-19T06:50:28-04:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
5x + 84 = 10x
84 = 10x - 5x
5x = 84
x = 84/5
x = 16 4/5
2015-03-19T06:52:04-04:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
5x + 84 = 10x
Subtract 5x to both sides:
84 = 5x
Divide 5 to both sides:
x = 16.8 | 291 | 971 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2017-04 | latest | en | 0.963129 |
https://www.physicsforums.com/threads/tough-motion-question-with-acceleration-time-and-distance.695705/ | 1,508,723,417,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825497.18/warc/CC-MAIN-20171023001732-20171023021732-00258.warc.gz | 954,130,885 | 18,246 | # Tough motion question with acceleration, time and distance
1. Jun 6, 2013
### incogserv
1. The problem statement, all variables and given/known data
A car 4m long came up behind a semi-trailer 20m long travelling at a steady rate of 72km/h. The car driver then overtook the truck. If the car pulled out from behind the truck with the front of the car 10m behind the rear of the truck and accelerated at 3.5 m/s2 until the rear of the car was 10m in front of the truck, how far would the car travel and how long would it take?
2. Relevant equations
v = u + at
v2 = u2 + 2ar
r = ut + 1/2 * at2
3. The attempt at a solution
What I've gotten so far is this:
• The back of the car is 34m behind the front of the truck
• They are travelling, initially, at 20m/s
• Therefore, the distance from the initial to final position is 44m (if both were stationary)
• The acceleration of the car is 3.5 m/s2
Could someone kindly lead me in the right direction?
Last edited: Jun 6, 2013
2. Jun 6, 2013
### voko
Very well so far.
Make use of the "if both were stationary" to solve it further. Is there a reference frame where this is true?
3. Jun 6, 2013
### incogserv
Sorry, I'm not sure what a reference frame is as I'm new to motion as part of physics (only in Year 9). Is it simply the direction of the vector? If so, no direction is given, and the vehicles are travelling in a straight line. I'll have another attempt at the question, concentrating more specifically on the "if both were stationary" comment.
4. Jun 6, 2013
### HallsofIvy
Staff Emeritus
There is NO "reference frame in which both are stationary" because they have different speeds.
(Well, initially they have the same speed and the truck maintains that speed so perhaps voko mean "in the reference frame of the truck".)
In the reference frame of the truck ("relative to the truck"), the truck's speed is 0 (any object's speed is 0 in its own refererncer frame), the car's speed is v= at= 3.5t so the distance traveled is d= 1.75t^2. The distance the rear of the car must travel is 44 m, as you say.
You could do this in the reference frame of the road- if you don't know "reference frames" that is probably how you would approach it. There the speed of the truck and the initial speed of the car is 20 m/s. In time t, the car will have moved 20t+ 1.75t^2 while the truck will have moved 20t meters. Now the car must move the 44 m above and the distance 20t that the truck moved.
You can, of course, do this in the reference frame of the car but it looks a bit odd. Now the car's speed is 0 and the truck will have a speed of -3.5t and so in time t will have moved -1.75 t^2. That must be equal to the distance the truck must go backward, relative to the car, -44 m. Of course, except that everything is negative, this is exactly the same as "relative to the truck".
Try doing all three ways and see that you get the same answers.
Last edited: Jun 6, 2013
5. Jun 6, 2013
### voko
Any motion is always with respect to SOMETHING. Typically one chooses some object as the "origin" and some directions as the "axes". This is a reference frame. I am sure this was told you when the concepts of displacement, velocity and acceleration were introduced.
The problem you have uses, implicitly, the road as the reference frame. In this frame, both the truck and car are not stationary, which makes analysis somewhat difficult.
But what if you choose the truck itself as a reference frame?
6. Jun 6, 2013
### ShreyasR
A reference frame is just a coordinate system from where you do the calculations. All the speeds and acceleration values are given with reference to the road. The truck is moving at 72 kmph with respect to the road. You can choose the truck as your frame of reference... If this is the case, you can say the road is moving backwards at 72 kmph with respect to the truck... (This is just to make you understand what is a frame of reference)
Take the origin as the front of the truck, and observe the back of the car (which will be accelerating from rest wrt truck at 3.5m/s2) and proceed with the calculations.
7. Jun 6, 2013
### incogserv
I haven't read what you guys have just said as I'm about to go to bed, but this is what I've done now:
Using r = ut + 1/2 * at2 and the quadratic formula,
1/2 * at2 + ut - r = 0
t = ( -u±√(u2- 4 * 1/2 * a * (-r)) ) / 3.5
∴ (if my calculations are correct...) t = ( ±2√(77) ) / 3.5 ≈ 5.01
I will continue tomorrow with the information you've just given :)
Last edited: Jun 6, 2013 | 1,219 | 4,520 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2017-43 | longest | en | 0.955776 |
bluefrogcreek.com | 1,695,321,221,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506029.42/warc/CC-MAIN-20230921174008-20230921204008-00430.warc.gz | 154,395,401 | 19,261 | ## A definitive guide to how much yarn you need for a C2C project and what size your project will be.
How much yarn do you need for your C2C project? How big will your project be in the end? Big questions with easy to find answers. All C2C patterns at Blue Frog Creek include a yarn guide listing the number of blocks for each color which will help you figure out approximately how much, and of what colors, you need.
#### How much yarn do I need?
First you need to know how much yarn you use in each block. The rest is simple math. I’m going to show you how.
#### First – Make a C2C swatch
The yarn you use, hook size, stitch and your personal gauge all factor in the amount of yarn you will need. Make your C2C swatch with all of your personal choices for the current project. This is the easiest way to get the information you need.
For example: I made a 5 x 5 block swatch using a 5mm hook, Red Heart yarn and a DC stitch.
#### Second – Measure your block size.
Your blocks should be square so you should be getting 1 number for the height and width. If your blocks are not square then you will need to adjust something. Blocks that are not square will skew a pattern made from squares. (Yes, of course, you can still do it if you want to. I just wanted to let you know what will happen.)
My blocks are ¾” high by ¾” wide.
#### Third – Measure your yarn
Frog your swatch. Measure the length of yarn that you used. Divide by the number of blocks that you had.
I used 516” of yarn which, divided by the 25 blocks, is almost 21” of yarn per block.
#### This is how much yarn you need
With your numbers use this calculation to determine the approximate amount needed for each color used. **Note: This doesn’t include yarn needed for traveling and weaving.
_______________ : _________________x____________________ = _____________ / 36” = ______________ (color): (# of blocks) multiplied by (inches in block) = (total inches) divide by 36″ = Yards Needed
So my project has 500 blocks of pink. I use 21″ per block. Multiply that by the 500 blocks I’m going to make. So I need 10,500 inches of yarn. Divided by 36″ in a yard I need 291.66 yards. Rounded up I need 292 yards of pink for my pattern.
Pink: 500 (# of blocks) x 21” (inches per block) = 10,500 (total inches) divided by 36” = 291.66 Total Yards
#### This is how big your project will be (approximately)
Use your block size to figure out the approximate size of your finished project. If you find that you will want a larger or smaller project you can adjust any of the factors as needed.
________________ x ______________ = ______________ (# of blocks across) multiplied by (your block width) = Total Width
________________ x ______________ = ______________ (# of blocks high) multiplied by (your block height) = Total Height
My blocks are ¾” wide by ¾” high. A project that is 64 blocks wide by 96 blocks high would be about 4′ by 6′.
Blocks wide: 64 x .75 = 48″ Total Width
Blocks high: 96 x .75 = 72″ Total Height
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• To: mathgroup at smc.vnet.net
• Subject: [mg106819] Re: [mg106792] The formula of Abraham Moivre
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Sun, 24 Jan 2010 05:41:14 -0500 (EST)
• References: <201001231236.HAA16448@smc.vnet.net>
```Here is a 2-step process which does it:
In[1]:= Clear[n, x, step1, step2];
In[2]:= step1 =
FullSimplify[ComplexExpand[(Cos[x] + I*Sin[x])^n],
Assumptions -> {Element[n, Integers], Element[x, Reals]}]
Out[2]= Cos[n Arg[E^(I x)]] + Sinh[n Log[E^(I x)]]
In[3]:= step2 = step1 /. {Arg[Exp[I*x_]] :> x, Log[Exp[I*x_]] :> I*x }
Out[3]= Cos[n x] + I Sin[n x]
The second step is manual and is correct under an assumption that -Pi<x<=Pi,
which we can safely take given that the original function is periodic.
Perhaps there are shorter and completely automatic ways based only on
built-in rules but I did not find them.
Regards,
Leonid
On Sat, Jan 23, 2010 at 4:36 AM, Arnold <sender999ster at gmail.com> wrote:
> How by means of Mathematica to transform (Cos [x] +I* Sin [x]) ^n in Cos
> [n*x] +I*Sin [n*x]?
>
> Thanks.
>
>
```
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#1
October 1st 05, 08:42 PM
kthenning Posts: n/a
Weighted Average Standard Deviation
I'm doing a customer survey where people have responded:
Agree strongly 331
Agree somewhat 100
Neither 50
Disagree somewhat 10
Disagree strongly 5
I want to assign a 1 to 5 score to each response (1=agree strongly) and get
the weighted average standard deviation using just the frequencys above. Is
this possible in Excel? If so, what would the equation be? I saw another
post about a wmean, wsd...but the equation returns a !NAME error.
#2
October 1st 05, 09:26 PM
Posts: n/a
kthenning wrote:
I'm doing a customer survey where people have responded:
Agree strongly 331
Agree somewhat 100
Neither 50
Disagree somewhat 10
Disagree strongly 5
I want to assign a 1 to 5 score to each response (1=agree strongly)
and get the weighted average standard deviation [...].
Is this possible in Excel?
There might be an easier way, but the following works,
and it straight-forwardly follows the math definitions.
Assume that A1:A5 has the values above, and B1:B5 has
the respective scores. Then the average score (C1) is:
=SUMPRODUCT(A1:A5,B1:B5)/(SUM(A1:A5)-1)
and the variance (C2) of the scores is:
=SUMPRODUCT(A1:A5,(B1:B5-C1)^2)/(SUM(A1:A5)-1)
The standard deviation is simply the square root of
the variance, namely:
=SQRT(C2)
Note: The formulas assume that you want to treat the
responses as samples. For the population average and
variance, remove "-1" in the denominator.
#3
October 1st 05, 09:44 PM
kthenning Posts: n/a
Thank you!!
" wrote:
kthenning wrote:
I'm doing a customer survey where people have responded:
Agree strongly 331
Agree somewhat 100
Neither 50
Disagree somewhat 10
Disagree strongly 5
I want to assign a 1 to 5 score to each response (1=agree strongly)
and get the weighted average standard deviation [...].
Is this possible in Excel?
There might be an easier way, but the following works,
and it straight-forwardly follows the math definitions.
Assume that A1:A5 has the values above, and B1:B5 has
the respective scores. Then the average score (C1) is:
=SUMPRODUCT(A1:A5,B1:B5)/(SUM(A1:A5)-1)
and the variance (C2) of the scores is:
=SUMPRODUCT(A1:A5,(B1:B5-C1)^2)/(SUM(A1:A5)-1)
The standard deviation is simply the square root of
the variance, namely:
=SQRT(C2)
Note: The formulas assume that you want to treat the
responses as samples. For the population average and
variance, remove "-1" in the denominator.
#4
October 2nd 05, 01:53 PM
Jerry W. Lewis Posts: n/a
#5
October 2nd 05, 05:03 PM
[email protected] Posts: n/a
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Related to electromagnetic radiation: Electromagnetic waves
energyenergy,
in physics, the ability or capacity to do work or to produce change. Forms of energy include heat, light, sound, electricity, and chemical energy. Energy and work are measured in the same units—foot-pounds, joules, ergs, or some other, depending on the system of
radiated in the form of a wavewave,
in physics, the transfer of energy by the regular vibration, or oscillatory motion, either of some material medium or by the variation in magnitude of the field vectors of an electromagnetic field (see electromagnetic radiation).
as a result of the motion of electric charges. A moving charge gives rise to a magnetic field, and if the motion is changing (accelerated), then the magnetic field varies and in turn produces an electric field. These interacting electric and magnetic fields are at right angles to one another and also to the direction of propagation of the energy. Thus, an electromagnetic wave is a transverse wave. If the direction of the electric field is constant, the wave is said to be polarized (see polarization of lightpolarization of light,
orientation of the vibration pattern of light waves in a singular plane. Characteristics of Polarization
Polarization is a phenomenon peculiar to transverse waves, i.e.
). Electromagnetic radiation does not require a material medium and can travel through a vacuum. The theory of electromagnetic radiation was developed by James Clerk Maxwell and published in 1865. He showed that the speed of propagation of electromagnetic radiation should be identical with that of lightlight,
visible electromagnetic radiation. Of the entire electromagnetic spectrum, the human eye is sensitive to only a tiny part, the part that is called light. The wavelengths of visible light range from about 350 or 400 nm to about 750 or 800 nm.
, about 186,000 mi (300,000 km) per sec. Subsequent experiments by Heinrich Hertz verified Maxwell's prediction through the discovery of radio waves, also known as hertzian waves. Light is a type of electromagnetic radiation, occupying only a small portion of the possible spectrumspectrum,
arrangement or display of light or other form of radiation separated according to wavelength, frequency, energy, or some other property. Beams of charged particles can be separated into a spectrum according to mass in a mass spectrometer (see mass spectrograph).
of this energy. The various types of electromagnetic radiation differ only in wavelength and frequency; they are alike in all other respects. The possible sources of electromagnetic radiation are directly related to wavelength: long radio waves are produced by large antennas such as those used by broadcasting stations; much shorter visible light waves are produced by the motions of charges within atomsatom
[Gr.,=uncuttable (indivisible)], basic unit of matter; more properly, the smallest unit of a chemical element having the properties of that element. Structure of the Atom
high-energy photons emitted as one of the three types of radiation resulting from natural radioactivity. It is the most energetic form of electromagnetic radiation, with a very short wavelength (high frequency).
, result from changes within the nucleusnucleus,
in physics, the extremely dense central core of an atom. The Nature of the Nucleus
Composition
Atomic nuclei are composed of two types of particles, protons and neutrons, which are collectively known as nucleons.
of the atom. In order of decreasing wavelength and increasing frequency, various types of electromagnetic radiation include: electric waves, radioradio,
transmission or reception of electromagnetic radiation in the radio frequency range. The term is commonly applied also to the equipment used, especially to the radio receiver.
electromagnetic radiation having a wavelength in the range from c.75 × 10−6 cm to c.100,000 × 10−6 cm (0.000075–0.1 cm).
invisible electromagnetic radiation between visible violet light and X rays; it ranges in wavelength from about 400 to 4 nanometers and in frequency from about 1015 to 1017 hertz.
, X raysX ray,
invisible, highly penetrating electromagnetic radiation of much shorter wavelength (higher frequency) than visible light. The wavelength range for X rays is from about 10−8 m to about 10−11
, and gamma radiation. According to the quantum theoryquantum theory,
modern physical theory concerned with the emission and absorption of energy by matter and with the motion of material particles; the quantum theory and the theory of relativity together form the theoretical basis of modern physics.
, light and other forms of electromagnetic radiation may at times exhibit properties like those of particles in their interaction with matter. (Conversely, particles sometimes exhibit wavelike properties.) The individual quantum of electromagnetic radiation is known as the photonphoton
, the particle composing light and other forms of electromagnetic radiation, sometimes called light quantum. The photon has no charge and no mass. About the beginning of the 20th cent.
and is symbolized by the Greek letter gamma. Quantum effects are most pronounced for the higher frequencies, such as gamma rays, and are usually negligible for radio waves at the long-wavelength, low-frequency end of the spectrum.
Energy transmitted through space or through a material medium in the form of electromagnetic waves. The term can also refer to the emission and propagation of such energy. Whenever an electric charge oscillates or is accelerated, a disturbance characterized by the existence of electric and magnetic fields propagates outward from it. This disturbance is called an electromagnetic wave. The frequency range of such waves is tremendous, as is shown by the electromagnetic spectrum in the table. The sources given are typical, but not mutually exclusive.
In theory, any electromagnetic radiation can be detected by its heating effect. This method has actually been used over the range from x-rays to radio. lonization effects measured by cloud chambers, photographic emulsions, ionization chambers, and Geiger counters have been used in the γ- and x-ray regions. Direct photography can be used from the γ-ray to the infrared region.
Electromagnetic spectrum
Frequency, Wavelength,
Hz m Nomenclature Typical source
1023 3 × 10-15 Cosmic photons Astronomical
1022 3 × 10-14 γ-rays Radioactive nuclei
1021 3 × 10-13 γ-rays, x-rays
1020 3 × 10-12 x-rays Atomic inner shell
Positron-electron annihilation
1019 3 × 10-11 Soft x-rays Electron impact on a solid
1018 3 × 10-10 Ultraviolet, x-rays Atoms in sparks
1017 3 × 10-9 Ultraviolet Atoms in sparks and arcs
1016 3 × 10-8 Ultraviolet Atoms in sparks and arcs
1015 3 × 10-7 Visible spectrum Atoms, hot bodies,
molecules
1014 3 × 10-6 Infrared Hot bodies, molecules
1013 3 × 10-5 Infrared Hot bodies, molecules
1012 3 × 10-4 Far-infrared Hot bodies, molecules
1011 3 × 10-3 Microwaves Electronic devices
1010 3 × 10-2 Microwaves, radar Electronic devices
109 3 × 10-1 Radar Electronic devices
Interstellar hydrogen
108 3 Television, FM radio Electronic devices
107 30 Short-wave radio Electronic devices
106 300 AM radio Electronic devices
105 3000 Long-wave radio Electronic devices
104 3 × 104 Induction heating Electronic devices
103 3 × 105 Electronic devices
100 3 × 106 Power Rotating machinery
10 3 × 107 Power Rotating machinery
1 3 × 108 Commutated direct current
0 Infinity Direct current Batteries
Fluorescence is effective in the x-ray and ultraviolet ranges. Bolometers, thermocouples, and other heat-measuring devices are used chiefly in the infrared and microwave regions. Crystal detectors, vacuum tubes, and transistors cover the microwave and radio frequency ranges. See Diffraction, Electromagnetic wave, Gamma rays, Heat radiation, Infrared radiation, Interference of waves, Light, Maxwell's equations, Polarization of waves, Reflection of electromagnetic radiation, Refraction of waves, Scattering of electromagnetic radiation, Ultraviolet radiation, Wave motion, X-rays
McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
Electromagnetic spectrum
A disturbance that can travel through a vacuum as well as through a material medium, light and radio waves being familiar forms. It consists of oscillating (time-varying) electric and magnetic fields with directions at right angles to each other and to the direction of propagation. The two fields are bound together, the time-varying electric and magnetic components regenerating each other in an endless cycle that moves from one point to the next through space. The radiation transfers energy and also momentum. It travels through a vacuum at the speed of light, c , which is a fundamental constant equal to about 3 × 105 km s–1. The speed is slightly reduced on entering a medium, such as air or glass.
Electromagnetic radiation is caused by the acceleration of charged particles, such as electrons. Its propagation through space can be fully described in terms of wave motion. Like other periodic waves, electromagnetic waves have a wavelength λ and a frequency ν, which are related by λν = c . Reflection, refraction, interference, and polarization can be explained in terms of wave motion. When radiation interacts with matter, however, it exhibits particle-like behavior, as when it undergoes absorption or emission. It thus has a dual wave–particle nature. A particulate nature was originally proposed by Newton but in its present form the concept is part of quantum theory. Light and other kinds of radiation interact with matter as quanta. A quantum of radiation of frequency ν transfers energy h ν and momentum h ν/c 2, where h is the Planck constant. The quantum of electromagnetic radiation is the photon. Light, etc., is thus absorbed by or emitted from atoms or molecules in the form of photons.
The range of frequencies (or wavelengths) of electromagnetic radiation is known as the electromagnetic spectrum (see illustration). The spectrum can be divided into various regions, which are not sharply delineated. These regions range from low-frequency low-energy radio waves through infrared radiation, light, ultraviolet radiation, X-rays, to high-frequency high-energy gamma rays. Most astronomical observations measure some form of electromagnetic radiation.
Collins Dictionary of Astronomy © Market House Books Ltd, 2006
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.
Classical radiation theory (Maxwell’s theory). The physical reasons for the existence of a free electromagnetic field (that is, a self-sustaining field that has become independent of the sources that induced it) are closely associated with the fact that electromagnetic waves propagate from sources—charges and currents —with a finite speed c (in a vacuum c˜3 X 1010 cm/sec) rather than instantaneously. If the radiation source (such as an alternating current) disappears at a certain instant, the field will not disappear instantaneously in the entire space: at points remote from the source it will disappear only after a finite time interval. It follows from Maxwell’s theory that a change in an electric field E in time gives rise to a magnetic field H, and the change in H gives rise to a vortex electric field. Hence it follows that only a variable electromagnetic field, in which both components—E and H—constantly excite each other by changing continuously, may be self-sustaining.
In the process of radiation an electromagnetic field carries energy away from the source. The energy flux density of the field (the quantity of energy per unit time passing through a unit area oriented perpendicular to the direction of the flux) is determined by the Poynting vector P, which is proportional to the vector product [EH].
The radiation intensity Eradis the energy removed from the source by the field per unit time. Its order of magnitude can be estimated by calculating the product of the area of the closed surface encompassing the source and the average value of the absolute flux density P on this surface (P˜EH). The surface is usually selected in the form of a sphere of radius R (its area is on the order of R2), and Erad is calculated from the limit R → ∞:
(E and H are the absolute values of the vectors E and H).
In order that this quantity does not disappear—that is, in order for a free electromagnetic field to exist far from the source —both E and H must not decrease more rapidly than \/R. This requirement is satisfied if moving charges under acceleration are the field sources. Near the charges the fields are Coulomb fields proportional to l/R2, but at large distances non-Coulomb fields Eand H, which attenuate as l/R, begin to play the primary role.
RADIATION OF A MOVING CHARGE. A point charge is the simplest field source. A resting charge has no radiation; nor may a uniformly moving charge (in a vacuum) be a source of radiation. However, a charge moving under acceleration does radiate. Direct calculations based on Maxwell’s equations show that the intensity of its radiation is
where e is the magnitude of the charge and a is its acceleration. (Here and below the Gaussian system of units is used.) Depending on the physical nature of the acceleration the radiation is sometimes given special names. For example, the radiation that arises during the deceleration of charged particles in matter as a result of the action of the Coulomb fields of automic nuclei and electrons is called bremsstrahlung. The radiation of a charged particle moving in a magnetic field that deflects its trajectory is called synchrotron radiation. It is observed, for example, in cyclic charged-particle accelerators.
In a particular case, when a charge undergoes a harmonic oscillation, the acceleration a is equal in magnitude to the product of the deviation of the charge from a state of equilibrium (x = x0 sin ωt, where x0 is the amplitude of the deviation of x) and the square of the frequency s. The radiation intensity, averaged with respect to time t, increases very rapidly (proportional to ω4) as the frequency increases:
ELECTRIC DIPOLE RADIATION. Two interconnected, co-oscillating opposite charges that are equal in magnitude are the simplest system that may serve as a source of radiation. They form a dipole with a variable moment. For example, if the charges of the dipole oscillate harmonically against each other, then the electric dipole moment changes according to the law d = d0 sin wt (ω is the frequency of oscillations, and do is the amplitude of moment d). The radiation intensity of such a dipole averaged with respect to the time t is
The radiation emanating from an oscillating dipole is anisotropic—that is, the energy emitted in various directions is not identical. Radiation is entirely absent along the axis of oscillations and is at a maximum at right angles to the axis of oscillations. For all intermediate directions the angular distribution of the radiation changes in proportion to sin2θ, where the angle θ is read from the direction of the axis of oscillations. If the direction of the axis of oscillations of a dipole changes over time, then the average angular distribution becomes more complex.
Real radiators usually include a set of charges. Precise consideration for all details of the motion of each charge in the study of radiation is unnecessary and often impossible. Indeed, radiation is defined by the values of the fields far from the source— that is, where the details of the distribution of the charges and currents in the radiator have a slight effect. This makes it possible to replace the true distribution of the charges with an approximate distribution. Consideration of a radiating system as a single charge, equal in magnitude to the sum of the charges of the system, is the crudest, “zero-order” approximation. In an electrically neutral system, the sum of whose charges is equal to zero, radiation is absent in this approximation. In the next approximation (the first), the positive and negative charges of the system “tend” imaginarily toward the centers of their distribution. For an electrically neutral system this means conceptual replacement by an electric dipole radiating according to (4). This approximation is called a dipole approximation, and the corresponding radiation is called electric dipole radiation.
ELECTRIC QUADRUPOLE AND HIGHER MULTIPOLE RADIATION. If a system of charges has no dipole radiation—for example, because the dipole moment is equal to zero—then it is necessary to take into account the next approximation, in which the system of charges (the radiation source) is regarded as a quadrupole. The simplest quadrupole is two dipoles that have moments of equal magnitude and opposite direction. An even more detailed description of a radiating system of charges is given by consideration of subsequent approximations, in which the charge distribution is described by multipoles of higher orders (a dipole is called a first-order multipole, a quadrupole a second-order multipole, and so on).
It is important to note that in each successive approximation the radiation intensity is approximately (c/v)2 times less than in the previous one (if, of course, it is not absent for some reason). If the radiator is nonrelativistic—that is, if all charges have velocities much less than the speed of light (v/c « 1)—then the lower, nonvanishing approximation plays the main role. Thus, if dipole radiation is present it is the primary radiation, and all other higher multipole corrections are extremely small and need not be taken into account. In the case of the radiation of relativistic particles, however, the description of radiation by means of multipoles becomes ineffective, since the contribution of higher-order multipoles ceases to be small.
MAGNETIC DIPOLE RADIATION. In addition to electric dipoles and higher multipoles, magnetic dipoles and multipoles may also be radiation sources (magnetic dipole radiation is generally the primary radiation). The distribution pattern of a magnetic field at a great distance from the circuit through which the current that gives rise to this field is flowing is similar to the distribution pattern of an electric field far from an electric dipole. The analogue of the electric dipole moment, the dipole magnetic moment M, is determined by the current strength I in the circuit and by the circuit’s geometry. For a plane circuit the absolute magnitude of the moment is M = (e/c )IS, where S is the area within the circuit. The formulas for the intensity of magnetic dipole radiation are almost the same as for electric radiation, except that they contain the magnetic moment M instead of the electric dipole moment d. Thus, if the magnetic moment changes according to the harmonic law M = M0 sin cat (for this the current strength I in the circuit must change harmonically), the radiation intensity averaged with respect to time is
Here M0 is the amplitude of the magnetic moment M.
The ratio of the magnetic and electric dipole moments is of the order of v/c, where v is the rate of motion of the charges forming the current; from this it follows that the intensity of magnetic dipole radiation is (c/v)2 times less than that of electric dipole radiation if, of course, the latter is present. Thus, the intensities of magnetic dipole and electric quadrupole radiation are of the same order of magnitude.
RADIATION OF RELATIVISTIC PARTICLES. The synchrotron radiation of charged particles in circular (ring) accelerators is one of the most important examples of radiation of relativistic particles. A sharp difference from nonrelativistic radiation is manifested here in the spectral composition of the radiation: if the revolution frequency of a charged particle in an accelerator is equal to ω (a nonrelativistic radiator would emit waves of the same frequency), then its radiation intensity has a maximum at a frequency ωmax ˜ ³3ω, where ³ = [1 — (v/c)2]-1/2; that is, when vc most of the radiation is found at frequencies higher than ω. Such radiation is directed nearly at a tangent to the orbit of the particle, mainly in the direction of its motion.
An ultrarelativistic particle may radiate electromagnetic waves even if it is moving in a straight line and uniformly (but only in matter, not in a vacuum!). This radiation, called Cherenkov radiation, arises if the velocity of a charged particle in a medium exceeds the phase velocity of light in this medium (uPhase = c/n, where n is the index of refraction of the medium). The radiation appears because the particle “overtakes” and breaks away from the field that gives rise to it.
Quantum radiation theory. It is has already been stated above that classical theory gives only an approximate description of radiation processes (the entire physical world is in principle a “quantum” world). However, physical systems also exist whose radiation cannot be described even approximately in conformance with experiments from the standpoint of classical theory. An important feature of such quantum systems as the atom or molecule is that their internal energy does not change continuously but may assume only certain values, forming a discrete set. The transition of a system from a state with one energy to a state with another takes place in a stepwise manner; because of the law of conservation of energy, upon such a transition a system must lose or acquire a certain “portion” of energy. This process is realized most often in the form of emission or absorption of a quantum of radiation—a photon—by the system. The energy of a quantum is Є³ =ħω where ħ is Planck’s constant (ħ = 1.05450 X 10-27 erg/sec), and ω is the angular frequency. A photon always acts as a unified whole, is emitted and absorbed “in its entirety,” in a single event, and has a definite energy, momentum, and spin (the projection of the angular momentum on the direction of the momentum)—that is, it has a number of corpuscular properties. At the same time the photon differs sharply from conventional classical particles in that it also has wave features. This dual character of the photon is a particular phenomenon of particle-wave dualism.
Quantum electrodynamics is a consistent quantum theory of radiation. However, many results that bear on the processes of the radiation of quantum systems can be obtained from the simpler semiclassical radiation theory. The formulas of the latter, according to the correspondence principle, should, within certain limits, give the results of classical theory for some limiting transition. Thus, a profound analogy is established between the quantities that characterize radiation processes in quantum and classical theories.
ATOMIC RADIATION. A system consisting of a nucleus and an electron moving in its Coulomb field must be in one of the discrete states (at a certain energy level). All states except the ground state (the state with the lowest energy) are unstable. An atom in an unstable (excited) state, even if isolated, passes into a state of lower energy. This quantum transition is accompanied by the emission of a photon; such radiation is called spontaneous radiation. The energy removed by the photon, Єϒ = ħω, is equal to the difference between the energies of the initial state and the final state j of the atom (ЄiЄj; Єi—Єj); the formula of N. Bohr for radiation frequencies follows from this:
It is important to note that such characteristics of spontaneous radiation as the direction of propagation (for a set of atoms, the angular distribution of their spontaneous radiation) and polarization do not depend on the radiation of other objects, such as an external electromagnetic field.
Bohr’s formula (6) defines the discrete set of frequencies, and consequently the wavelengths, of atomic radiation. It explains why the spectra of atomic radiation have the well-known “line” character—each line of the spectrum corresponds to one of the quantum transitions of the atoms of the particular substance.
RADIATION INTENSITY. In quantum theory, as in classical theory, electric dipole and higher multipole radiation may be examined. If a radiator is nonrelativistic, the primary radiation is the electric dipole radiation whose intensity is determined by a formula close to the classical formula:
The quantities dij, which are a quantum analogue of the electric dipole moment, are found to be nonzero only when certain relations exist between the quantum numbers of the initial state /’ and the final state j (the selection rules for dipole radiation). Quantum transitions that satisfy such selection rules are called allowed transitions (the allowed electric dipole radiation is actually meant). By contrast, transitions of higher multipole levels are said to be forbidden. This prohibition is relative: forbidden transitions have a relatively low probability—that is, the radiation intensity corresponding to them is small. The states from which transitions are “forbidden” are comparatively stable (long-lived); they are called metastable states.
Quantum radiation theory makes possible an explanation not only of the difference in intensity of various lines but also of the intensity distribution within each line, and in particular the width of spectral lines.
Not only atoms but also more complex quantum systems may be sources of electromagnetic radiation. The general methods for describing the radiation of such systems are the same as those used in the study of atoms, but the specific features of the radiation are extremely diverse. For example, molecular radiation has more complex spectra than does atomic radiation. High energy of individual quanta (³-quanta) and comparatively low radiation intensity are typical of the radiation of atomic nuclei.
Electromagnetic radiation frequently also arises during mutual transformations of elementary particles (such as the annihilation of electrons and positrons and the decay of the neutral pi-meson).
### REFERENCES
Tamm, I.E. Osnovy teorii elektrichestva, 7th ed. Moscow, 1957.
Ivanenko, D., and A. Sokolov. Klassicheskaia teoriia polia. Moscow-Leningrad, 1949.
Ivanenko, D., and A. Sokolov. Kvantovaia teoriia polia. Moscow-Leningrad, 1952.
Akhiezer, A. I., and V.B. Berestetskii. Kvantovaia elektrodinamika, 2nd ed. Moscow, 1959.
Landau, L. D., and E.M. Lifshits. Teoriia polia, 5th ed. Moscow, 1967. (Teoreticheskaia fizika, vol. 2.)
V. I. GRIGOR’EV
[i¦lek·trō·mag′ned·ik ‚rād·ē′ā·shən]
(electromagnetism)
Electromagnetic waves and, especially, the associated electromagnetic energy.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The energy that radiates from all things in nature and from man-made electrical and electronic systems. Electromagnetic radiation includes cosmic rays, gamma rays, x-rays, ultraviolet light, visible light, infrared light, radar, microwaves, TV, radio, cellphones and all electronic transmission systems. Electromagnetic radiation is made up of an electromagnetic field (EMF), which comprises an electric field and a magnetic field that move at right angles to each other at the speed of light. See spectrum, microwave and electromagnetic hypersensitivity.
Copyright © 1981-2019 by The Computer Language Company Inc. All Rights reserved. THIS DEFINITION IS FOR PERSONAL USE ONLY. All other reproduction is strictly prohibited without permission from the publisher.
References in periodicals archive ?
Mechanism of Electromagnetic Radiation in Predicting Strain-Type Rockburst
Oscillating circuits consumed radiant energy from the external environment and convert it into heat protecting living space by its electromagnetic shielding in a wide range of specific frequency of environment electromagnetic radiation.
What separates one type of electromagnetic radiation from another is its wavelength.
And the bulk of the research cited by the American Cancer Society has focused on direct and prolonged exposure to radio-frequency electromagnetic radiation in general, not on cell towers and their effects specifically.
Although no-one has yet conclusively proved a correlation between electromagnetic radiation and leukaemia, there is plenty of circumstantial evidence.
One theory is exposure to electromagnetic radiation cuts production of a hormone called melatonin.
In addition, some 3M filters reduce screen glare, block ELF/VLF E-field electromagnetic radiation, and prevent static and dust build-up when properly grounded.
Because it is mobile, it can protect VIPs in transit, military convoys, sensitive venues, and fixed installations by effectively emitting a protective shield of electromagnetic radiation. Other units in the BombJammer product line include the VIP 200, which is built into a briefcase and jams radio-frequency-controlled bombs; the VIP 600, which is built into a military backpack and designed for tactical use; and the VIP 900, a stationary system for protecting military and government installations, arenas, and transit stations.
One of his interests is studying the interaction of electromagnetic radiation and genetic material to determine how electric fields from cell phones, television sets, computers, and power lines can alter our DNA.
For example, you will find new or redone sections on indoor air quality, environmental justice, endangered species, multiple chemical sensitivities, electromagnetic radiation, disasters, and ergonomics.
Inhabitants around the radio's transmission center alleged that its levels of electromagnetic radiation had increased the risk of cancer in children.
* Complete an analysis of applicable regulations and other requirements, such as Hazards of Electromagnetic Radiation to Ordnance (HERO) certification (June 2004)
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Open / Close | 6,212 | 29,945 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2021-17 | longest | en | 0.902052 |
https://www.mecharithm.com/tag/screw-theory/ | 1,685,824,891,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649343.34/warc/CC-MAIN-20230603201228-20230603231228-00357.warc.gz | 945,416,396 | 27,170 | ### Forward Kinematics in Robotics Using Screw Theory
Can you recall a time when you were frustrated when attempting to compute the forward kinematics for robotic systems? Did you find it frustrating to assign coordinate frames to each link when robots become more sophisticated? The frustration caused by assigning coordinate frames for each link while solving the forward kinematics of robotic systems using methods like Denavit-Hartenberg is REAL. If your answer to these questions is yes, and you're tired of cumbersome methods like Denavit-Hartenberg to calculate the forward kinematics of robotic chains, this lesson is for you. The Denavit-Hartenberg is one of the methods to derive the forward…
### Screws: a Geometric Description of Twists in Robotics
In the previous lesson, we learned about velocities in robotics. We became familiar with angular and linear velocities and saw that stacking them together gives us the twist. We also saw how we could change the frame of reference for angular velocities and twists. This lesson is about screws as a geometric interpretation for twists and how they can be used to express configurations in robotics. This lesson is part of the series of lessons on foundations necessary to express robot motions. For the complete comprehension of the Fundamentals of Robot Motions and the tools required to represent the configurations,…
### Velocities in Robotics: Angular Velocities & Twists
In the previous lesson, we saw an introduction to screw theory and its applications in robotics. We saw that integrating a constant twist over time gives us the configuration. We also became familiar with the exponential coordinates of robot motions, and we saw that in order to define the screw axis, we need to understand angular and linear velocities. In this lesson, we will become familiar with the concept of velocities in robotics, and we will study angular velocities and twists. This lesson is part of the series of lessons on foundations necessary to express robot motions. For the complete…
### Screw Motion and Exponential Coordinates of Robot Motions
This lesson is part of the series of lessons on foundations necessary to express robot motions. For the complete comprehension of the Fundamentals of Robot Motions and the tools required to represent the configurations, velocities, and forces causing the motion, please read the following lessons (note that more lessons will be added in the future): https://www.mecharithm.com/category/fundamentals-of-robotics/fundamentals-of-robot-motions/ Also, reading some lessons from the base lessons of the Fundamentals of Robotics course are deemed invaluable. In this lesson, we will see an introduction to screw motion in robotics, and we will also see how we can define exponential coordinates for robot motions. This is… | 538 | 2,826 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2023-23 | latest | en | 0.918537 |
https://forum.allaboutcircuits.com/threads/superposition-rule.161009/#post-1407412 | 1,638,004,822,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358153.33/warc/CC-MAIN-20211127073536-20211127103536-00441.warc.gz | 343,788,995 | 18,875 | # Superposition Rule
#### AndrieGnd
Joined Jun 25, 2019
52
Hello gentlemen ! , I'm not assure if this related to math or not but I think so.
my professor wrote a question with given equation as this: E=E1^x +E2^y , which E is electrical field.
he said afterwards, we will deal with the solution of this question as two fields separately, which means:
solving over E1 and gets its soltuion.
solving over E2 and gets its solution.
the total solution is the sum of the two solution I said above.
I totally agree with him, but what's confusing me maybe E1 and E2 is affecting each other once they are applied on the same time so we can't solve the problem as solution of E1,E2 separately because they are affecting one eachother while applying them altogether.
So I'm asking maybe there's relation between E1,E2 once we are applying them together and didn't give us information about that .. so how we still use the superposition Rule although it might be relation between E1,E2 ! (( in the question didn't give us information if there's a relation between E1,E2))
Any help?!
Last edited:
#### AndrieGnd
Joined Jun 25, 2019
52
Maybe we are assuming that we don't have a relation between two elements(E1,E2) ? so we can solve problem separately at each element?! but if so, in waves for example we get a interference between two waves .. so we can't separate one wave from another because they've a relation between eachother once they applied altogether (we get non-constructive interference)
#### MrAl
Joined Jun 17, 2014
8,543
Hi,
Well if he said to use superposition then i would do that.
Also, are the two fields orthogonal? That would be a consideration but if he already said how to do it then do it that way. | 412 | 1,720 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2021-49 | latest | en | 0.969305 |
https://math.stackexchange.com/questions/3049003/simple-continuous-game-or-not | 1,571,616,181,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987750110.78/warc/CC-MAIN-20191020233245-20191021020745-00074.warc.gz | 608,662,066 | 31,188 | # Simple continuous game or not?
Two players simultaneously pick a number from [0, 1]. Payoff of the first player (equal to the loss of the second) is the distance between those numbers.
1. Does there exist pure-strategy Nash equilibrium?
2. Does there exist mixed-strategy Nash equilibrium? How many?
I found value of the game v=1/2, pure optimal strategy for the second player y=1/2 and the mixed optimal strategy for the first player x={0, 1} with probabilities p=(1/2, 1/2).
I am a bit stuck with finding other mixed strategies, could you help me, please?
1. There is no pure-strategy Nash equilibrium: Assume player 1 choose $$a\in[0,1]$$ and player 2 choose $$b\in[0,1]$$, show that either player 1 or player 2 can do better. | 195 | 736 | {"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": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2019-43 | latest | en | 0.911003 |
http://boingboing.net/2009/11/17/logicomix-an-epic-se.html | 1,467,179,063,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783397567.28/warc/CC-MAIN-20160624154957-00042-ip-10-164-35-72.ec2.internal.warc.gz | 40,718,447 | 23,130 | # Logicomix: An Epic Search for Truth
When I found out that a graphic novel about the life of Bertrand Russell was in the works, I imagined it would be interesting, but I never thought it would be as spellbinding as it turned out to be. Logicomix, created by a team of Greek artists and writers is full color graphic novel about Bertrand Russell and his ardent quest for the logical foundation of mathematics. The creators of the graphic novel put themselves into the story, between chapters of Russell's life, to discuss their thoughts on key moments. It's a clever and useful way to add additional context to the story.
The book is 352 pages long -- 10 pages less than what it took Russell and Whitehead to prove that 1+1 = 2 in their book Principia Mathematica, but I was tearing through it to find out what happened. Afterwards, I went back to admire the artwork, which is masterfully composed and filled with terrific architecture and other detials. All-in-all, this was a surprisingly terrific book.
### 23
1. Anonymous says:
Does the book explain how Godel dismantled Russell’s life work irrevocably? It’s a pretty important lesson that Russell _should_ have learned…
2. Xopher says:
Russell and Whitehead and Hegel and Kant:
Maybe I shall, and maybe I shan’t.
Maybe I shan’t, and maybe I shall:
Kant, Russell, Whitehead, Hegel et al.
—The Space Child’s Mother Goose
3. Anonymous says:
Personally, I recommend this one. It’s a fun read, and has a compelling story. Though it’s a bit more self-referential than I bargained for.
4. Keneke says:
A spoonful of sugar helps the medicine go down; that’s what graphic novels are turning into. And the problem is, it may be “medicine”, it may be “poison”, it may be nothing. I happen to think this is a good topic though.
5. Joe says:
Anonymous #1: Russell’s work led to Gödel’s work; Gödel built on Russell. The comic illustrates Russell’s paradox about the set of all sets not containing themselves. The Principia Mathematica was an attempt to eliminate this problem by eliminating self-reference, and Gödel showed how to re-introduce self-reference in a way that cannot be defeated. But Gödel couldn’t have accomplished what he did without building on Russell.
And now you arrogantly state that there’s an important lesson that Russell should have learned. But Russell learned it when the rest of the world did, when Gödel shared it.
Furthermore, the fact that Russell didn’t succeed in his principal aim (to construct a paradox-free foundation for mathematics) doesn’t eliminate the value of the Principia Mathematica.
6. AnotherBeaver says:
I bought it and knew ABSOLUTELY NOTHING about the subject. I mean nothing. I had seen a panel on a website and noticed the word Tautology and had no idea what it meant. I looked the word up to see what it meant then I read a snippet about the comic and decided to get it.
I read it straight through in one sitting. I was and am fascinated by it. I had always assumed math had been figured out thousands of years ago and that the rules were set and were unquestionable. I had no idea so much had happened so recently, relatively.
I feel like I’ve discovered a hidden history, hidden to me, that I am going to read up on.
I’ve lent it out a few times already.
7. jazzbo says:
#5 Joe, please ping me when they make Principia a graphic novel.
8. MattF says:
I don’t know where the claim that Whitehead and Russell proved 1 + 1 = 2 on page 342 comes from– but in fact the proof of 1 + 1 = 2 occurs on page 83 of Volume 2. Since Volume 1 has 674 pages, you’re off by about a factor of two. For the record, 1 + 1 = 2 is theorem *110.643– W&R comment “The above proposition is occasionally useful. It is used at least three times, in *113.66 and *120.123.472.”
1. AnotherBeaver says:
He said “342 pages to prove it.”
Anyways, all of this makes me realize what it must feel like for my mother to try and use the computer. Fish out of water.
1. MattF says:
Even leaving out introductory and expository stuff it takes some 600 pages for W&R to get to 1 + 1 = 2. It should be said that modern theories of cardinal addition get to that point a lot faster– and then go on to the interesting stuff involving infinite cardinals and ordinals. Also, Whitehead and Russell put a lot of effort into proving all the statements they will need in propositional logic, but in the modern world we just look at truth tables.
9. Mark Frauenfelder says:
Hi Matt — I think I was off by 10 pages or so, not 300. But if you are correct you should clean up the error on Wikipedia!
“From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2.” – Volume I, 1st edition, page 379 (page 362 in 2nd edition; page 360 in abridged version).
1. MattF says:
It’s a somewhat obscure point because nowadays, numbers are defined a la von Neumann as specific sets– e.g., 0 = empty set, 1 = ‘the set whose only member is the empty set’ = {empty set}, 2 = {{empty set}, empty set}, and so forth. But I’ll look at the Wikipedia entry and see if it’s misleading.
10. Roy Trumbull says:
Russell could be brilliant but there’s a few of his ideas I’m glad we didn’t adopt.
In the essay “The Future of Mankind” he argued that the U.S. and Britain should use their military edge and the bomb to attack Russia and unify the world under one government.
His essay “The Superior Virtue of the Oppressed” should be read by everyone. He nails a very widespread bit of fuzzy thinking that was being applied to many.
11. jerwin says:
I don’t have the book; I’ve only seen the Amazon previews. But it does remind me of “Godot Action Comics”
Here’s Episode #37: The Wrath of Vladimir.
http://www.hdschellnack.de/?p=680
12. Anonymous says:
How much of a look-in does Frege get here? From the various descriptions it seems like he’s not getting quite the amount of credit he deserves.
1. Anonymous says:
The book is a mathatical biography of Russell, and it takes as its first high point Russell’s letter to Frege, and it looks at the mental illness so common among logicians. It doesn’t go into Cantor, Frege, or especially Gödel in enough detail to really be a comprehensive story about mathematical logic, but the narrative holds together very well, so I’d definitely recommend it.
13. Anonymous says:
One of the two authors here, Christos Papadimitriou, is known not for his writing or illustrations, but for his work in theoretical computer science. Just some relevant credentials that were missing.
14. Anonymous says:
@ Joe
No arguments from me on any of your points. After re-reading my post (and yours) I realize that my question came off as rhetorical. I actually was/am wondering if/how the book portrays Russell’s reaction when his proposition was disproved Godel.
Thanks for your post as it did lead me to do a little more digging on BR. Cheers.
15. Anonymous says:
Check out the book’s website, there’s loads of information there on the story, the creators, and on how the book was made, as well as news updates, reviews, and a list of foreign sales, etc. http://www.logicomix.com
16. Tzctlp says:
One of the authors, Apostolos Doxiadis, wrote “Uncle Petros and Goldbach’s Conjecture: A Novel of Mathematical Obsession” which is a delicious book about the nature of mathematical genius, family relationships and complex mathematical concepts.
It is what the horrible “Godel, Escher, Bach: An Eternal Golden Braid” should have been.
17. Anonymous says:
I am straying into politics here, but it is related.
This graphic novel reinforces Bertrand Russell’s status as an intellectual hero. The truth is more complicated.
He was for “scientific” and “logical” SLAVERY through horrific social engineering techniques. His work in mathematics might be significant but, like many others, politically, he took “logic” too far to where it seems “logical” to enslave the majority of the planet for the pleasure of a select few. He was a Fabian Socialist (for slow and incremental rise of global authoritarian governence) and supported the destruction of families in favor of State influence over the individual and the futher development of the worldwide scientific dictatorship, a New World Order, over the global population using psychological mass mind control techniques as late as 1953. In particular, read “Proposed Roads to Freedom” (1918) and “The Impact of Science on Society” (1953).
18. Anonymous says:
While the Fabians had tremendous problems, mostly the fact that they saw an entrenched wealthy class voluntarily giving up their power by reform… i don’t think it was their belief in socialism that would give rise to a “new world order” in the way you think… capitalism has already created a world order, it is in desperate need of a new and better order anyways.
The thing people don’t understand about the idea of a state, is; whose state is it? What is a state? A state is an institution of one class to oppress another. We currently live in a state where the wealthy live parasitically off of those who do the work. Socialism would be a worker’s state, meaning those who do the work decide how that work is done, yes its oppressing the wishes of the wealthy who wish to exploit that work, but too many years of unemployment and seeing Detroiter’s live like rats, makes think they deserve a little oppression.
Also a worker’s state would be the first state in history where where the government is run by the majority, where the oppression of the privileged is used to benefit and raise up the overwhelmingly vast number of people who live in utter poverty. As people are given an equal playing field, class would disappear and so would the state as there would be no exploitation to enforce. Bosses would cease to exist, replaced by administrative workers who would have no more authority over a person then anyone else in society would have.
What happened in Russia, which is always the crap people bring up, was the work of capitalism, not those who tried to free the Russian people from the czar or foreign investors who were turning Russia into a wasteland in world war one. Stalin was the best thing that ever happened to Britain and American Capitalists. It meant that all their effort to crush the revolution was not in vain. They had succeeded in destroying so much of the infrastructure of the country, reducing to almost nothing. Imagine if there was no roads, no electricity, everyone in the cities had fled to the country just to eat due to a famine (induced by foriegn backed civil war and a blockaid, which united “bitter” enemies like Germany and Japan with France and England… its funny how things work out when rich people see poor people doing something), imagine if the town you lived in was in this situation, imagine trying to conduct voting and elect people and run a government when anyone who could, was trying to get the hell out just to survive, who could think of discussing which political positions should be taken, when they couldn’t find enough bread to fill their aching bellies! If you look at the government after the insurrection but before the civil war, you see a government which is the freest government the world has seen since we stepped out of tribal life. Women were given the right to divorce, equal pay and voting rights… well before the “developed world”, they allowed any country which had been conquered by the czar to leave and form their own government, which some did, some didn’t. They based their government around soviets. Soviet isn’t another word for Russian, it means council. Councils at workplaces, in the army and amongst the peasants, councils of producers and councils of consumers, who argued openly about how to proceed, a lively and well functioning worker’s democracy.
After the civil war… chaos, absolute and utter chaos. Millions had died in the service of the Entente in WW1, their was already a widespread collapse of industry and the railroad supply system under pressure of war.
After the civil war, nothing really remained. The money was worthless, they couldn’t buy anything anyways because they had an embargo and block aid put on them. They were forced to give up most of the Ukraine to end WW1, which was where much of the grain and oil was… they encountered privileged elements emboldened by civil war, sabotaging industry at every moment, dragging their feet, speculating and stealing food. They had to rely on these same elements to develop industry because their was no education system for the masses under the czar. No way of educating new people in areas of specialty. They were trapped. Either complete failure of the revolution, and the return of Masters and slaves, complete with bloody retribution, or the communists must take control themselves.
The Bolsheviks took control over government or it would collapse. In doing so they appointed people they trusted, and they appointed people they trusted, well with so few people around that had any competency in the actual day to day running of things, eventually a lot of untrustworthy people slipped in. A bureaucracy developed. Lenin, and Trotsky warned, that if there wasn’t another revolution (their hope was Germany), the bureaucracy would swallow the revolution and the Communist Party. The revolution in Germany failed and the Communist Party were eaten whole. Stalin became the representation of this bureaucracy, and killed off nearly every member of the old Bolsheviks who helped bring about the revolution, with the participation of foreign backing. Stalin was won over to the idea of nationalism, and turned his back on the laboring people of the world.
Sorry to rant, but with a looming depression people need to know their history and quit all this red baiting bullshit that has spread like wildfire.
19. Anonymous says:
Russell lived to be 97 years old. His opinions changed a lot over that time. I just finished the book, and it is wonderful, telling his story up to the beginning of WW2. Sure, Russell said some off-colour things but this is the story of his life, to enjoy it you don’t have to hero worship him (though I do). | 3,137 | 14,138 | {"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} | 2.53125 | 3 | CC-MAIN-2016-26 | longest | en | 0.959242 |
https://www.simscale.com/blog/natural-frequency-vortex-shedding/ | 1,721,591,896,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517768.40/warc/CC-MAIN-20240721182625-20240721212625-00590.warc.gz | 839,964,338 | 26,995 | Required field
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• # Natural Frequency and Vortex Shedding: Solving Design Dilemmas
Natural Frequency and Vortex Shedding: Solving Design Dilemmas
Natural frequency analyses are used to determine the dynamic properties of a system and to identify its resonant frequencies. Some frequencies can cause elements to ‘sing.’ Imagine the sound of a guitar string being strummed. Because we understand a guitar string’s resonant frequencies, we are able to harness it, and subsequently make music. This can also be exampled by microwave ovens. Microwaves in microwave ovens have an equal frequency to the frequency of water molecules. As these molecules are oscillated and gain kinetic energy, the temperature of food rises.
At the same time, we can also use this knowledge of natural frequency to dampen an object’s resonant frequencies and vibrations. As engineers, natural frequency analysis, or modal frequency analysis, of planned structures or buildings is imperative to avoid disasters. For example, the construction of the Tacoma Narrows Bridge in 1940 failed to take into consideration the bridge’s natural frequency, and as normal wind speeds produced an aeroelastic flutter, the suspension bridge disastrously collapsed after 5 short months. In the case of the Tacoma Bridge, proactively dampening the bridge’s natural frequency would have proven to be a strategic design move.
## How to Use CFD and FEA Together
With SimScale, using both CFD (computational fluid dynamics) and FEA (finite element analysis) is possible on our platform. While CFD can simulate airflow on and around a structure (i.e., wind loading) FEA simulates what the acting forces do internally to that same structure (i.e., vibrations). The case below evaluates a building using FEA for natural frequency analysis to determine its modal frequencies, and then compares the findings with the results of a CFD vortex shedding simulation.
Learn how to leverage the cloud-based SimScale platform to optimize your design based on accurate results and ensure pedestrian wind comfort and safety.
## Case Study: Skyscraper Simulation with CFD and FEA
The project features an 80m structure with 30 floors at 2.5m intervals, 8 columns across the entire length, and is presumably planned to be built in an existing cityscape. The building is constrained only at the bottom with fixed supports in the ground, and is made entirely out of concrete. This was an assumption for the sake of testing.
## FEA Simulation for Natural Frequency Analysis
The initial aim of the simulation project is to solve two questions using frequency analysis: What are the modal frequencies? And how could the wind loads on the building excite the structure?
In order to determine this, FEA is first needed to determine the frequency response, or modal frequencies (eigenmodes) of the structure. The simulation is shaded by displacement where blue represents zero displacement and red represents a large amount of movement. This visualization is important in pinpointing where the design needs to be changed if it is deemed necessary.
## Initial Modal Frequency Findings with FEA
The simulation took 9 minutes to run in total, giving exceptionally quick results. This included a graph of frequencies the building is going to respond to, which can later be compared with the CFD simulation findings.
The first 4 modes listed show how the structure is predicted to move at these particular eigenmodes. As you can see in the image below, the simulation revealed that the structure’s movements are very varied.
To further delve into the current design dilemma, CFD simulation is then used to calculate and predict vortex shedding and the forces on the structure.
## CFD Simulation for Vortex Shedding Analysis
Similar to before, the project is set up with the same structural parameters. The simulation uses transient as well as turbulent flow using the incompressible LBM solver within the SimScale platform. The boundary conditions form the conditions of the virtual wind tunnel. An inlet profile is used where the inlet velocity is maxed out at 36.6m/s at 37m from the ground, the outlet is a pressure outlet, and the sidewalls have no friction. Three studies are then run for the purpose of the simulation; wind in x-direction from the left, at a 45-degree angle, and finally at a 90-degree angle. The simulation predicts the vortex shedding frequencies for each wind direction, and once extracted, these frequencies are compared to the modes from the previous analysis.
## Vortex Shedding Results
The simulation found that there are significant forces acting upon the structure, and large flow variations.
## CFD vs. Frequency Response Results
In two particular modes, the airflow velocity would excite the natural frequencies, creating an obvious design flaw as the actual structure would move. Therefore, some design changes must be made.
## Conclusion
The FEA and CFD comparative simulations found that there were two modal frequencies that cross over with transient wind loads. This design could then be modified in two ways in order to mitigate vibrations and motion; through internal or external modification. Internal changes could include dampening the structure with a pendulum or similar dampening device. External changes could be the redesigning of the entirety of the structure, specifically looking at the 12th and 15th modes as noted in the table above, to alter the path of the wind around the structure and the lateral forces working against it.
Watch our recent webinar recording by filling out a short form here and check out our published slide deck for more information.
• ## Other 'Computational Fluid Dynamics (CFD)' Stories
Your hub for everything you need to know about simulation and the world of CAE | 1,207 | 6,100 | {"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-2024-30 | latest | en | 0.914474 |
https://bpwnjfoundation.org/and-pdf/970-commercial-mathematics-and-statistics-class-11-pdf-730-598.php | 1,642,489,198,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300805.79/warc/CC-MAIN-20220118062411-20220118092411-00331.warc.gz | 205,163,038 | 8,817 | Commercial Mathematics And Statistics Class 11 Pdf
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These solutions for Statistics are extremely popular among Class 11 Commerce students for Math Statistics Solutions come handy for quickly completing your homework and preparing for exams. Mean of the data,. The deviations of the respective observations from the mean are.
The answers for the Balbharati books are the best study material for students.
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. You are using an out of date browser. It may not display this or other websites correctly. You should upgrade or use an alternative browser. Business Mathematics class 11 eBook and lecture notes contains the following key topics:.
Business mathematics ebook - class Last edited by a moderator: Aug 7, Joined Jun 21, Messages 1 Reaction score 0 Points 0. I want 11th state board maths guide not book in pdf only.
Aaditya04 New Member. Joined Jul 3, Messages 1 Reaction score 0 Points 0. Hey Buddies!! I am sharing the complete study material for Business Mathematics for class 11 students. The attached PDF file contains comprehensive lecture notes for your preparation of Business Mathematics subject for class 11 exams. Business Mathematics class 11 ebook and lecture notes contains the following topics: Yes i too need a guide for bm.
CBSE Class 11 and 12 students can opt for Applied Mathematics from this session
CBSE already offers two levels of Mathematics — basic easy and standard tough — for students at the level of Class Basic is for those who do not want to continue studying Maths after Class 10 and standard is for those who want to continue with the subject. This was introduced last year on the basis of recommendations from experts. Applied Mathematics is more about practical application of the subject. The idea behind introducing this subject is to make it relevant for those who do not want to study core Mathematics but use it for data interpretation, business, finance, graphical representation and other similar things. It has been observed that the existing syllabus of Mathematics aligns well with Science subjects, but does not align well with Commerce or Social Science-based subjects in university education.
Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting , inventory management , marketing , sales forecasting , and financial analysis. Mathematics typically used in commerce includes elementary arithmetic , elementary algebra , statistics and probability. For some management problems, more advanced mathematics - such as calculus , matrix algebra and linear programming - is applied. Business mathematics, sometimes called commercial math or consumer math , is a group of practical subjects used in commerce and everyday life. In schools, these subjects are often taught to students who are not planning a university education. In the United States, they are typically offered in high schools and in schools that grant associate's degrees ; elsewhere they may be included under business studies.
Add to cart. Sign Up Login. SchoolConnects 3 friends. Other Chapters For 11th Operations Management. Operations management is an area of management concerned with designing and controlling the Marketing is the study and management of exchange relationships. Marketing is used to create,
AHSEC - Class 11: Commercial Mathematics and Statistics Selected Questions for Feb' 2017 Exam
Class 11 Maths Notes are available here for all the students. They can also find notes for other subjects such as Biology, Physics and Chemistry for all the chapters. Specifically, in Maths, there are important points such as formulas, equations, identities, properties, theorem, etc. These revision notes have been prepared by our expert teachers with respect to CBSE Syllabus and guidelines. This will also be helpful for students when they will reach the 12th grade, as most of the concepts are inter-related with each other.
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Choosing the right books will help you understand the concepts in-depth and score better in the class 11 exams. But opting for the right books is difficult as there are many books available in both online and offline. To help you out in finding the right book, we have curated the list of best 11th Commerce Books for Accountancy, Business Studies, English, Mathematics, and more. The following books are prescribed by the boards as they are designed as per the latest Class 11 Accountancy Syllabus. You are suggested to follow these books which are as per the latest Class 11 Business Studies Syllabus.
Тут рядом полицейский участок.
ГЛАВА 110 Невидящими глазами Джабба смотрел на распечатку, которую ему вручила Соши. Он побледнел и вытер рукавом пот со лба. - Директор, у нас нет выбора. Мы должны вырубить питание главного банка данных. - Это невозможно, - сказал директор.
Эти слова были встречены полным молчанием. Лицо Стратмора из багрового стало пунцовым. Сомнений в том, кого именно обвиняет Чатрукьян, не. Единственный терминал в шифровалке, с которого разрешалось обходить фильтры Сквозь строй, принадлежал Стратмору. Когда коммандер заговорил, в его голосе звучали ледяные нотки: - Мистер Чатрукьян, я не хочу сказать, что вас это не касается, но фильтры обошел .
ARA обслуживает в основном американских клиентов. Вы полагаете, что Северная Дакота может быть где-то. - Возможно.
Скоростной карт фирмы Кенсингтон повернул за угол и остановился. Сзади, перпендикулярно туннелю, начинался коридор, едва освещаемый красными лампочками, вмонтированными в пол. - Пойдемте, - позвал Бринкерхофф, помогая Сьюзан вылезти. Она шла следом за ним точно в тумане. Коридор, выложенный кафельными плитками, довольно круто спускался вниз, и Сьюзан держалась за перила, стараясь не отставать.
Он не предложил вам больницы поприличнее. - На этой его чертовой тарантайке. Нет уж, увольте.
Джабба открыл рот. - Но, директор, ведь это… - Риск, - прервал его Фонтейн.
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1. Landabbremo 07.06.2021 at 14:09
Nts sample paper for sub engineer civil pdf english grammar by wren and martin free download pdf
2. Brandon G. 09.06.2021 at 06:07 | 1,547 | 6,635 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2022-05 | latest | en | 0.893961 |
https://www.protopie.io/blog/protopie-school-formula-basics-part-2 | 1,723,002,568,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640667712.32/warc/CC-MAIN-20240807015121-20240807045121-00846.warc.gz | 721,693,529 | 36,002 | Lesson 7: Formula Basics II
Learn how to use Formulas in ProtoPie to add more dynamic interactions into your prototypes.
Jeff Clarke, UX Designer & ProtoPie EducatorMarch 30, 2022
In Part 1, you learned how to use Formulas to join text together. Now we're going to delve deeper and do some more complex calculations.
What you'll learn
By the end of this tutorial you'll have learned:
• How to create a Formula to perform mathematical calculations
• An introduction to Functions
Time to complete: ≤15 minutes
From Text to Mathematical Calculations
Using the same Pie, open Scene 3 - Calculate. This Scene has two input fields and four buttons. What we'd like is for the user to input a number in each field, and then select the calculation they'd like to perform — in our case, Addition, Subtraction, Multiplication or Division. We're going to have our Pie make the desired calculation and display the result below the buttons.
• Add a Text Response to the Result Layer.
• Since we are once again working with input that we don't yet know, we'll want to use a Formula. Choose Formula in the drop down below Content.
• Click the box below it and you'll see our familiar ∫x icon. Click it to expand the Formula input box.
• Like we did previously, click the icon that appears near the right end of the Formula box and choose the `Number 1` layer.
• We'd like to access the `text` property of this layer. Type the dot `.` character to reveal all of the properties for the `Number 1` Layer. Scroll down and choose text. Type `+` to tell ProtoPie you want to do some addition. Click the icon again and this time pick the `Number 2` layer. Type `.` and pick the `text` property.
Click OK to commit your Formula.
Let's Preview this. Enter a number in both input fields and click the `+` action button.
That... didn't work, did it? Instead of adding or two numbers and giving us the sum, ProtoPie instead joined the two numbers together. In my example, 5 + 6 gave me 56, not 11!
Why did this happen?
If you recall from Part 1, the `+` character in your Formula was used to tell ProtoPie you'd like to join some text together. Confusingly, it is also used when you'd like to add two numbers arithmetically. ProtoPie is intelligently trying to guess what type of operation you'd like to do, but in this case ProtoPie got it wrong. As the name might suggest, ProtoPie is treating the `text` property of the `Number 1` and `Number 2` fields as text, not as numbers, and therefore assumes you're trying to join two pieces of text together.
We can fix this by explicitly telling ProtoPie how to treat the `text` properties. We can use something called a Function to do this. A Function is a fancy name for a predefined set of instructions. We'd like one that Tells ProtoPie that the `text` properties should be treated as numbers.
• Click the ∫x icon to modify your formula. Click the `?` icon at the right end of the Formula entry box to open the documentation for Formulas in your browser.
• In the left-hand panel navigate to Formulas → Functions.
These are all of the Functions available in ProtoPie. When you're done this tutorial, take some time to explore all of the available Functions you can use in your Formulas.
• Scroll down to the Type Conversion section and look for the `number(source:TEXT)` function.
• All functions have a similar format:
• The name of the function, in this case `number`
• One or more parameters you supply to the function as input, enclosed in brackets (e.g., `(source:TEXT)`). What this means is that this function takes in a single parameter, and that parameter must be in text format. If a function takes multiple parameters, they are separated by a comma (e.g., `format(value:NUMBER,format:TEXT)` take two parameters, a number and some text).
• What type of information the function will give you back after it executes (e.g. `-> NUMBER`).
Since we have text and we'd like to convert it to a number, this function does exactly what we need! It takes in some text, and converts it to a number.
Let's Preview this again, and see it it fixed our problem.
Bingo!
All we need to do now is make similar interactions for our remaining buttons. You could go the long way and repeat all of the above steps again, but a faster way is to duplicate the work we've already done, and just modify it for the specific action.
• Click the Tap trigger in order select it. Right-click and choose Duplicate.
💡 Pro-tip: `cmd + D` on Mac or `ctrl + D` on Windows does the same thing.
Before we move on, we now have two Tap Triggers that are named the same thing. Let's rename then so that they are easier to understand. Double click the Trigger's label to rename the first one to Tap Add and the second one to Tap Subtract.
Let's modify our duplicated Trigger to work with the Subtract button and perform a subtraction action.
• Click the Tap Subtract Trigger to select it, and re-associate it with the Subtract Layer.
• Click the Text Response underneath it, and modify the formula to subtract instead of add. Change the `+` character to `-`
Do this two more times for the multiplication and division actions. By now you've likely realized that there is no multiply character on your keyboard, nor is there a divide character. Programmers solved this a long time ago by using `*` to represent multiplication, and `/` for division. Your Formulas should look like these respectively:
Formula: Multiplication
Formula: Division
If you Preview this, you should be able to execute all four actions against your numbers. And if you change your numbers to something else, your math will still work. That's the power of using Formulas!
A note on white space
In our formulas above we didn't use spaces around our operators (`+`, `-`, `*`, and `/` are all called operators). As your formulas get more complicated, this can make them harder to read. It's perfectly fine to rewrite a formula that looks like this:
like this (notice the spaces around the `*` character):
Both will do exactly the same thing, but the second one is a little easier to read. In fact you can add white space in many other places. Nothing wrong with this, for example:
ProtoPie is even smart enough to figure out what you mean by this:
There are a few places where white space does matter, though. We already covered the difference between `"Hello,"` and `"Hello, "`. Also, if you try to do this:
ProtoPie will not like this. Variable names can't have spaces in them. ProtoPie interprets this thinking that you are trying to use three different variables, none of which can be found. ProtoPie tries to help you by underlining the problem areas with a red zig-zag. Whenever you run into problems with your Formulas, checking for the red zig-zag underline is a great place to start.
"There you go! Easy as " + Type of Pie.text + " Pie!"
You should now have a good grasp on how you can use formulas to make your Pies incredibly lifelike. You do not need to stick to static values, as the ability to use Formulas can be found almost anywhere in ProtoPie — just look for the ∫x icon. Take some time to explore all the ways you can use Formulas to take your experiences to the next level!
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Abhas Sinha ∙ 7 min read | 1,708 | 7,501 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2024-33 | latest | en | 0.901279 |
https://mathematica.stackexchange.com/questions/58619/add-to-the-last-digit-a-number | 1,656,779,376,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104189587.61/warc/CC-MAIN-20220702162147-20220702192147-00779.warc.gz | 428,960,992 | 64,934 | # Add to the last digit a number
I have data from a Multimeter that has a precision of 0.6%rdg+4dgt. So i want to take the last digit of, say, 12.007 and add 4 to the last digit like 12.011. I'm doing RealDigits[12.007,10,5][[1,-1]]add 4 and then somehow withFromDigits get the result...it seems trivial but i don't see how.
Perhaps something like:
ClearAll[func];
func[add_, pos_: (-1)] := N@FromDigits@MapAt[# + add &, RealDigits[##], {{1, pos}}] &
func[4, -1][12.007, 10, 5]
(* 12.011 *)
func[4, -3][12.707, 10, 5]
(* 13.107 *)
• it works fine but i want to use it in a rule like {a_,b_}->{a,fun[4,-1]@b}but it seems that first apply the function to a and then the substitution rule. Sep 1, 2014 at 14:11
• @Kafkarudo, can you give an example for the list you are trying to transform? Btw, perhaps you need :> instead of ->?
– kglr
Sep 1, 2014 at 14:23
• yep, the :> did it! thank a lot. Sep 1, 2014 at 14:28 | 333 | 917 | {"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} | 2.859375 | 3 | CC-MAIN-2022-27 | latest | en | 0.815223 |
https://eandbsoftware.org/significance/48293_3643.aspx | 1,669,801,492,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710734.75/warc/CC-MAIN-20221130092453-20221130122453-00789.warc.gz | 251,633,053 | 17,403 | Two key assumptions are that the distributions are at least ordinal in nature and that they are identical, internal customers and employees.
Bootstrap samples t test based on the appropriate steps outlined about
The area in red is called the rejection region. Just one tailed hypothesis completely changes based on one tailed tests for rejection rate for common significance becomes. Is it obligatory to participate in conference if accepted?
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What should i do now? Here is the table of critical values for the Pearson correlation. On the other hand, at one point in time, and a host of other problems will be obvious from the density trace on the histogram. The larger the t score, perhaps the finding is not really rare.
Calculate the t value, the data transformed to the log scale appeared to be approximately normally distributed.
Build a two? From Online Java ClassSchema Xml. Char ArrayMachine Learning Mastery Pty.
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Compute summary statistics texts for moses extreme as a table, interpret it together: charts will report.
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Inferences for small, and bootstrap histograms section on our sample size that separates these decimals are.
• It is possible that the two means could come from the same population and have the same difference.
To obtain these two tailed tests are sampled from tables available in table at least for interpreting statistics?
Order Tracking WereTreaties Were BrokenIf two tests?
What we say that? How can have, t test significance table two tailed or below table? So, you may want to see if the number of older siblings is different for students who have higher GPAs than for students who have lower GPAs. Ci provides bootstrap distributions, two tailed hypothesis?
Some very helpful information available here! You should select one of the following four situations based on the status of the normality and equal variance assumptions. Earphones and to reject ho, if your population means or only.
Check your significance? If the same amount of tails and validity of observations about the tail or view of the previous plots of t table lookup is. Imagine that the null hypothesis is true; that is, select File, take a look and see how it compares to the one you calculated from the data.
Degrees of freedom must be a positive number! Your significance needs to.
Most would choose the nonparametrictest. Draw a normal curve, or the rejection of the null hypothesis when it is in facttrue. With larger sample sizes, that this is only one statistic, it is appropriate for the vast majority of research studies. If it directly from encyclopaedia britannica newsletter to learn more than or alternative hypotheses are different from another group that there are. The unranked anova on all three alternative hypothesis should appear with a researcher assumes that there will explain what do as such misuses so? The following are typical hypothesis for means, strictly speaking, while rejecting significance may give us a false sense of confidence that the finding does not exist.
Check the Testcheck box. How are identical for students because statistics are on subjective interpretations are present each variable types. For students reported in doing so, t distribution based on how about a draft was successfully deleted, it could possibly be determined by. | 2,043 | 10,829 | {"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 | 3 | CC-MAIN-2022-49 | latest | en | 0.937674 |
http://www.t-vec.com/forums/viewtopic.php?p=20 | 1,544,387,445,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823009.19/warc/CC-MAIN-20181209185547-20181209211547-00330.warc.gz | 555,048,058 | 6,417 | ## Floating-point precision
A place for discussing topics that do not fit into the other VGS categories
### Floating-point precision
Hi,
I want to know how TVGS decide the floating-point precision.
For example,if the expression is:
a > 10.0
the type of "a" is double.
How to decide the low bound or high bound?
jack
Posts: 16
Joined: Sat Mar 15, 2008 9:59 am
### Re: Floating-point precision
The subject of floating point precision in VGS is pretty complicated. There are many rules and relationships that go into determining the current precision of a variable. First, let me address your specific question about
if the expression is:
a > 10.0
the type of "a" is double.
How to decide the low bound or high bound?
VGS starts with the data type of the variable involved. The IEEE Float64 (double) and IEEE Float32 (single/float) standards are the starting point. FLoat64 representation has about 15.5 decimal digits of precision to start with. Float32 has only about 5.5 decimal digits. At this point, VGS only assumes 14 and 5 digits, respectively, as a starting point. Now, with respect to your question
How to decide the low bound or high bound?
If the user does not specify a range for "a" then VGS will default the low and high bound range values to +/- 1.0e+012 (double) and +/- 1.0E+004 (floats) so that at the boundaries a variable sill has 4 and 1 digits of precision below the decimal point. For example if "a" is a double then its default domain, at its low/high values, can expect to be able to represent values with these digits
xxxxxxxxxx.xxxx
If "a" was a single/float type, then it will be able to represent maximum and minimum values with these digits
xxxx.x
These default limits +/- 1.0e+012 (double) and +/- 1.0E+004 (floats) have been chosen based on about 20 years of VGS development experience. This does not mean that TTM model can not work with numbers that are of greater magnitudes. However, to do so requires use of user-defined data types rather than default data types.
Now, these limits and precisions are only starting point values. If "a" is involved in relationships with any other variables and/or computational operators, its expected precision value can grow towards fewer digits of precision due to round-off errors in the computations and due to inequality relationships with other variables. This precision information is used in the determination of the new high/low bound limits when "a" is in a relationship such as
a > 10.0
In order to insure that all single point values for "a" will satisfy the a > 10.0 relationship in the actual executing code on the target platform, VGS will converge the domain of "a" to a low bound value based on the current precision knowledge about "a" and also based on the magnitude of the constant or variable that "a" is being compared with. In this case, because the initial low_bound for "a" was -1.0e+012 its initial precision setting only included a few places to the right of the decimal point. In addition, because it is being compared to a number 10.0 that has a magnitude a couple places to the left of the decimal point the resulting low bound, after comparison with 10.0 will be 1.02e+001. However, if the initial domain for "a" was +/-1.0e+004 and "a" was still a double, then its initial precision would include a larger number of decimal places to the right of the decimal point and its low bound after comparison to 10.0 would instead be 1.000000001e+001.
The subject of floating point precision/tolerance is too complex for a User's Forum reply, and the algorithms used to determine this informaion is also very proprietary. But I hope my reply does provide enough information to gain a basic understanding about the topic and answers your questions to your satisfaction.
busser
Posts: 52
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# Chapter 30
Chapter 30. Sources of the Magnetic Field. 30.1 Biot-Savart Law – Introduction. Biot and Savart conducted experiments on the force exerted by an electric current on a nearby magnet They arrived at a mathematical expression that gives the magnetic field at some point in space due to a current.
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## Chapter 30
E N D
### Presentation Transcript
1. Chapter 30 Sources of the Magnetic Field
2. 30.1 Biot-Savart Law – Introduction • Biot and Savart conducted experiments on the force exerted by an electric current on a nearby magnet • They arrived at a mathematical expression that gives the magnetic field at some point in space due to a current
3. Biot-Savart Law – Set-Up • The magnetic field is at some point P • The length element is • The wire is carrying a steady current of I Please replace with fig. 30.1
4. Biot-Savart Law – Observations • The vector is perpendicular to both and to the unit vector directed from toward P • The magnitude of is inversely proportional to r2, where r is the distance from to P
5. Biot-Savart Law – Observations, cont • The magnitude of is proportional to the current and to the magnitude ds of the length element • The magnitude of is proportional to sin q, where q is the angle between the vectors and
6. Biot-Savart Law – Equation • The observations are summarized in the mathematical equation called the Biot-Savart law: • The magnetic field described by the law is the field due to the current-carrying conductor • Don’t confuse this field with a field external to the conductor
7. Permeability of Free Space • The constant mo is called the permeability of free space • mo = 4p x 10-7 T. m / A
8. Total Magnetic Field • is the field created by the current in the length segment ds • To find the total field, sum up the contributions from all the current elements I • The integral is over the entire current distribution
9. Biot-Savart Law – Final Notes • The law is also valid for a current consisting of charges flowing through space • represents the length of a small segment of space in which the charges flow • For example, this could apply to the electron beam in a TV set
10. Compared to • Distance • The magnitude of the magnetic field varies as the inverse square of the distance from the source • The electric field due to a point charge also varies as the inverse square of the distance from the charge
11. Compared to , 2 • Direction • The electric field created by a point charge is radial in direction • The magnetic field created by a current element is perpendicular to both the length element and the unit vector
12. Compared to , 3 • Source • An electric field is established by an isolated electric charge • The current element that produces a magnetic field must be part of an extended current distribution • Therefore you must integrate over the entire current distribution
13. for a Long, Straight Conductor • The thin, straight wire is carrying a constant current • Integrating over all the current elements gives
14. for a Long, Straight Conductor, Special Case • If the conductor is an infinitely long, straight wire, q1= p/2 and q2= -p/2 • The field becomes
15. for a Long, Straight Conductor, Direction • The magnetic field lines are circles concentric with the wire • The field lines lie in planes perpendicular to to wire • The magnitude of the field is constant on any circle of radius a • The right-hand rule for determining the direction of the field is shown
16. for a Curved Wire Segment • Find the field at point O due to the wire segment • I and R are constants • q will be in radians
17. for a Circular Loop of Wire • Consider the previous result, with a full circle • q = 2p • This is the field at the center of the loop
18. for a Circular Current Loop • The loop has a radius of R and carries a steady current of I • Find the field at point P
19. Comparison of Loops • Consider the field at the center of the current loop • At this special point, x = 0 • Then, • This is exactly the same result as from the curved wire
20. Magnetic Field Lines for a Loop • Figure (a) shows the magnetic field lines surrounding a current loop • Figure (b) shows the field lines in the iron filings • Figure (c) compares the field lines to that of a bar magnet
21. 30.2 Magnetic Force Between Two Parallel Conductors • Two parallel wires each carry a steady current • The field due to the current in wire 2 exerts a force on wire 1 of F1 = I1ℓB2 PLAY ACTIVE FIGURE
22. Magnetic Force Between Two Parallel Conductors, cont. • Substituting the equation for gives • Parallel conductors carrying currents in the same direction attract each other • Parallel conductors carrying current in opposite directions repel each other
23. Magnetic Force Between Two Parallel Conductors, final • The result is often expressed as the magnetic force between the two wires, FB • This can also be given as the force per unit length:
24. Definition of the Ampere • The force between two parallel wires can be used to define the ampere • When the magnitude of the force per unit length between two long, parallel wires that carry identical currents and are separated by 1 m is 2 x 10-7 N/m, the current in each wire is defined to be 1 A
25. Definition of the Coulomb • The SI unit of charge, the coulomb, is defined in terms of the ampere • When a conductor carries a steady current of 1 A, the quantity of charge that flows through a cross section of the conductor in 1 s is 1 C
26. 30.4 Magnetic Field of a Solenoid • A solenoid is a long wire wound in the form of a helix • A reasonably uniform magnetic field can be produced in the space surrounded by the turns of the wire • The interior of the solenoid
27. Magnetic Field of a Solenoid, Description • The field lines in the interior are • nearly parallel to each other • uniformly distributed • close together • This indicates the field is strong and almost uniform
28. Magnetic Field of a Tightly Wound Solenoid • The field distribution is similar to that of a bar magnet • As the length of the solenoid increases • the interior field becomes more uniform • the exterior field becomes weaker
29. Ideal Solenoid – Characteristics • An ideal solenoid is approached when: • the turns are closely spaced • the length is much greater than the radius of the turns
30. Ampere’s Law Applied to a Solenoid • Ampere’s law can be used to find the interior magnetic field of the solenoid • Consider a rectangle with side ℓ parallel to the interior field and side w perpendicular to the field • This is loop 2 in the diagram • The side of length ℓ inside the solenoid contributes to the field • This is side 1 in the diagram
31. Ampere’s Law Applied to a Solenoid, cont. • Applying Ampere’s Law gives • The total current through the rectangular path equals the current through each turn multiplied by the number of turns
32. Magnetic Field of a Solenoid, final • Solving Ampere’s law for the magnetic field is • n = N / ℓ is the number of turns per unit length • This is valid only at points near the center of a very long solenoid
33. 30.5 Magnetic Flux • The magnetic flux associated with a magnetic field is defined in a way similar to electric flux • Consider an area element dA on an arbitrarily shaped surface
34. Magnetic Flux, cont. • The magnetic field in this element is • is a vector that is perpendicular to the surface • has a magnitude equal to the area dA • The magnetic flux FB is • The unit of magnetic flux is T.m2 = Wb • Wb is a weber
35. Magnetic Flux Through a Plane, 1 • A special case is when a plane of area A makes an angle q with • The magnetic flux is FB = BA cos q • In this case, the field is parallel to the plane and F = 0 PLAY ACTIVE FIGURE
36. Magnetic Flux Through A Plane, 2 • The magnetic flux is FB = BA cos q • In this case, the field is perpendicular to the plane and F = BA • This will be the maximum value of the flux • Use the active figure to investigate different angles PLAY ACTIVE FIGURE
37. 30.6 Gauss’ Law in Magnetism • Magnetic fields do not begin or end at any point • The number of lines entering a surface equals the number of lines leaving the surface • Gauss’ law in magnetism says the magnetic flux through any closed surface is always zero:
38. 30.7 Displacement Current and the General Form of Ampère’s Law • Displacement Current • Ampere’s law in the original form is valid only if any electric fields present are constant in time • Maxwell modified the law to include time-saving electric fields • Maxwell added an additional term which includes a factor called the displacement current, Id
39. Displacement Current, cont. • The displacement current is not the current in the conductor • Conduction current will be used to refer to current carried by a wire or other conductor • The displacement current is defined as • FE = òE . dA is the electric flux and eo is the permittivity of free space
40. Ampere’s Law – General Form • Also known as the Ampere-Maxwell law
41. Ampere’s Law – General Form, Example • The electric flux through S2 is EA • A is the area of the capacitor plates • E is the electric field between the plates • If q is the charge on the plate at any time, FE = EA = q/eo
42. Ampere’s Law – General Form, Example, cont. • Therefore, the displacement current is • The displacement current is the same as the conduction current through S1 • The displacement current on S2 is the source of the magnetic field on the surface boundary
43. Ampere-Maxwell Law, final • Magnetic fields are produced both by conduction currents and by time-varying electric fields • This theoretical work by Maxwell contributed to major advances in the understanding of electromagnetism
44. 30.8 Magnetic Moments • In general, any current loop has a magnetic field and thus has a magnetic dipole moment • This includes atomic-level current loops described in some models of the atom • This will help explain why some materials exhibit strong magnetic properties
45. Magnetic Moments – Classical Atom • The electrons move in circular orbits • The orbiting electron constitutes a tiny current loop • The magnetic moment of the electron is associated with this orbital motion • is the angular momentum • is magnetic moment
46. Magnetic Moments – Classical Atom, 2 • This model assumes the electron moves • with constant speed v • in a circular orbit of radius r • travels a distance 2pr in a time interval T • The current associated with this orbiting electron is
47. Magnetic Moments – Classical Atom, 3 • The magnetic moment is • The magnetic moment can also be expressed in terms of the angular momentum
48. Magnetic Moments – Classical Atom, final • The magnetic moment of the electron is proportional to its orbital angular momentum • The vectors and point in opposite directions • Because the electron is negatively charged • Quantum physics indicates that angular momentum is quantized
49. Magnetic Moments of Multiple Electrons • In most substances, the magnetic moment of one electron is canceled by that of another electron orbiting in the same direction • The net result is that the magnetic effect produced by the orbital motion of the electrons is either zero or very small
50. Electron Spin • Electrons (and other particles) have an intrinsic property called spin that also contributes to their magnetic moment • The electron is not physically spinning • It has an intrinsic angular momentum as if it were spinning • Spin angular momentum is actually a relativistic effect
More Related | 2,565 | 11,537 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2024-18 | latest | en | 0.894428 |
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1. ### Multiple temperature reservoirs
I have a problem: A typical compartment domestic refrigerator with freezer can be represented by 3 temperature reservoirs connected to the cyclic device which absorbs W' of work. - cool box at Tc = +279K from which Q'c heat is extracted - freezer at Tf = -269k from which a further Q'f...
2. ### Principal stresses help ?
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3. ### Principal stresses help ?
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7. ### To find the sum of a fourier series ?
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8. ### Please check my solution
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9. ### Please check this differentiation result
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12. ### Would this work ?
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Designing folding legs for a bunk bed..... Im having trouble finding a suitable hinge mechanism which would allow 2 legs under a bed to be locked and pulling them down into a vertical position they would lock. Does anyone have any ideas or links to a suitable hinge design. Thanks | 1,131 | 4,516 | {"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} | 3.296875 | 3 | CC-MAIN-2021-49 | latest | en | 0.915172 |
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A119407 Number of nonempty subsets of {1,2,...,n} with no gap of length greater than 4 (a set S has a gap of length d if a and b are in S but no x with a < x < b is in S, where b-a=d). 3
1, 3, 7, 15, 31, 62, 122, 238, 462, 894, 1727, 3333, 6429, 12397, 23901, 46076, 88820, 171212, 330028, 636156, 1226237, 2363655, 4556099, 8782171, 16928187, 32630138, 62896622, 121237146, 233692122, 450456058, 868281979, 1673667337, 3226097529, 6218502937, 11986549817, 23104817656 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 COMMENTS The numbers of subsets of {1,2,...,n} with no gap of length greater than d, for d=1,2 and 3, seem to be given in A000217, A001924 and A062544, respectively. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,-1,1). FORMULA G.f. for number of nonempty subsets of {1,2,...,n} with no gap of length greater than d is x/((1-x)*(1-2*x+x^(d+1))). - Vladeta Jovovic, Apr 27 2008 From Michael Somos, Dec 28 2012: (Start) G.f.: x/((1-x)^2*(1-x-x^2-x^3-x^4)) = x/((1-x)*(1-2*x+x^5)). First difference is A107066. (End) a(n-3) = Sum_{k=0..n} (n-k)*A000078(k) for n>3. - Greg Dresden, Jan 01 2021 EXAMPLE G.f. = x + 3*x^2 + 7*x^3 + 15*x^4 + 31*x^5 + 62*x^6 + 122*x^7 + 238*x^8 + 462*x^9 + ... MATHEMATICA Rest@CoefficientList[Series[x/((1-x)*(1-2*x+x^5)), {x, 0, 40}], x] (* G. C. Greubel, Jun 05 2019 *) LinearRecurrence[{3, -2, 0, 0, -1, 1}, {1, 3, 7, 15, 31, 62}, 40] (* Harvey P. Dale, Dec 04 2019 *) PROG (PARI) {a(n) = if( n<0, n = -n; polcoeff( x^5 / ((1 - x)^2 * (1 + x + x^2 + x^3 - x^4)) + x * O(x^n), n), polcoeff( x / ((1 - x)^2 * (1 - x - x^2 - x^3 - x^4)) + x * O(x^n), n))} /* Michael Somos, Dec 28 2012 */ (PARI) my(x='x+O('x^40)); Vec(x/((1-x)*(1-2*x+x^5))) \\ G. C. Greubel, Jun 05 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x/((1-x)*(1-2*x+x^5)) )); // G. C. Greubel, Jun 05 2019 (Sage) a=(x/((1-x)*(1-2*x+x^5))).series(x, 40).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jun 05 2019 CROSSREFS Cf. A000217, A001924, A062544, A107066. Sequence in context: A218281 A057703 A006739 * A224521 A269167 A261586 Adjacent sequences: A119404 A119405 A119406 * A119408 A119409 A119410 KEYWORD nonn AUTHOR John W. Layman, Jul 25 2006 EXTENSIONS Terms a(25) onward added by G. C. Greubel, Jun 05 2019 STATUS approved
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Last modified September 17 16:32 EDT 2021. Contains 347487 sequences. (Running on oeis4.) | 1,161 | 2,903 | {"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-2021-39 | latest | en | 0.634549 |
https://discourse.mcneel.com/t/laser-cutting-nurbs-curve/623 | 1,544,423,590,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823318.33/warc/CC-MAIN-20181210055518-20181210081018-00217.warc.gz | 592,393,102 | 4,204 | # Laser cutting NURBS curve
#1
Greetings -
Have curve “A” detailed as follows:
Geometry:
Valid curve.
Closed polycurve with 8 curve segments.
Segment 1:
Open NURBS curve
start = (-7.07029,-2.24453,0)
end = (-5.75547,-0.929714,0)
degree = 3
control points: non-rational, count=724
knots: non-uniform, domain = 6134.88 to 6854.88
clamped at start and end
Segment 2: …
[snip]
Eight similar segments totaling 8x724 = 5792 control points.
This curve severely bogs down the laser cutter.
Offset curve “A” some small amount (say .001”) and get curve “B” detailed as follows:
Geometry:
Valid curve.
Closed NURBS curve
start = (-5.7564,-0.929332,0)
end = (-5.7564,-0.929332,0)
degree = 3
control points: non-rational, count=1567 (1 duplicate)
knots: non-uniform, domain = 0 to 26.9605
clamped at start and end
That’s it – just 1567 control points in a nearly-identical shaped curve “B” which laser cuts nicely.
Question: How to convert curve “A” to the characteristics of curve “B” in-place?
Tried several approaches to no avail – offsetting to both sides then “tweening”, rebuilding, change degree, convert, ConvertToBeziers, etc…
It’s apparently possible to simplify this curve from ~6000 control points to ~1500 control points without changing its shape.
Thanks,
Tom Longtin
#2
First thing I might try is FitCrv with a max deviation tolerance you can manage. Set the angle tolerance so it doesn’t smooth over the kinks.
I assume that the curve has kinks in it and that’s why Rebuild doesn’t work for you, because otherwise, with that high a point count, I think it would also not alter the shape too much if you reduced the point count significantly with Rebuild.
If you can, post the curve in question and someone will look…
–Mitch
#3
I always use “convert” on anything that’s not already straight lines and/or pure arcs before I export. I use it with the angle tolerance set to zero… which allows the arc segments to not be perfectly tangent, but I crank up the tolerance to about 0.001 which keeps plenty accurate enough for all my uses, and it certainly stays completely smooth on a visual level to the human eye.
#4
Thanks, Guys - Got best results with FitCrv:
Fitting tolerance <0.0010> ( DeleteInput=No Degree=3 OutputLayer=Input AngleTolerance=0.001 ):
Reduced control points from ~6000 to ~1000 in a nearly-identical curve - laser cutter happy now!
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# Paleontologists believe that fragments of a primate jawbone unearthed
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Re: Paleontologists believe that fragments of a primate jawbone unearthed [#permalink]
rpfinley
Paleontologists believe that fragments of a primate jawbone unearthed in Burma and estimated at 40 to 44 million years old provide evidence of a crucial step along the evolutionary path that led to human beings.
(A) at 40 to 44 million years old provide evidence of
at isn't the right usage therefore out
(B) as being 40 to 44 million years old provides evidence of
being is a huge red flag as always in addition provides isn't the right usage therefore out
(C) that it is 40 to 44 million years old provides evidence of what was
THe right idom is to be therefore out
(D) to be 40 to 44 million years old provide evidence of
The idiom is perfect therefore our answer
(E) as 40 to 44 million years old provides evidence of
as isn't the right idiom therefore out
THerefore IMO D
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Re: Paleontologists believe that fragments of a primate jawbone unearthed [#permalink]
2
Kudos
BLTN
GMATNinja
Dear Charles,
could you elaborate, are the following sentences correct?
- Company was estimated at \$3 million
- The power of hydroelectric station is estimated at 13 MW
If no, why the official GMAT question utilized this construction in the Non-underlined portion of the sentence?
- With surface temperatures estimated at minus 230 degrees Farenheit, Jupiter's moon Europa has long been considered far too cold to support life, and with 60 square miles of water though to be frozen from top to bottom
The value of a company could be estimated at \$3 million, but the company itself? Nah.
For the second sentence, something like "the energy expenditure" or "usage" might make a little more sense than "power," but I wouldn't say it's fundamentally wrong.
Two practical points to keep in mind: 1) don't waste energy evaluating the non-underlined portion of sentences! You can't change them. And there are too many possible constructions to try to internalize what's acceptable and what isn't.
2) Just ask yourself whether what you're reading, if interpreted literally, is logical. If it's illogical, eliminate the answer. If it's logical, or if you're just not sure, hang on to it, and look for other issues. That's it. No memorization or agonizing required.
I hope that helps!
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Re: Paleontologists believe that fragments of a primate jawbone unearthed [#permalink]
“Estimated to be” is correct and is preferred over “estimated at”
arpanpatnaik
zazoz
Hi guys! just a refresher, enjoy!
Paleontologists believe that fragments of a primate jawbone unearthed in Burma and estimated at 40 to 44 million years old provide evidence of a crucial step along the evolutionary path that led to human beings.
(A) at 40 to 44 million years old provide evidence of
(B) as being 40 to 44 million years old provides evidence of
(C) that it is 40 to 44 million years old provides evidence of what was
(D) to be 40 to 44 million years old provide evidence of
(E) as 40 to 44 million years old provides evidence of what was
OA: D
I guess the trick is to understand the difference between 'estimated at' and 'estimated to be'. Since at is a preposition, it should be followed by a noun, whereas 40 to 40 million years old is not. Hence the structure is inaccurate. Furthermore 'estimated to be' is the proper idiomatic usage which includes the infinitive to make sure a valid range can be described.
Good one zazoz!
Regards,
A
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Re: Paleontologists believe that fragments of a primate jawbone unearthed [#permalink]
Question sentence - > "Paleontologists believe that fragments of a primate jawbone unearthed in Burma and estimated at 40 to 44 million years old provide evidence of a crucial step along the evolutionary path that led to human beings."
My Query - >
I may be wrong here, but isn't this sentence a fragment(without a working verb).
Please correct me if I am incorrect, but according to my understanding "fragments of a primate jawbone" is the subject( thing about which the statement is made ) of the sentence.
AND
In the question there is no working verb expressing an action, an occurrence, or a state of being of the subject. But in the correct choice "to be" is the working verb.
Can you please confirm if my understanding is correct? If not, can you please explain how am I incorrect.
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Re: Paleontologists believe that fragments of a primate jawbone unearthed [#permalink]
1
Kudos
gmdsat
No, the sentence core of A is the same as that of D: Paleontologists believe that fragments provide evidence. The "estimated" portion is a modifier, and so nothing in there is working as a verb for the main subject. Also, "to be" can never be the main verb of a sentence. It must be conjugated!
The only difference at this point is one of idiom: we say "estimated to be" a certain age, not "estimated at."
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Re: Paleontologists believe that fragments of a primate jawbone unearthed [#permalink]
1
Kudos
gmdsat
Question sentence - > "Paleontologists believe that fragments of a primate jawbone unearthed in Burma and estimated at 40 to 44 million years old provide evidence of a crucial step along the evolutionary path that led to human beings."
My Query - >
I may be wrong here, but isn't this sentence a fragment(without a working verb).
Please correct me if I am incorrect, but according to my understanding "fragments of a primate jawbone" is the subject( thing about which the statement is made ) of the sentence.
AND
In the question there is no working verb expressing an action, an occurrence, or a state of being of the subject. But in the correct choice "to be" is the working verb.
Can you please confirm if my understanding is correct? If not, can you please explain how am I incorrect.
Hello gmdsat,
We hope this finds you well.
To clarify, in Option A the verb "provide" is the active verb that acts upon the subject noun "fragments".
The same is true in Option D - the correct answer choice - and, in fact, "unearthed" and "estimated to be" are both past participles acting as modifiers.
We hope this helps.
All the best!
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Re: Paleontologists believe that fragments of a primate jawbone unearthed [#permalink]
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1 17.0 Linear Regression 1 Answer Questions Lines Correlation Regression
2 17.1 Lines The algebraic equation for a line is Y = β 0 + β 1 X 2 The use of coordinate axes to show functional relationships was invented by René Descartes ( ). He was an artillery officer, and probably got the idea from pictures that showed the trajectories of cannonballs.
3 17.2 Correlation 3 Sir Francis Galton explored Africa, invented eugenics, studied whether ships that carried missionaries were less likely to be lost at sea, pioneered birth-and-death models and meteorology, and was Charles Darwin s cousin. He also was the first to conceive of linear regression (although he did not have the mathematical skill to develop the formulae, and got a friend of his at Cambridge to do the derivations).
4 Correlation is a measure of the strength of the linear association between two continuous variables. An early example studied the relationship between the height of fathers and the height of sons. 4 Clearly, tall fathers tend to have tall sons, and short fathers tend to have short sons. If the father s height were a perfect predictor of the son s height, then all father-son pairs would lie on a straight line in a scatterplot. Regression fits a line to the points in a scatterplot. The term comes from the father-son example. An exceptionally tall father tends to have sons that are shorter than himself; an exceptionally short father tends to have sons that are taller than himself. Thus the sons height tend to regress towards the mean.
5 The sample correlation coefficient r measures the strength of the linear association between X and Y values in a scatterplot. If the absolute value of the correlation is near 1, then knowing one variable determines the other variable almost perfectly (if the relationship is linear). r lies between -1 and 1, inclusive. 5 r equals 1 iff all points lie on a line with positive slope. r equals -1 iff all points lie on a line with negative slope. non-zero r does not imply a causal relationship. The square of the correlation is called the coefficient of determination. It is the proportion of the variation in Y that is explained by knowledge of X.
6 6
7 To estimate the true correlation coefficient, define SS xx = (x i x) 2 = x 2 i n x 2 SS yy = (y i ȳ) 2 = y 2 i nȳ 2 SS xy = (x i x)(y i ȳ) = x i y i n xȳ. 7 Note: if divided by n 1, these are the sample versions of the variances and the covariance. So there s no need to memorize. Then the sample correlation is r = SS xy SSxx SS yy. One can show that the coefficient of determination r 2 is the proportion of the variance in Y that is explained by knowledge of X.
8 Correlations are often high when some factor affects both X and Y. GPA and SAT scores are both affected by IQ. number of hours spent listening to Rob Zombie and GPA are both affected by lifestyle. 8 It is hard to argue that correlation implies causation. GPA does not cause SAT, and Rob Zombie does not hurt GPA. But sometimes, there might be a causal link. Hours of study are probably correlated with GPA, and it seems likely to be causal. Ecological correlations occur when X or Y or both is an average, proportion, or a percentage for a group. Here causation is especially difficult to show. The original link between smoking and lung cancer was an ecological correlation (Doll, 1955). The scatterplot showed the lung cancer rate against the proportion of smokers for 11 different countries.
9 9
10 17.3 Regression The mathematical model for regression assumes that: 1. Each point (X i, Y i ) in the scatterplot satisfies: Y i = β 0 + β 1 X i + ǫ i 10 where the ǫ i have a normal distribution with mean zero and (usually) unknown standard deviation. 2. The errors ǫ i are independent. 3. The X i values are measured without error. (Thus all error occurs in the vertical direction.) The response variable is labeled Y. This is sometimes called the dependent variable. The explanatory variable is labeled X. This is sometimes called the independent variable, or the covariate.
11 Regression tries to fit the best straight line to the data. Specifically, it fits the line that minimizes the sum of the squared deviations from each point to the line, where deviation is measured in the vertical direction. Note: This does not measure deviation as the perpendicular distance from the point to the line. 11
12 How does one find the estimates ˆβ 0 and ˆβ 1 of the coefficients in the regression equation? We need to get the values that minimize the sum of the squared vertical distances. (Gauss, of course.) The sum of the squared vertical distances is 12 f(β 0, β 1 ) = n [Y i (β 0 + β 1 X i )] 2. i=1 So take the derivative of f(β 0, β 1 ) with respect to β 0 and β 1, set these equal to zero, and solve. One finds that: ˆβ 0 = Ȳ ˆβ 1 X; ˆβ1 = SS xy /SS xx.
13 The regression line predicts the average value of Y for a specific value of X. This is not the same as saying that an individual s value lies on the line. An individual is likely to be far from the line. 13 Under our assumptions, the distance of an individual from the regression line is normally distributed with mean 0 and standard deviation σ ǫ. We do not know the true σ ǫ, but we can estimate it from the sample standard deviation of the residuals. The residuals are the {ˆǫ i = y i ŷ i }, where ŷ i is the value predicted by the regression line. This difference is the estimated error ˆǫ i for the ith observation. Then ˆσ ǫ = 1 n (y i ŷ i ) n 2 2. Why do we divide by n 2? i=1
14 Recall that SS x = n i=1 (X i X) 2. Then a two-sided 100(1 α)% confidence interval on the location of the true regression line at x is ˆβ 0 + ˆβ 1 (x X) 2 1 x ± ˆσ ǫ + t n 2,α/2. n SS x 14 A two-sided 100(1 α)% prediction interval on the location of an individual whose value of the explanatory variable is x is ˆβ 0 + ˆβ 1 x ± ˆσ ǫ (x X) 2 + t n 2,α/2. n SS x One-sided intervals are formed in the obvious way. If the sample size is large, you use the z-table instead of the t n 2 -table. And if you sample without replacement, you can use the FPCF to multiply ˆσ ǫ. The ˆσ ǫ is sometimes called root mean squared error or rmse.
15 Example 1.a: The DUS want to set 95% confidence intervals on the starting salaries (in thousands) of Duke statistics majors as a function of their GPA. Based on the 15 people who majored last year, we find β 0 = 20 and ˆβ 1 = 10. The rmse was 4, SS x = 4, X = 3.2. What is the average starting salary for people who have GPAs of 3.5? 15 ˆβ 0 + ˆβ 1 1 x ± ˆσ ǫ n (x X) 2 + SS x t n 2,α/2 = ± ( ) The DUS is 95% confident that the mean starting salary is between L = \$52.42K and U = \$57.58K.
16 Example 1.b: Poindexter has a GPA of 3.5 and asks the DUS to set a 95% prediction interval on his starting salary. 16 ˆβ 0 + ˆβ 1 x ± ˆσ ǫ n = ± 4 (x X) 2 + SS x t n 2,α/2 + ( ) The DUS is 95% confident that his starting salary will be between L = \$45.98K and U = \$64.02K. Note that for both intervals, the uncertainty increases as one tries to set intervals for x-values that are far from X. This is reasonable if there is a certain amount of wigggle error in the fitted regression line, the magnitude of the error increases with distance from X.
17 Be aware that regressing weight as a function of height gives a different regression line than regressing height against weight. If your best estimate of the weight of a man who is 5 10 is 170 pounds, that does not mean that the best estimate of the height of a man who weighs 170 pounds is The regression fallacy mistakenly argues that there is some effect or force that causes sons to be more average than their fathers. In fact, this is only the natural operation of random chance. Consider scores on a first and second exam, and also the father-son height example. What can you say about the performance of baseball players in the first and second halves of the season? Or stock-traders, or new employees?
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# Despite what was hoped, the introduction of a sixty-five
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Despite what was hoped, the introduction of a sixty-five [#permalink]
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19 Jul 2011, 21:37
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Despite what was hoped, the introduction of a sixty-five mile per hour speed limit is reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution from the decreased amount of time trucks spend on the road.
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less polluting
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution
E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution
The question is, whats the guiding rule in such constructions and why the answer is what it is.
[Reveal] Spoiler: OA
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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19 Jul 2011, 22:09
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jn.mohit wrote:
@sudhir18n can you please eloborate more on 'C' and how 'E' is much better than 'C'
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution..........uses the wrong idiom and does not follow the rule of parallelism
Observe both C and E.
C: not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution
E:not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution
Not reducting THE congestion vs not reducing congestion
subtle difference..
Not reducting THE congestion : This means reducing X to do Y
is it contributing to save gas : this should be in the form of : is it contributing the saving of gas .. to be parallel
E makes those changes- Reducing congestion and contributing to lower gas costs...
hope this helps.
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Re: Despite what was hoped, the introduction of a sixty-five [#permalink]
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15 May 2012, 23:29
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RohitKalla wrote:
Despite what was hoped, the introduction of a sixty-five mile per hour speed limit is reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution from the decreased amount of time trucks spend on the road.
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less polluting
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution
E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution
The question is, whats the guiding rule in such constructions and why the answer is what it is.
+1 for E.
Here is the explanation:
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution--> wrong,it is neither ... nor.
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less pollution--> it doesnot makes sense with the clause after the second comma.
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution-->The use of and makes it wrong.
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution-->for the argument to be true, idiomatically neither should be accompanied by nor.hence this one is wrong.
E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution--> this one is correct.
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Re: Despite what was hoped, the introduction of a sixty-five [#permalink]
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04 Jun 2017, 20:42
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Expert's post
techiesam wrote:
GMATNinja,
GMATNinjaTwo
daagh
Flawed question.
Contribute to + noun is correct. The preposition "to" after contribute is not the same "to" you see in an infinite - it is a preposition that requires a noun as the object of preposition. - Contribute to + verb is wrong. The mistake is similar to the following that we often use at the end of a letter:
Looking forward to see you... wrong. ("looking forward to" requires a noun.)
Looking forward to seeing you.... correct. (gerund "seeing" is a noun and is hence alright)
Similarly "contribute to" requires a noun - usage of gerund "lowering" instead of verb "lower" is required.
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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19 Jul 2011, 21:55
@sudhir18n can you please eloborate more on 'C' and how 'E' is much better than 'C'
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution..........uses the wrong idiom and does not follow the rule of parallelism
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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19 Jul 2011, 23:42
I too agree with E...thanks sudhir18n
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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20 Jul 2011, 05:13
[quote="sudhir18n"][quote="jn.mohit"]
Not reducing THE congestion vs not reducing congestion
subtle difference..
Not reducing THE congestion : This means reducing X to do Y What do you mean by this?
I haven't really got what you explained for the usage of "THE".. A lil more explanation please...
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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20 Jul 2011, 13:53
Good question and very good explanation by Sudhir!
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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20 Jul 2011, 17:15
+1 E
I eliminated choice C because "save gas" is not the real meaning of the sentence.
Good question.
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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07 Sep 2011, 11:57
Quote:
Despite what was hoped, the introduction of a sixty-five mile per hour speed limit is reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution from the decreased amount of time trucks spend on the road.
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less polluting
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution
E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution
*note: not necessary that 'nor' be used with 'neither'
Quote:
RohitKalla wrote:
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution.........does not follow the correct idiomatic usage... neither X nor Y.
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less polluting............follow the correct idiomatic usage neither X nor Y, and uses an incorrect tense 'polluting'- thus is incorrect
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution..........uses the wrong idiom and does not follow the rule of parallelism
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution............wrong on the use of tense 'it is less pollution'
E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution...........unconventional but the most clear and concise option
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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29 Sep 2011, 00:10
RohitKalla wrote:
Despite what was hoped, the introduction of a sixty-five mile per hour speed limit is reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution from the decreased amount of time trucks spend on the road.
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less polluting
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution
E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution
The question is, whats the guiding rule in such constructions and why the answer is what it is.
It's tough question.
I also chose C. But Sudhir's explanation is impressive.
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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19 Oct 2011, 06:29
Toughie, i selected C
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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24 Oct 2011, 05:59
+1 for E.
Elimination of other choices is the way to go in this problem, rather than picking the correct choice.
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Re: One of the Kind of SC that cause congestion in my brain [#permalink]
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29 Oct 2011, 04:38
RohitKalla wrote:
Despite what was hoped, the introduction of a sixty-five mile per hour speed limit is reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution from the decreased amount of time trucks spend on the road.
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less polluting
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution
E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution
The question is, whats the guiding rule in such constructions and why the answer is what it is.
+1 for E. E uses correlative conjunctions most idiomatically.
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16 May 2012, 00:52
"E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution--> this one is correct. "
But what you suggest is: neither A nor B or C.
Shouldn't it be: neither A nor B nor C??
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Re: Despite what was hoped, the introduction of a sixty-five [#permalink]
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20 Sep 2012, 12:36
E) not reducing congestion on rural highways, nor is it contributing to lower gas costs for truck companies or less pollution
I see that this choice violates parallelism. it should've been "nor contributing" if it is to be parallel to "not reducing"
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Re: Despite what was hoped, the introduction of a sixty-five [#permalink]
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28 Jan 2013, 00:35
Despite what was hoped, the introduction of a sixty-five mile per hour speed limit is reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution from the decreased amount of time trucks spend on the road.
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less polluting
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution
E) not reducing congestion on rural highways, nor is it contributing to {lower gas costs for truck companies or less pollution}
In C, the use of "and" changes the meaning.
But regardless of this error, one thing that I noticed is that in E, we are talking about "gas costs", whereas in the original choie we are talking about its "amount".
Hasn't the answer choice E deviated from the sense?
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Re: Despite what was hoped, the introduction of a sixty-five [#permalink]
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28 Jan 2013, 00:55
Marcab wrote:
Despite what was hoped, the introduction of a sixty-five mile per hour speed limit is reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution from the decreased amount of time trucks spend on the road.
A) reducing neither congestion on rural highways, or it is not contributing to save gas for trucking companies and less pollution
B) reducing neither the congestion on rural highways nor is it contributing to lower gas costs for trucking companies, or to less polluting
C) not reducing the congestion on rural highways nor is it contributing to save gas for trucking companies, and it is not lessening the pollution
D) not reducing the congestion on rural highways, it is not contributing to savings on gas for trucking companies, it is less pollution
E) not reducing congestion on rural highways, nor is it contributing to {lower gas costs for truck companies or less pollution}
In C, the use of "and" changes the meaning.
But regardless of this error, one thing that I noticed is that in E, we are talking about "gas costs", whereas in the original choie we are talking about its "amount".
Hasn't the answer choice E deviated from the sense?
Not really.
The meaning of the sentence is : The hope was to get following benefits by imposing speed limit : 1. reduced congestion 2. lowered gas consumption 3. reduced pollution. But none of these has happened.
Actually apart from meaning, only E retains the grammatical structure. Notice C has three elements connected with not, nor, and. While in E there are 2 elements connected with not-nor and second elements itself has 2 elements connected with or. Perfectly done.
Therefore Ans E it is.
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28 Jan 2013, 01:12
I don't have any problem with the grammatical construction of E. The only think that is bothering me here is the use of "gas costs". We were originally concerned with the saving of gas.
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28 Jan 2013, 01:19
Marcab wrote:
I don't have any problem with the grammatical construction of E. The only think that is bothering me here is the use of "gas costs". We were originally concerned with the saving of gas.
Logically both mean same things isnt it? If you are saving gas your are saving gas cost. Not everyone is environmentalist but still wants a car with better mileage?
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26 Math Castroconde Chapter 6 1. 2. 3. Name: I.D.#: 4 3 1 3 4 , y = , z = 2 are mutually orthogonal and find a nonzero Show that x = 2 1 3 1 2 4 vector w in R 4 such that {x, y, z w} is an orthogonal set. 1 1 3 Let u = 1 , w = 1 , v = 1 . Let W = span{u, w}. 1 0 1 a. Show that {u, w} is an orthogonal basis for W. b. Find projW v . c. Find the distance from v to W. Let W be the...
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26 Math Castroconde Chapter 6 1. 2. 3. Name: I.D.#: 4 3 1 3 4 , y = , z = 2 are mutually orthogonal and find a nonzero Show that x = 2 1 3 1 2 4 vector w in R 4 such that {x, y, z w} is an orthogonal set. 1 1 3 Let u = 1 , w = 1 , v = 1 . Let W = span{u, w}. 1 0 1 a. Show that {u, w} is an orthogonal basis for W. b. Find projW v . c. Find the distance from v to W. Let W be the subspace of R 3 represented by the plane with equation x + y + z =0. 1 1 Show that B = 0 , 1 is a basis for W and use it to construct an orthonormal 1 0 basis W. 4. Find for the orthogonal complement W of the subspace W of question 3. 5. Assume A and B are n x n orthogonal matrices, and let k be any nonzero real number. Determine if the matrices kA, A + B, and AB are orthogonal by proving that each is or by providing a counter example if it is not. 6. 3 1 1 1 , u = 2 , w = 4 , and let W = {v, u, w}. Let v = 1 1 7 a. b. c. 7. Show that W is an orthogonal set. Using the elements of W, construct an orthogonal matrix A. Find A1 . 1 2 3 1 4 , b = 1 . Find a least-squares solution of Ax = b. Let A = 1 2 5
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Feb 9 2010ME 3281 Spring 2010PROBLEM SET 54.20Wilson Santiago
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Feb 9 2010ME 3281 Spring 2010PROBLEM SET 6Wilson SantiagoFeb 9 2010ME 3281 Spring 2010Wilson SantiagoFeb 9 2010ME 3281 Spring 2010Wilson SantiagoFeb 9 2010ME 3281 Spring 2010Wilson Santiago
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7.24
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s=tf('s');H1 = (s-1)/(s+1);subplot(321)bode(H1);grid onsubplot(322)pzmap(H1);grid onH2 = (s+1)*(s+1)/s/(s+5);subplot(323)bode(H2);grid onsubplot(324)pzmap(H2);grid onH3 = s/(s*s+.2*s+100)/(s*s+.2*s+100);subplot(325)bode(H3);grid onsubplot(32
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University of Minnesota Crookston - ME - 3281 | 4,627 | 15,908 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2013-20 | latest | en | 0.871659 |
http://www.geekviewpoint.com/java/sorting/bucketsort | 1,713,276,277,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817095.3/warc/CC-MAIN-20240416124708-20240416154708-00331.warc.gz | 45,702,617 | 9,996 | # Bucket Sortby Isai Damier, Android Engineer @ Google
```/*****************************************************************************
* Author: Isai Damier
* Title: Bucketsort
* Project: geekviewpoint
* Package: algorithms
*
* Statement:
* Given a disordered list of integers, rearrange them in natural order.
*
* Sample Input: {8,5,3,1,9,6,0,7,4,2,5}
* Sample Output: {0,1,2,3,4,5,6,7,8,9,5}
*
* Time Complexity of Solution:
* Best Case O(n); Average Case O(n); Worst Case O(n).
*
* Approach:
* If it sounds too good to be true, then most likely it's not true.
* Bucketsort is not an exception to this adage. For bucketsort to work at
* its blazing efficiency, there are multiple prerequisites. First the
* hash function that is used to partition the elements need to be very
* good and must produce ordered hash: if i < k then hash(i) < hash(k).
* Second, the elements to be sorted must be uniformly distributed.
*
* The aforementioned aside, bucket sort is actually very good considering
* that counting sort is reasonably speaking its upper bound. And counting
* sort is very fast. The particular distinction for bucket sort is that
* it uses a hash function to partition the keys of the input array, so
* that multiple keys may hash to the same bucket. Hence each bucket must
* effectively be a growable list; similar to radix sort.
*
* Numerous Internet sites, including university pages, have erroneously
* written counting sort code and call them bucket sort. Bucket sort uses
* a hash function to distribute keys; counting sort creates a bucket for
* each key. Indeed there are perhaps greater similarities between radix
* sort and bucket sort, than there are between counting sort and bucket sort.
*
* In the presented program Java's Collections.sort(C) is used to sort each
* bucket. This is to inculcate that the bucket sort algorithm does not
* specify which sorting technique to use on the buckets. A programmer may
* choose to continuously use bucket sort on each bucket until the
* collection is sorted (in the manner of the radix sort program below).
* Whichever sorting method is used on the buckets, bucket sort still
* tends toward O(n).
*
****************************************************************************/
public void bucketsort(int[] input) {
//get hash codes
final int[] code = hash(input);
//create and initialize buckets to ArrayList: O(n)
List<Integer>[] buckets = new List[code[1]];
for (int i = 0; i < code[1]; i++) {
buckets[i] = new ArrayList<Integer>();
}
//distribute data into buckets: O(n)
for (int i : input) {
}
/**
* Sort each bucket: O(n).
* I mentioned above that the worst case for bucket sort is counting
* sort. That's because in the worst case, bucket sort may end up
* with one bucket per key. In such case, sorting each bucket would
* take 1^2 = O(1). Even after allowing for some probabilistic
* variance, to sort each bucket would still take 2-1/n, which is
* still a constant. Hence, sorting all the buckets takes O(n).
***/
for (List bucket : buckets) {
Collections.sort(bucket);
}
int ndx = 0;
//merge the buckets: O(n)
for (int b = 0; b < buckets.length; b++) {
for (int v : buckets[b]) {
input[ndx++] = v;
}
}
}
private int[] hash(int[] input) {
int m = input[0];
for (int i = 1; i < input.length; i++) {
if (m < input[i]) {
m = input[i];
}
}
return new int[]{m, (int) Math.sqrt(input.length)};
}
private int hash(int i, int[] code) {
return (int) ((double) i / code[0] * (code[1] - 1));
}```
```import org.junit.Test;
import static org.junit.Assert.*;
public class SortingTest {
@Test
public void testBucketsort() {
System.out.println(""bucketsort"");
int[] A = {8, 5, 3, 1, 9, 6, 0, 7, 4, 2, 5};
Sorting instance = new Sorting();
instance.bucketsort(A);
for (int i = 1; i < A.length; i++) {
if (A[i - 1] > A[i]) {
fail(""bucketsort method fails."");
}
}
}
}``` | 1,021 | 3,887 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2024-18 | latest | en | 0.875204 |
https://www.thestudentroom.co.uk/showthread.php?page=37&t=4118695 | 1,558,352,881,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232255943.0/warc/CC-MAIN-20190520101929-20190520123929-00508.warc.gz | 957,815,532 | 37,673 | # Edexcel AS/A2 Mathematics M2 - 17th June 2016 - Official ThreadWatch
Announcements
2 years ago
#721
(Original post by nitromeguy)
Answers to edexcel m2 uk paper
1 a) 4ms-2 b) 11/3
2) P =4900 R = 784 d= 53.1
3) c= 10/3
4) x =0.83m, angle 113.6
5) a) friction = (5gdsinthetacostheta)/4
Reaction= (5g/4)(4-dcos^2theta)
b) d = 2.56m
6)a) lambda = 30/7 b) speed 10.4 angle 73.6
7) a) Va = 3u/20 Vb = 21u/10 b) e=1/14 c) no since moving at same speed in same direction
In question 6bi, is the question measured clockwise? As in would 73.6 from i be the same as 163.6 from j
0
2 years ago
#722
So frustrating. Got all of it right except for the first question which I completely ****ed up. Hopefully I'll get get some method marks since I had the right method but slipped up at a point. If I get 90 I'll be over the moon lol
0
2 years ago
#723
People generally found it very tricky so hopefully boundaries will be low (centre of mass question was peaaaaaaaak)
0
2 years ago
#724
(Original post by target21859)
I hate having to wait so long for results day. It's the worst. Tbh I did well in fp2 and I find fp3 easier than fp2 so I should be fine. I've got S2 as back up any way but I need to start revising for that
Egh, I know, I just try to put results day out of my mind until it actually arrives. If you’ve done well in FP2 then you’ll have got some pretty high UMS there, it was a tough paper. I’m generally OK with FP3 but I really don’t like the loci problems they set in the conics questions.
0
2 years ago
#725
What grade would mid 40s be? (44-46ish) Would that be a D?
0
2 years ago
#726
You're all welcome, I'm helping the grade boundaries get lower .
Also, for question 6, I couldn't figure out a value for lambda so I just used lambda = 3 then went onto part b using this value. How many marks would I gain from part b for using this.
0
2 years ago
#727
(Original post by Craig1998)
You're all welcome, I'm helping the grade boundaries get lower .
Also, for question 6, I couldn't figure out a value for lambda so I just used lambda = 3 then went onto part b using this value. How many marks would I gain from part b for using this.
I would say if you did the right method you might not lose anything
0
2 years ago
#728
How many marks do you guys reckon I'll lose for adding the mass of the 2 shapes together then dividing by the total mass of the shapes (rather than subtracting the mass of the triangle from the mass of the sector then dividing). It means I got the distance from AD wrong and ofc the angle as a follow on from that. In terms of method, attempted to find the angle using tan-1 and that the angle in the triangle was 45 - my table of masses was also correct. Is about -4 marks fair? (out of 9)
0
2 years ago
#729
(Original post by pixelwulf)
What grade would mid 40s be? (44-46ish) Would that be a D?
Yup. C was 50 last yr
0
2 years ago
#730
Hmmmmmmhmmm, pretty relieved, because I was so stressed going in to the test, however I got 70.0 for Q)6 so it looks like a made a ittle error somewhere, but hopefully I won't loose too many marks for that... I know I've also lost 2 marks at the beginning for a silly error.
0
2 years ago
#731
(Original post by Craig1998)
You're all welcome, I'm helping the grade boundaries get lower .
Also, for question 6, I couldn't figure out a value for lambda so I just used lambda = 3 then went onto part b using this value. How many marks would I gain from part b for using this.
I did the exact same thing loool, I'm expecting no marks from that question to be fair
0
2 years ago
#732
Can someone tell me how to do 2b?
Just to make sure because I think I got 531
0
2 years ago
#733
(Original post by mani119)
Can someone tell me how to do 2b?
Just to make sure because I think I got 531
1/2m12.5^2= mgdsin+ dR
1
2 years ago
#734
(Original post by Mathlete2198)
Hi guys,
So I'm supposed to be revising for C3, but I remembered all the questions from 1-6. I'm really sad, sorry. If anyone remembers Q7 holla at me.
I hope that these are right, but remember, I'm a student just like you guys!
If you have any questions let me know.
Thanks a lot, hopefully more people can see this
0
2 years ago
#735
Q5 said write in terms d g theta I didn't do moments therefore never got d But my R and P was still correct how many marks lost??
0
2 years ago
#736
nitromeguy Q5 said write in terms d g theta I didn't do moments therefore never got d But my R and P was still correct how many marks lost??
0
2 years ago
#737
Damn damn damn damn, I got the i and j vectors the wrong way around, I said 3 was it's inital vertical speed. If all my working is correct how many marks could I lose ? 3 for answer marks?
0
2 years ago
#738
Predictions for full ums? what mark out of 75 do you lot think it'll be?
0
2 years ago
#739
(Original post by CD1998)
I would say if you did the right method you might not lose anything
I'll lose all the accuracy marks, I know that (I was just thinking I need to get some more method marks when I rushed to get that part done).
Tbh I did it last year in M1 with the lift question, couldn't do part a but I had a method for part b (they were both only 4 marks I think), so I could get 1-2 extra marks in part b using a random answer for part a.
0
2 years ago
#740
For 6bi I said that the angle for direction is 73 Degrees below the HORZONTAl is this correct?
0
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# If x, y and z are nonzero number
Author Message
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If x, y and z are nonzero number [#permalink]
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13 Jan 2013, 05:21
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### HideShow timer Statistics
If x, y and z are nonzero numbers and x – 2y = –z, which of the following is equal to 2?
A (x-y)/z
B (x+y)/z
C (x-z)/y
D (z-x)/y
E (z+y)/-x
[Reveal] Spoiler: OA
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Re: If x, y and z are nonzero number [#permalink]
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13 Jan 2013, 05:30
Ok. I plugged in x=5 y=3 so 5-2(3)=5-6=-1 therefor z=1
a. (5-3)/1=2
b. (5+3)/1=8
i get A. Can you please explain?
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Re: If x, y and z are nonzero number [#permalink]
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13 Jan 2013, 06:31
1
KUDOS
Expert's post
maglian wrote:
If x, y and z are nonzero numbers and x – 2y = –z, which of the following is equal to 2?
A (x-y)/z
B (x+y)/z
C (x-z)/y
D (z-x)/y
E (z+y)/-x
None of the options equal to 2 if x=2, y=4 and z=6. Can you please check the question?
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Re: If x, y and z are nonzero number [#permalink]
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15 Jan 2013, 08:36
2
KUDOS
after re-arranging the variables, 2 should be = (x+z)/(y)
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Re: If x, y and z are nonzero number [#permalink]
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Re: If x, y and z are nonzero number [#permalink]
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14 May 2016, 02:03
What is the answer? When I solve the equation all I get is x+z/y.
Re: If x, y and z are nonzero number [#permalink] 14 May 2016, 02:03
Display posts from previous: Sort by | 1,127 | 3,397 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2017-04 | latest | en | 0.782273 |
https://oeis.org/A133845 | 1,556,143,939,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578663470.91/warc/CC-MAIN-20190424214335-20190425000335-00496.warc.gz | 504,068,338 | 3,604 | This site is supported by donations to The OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A133845 Decimal expansion of maximum possible value of A B C-8 omega^3. 1
4, 4, 0, 0, 5, 3, 4, 6, 7, 0, 5, 2, 4, 9, 2, 3, 0, 2, 3, 9, 1, 3, 3, 4, 5, 2, 6, 5, 1, 8, 6, 1, 7, 4, 9, 9, 1, 6, 8, 2, 8, 1, 3, 7, 6, 8, 0, 2, 6, 6, 9, 8, 8, 1, 8, 9, 4, 2, 7, 2, 4, 6, 9, 3, 0, 7, 5, 2, 2, 0, 2, 1, 8, 7, 0, 0, 0, 3, 7, 1, 9, 6, 4, 6, 2, 7, 6, 9, 7, 5, 8, 9, 2, 3, 0, 7, 5, 8, 6, 3, 4, 8, 5, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET 0,1 LINKS Eric Weisstein's World of Mathematics, Yff Conjecture EXAMPLE 0.44005346705249230239... MATHEMATICA f[a_] := a^2*(Pi - 2*a) - 8*ArcCot[2*Cot[a] - Cot[2*a]]^3; a0 = a /. FindRoot[f'[a] == 0, {a, 3/2}, WorkingPrecision -> 110]; RealDigits[f[a0], 10, 105] // First (* Jean-François Alcover, Feb 07 2013, after Eric W. Weisstein *) CROSSREFS Cf. A133844. Sequence in context: A200505 A285242 A143266 * A282289 A291696 A291649 Adjacent sequences: A133842 A133843 A133844 * A133846 A133847 A133848 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Sep 26 2007 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
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Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.) | 688 | 1,505 | {"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-2019-18 | latest | en | 0.591551 |
https://nrich.maths.org/public/leg.php?code=149&cl=2&cldcmpid=8171 | 1,438,489,727,000,000,000 | text/html | crawl-data/CC-MAIN-2015-32/segments/1438042988962.66/warc/CC-MAIN-20150728002308-00237-ip-10-236-191-2.ec2.internal.warc.gz | 880,375,829 | 9,753 | # Search by Topic
#### Resources tagged with Area similar to Now and Then:
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### There are 88 results
Broad Topics > Measures and Mensuration > Area
##### Stage: 3 Challenge Level:
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
### Shaping It
##### Stage: 1 and 2 Challenge Level:
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
### All in a Jumble
##### Stage: 3 Challenge Level:
My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
### Rope Mat
##### Stage: 2 Challenge Level:
How many centimetres of rope will I need to make another mat just like the one I have here?
### Cutting it Out
##### Stage: 1 and 2 Challenge Level:
I cut this square into two different shapes. What can you say about the relationship between them?
### Uncanny Triangles
##### Stage: 2 Challenge Level:
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
### Fit These Shapes
##### Stage: 1 and 2 Challenge Level:
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
### Area and Perimeter
##### Stage: 2 Challenge Level:
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
### More Transformations on a Pegboard
##### Stage: 2 Challenge Level:
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
### Geoboards
##### Stage: 2 Challenge Level:
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
### Making Squares
##### Stage: 2 Challenge Level:
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
### A Day with Grandpa
##### Stage: 2 Challenge Level:
Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?
### Lawn Border
##### Stage: 1 and 2 Challenge Level:
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
### Great Squares
##### Stage: 2 and 3 Challenge Level:
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
### Two Squared
##### Stage: 2 Challenge Level:
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
### Numerically Equal
##### Stage: 2 Challenge Level:
Can you draw a square in which the perimeter is numerically equal to the area?
### Tiles on a Patio
##### Stage: 2 Challenge Level:
How many ways can you find of tiling the square patio, using square tiles of different sizes?
### Tiling
##### Stage: 2 Challenge Level:
An investigation that gives you the opportunity to make and justify predictions.
### Making Boxes
##### Stage: 2 Challenge Level:
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
### Fencing Lambs
##### Stage: 2 Challenge Level:
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
### Dicey Perimeter, Dicey Area
##### Stage: 2 Challenge Level:
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
### Tiles in the Garden
##### Stage: 2 Challenge Level:
How many tiles do we need to tile these patios?
### Cover the Tray
##### Stage: 2 Challenge Level:
These practical challenges are all about making a 'tray' and covering it with paper.
### Warmsnug Double Glazing
##### Stage: 3 Challenge Level:
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
### Through the Window
##### Stage: 2 Challenge Level:
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
### Fitted
##### Stage: 2 Challenge Level:
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
### Triangle Relations
##### Stage: 2 Challenge Level:
What do these two triangles have in common? How are they related?
### Ribbon Squares
##### Stage: 2 Challenge Level:
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
### It Must Be 2000
##### Stage: 2 Challenge Level:
Here are many ideas for you to investigate - all linked with the number 2000.
### The Big Cheese
##### Stage: 2 Challenge Level:
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
### Torn Shapes
##### Stage: 2 Challenge Level:
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
### My New Patio
##### Stage: 2 Challenge Level:
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
### Fence It
##### Stage: 3 Challenge Level:
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
### From One Shape to Another
##### Stage: 2
Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.
### Transformations on a Pegboard
##### Stage: 2 Challenge Level:
How would you move the bands on the pegboard to alter these shapes?
### Inside Seven Squares
##### Stage: 2 Challenge Level:
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
### Isosceles Triangles
##### Stage: 3 Challenge Level:
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
### Framed
##### Stage: 3 Challenge Level:
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
### Different Sizes
##### Stage: 1 and 2 Challenge Level:
A simple visual exploration into halving and doubling.
### Shape Draw
##### Stage: 2 Challenge Level:
Use the information on these cards to draw the shape that is being described.
### Dissect
##### Stage: 3 Challenge Level:
It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?
### Wrapping Presents
##### Stage: 2 Challenge Level:
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
### Triangle Island
##### Stage: 2 Challenge Level:
You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?
### Tiling Into Slanted Rectangles
##### Stage: 2 and 3 Challenge Level:
A follow-up activity to Tiles in the Garden.
### Extending Great Squares
##### Stage: 2 and 3 Challenge Level:
Explore one of these five pictures.
### Fencing
##### Stage: 2 Challenge Level:
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
### How Random!
##### Stage: 2 Challenge Level:
Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?
### A Square in a Circle
##### Stage: 2 Challenge Level:
What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
### Poly-puzzle
##### Stage: 3 Challenge Level:
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas. | 1,960 | 8,744 | {"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} | 3.78125 | 4 | CC-MAIN-2015-32 | longest | en | 0.905964 |
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## Question number: 59
» Physics » Source of Energy
MCQ▾
### Question
The site of a hydroelectric plant should be chosen carefully because it
### Choices
Choice (4) Response
a.
produces a large amount of carbon mono-oxide and carbon dioxide
b.
affects the organism of region
c.
produces a large amount of electricity
d.
is expensive
## Question number: 60
» Physics » Sound
MCQ▾
### Question
In a medium, sound travels 2 km in 3 s and in air, it travels 3 km in 10 s. The ratio of the wavelength of sound in the two medium is
### Choices
Choice (4) Response
a.
1: 18
b.
8: 1
c.
1: 8
d.
20: 9
## Question number: 61
» Physics » Sound
MCQ▾
### Question
Sonar emits which of the following waves?
### Choices
Choice (4) Response
a.
Light waves
b.
Magnetic waves
c.
d.
Ultrasonic waves
## Question number: 62
» Physics » Sound
MCQ▾
### Question
Which of the following is the longitudinal wave?
### Choices
Choice (4) Response
a.
Water waves
b.
Waves on plucked string
c.
Sound waves
d.
Light waves
## Question number: 63
» Physics » Light
MCQ▾
### Question
Two plane mirrors are inclined to each other at an angle of as shown in figure. A ray of light falls on the mirror at angle and after reflection, falls on the other mirror from which it get reflected by angle i. The value of third angle is?
### Choices
Choice (4) Response
a.
b.
c.
d.
## Question number: 64
» Physics » Motion and Force
MCQ▾
### Question
The figure shown below depicts the distance travelled by a body as a function of time.
The average speed and maximum speed between 0 and 20 s are
### Choices
Choice (4) Response
a.
2.0 m/s, 2.6 m/s respectively
b.
1 m/s, 2.0 m/s respectively
c.
1.3 m/s, 2.0 m/s respectively
d.
1 m/s, 1.6 m/s respectively
f Page | 603 | 2,166 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2018-22 | latest | en | 0.755448 |
http://catdumps.blogspot.com/2010/02/gmat-question-of-day_18.html | 1,503,543,873,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886126027.91/warc/CC-MAIN-20170824024147-20170824044147-00363.warc.gz | 70,343,617 | 10,874 | Thursday, February 18, 2010
GMAT Question of the day
The numerator of a fraction is a multiple of two nos. One of the nos. is greater
than other by 2. The greater no. is smaller than the denominator by 1. If the
denominator is given as 5 + c (c is a constant), then the minimum value of the
fraction is
(a) 2
(b) –2
(c) –1/2
(d) 1/2
The fraction can be written as F = (4 + c) (2 + c) / (5 + c)
Put 5 + c = t or c = t – 5
∴ F = (t – 3) (t – 1)/t
= (t^2 – rt + 3)/t
= (t^2 – 4t + 4 – 1)/t
= (t – 2)^2/ t – 1/t
Hence, the given expression is minimum, if the square term is equal to zero
∴(t-2)/t = 0 or t = 2 | 246 | 608 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2017-34 | longest | en | 0.903455 |
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Dr. Hackney STA Solutions pg 133
# Dr. Hackney STA Solutions pg 133 - 8-12Solutions Manual for...
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Unformatted text preview: 8-12Solutions Manual for Statistical Inference8.26 a. We will prove the result for continuous distributions. But it is also true for discrete MLRfamilies. Forθ1> θ2, we must showF(x|θ1)≤F(x|θ2). Nowddx[F(x|θ1)-F(x|θ2)] =f(x|θ1)-f(x|θ2) =f(x|θ2)f(x|θ1)f(x|θ2)-1.Becausefhas MLR, the ratio on the right-hand side is increasing, so the derivative can onlychange sign from negative to positive showing that any interior extremum is a minimum.Thus the function in square brackets is maximized by its value at∞or-∞, which is zero.b. From Exercise 3.42, location families are stochastically increasing in their location param-eter, so the location Cauchy family with pdff(x|θ) = (π[1+(x-θ)2])-1is stochasticallyincreasing. The family does not have MLR.8.27 Forθ2> θ1,g(t|θ2)g(t|θ1)=c(θ2)c(θ1)e[w(θ2)-w(θ1)]twhich is increasing intbecausew(θ2)-w(θ1)>0. Examples include n(θ,1), beta(θ,1), andBernoulli(θ)....
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Ask a homework question - tutors are online | 415 | 1,307 | {"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-2018-09 | latest | en | 0.746436 |
https://www.cscodehelp.com/%E7%A7%91%E7%A0%94%E4%BB%A3%E7%A0%81%E4%BB%A3%E5%86%99/cs%E4%BB%A3%E8%80%83%E7%A8%8B%E5%BA%8F%E4%BB%A3%E5%86%99-compiler-osu-cse-2421-4/ | 1,722,816,413,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640417235.15/warc/CC-MAIN-20240804230158-20240805020158-00864.warc.gz | 561,243,368 | 16,033 | # CS代考程序代写 compiler OSU CSE 2421
OSU CSE 2421
Computer Systems: A Programmer’s Perspective, 3rd Edition,
Chapter 1 thru Section 1.3
Pointers on C,
Chapter 5 thru Section 5.1.3, 5.3 through the end of the chapter
J.E.Jones
OSU CSE 2421
lvalue/Lvalue/L-value: That operand found on the left side of the assignment operator.
◦ All L-values must be modifiable since they are being assigned a value.
rvalue/Rvalue/R-value: That expression found on the right side of the assignment operator.
◦ R-values can be constants, expressions, be a return value from a function, etc.
J. E. Jones
OSU CSE 2421
Operator =
+
*
/
%
>
>=
< <= == != && || ! ++ Category Assignment Mathematical Mathematical Mathematical Mathematical Mathematical Comparison Comparison Comparison Comparison Comparison Comparison Logical Logical Logical Mathematical Duty Operator Category ‐‐ Mathematical Duty Decrement by 1 Equals Addition & Subtraction | Multiplication ^ Division << Modulo >>
Bitwise Bitwise Bitwise Bitwise Bitwise Bitwise Unary Unary Unary Unary Unary
AND
Inclusive OR
Exclusive OR
Shift bits left
Shift bits right
One’s Complement Positive
Negative
Pointer
Returns size of an object Element Access
Pointer element Access odd ‘if’ expression;
not often used
Greater than
Greater than or equal to Less than
Less than or equal to
is equal to
is not equal to
AND
OR
NOT
Increment by 1
~
+
* & sizeof
. Structure ‐> Structure ?: Conditional
J. E. Jones
OSU CSE 2421
C operators can be classified according to the number of operands which they take.
C has unary operators, binary operators, and one ternary operator (the conditional operator ? : )
The operands of C operators are expressions, which can be constants, variables, or expressions which contain one or more operators.
Expressions will always be evaluated by the code which the compiler generates; that is, an expression has a value (which has a type, of course).
There is a table of operators posted on Piazza which shows which operators are unary, binary or ternary, and the precedence and associativity of each operator (precedence/associativity covered below).
J. E.4Jones
OSU CSE 2421
Precedence refers to the relationship between two operators in terms of the order in which the operations are performed.
Precedence is a binary relation, that is, it is defined with respect to pairs of (adjacent) operators. Binary operators are adjacent if they have one operand in common; unary operators are adjacent if they have the same operand.
We can always enforce a precedence different from the precedence specified by the language for 2 operators by using parentheses, because operations inside parentheses are done first (Have the highest precedence).
If two adjacent operators have the same precedence, then associativity is relevant.
L-R associativity means that the operation specified by the leftmost operator is done first, and then the one specified by the rightmost operator. R-L associativity, of course, means the opposite order.
Bottom Line: P&A in C is just like math class, but there are a few “new” operators
J. E. Jones
OSU CSE 2421
#include
/* program to show associativity of the “/” operator */ int main() {
}
float num1;
float num2;
float num3;
num1 = 2.0 / 1.0 / 2.0;
num2 = (2.0 / 1.0) / 2.0;
num3 = 2.0 / (1.0 / 2.0); printf(“num1 is: %f
”, num1); printf(“num2 is: %f
”, num2); printf(“num3 is: %f
”, num3);
What is printed?
J. E.6Jones
OSU CSE 2421
#include
/* program to show associativity of the “/” operator */ int main() {
}
float num1;
float num2;
float num3;
num1 = 2.0 / 1.0 / 2.0;
num2 = (2.0 / 1.0) / 2.0;
num3 = 2.0 / (1.0 / 2.0); printf(“num1 is: %f
”, num1); printf(“num2 is: %f
”, num2); printf(“num3 is: %f
”, num3);
/* num1 is: 1.000000 */
J. E.7Jones
OSU CSE 2421
#include
/* program to show associativity of the “/” operator */ int main() {
float num1;
float num2;
float num3;
num1 = 2.0 / 1.0 / 2.0;
num2 = (2.0 / 1.0) / 2.0;
num3 = 2.0 / (1.0 / 2.0); printf(“num1 is: %f
”, num1); printf(“num2 is: %f
”, num2);
/* num1 is: 1.000000 */
/* num2 is: 1.000000
Result with L-R associativity */
printf(“num3 is: %f
”, num3); }
J. E.8Jones
OSU CSE 2421
#include
/* program to show associativity of the “/” operator */ int main() {
}
float num1;
float num2;
float num3;
num1 = 2.0 / 1.0 / 2.0;
num2 = (2.0 / 1.0) / 2.0;
num3 = 2.0 / (1.0 / 2.0); printf(“num1 is: %f
”, num1); printf(“num2 is: %f
”, num2);
/* num1 is: 1.000000 */
/* num2 is: 1.000000
Result with L-R associativity */
printf(“num3 is: %f
”, num3);
/* num3 is: 4.000000
Result with R-L associativity */
J. E.9Jones
OSU CSE 2421
Let’s see how an expression is evaluated, using the precedence and associativity in C.
Suppose, before this statement is executed, ◦ a=1,b=3,andc=5,then
d = ++a * c + b++;
How does the compiler determine the order of operations?
J. E. Jones
OSU CSE 2421
How does the compiler determine the order of operations?
We can take the view that the compiler does the binary operation with the highest precedence first, then next highest, but expressions with unary operators are not evaluated until they need to be, in order to evaluate a larger expression of which they are a part.
We will also suppose that operands of binary operators are evaluated left to right (this is true for most compilers, and it is true for ours).
A good practice is to use parentheses to show the order of evaluation, starting with the binary operator which has the highest precedence, and going to the lowest, considering associativity where necessary.
So, let’s try to parenthesize the binary operators in the expression above, after parenthesizing all unary operator expressions (unary operators have higher precedence than all binary operators generally).
J. E. Jones
OSU CSE 2421
Parenthesize unary operators:
d = (++a) * c + (b++);
Precedence of binary operators: * first, then +, then = Now we can add the rest of the parentheses:
d = ((++a) * c) + (b++);
What is d after execution of this statement (Remember, before this statement, a = 1, b = 3, and c = 5)?
J. E. Jones
OSU CSE 2421
Value of expression 253
(d = ((++a) * c) + (b++)); d = (2 * 5) + 3
So, d has the value 13 and after the statement is executed
(a = 2, b = 4, and c = 5)
J. E. Jones
OSU CSE 2421
void main() {
[jones.5684@cse-fac2 test]\$ precedence d = 13, when no parens are used.
a=2, b=4, c=5
d = 13, when some parens are used. a=2, b=4, c=5
}
int a, b, c, d;
a=1;
b=3;
c=5;
d = ++a * c + b++;
printf(“d = %d, when no parens are used.
”, d); printf(“a=%d, b=%d, c=%d
”, a, b, c);
d = 13, when all parens are used. a=2, b=4, c=5 [jones.5684@cse-fac2 test]\$
a=1;
b=3;
c=5;
d = (++a) * c + (b++);
printf(“d = %d, when some parens are used.
”, d); printf(“a=%d, b=%d, c=%d
”, a, b, c);
a=1;
b=3;
c=5;
d = (((++a) * c) + (b++));
printf(“d = %d, when all parens are used.
”, d); printf(“a=%d, b=%d, c=%d
”, a, b, c);
J. E. Jones
OSU CSE 2421
In C, assignments are expressions. This means that an assignment expression, just as any expression, has a value, which is the value of the rightmost expression.
Assignment operator has lowest precedence (except for the comma operator) Embedded assignments – legal anywhere an expression is legal.
◦ This allows multiple assignment: a = b = 1; /*R-L associativity */
◦ We’ll see how these are used in C a bit later.
◦ Other assignment operators (compound assignment operators) – same associativity – R-L
+= , –= , *= , /= , %=
e.g., a += 6; equivalent to a = a + 6;
NOTE: Using an assignment operator (=) is legal anywhere it is legal to compare for equality (==), so it is not a syntax error (some compilers may give a warning, although stdlinux compiler will not!!!).
J. E. Jones
OSU CSE 2421
In Spring 1993, in the Operating System development group at SunSoft, we had a “priority-one” bug report come in describing a problem in the asynchronous I/O library. The bug was holding up the sale of \$20 million worth of hardware to a customer who specifically needed the library functionality, so we were extremely motivated to find it. After some intensive debugging sessions, the problem was finally traced to a statement that read:
x==2;
It was a typo for what was intended to be an assignment statement. The programmer’s finger had bounced on the “equals’ key, accidentally pressing it twice instead of once. The statement as written compared x to 2, generated true or false, and discarded the result.
C is enough of an expression language that the compiler did not complain about a statement which evaluated an expression, had no side-effects, and simply threw away the result. We didn’t know whether to bless our good fortune at locating the problem, or cry with frustration at such a common typing error causing such an expensive problem
J. E. Jones
OSU CSE 2421
• Mathematical Symbols
• +-*/%
• addition, subtraction, multiplication, division, modulus • Works for both integers and float
• +-*/
• / operator performs
integer division if both operands are integer, i.e., truncates answer So that there is only an integer result;
otherwise, if at least one operand is float, performs floating point division (i.e., implicit casting is used) result contains whole number and fractional decimal result.
• %operatordividestwointegeroperandsandgivesintegerresultofthe remainder
• Associativity – L-R.
• Precedence:
1. Anything inside () 2. * / %
3. + –
J. E. Jones
OSU CSE 2421
++aanda++havethebehaviorofa=a+1 ◦ (difference is WHEN increment occurs)
–aanda–havethebehaviorofa=a–1 ◦ (difference is WHEN decrement occurs)
[Postfix operators have higher precedence than prefix operators]
NOTEPOSITIONOFOPERATORANDWHATITMEANS
◦ ++a
◦ –a
◦ a++
◦ a–
◦ ++a–
a is incremented BEFORE a is evaluated in the expression
a is decremented BEFORE a is evaluated in the expression
a is incremented AFTER a is evaluated in the expression
a is decremented AFTER a is evaluated in the expression
most compilers will accept, but behavior is undefined/inexact (pick a compiler and roll the dice.)
In both examples below, the final value of a is 2
int main() int main() {{
int a = 1;
printf (“ a is %d”, ++a); return 0;
int a = 1;
printf (“ a is %d”, a++); return 0;
}}
/* 2 will be printed */ /* 1 will be printed */
J. E. Jones
OSU CSE 2421
What values occur here? ◦ If a=4, c=4, b=3,
◦ z=(a++>c)||(++b<=a) J. E. Jones OSU CSE 2421 What values occur here? ◦ If a=4, c=4, b=3, ◦ z=(a++>c)||(++b<=a) ◦ z=(4>4)||(4<=5) (4 > 4) evaluates to 0 (or false), a increments to 5 after evaluation
b increments to 4 before evaluation, (4 <= 5) evaluates to 1 (or true) J. E. Jones OSU CSE 2421 What values occur here? ◦ If a=4, c=4, b=3, ◦ z=(a++>c)||(++b<=a) ◦ z=(4>4)||(4<=5) (4 > 4) evaluates to 0 (or false), a increments to 5 after evaluation
b increments to 4 before evaluation, (4 <= 5) evaluates to 1 (or true) ◦ z = 0 || 1 J. E. Jones OSU CSE 2421 What values occur here? ◦ If a=4, c=4, b=3, ◦ z=(a++>c)||(++b<=a) ◦ z=(4>4)||(4<=5) (4 > 4) evaluates to 0 (or false), a increments to 5 after evaluation
b increments to 4 before evaluation, (4 <= 5) evaluates to 1 (or true) ◦ z = 0 || 1 ◦ z=1,a=5,c=4,b=4 J. E. Jones OSU CSE 2421 What values occur here? ◦ If a=4, c=4, b=3, ◦ z=(a++<=c)||(++b<=a) ◦ z=(4<=4)||(4<=5) (4 > 4) evaluates to 1 (or true), a increments to 5 after evaluation 2nd expression doesn’t execute because of short circuit
◦ z = 1 || unknown (don’t care)
◦ z=1,a=5,c=4,b=3
J. E. Jones | 3,570 | 11,442 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2024-33 | latest | en | 0.841111 |
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Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne | 838 | 2,397 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2021-21 | longest | en | 0.838366 |
https://datascience.stackexchange.com/questions/84718/why-the-sigmoid-activation-function-results-in-sub-optimal-gradient-descent | 1,701,233,786,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100056.38/warc/CC-MAIN-20231129041834-20231129071834-00516.warc.gz | 246,773,272 | 43,119 | Why the sigmoid activation function results in sub-optimal gradient descent?
I need some help understanding the second shortcoming of the sigmoid activation function as described in this video from Stanford. She says that because the output of sigmoid is always positive, that any gradients flowing back from a neuron following a sigmoid will all share the same sign as the upstream gradient flowing into that neuron. She then says that a consequence of these weight updates sharing the same sign is a sub-optimal zigzag gradient descent path.
I understand this phenomenon when zoomed in on a single neuron. However, since upstream gradients flowing into a layer can be of different signs, it's still possible to get a healthy mixture of positive and negative weight updates in a layer. Therefore, I'm having trouble understanding how using sigmoid results in this zigzag descent path, except for in the case where the upstream gradients are all of the same sign (which intuitively seems uncommon). It seems to me that if this suboptimal descent is important enough to be highlighted in the lecture, that it must be more common than that.
I'm wondering if the issue is "reduced entropy" among the weight updates, rather than all weight updates in the network sharing the same sign. That is, zigzagging in a subset of the dimensions. For example, say a network using sigmoid has four weights in a layer with two neurons: w1, w2, w3, and w4. The updates to w1 and w2 could be positive, while the updates to w3 and w4 could be negative if the two upstream gradients differ in sign. However, it wouldn't be possible for w1 and w3 to be positive, and w2 and w4 to be negative. Is this the limitation of sigmoid that the Stanford lecture is referring to, assuming the second combination of weight updates was the optimal one?
• Yes, the lecturer is refering to a single neuron. It's true that in the same layer we could have different signs of updates. However, by using sigmoid function, all the weights connecting to a single neuron will be updated increasing its value or decreasing it (and not both at the same time) $\rightarrow$ zig-zagging in order to reach the optimal value of the weights. Oct 31, 2020 at 8:26
• Thanks Javier. To make sure I understand your response, are you saying it’s correct that with sigmoid we zigzag in a subset of dimensions? That is, constraining the gradients flowing back from a single node to share the same sign is enough to cause the behavior, regardless of what the rest of the network is doing? Oct 31, 2020 at 15:57
• Yes, I think we are on the same page. Concretely, this happens because the update of a weight that connects a neuron $j$ with a neuron $k$ is given by a quantity proportional to: $$\frac{\partial C}{\partial w^l_{kj}}= \delta^l_k \,\,a_j^{l-1}$$ Where $C$ is the cost function, $a_j^{l-1}$ the activation of the neuron $j$ and $\delta^l_k$ the "error" term for the neuron $k$. $\delta^l_k$ is just a scalar, hence, if all $a_j^{l-1}$ are positive (this happens with sigmoid), then the updates of all the weights that connect to a neuron $k$ will have the same sign Oct 31, 2020 at 16:12
• Thanks for your comments Javier. It seems I can't mark a comment as an answer though. If you'd like to re-post this as an answer, I'll accept it. Nov 1, 2020 at 18:01
1 Answer
Two primary reasons sigmoid is a sub-optimal activation function for gradient descent:
1. A node's activation saturates at either tail of 0 or 1. The resulting gradient is very small at those points, thus a very small learning signal.
2. The maximum gradient is .25. Since this value is less than 1, the error signal is attenuated and can result in vanishing gradients after many layers of backpropagation.
• It might be useful to add that during backprop, the gradient is typically multiplied by the derivative of the activation function. Jun 22 at 8:51
• Also, a logistic sigmoid at the end of the network (in combination with binary cross-entropy) is not that much of a problem. (see e.g. this answer for some intuition) Jun 22 at 8:53 | 956 | 4,066 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2023-50 | longest | en | 0.926307 |
http://www.netlib.org/lapack/explore-3.1.1-html/dgbcon.f.html | 1,537,746,804,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267159938.71/warc/CC-MAIN-20180923232129-20180924012529-00016.warc.gz | 364,771,953 | 3,519 | ``` SUBROUTINE DGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
\$ WORK, IWORK, INFO )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
*
* .. Scalar Arguments ..
CHARACTER NORM
INTEGER INFO, KL, KU, LDAB, N
DOUBLE PRECISION ANORM, RCOND
* ..
* .. Array Arguments ..
INTEGER IPIV( * ), IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DGBCON estimates the reciprocal of the condition number of a real
* general band matrix A, in either the 1-norm or the infinity-norm,
* using the LU factorization computed by DGBTRF.
*
* An estimate is obtained for norm(inv(A)), and the reciprocal of the
* condition number is computed as
* RCOND = 1 / ( norm(A) * norm(inv(A)) ).
*
* Arguments
* =========
*
* NORM (input) CHARACTER*1
* Specifies whether the 1-norm condition number or the
* infinity-norm condition number is required:
* = '1' or 'O': 1-norm;
* = 'I': Infinity-norm.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KL (input) INTEGER
* The number of subdiagonals within the band of A. KL >= 0.
*
* KU (input) INTEGER
* The number of superdiagonals within the band of A. KU >= 0.
*
* AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
* Details of the LU factorization of the band matrix A, as
* computed by DGBTRF. U is stored as an upper triangular band
* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
* the multipliers used during the factorization are stored in
* rows KL+KU+2 to 2*KL+KU+1.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
*
* IPIV (input) INTEGER array, dimension (N)
* The pivot indices; for 1 <= i <= N, row i of the matrix was
* interchanged with row IPIV(i).
*
* ANORM (input) DOUBLE PRECISION
* If NORM = '1' or 'O', the 1-norm of the original matrix A.
* If NORM = 'I', the infinity-norm of the original matrix A.
*
* RCOND (output) DOUBLE PRECISION
* The reciprocal of the condition number of the matrix A,
* computed as RCOND = 1/(norm(A) * norm(inv(A))).
*
* WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
*
* IWORK (workspace) INTEGER array, dimension (N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LNOTI, ONENRM
CHARACTER NORMIN
INTEGER IX, J, JP, KASE, KASE1, KD, LM
DOUBLE PRECISION AINVNM, SCALE, SMLNUM, T
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IDAMAX
DOUBLE PRECISION DDOT, DLAMCH
EXTERNAL LSAME, IDAMAX, DDOT, DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DLACN2, DLATBS, DRSCL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KL.LT.0 ) THEN
INFO = -3
ELSE IF( KU.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
INFO = -6
ELSE IF( ANORM.LT.ZERO ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGBCON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
RCOND = ZERO
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
ELSE IF( ANORM.EQ.ZERO ) THEN
RETURN
END IF
*
SMLNUM = DLAMCH( 'Safe minimum' )
*
* Estimate the norm of inv(A).
*
AINVNM = ZERO
NORMIN = 'N'
IF( ONENRM ) THEN
KASE1 = 1
ELSE
KASE1 = 2
END IF
KD = KL + KU + 1
LNOTI = KL.GT.0
KASE = 0
10 CONTINUE
CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.KASE1 ) THEN
*
* Multiply by inv(L).
*
IF( LNOTI ) THEN
DO 20 J = 1, N - 1
LM = MIN( KL, N-J )
JP = IPIV( J )
T = WORK( JP )
IF( JP.NE.J ) THEN
WORK( JP ) = WORK( J )
WORK( J ) = T
END IF
CALL DAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
20 CONTINUE
END IF
*
* Multiply by inv(U).
*
CALL DLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
\$ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ),
\$ INFO )
ELSE
*
* Multiply by inv(U').
*
CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
\$ KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ),
\$ INFO )
*
* Multiply by inv(L').
*
IF( LNOTI ) THEN
DO 30 J = N - 1, 1, -1
LM = MIN( KL, N-J )
WORK( J ) = WORK( J ) - DDOT( LM, AB( KD+1, J ), 1,
\$ WORK( J+1 ), 1 )
JP = IPIV( J )
IF( JP.NE.J ) THEN
T = WORK( JP )
WORK( JP ) = WORK( J )
WORK( J ) = T
END IF
30 CONTINUE
END IF
END IF
*
* Divide X by 1/SCALE if doing so will not cause overflow.
*
NORMIN = 'Y'
IF( SCALE.NE.ONE ) THEN
IX = IDAMAX( N, WORK, 1 )
IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
\$ GO TO 40
CALL DRSCL( N, SCALE, WORK, 1 )
END IF
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM.NE.ZERO )
\$ RCOND = ( ONE / AINVNM ) / ANORM
*
40 CONTINUE
RETURN
*
* End of DGBCON
*
END
``` | 1,974 | 5,797 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-39 | latest | en | 0.723383 |
https://de.mathworks.com/matlabcentral/profile/authors/9134567?s_tid=cody_local_to_profile | 1,606,870,365,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141685797.79/warc/CC-MAIN-20201201231155-20201202021155-00408.warc.gz | 231,984,119 | 20,907 | Community Profile
# jianrui fan
51 total contributions since 2019
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Breaking Out of the Matrix
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I Plead the Fifth
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Is this is a Tic Tac Toe X Win?
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mehr als ein Jahr ago | 1,607 | 5,923 | {"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-2020-50 | latest | en | 0.45539 |
https://istopdeath.com/evaluate-3-1466/ | 1,675,839,214,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500719.31/warc/CC-MAIN-20230208060523-20230208090523-00545.warc.gz | 327,765,162 | 15,059 | # Evaluate 3.14*6*6
3.14⋅6⋅6
Multiply 3.14 by 6.
18.84⋅6
Multiply 18.84 by 6.
113.04
Evaluate 3.14*6*6 | 63 | 103 | {"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-2023-06 | latest | en | 0.520366 |
https://cu-numpde.github.io/fall22/slides/2022-09-21-transient.html | 1,670,598,701,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711417.46/warc/CC-MAIN-20221209144722-20221209174722-00361.warc.gz | 217,413,841 | 7,409 | 2022-09-21 Transient Intro#
Last time#
• Structured by-hand differentiation
• Concept of PDE-based inference (inverse problems)
• The Blasius problem (activity)
Today#
• Blasius working session
• Intro to transient problems
• Stability diagrams
• Energy dissipation
• $$A$$ and $$L$$ stability
using Plots
default(linewidth=3)
using LinearAlgebra
using SparseArrays
using Zygote
function vander(x, k=nothing)
if k === nothing
k = length(x)
end
V = ones(length(x), k)
for j = 2:k
V[:, j] = V[:, j-1] .* x
end
V
end
vander (generic function with 2 methods)
Compressible Blasius boundary layer#
• Activity will solve this 1D nonlinear PDE
Ordinary Differential Equations#
Given initial condition $$u_0 = u(t=0)$$, find $$u(t)$$ for $$t > 0$$ that satisfies
$\dot u \equiv \frac{\partial u}{\partial t} = f(t, u)$
Application
$$u$$
$$f$$
Orbital dynamics
position, momentum
conservation of momentum
Chemical reactions
concentration
conservation of atoms
Epidemiology
infected/recovered population
transmission and recovery
Heat transfer
temperature
conservation of energy
Seismology
displacement, momentum
conservative of momentum
Solving differential equations#
Linear equations#
$\dot u = A(t) u + \text{source}(t)$
• Autonomous if $$A(t) = A$$ and source independent of $$t$$
• Suppose $$u$$ and $$a = A$$ are scalars: $$u(t) = e^{at} u_0$$
Can do the same for systems#
$y(t) = e^{A t} y_0$
What does it mean to exponentiate a matrix?#
Taylor series!
$e^A = 1 + A + \frac{A^2}{2} + \frac{A^3}{3!} + \dotsb$
and there are many practical ways to compute it.
Question#
Suppose that the diagonalization $$A = X \Lambda X^{-1}$$ exists and derive a finite expression for the matrix exponential using the scalar exp function.
Forward Euler method#
function ode_euler(f, u0; tfinal=10., h=0.1)
u = copy(u0)
t = 0.
thist = [t]
uhist = [u0]
while t < tfinal
tnext = min(t+h, tfinal)
h = tnext - t
u += h * f(t, u)
t = tnext
push!(thist, t)
push!(uhist, u)
end
thist, hcat(uhist...)
end
ode_euler (generic function with 1 method)
f1(t, u; k=11) = -k * (u .- cos(t))
thist, uhist = ode_euler(f1, [.5], tfinal=10, h=.2)
scatter(thist, uhist[1,:])
plot!(cos) | 690 | 2,198 | {"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} | 3.34375 | 3 | CC-MAIN-2022-49 | latest | en | 0.698696 |
http://www.reference.com/browse/coefficient+of+performance | 1,432,437,867,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207927824.81/warc/CC-MAIN-20150521113207-00261-ip-10-180-206-219.ec2.internal.warc.gz | 692,121,386 | 17,709 | Definitions
# Coefficient of performance
The coefficient of performance, or COP (sometimes CP), of a heat pump is the ratio of the change in heat at the "output" (the heat reservoir of interest) to the supplied work:
$COP = frac$
{Delta W}>
where
• $|Delta Q|$ is the change in heat at the heat reservoir of interest, and
• $Delta W$ is the work consumed by the heat pump.
(Note: COP has no units, therefore in this equation, heat and work must be expressed in the same units.)
The COP for heating and cooling are thus different, because the heat reservoir of interest is different. When one is interested in how well a machine cools. For example, the COP is the ratio of the heat removed from the cold reservoir to input work. However, for heating, the COP is the ratio of the heat removed from the cold reservoir plus the heat added to the hot reservoir by the input work to input work:
$COP_\left\{heating\right\}=frac$
$COP_\left\{cooling\right\}=frac$
>{Delta W}
where
• $Delta Q_\left\{cold\right\}$ is the heat moved from the cold reservoir (to the hot reservoir).
## Derivation
According to the first law of thermodynamics, in a reversible system we can show that $Q_\left\{hot\right\}=Q_\left\{cold\right\}+W$ and $W=Q_\left\{hot\right\}-Q_\left\{cold\right\}$, where $Q_\left\{hot\right\}$ is the heat given off by the hot heat reservoir and $Q_\left\{cold\right\}$ is the heat taken in by the cold heat reservoir.
Therefore, by substituting for W,
$COP_\left\{heating\right\}=frac\left\{Q_\left\{hot\right\}\right\}\left\{Q_\left\{hot\right\}-Q_\left\{cold\right\}\right\}$
For a heat pump operating at maximum theoretical efficiency (i.e. Carnot efficiency), it can be shown that $frac\left\{Q_\left\{hot\right\}\right\}\left\{T_\left\{hot\right\}\right\}=frac\left\{Q_\left\{cold\right\}\right\}\left\{T_\left\{cold\right\}\right\}$ and $Q_\left\{cold\right\}=frac\left\{Q_\left\{hot\right\}T_\left\{cold\right\}\right\}\left\{T_\left\{hot\right\}\right\}$, where $T_\left\{hot\right\}$ and $T_\left\{cold\right\}$ are the temperatures of the hot and cold heat reservoirs respectively.
Hence, at maximum theoretical efficiency,
$COP_\left\{heating\right\}=frac\left\{T_\left\{hot\right\}\right\}\left\{T_\left\{hot\right\}-T_\left\{cold\right\}\right\}$
Similarly,
$COP_\left\{cooling\right\}=frac\left\{Q_\left\{cold\right\}\right\}\left\{Q_\left\{hot\right\}-Q_\left\{cold\right\}\right\} =frac\left\{T_\left\{cold\right\}\right\}\left\{T_\left\{hot\right\}-T_\left\{cold\right\}\right\}$
It can also be shown that $COP_\left\{cooling\right\}=COP_\left\{heating\right\}-1$. Note that these equations must use the absolute temperature, such as the Kelvin scale.
$COP_\left\{heating\right\}$ applies to heat pumps and $COP_\left\{cooling\right\}$ applies to air conditioners or refrigerators. For heat engines, see Efficiency. Values for actual systems will always be less than these theoretical maximums.
## Example
A geothermal heat pump operating at $COP_\left\{heating\right\}$ 3.5 provides 3.5 units of heat for each unit of energy consumed (e.g. 1 kW consumed would provide 3.5 kW of output heat). The output heat comes from both the heat source and 1 kW of input energy, so the heat-source is cooled by 2.5 kW, not 3.5 kW.
A heat pump of $COP_\left\{heating\right\}$ 3.5, such as in the example above, could be less expensive to use than even the most efficient gas furnace.
A heat pump cooler operating at $COP_\left\{cooling\right\}$ 2.0 removes 2 units of heat for each unit of energy consumed (e.g. such an air conditioner consuming 1 kW would remove heat from a building's air at a rate of 2 kW).
The COP of heat pumps compares favorably with high-efficiency gas-burning furnaces (90-99% efficient), and electric heating (100%), but the full costs of the energy consumed must be considered, and energy from gas is typically much less expensive than that from electricity.
Search another word or see coefficient of performanceon Dictionary | Thesaurus |Spanish | 1,188 | 4,006 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 23, "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-2015-22 | latest | en | 0.821385 |
https://tex.stackexchange.com/questions/481978/how-to-write-the-block-matrix-in-latex/481981 | 1,721,845,208,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518427.68/warc/CC-MAIN-20240724171328-20240724201328-00641.warc.gz | 495,636,473 | 41,481 | # How to write the block matrix in LaTex? [duplicate]
I wish to write the following block matrix in LaTex.
I have been trying a bunch of stuff, but none of it seems to work. In particular, I tried the following:
\begin{bmatrix}
0 & -1& & & & & 0 & & & &\\
1 & 0 & & & & & & & & &\\
& & \cdot & & & & & & & &\\
& & & \cdot & & & & & & &\\
& & & & \cdot & & & & & &\\
& & & & & 0 & 1 & & & &\\
& & & & &-1 & 0 & & & &\\
& & & & & & & \cdot & & &\\
& & & & & & & & \cdot & & \\
& & & & & & & & & \cdot & \\
0 & & & & & & & & & & 0\\
\end{bmatrix}
But this is pretty ugly and so any suggestions will be much appreciated.
Perhaps
$\left(\begin{array}{cccccc} \left[\begin{array}{cc} 0 & 1\\ -1 & 0 \end{array}\right] & & & & & 0\\ & \ddots\\ & & \left[\begin{array}{cc} 0 & 1\\ -1 & 0 \end{array}\right]\\ & & & 0\\ & & & & \ddots\\ 0 & & & & & 0 \end{array}\right)$
• Thank you so much! Commented Mar 28, 2019 at 20:45
Just for the fun of it! :-)
\documentclass{article}
\usepackage{amsmath,array}
\begin{document}
$\begin{pmatrix} \newcommand{\lr}[1]{\multicolumn{1}{|c}{#1}} \newcommand{\rr}[1]{\multicolumn{1}{c|}{#1}} \; \begin{array}{@{}*{10}{c}@{}} \cline{1-2} \lr{0} & \rr{1} &&&&&&&& \raisebox{-1em}[0pt][0pt]{0}\\ \lr{-1} & \rr{0} \\ \cline{1-2} && \ddots \\ \cline{4-5} &&& \lr{0} & \rr{1} \\ &&& \lr{-1} & \rr{0} \\ \cline{4-5} &&&&& 0 \\[-1ex] &&&&&& \ddots \\ &&&&&&& 0 \\[-1ex] &&&&&&&& \ddots \\ \multicolumn{2}{c}{0} &&&&&&&& 0 \end{array} \;\; \end{pmatrix}$
\end{document}
• You guys are the best! Commented Mar 28, 2019 at 22:40
• @model_checker I'm certainly not the best. Here is world excellence. Commented Mar 28, 2019 at 22:50
• I am sorry! Last I checked there was an objection to your answer. But it's also great! Commented Mar 28, 2019 at 22:53
• @model_checker Don't worry. I have put two & in addition. :-) but now it is correct. Commented Mar 28, 2019 at 23:02
Here there is my proposal as the original picture using \bmatx command that replace a boxed matrix.
\documentclass{article}
\usepackage{mathtools}
\newcommand{\bmatx}{\boxed{\begin{matrix} 0& 1 \\ -1& 0\end{matrix}}}
\begin{document}
$\begin{pmatrix} \, \bmatx& & & & & & & 0 \\ & \ddots& & & & \\ & & \bmatx & & & & \\ & & & \ddots& & &\\ & & & & 0 & &\\ & & & & & & \ddots\\ 0 & & & & & & & 0 \end{pmatrix}$
\end{document}
The best code is provided thanks to the precious comment of @Bernard.
• In my opinion, you shouldn't add an empty 3rd column in the definition of \bmatx\ Commented Mar 28, 2019 at 21:24
• Your comment not is an opinion :-) ...it is truly correct. :-) Commented Mar 28, 2019 at 21:30
Here's another solution. It uses a pmatrix environment for the overall matrix and a custom macro called \blockmat for the 2x2 inner matrices.
\documentclass{article}
\usepackage{array,amsmath}
\newcommand\blockmat{%
\begin{array}{|@{\,}rr@{\,}|}
\hline 0 & 1^{\mathstrut} \\ -1 & 0 \\ \hline
\end{array}}
\begin{document}
$\begin{pmatrix} \blockmat & & & & & 0 \\ & \ddots & & & & \\ & & \blockmat & & & \\ & & & 0 & & \\ & & & & \ddots & \\ 0 & & & & & 0 \\ \end{pmatrix}$
\end{document}
Here's a solution using TikZ that will work in all kinds of context, not just matrices, to draw boxes. You just need to put \tl in the point where the top-right corner is supposed to be and \br where the bottom-right will be. You can also use any TikZ feature to modify your box. Obviously this needs to be fine tuned depending on what exactly you're using it for (spacing etc.).
\newcounter{textbox}
\def\tl{\stepcounter{textbox}\tikzmarknode{a\thetextbox}{\strut}}
\def\br{\tikzmarknode{b\thetextbox}{\strut}\begin{tikzpicture}[overlay, remember picture]\draw (a\thetextbox.north west) rectangle (b\thetextbox.south east);\end{tikzpicture}}
The spacing in this version is not optimized for matrices, but you can use
\tikzmarknode{b\thetextbox}{\strut}\begin{tikzpicture}[overlay, remember picture]\draw ($(a\thetextbox.north west)+(-0.4\arraycolsep,0ex)$) rectangle ($(b\thetextbox.south east)+(0.4\arraycolsep,0ex)$);\end{tikzpicture}
to add extra space.
Full code:
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usetikzlibrary{tikzmark,calc}
\newcounter{textbox}
\def\tl{\stepcounter{textbox}\tikzmarknode{a\thetextbox}{\strut}}
\def\br{\tikzmarknode{b\thetextbox}{\strut}\begin{tikzpicture}[overlay, remember picture]\draw (a\thetextbox.north west) rectangle (b\thetextbox.south east);\end{tikzpicture}}
\begin{document}
$\begin{bmatrix} \tl0 &-1 & & & & & & & & 0 \\ 1 & 0\br & & & & & & & & \\ & & \cdot & & & & & & & \\ & & & \cdot & & & & & & \\ & & & & \cdot & & & & & \\ & & & & &\tl0 & 1 & & & \\ & & & & &-1 & 0\br & & & \\ & & & & & & & \cdot & & \\ & & & & & & & & \cdot & \\ 0 & & & & & & & & & \cdot \\ \end{bmatrix}$
\end{document} | 1,873 | 5,400 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2024-30 | latest | en | 0.415083 |
https://www.quizzes.cc/metric/percentof.php?percent=80.8&of=527 | 1,590,796,346,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347406785.66/warc/CC-MAIN-20200529214634-20200530004634-00045.warc.gz | 860,412,969 | 3,247 | What is 80.8 percent of 527?
How much is 80.8 percent of 527? Use the calculator below to calculate a percentage, either as a percentage of a number, such as 80.8% of 527 or the percentage of 2 numbers. Change the numbers to calculate different amounts. Simply type into the input boxes and the answer will update.
80.8% of 527 = 425.816
Calculate another percentage below. Type into inputs
Find number based on percentage
percent of
Find percentage based on 2 numbers
divided by
Calculating eighty point eight of five hundred and twenty-seven How to calculate 80.8% of 527? Simply divide the percent by 100 and multiply by the number. For example, 80.8 /100 x 527 = 425.816 or 0.808 x 527 = 425.816
How much is 80.8 percent of the following numbers?
80.8 percent of 527.01 = 42582.408 80.8 percent of 527.02 = 42583.216 80.8 percent of 527.03 = 42584.024 80.8 percent of 527.04 = 42584.832 80.8 percent of 527.05 = 42585.64 80.8 percent of 527.06 = 42586.448 80.8 percent of 527.07 = 42587.256 80.8 percent of 527.08 = 42588.064 80.8 percent of 527.09 = 42588.872 80.8 percent of 527.1 = 42589.68 80.8 percent of 527.11 = 42590.488 80.8 percent of 527.12 = 42591.296 80.8 percent of 527.13 = 42592.104 80.8 percent of 527.14 = 42592.912 80.8 percent of 527.15 = 42593.72 80.8 percent of 527.16 = 42594.528 80.8 percent of 527.17 = 42595.336 80.8 percent of 527.18 = 42596.144 80.8 percent of 527.19 = 42596.952 80.8 percent of 527.2 = 42597.76 80.8 percent of 527.21 = 42598.568 80.8 percent of 527.22 = 42599.376 80.8 percent of 527.23 = 42600.184 80.8 percent of 527.24 = 42600.992 80.8 percent of 527.25 = 42601.8
80.8 percent of 527.26 = 42602.608 80.8 percent of 527.27 = 42603.416 80.8 percent of 527.28 = 42604.224 80.8 percent of 527.29 = 42605.032 80.8 percent of 527.3 = 42605.84 80.8 percent of 527.31 = 42606.648 80.8 percent of 527.32 = 42607.456 80.8 percent of 527.33 = 42608.264 80.8 percent of 527.34 = 42609.072 80.8 percent of 527.35 = 42609.88 80.8 percent of 527.36 = 42610.688 80.8 percent of 527.37 = 42611.496 80.8 percent of 527.38 = 42612.304 80.8 percent of 527.39 = 42613.112 80.8 percent of 527.4 = 42613.92 80.8 percent of 527.41 = 42614.728 80.8 percent of 527.42 = 42615.536 80.8 percent of 527.43 = 42616.344 80.8 percent of 527.44 = 42617.152 80.8 percent of 527.45 = 42617.96 80.8 percent of 527.46 = 42618.768 80.8 percent of 527.47 = 42619.576 80.8 percent of 527.48 = 42620.384 80.8 percent of 527.49 = 42621.192 80.8 percent of 527.5 = 42622
80.8 percent of 527.51 = 42622.808 80.8 percent of 527.52 = 42623.616 80.8 percent of 527.53 = 42624.424 80.8 percent of 527.54 = 42625.232 80.8 percent of 527.55 = 42626.04 80.8 percent of 527.56 = 42626.848 80.8 percent of 527.57 = 42627.656 80.8 percent of 527.58 = 42628.464 80.8 percent of 527.59 = 42629.272 80.8 percent of 527.6 = 42630.08 80.8 percent of 527.61 = 42630.888 80.8 percent of 527.62 = 42631.696 80.8 percent of 527.63 = 42632.504 80.8 percent of 527.64 = 42633.312 80.8 percent of 527.65 = 42634.12 80.8 percent of 527.66 = 42634.928 80.8 percent of 527.67 = 42635.736 80.8 percent of 527.68 = 42636.544 80.8 percent of 527.69 = 42637.352 80.8 percent of 527.7 = 42638.16 80.8 percent of 527.71 = 42638.968 80.8 percent of 527.72 = 42639.776 80.8 percent of 527.73 = 42640.584 80.8 percent of 527.74 = 42641.392 80.8 percent of 527.75 = 42642.2
80.8 percent of 527.76 = 42643.008 80.8 percent of 527.77 = 42643.816 80.8 percent of 527.78 = 42644.624 80.8 percent of 527.79 = 42645.432 80.8 percent of 527.8 = 42646.24 80.8 percent of 527.81 = 42647.048 80.8 percent of 527.82 = 42647.856 80.8 percent of 527.83 = 42648.664 80.8 percent of 527.84 = 42649.472 80.8 percent of 527.85 = 42650.28 80.8 percent of 527.86 = 42651.088 80.8 percent of 527.87 = 42651.896 80.8 percent of 527.88 = 42652.704 80.8 percent of 527.89 = 42653.512 80.8 percent of 527.9 = 42654.32 80.8 percent of 527.91 = 42655.128 80.8 percent of 527.92 = 42655.936 80.8 percent of 527.93 = 42656.744 80.8 percent of 527.94 = 42657.552 80.8 percent of 527.95 = 42658.36 80.8 percent of 527.96 = 42659.168 80.8 percent of 527.97 = 42659.976 80.8 percent of 527.98 = 42660.784 80.8 percent of 527.99 = 42661.592 80.8 percent of 528 = 42662.4 | 1,801 | 4,221 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2020-24 | latest | en | 0.860541 |
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Get Full Access to Explorations In College Algebra - 5 Edition - Chapter 2 - Problem 41
Get Full Access to Explorations In College Algebra - 5 Edition - Chapter 2 - Problem 41
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Solved: In 3241, give an example of a function or
ISBN: 9780470466445 178
Solution for problem 41 Chapter 2
Explorations in College Algebra | 5th Edition
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Problem 41
In 3241, give an example of a function or functions with the specified properties. Express your answers using equations, and specify the independent and dependent variables. Five data points for which the average rates of change between consecutive points are positive and the sequential points are increasing at a decreasing rate
Step-by-Step Solution:
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Week12(Ithink) TESTMONDAY WEDNESDAY Microplasmas–bacteriawithoutcellwallswithsmallgenomes,485genes Wantedtoputgenomeofoneorganismintoanothertomakeitthefirstone Endonucleaseusedtocut5’endofsinglestrandsoyoucananneal2chromosome partstogethertobuildchromosomefragments Yeastcombinedthemintoacircle Transformrelatedspecies(looklikeeyeballs)membraneandcytoplasmofone organismwithacompletelyartificiallysynthesizedgenome Determineifthegeneswereessential,non-essential,orquasi-essential Hadtoreturnsomenon-essentialgenesbecausethecellwouldnotgrow Theythinkthereneededtoberedundancyoffunction Sometheycoulddeletethattheythoughtwereessential Putgenesinto4groupsoffunction(cytosolicmetabolism,cellmembrane, preservationofgenomeinformation,andexpressionofgenomeinformation [Largest]) NOTTALKINGABOUTRNA FRIDAY Guestlecture HowtoderiveGMOs Humanshave25,000genes.“Wehavethegenomesequenced”=don’tknowexactly whattheydo,blueprintinworkingdocument 20chromosomesofproteins • Recombinationattelomere • GlycinemaxfromGlycinesoja–tookalotofworktogetridofnonneeded genes • Teosinte–cornismoredifferentthanhumansandchimps VariationatUNL • Conventionalhas57000genesandroundupreadyhas57001genes • Planthybridsandputmaleandfemalechromintosisterchromatidstoget recombination • Promotertellsgenewhere,when,andhowmuchtoproducegene • IntegrationeventXregeneration=functionaltransformant • Planttissueculture–cangothroughsomaticembryogenesis(monocots)or organogenesis(formshootorroot,thenflipit,dicots) • Planttransformation– o Microprojectilebombardment–mostcommon o Agrobacterium-mediatedtransformation–bacteriacellformsextreme growth § Abunchofproteinsinvolved(took10labs20yearstofigure out) § Chemotaxis–helpsignalsfromplantandmovestowardthe higherconcentration § ThisactivatesagenetomaketDNAthatmovesthroughthe pore § Resultsincrowngall o Say“heyletstakeoutthesebadgenesandputinthegeneswewantin theplantandletitreplicateandsendittotheplantcells!” o CutandpastegenesintobinaryvectorsinsteadofintegratingintoTi plasmid. • Hairyroots–likeasweetpotato,naturalGMO • Bolistics–byastrawberrybreeder o Nobiologicalprocess,justshootitinlikeashotgun Crossblackflowerandblackandwhiteandgetallwhite–endogenousgenes Zincfinger–makeupdependsonwherewillbind. • Makegeneediting Agrobacteriumuse4proteinpathway Bacteria–sitonneedle3proteinandwhattheyinsertistranscriptionactors. • Effectorsthatactastranscriptionfactorshavemanylittleparts. CRISPR–adaptiveimmunesystem Zincfinger Talons Cas
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ISBN: 9780470466445
The full step-by-step solution to problem: 41 from chapter: 2 was answered by , our top Math solution expert on 12/23/17, 04:55PM. This textbook survival guide was created for the textbook: Explorations in College Algebra, edition: 5. The answer to “In 3241, give an example of a function or functions with the specified properties. Express your answers using equations, and specify the independent and dependent variables. Five data points for which the average rates of change between consecutive points are positive and the sequential points are increasing at a decreasing rate” is broken down into a number of easy to follow steps, and 51 words. Explorations in College Algebra was written by and is associated to the ISBN: 9780470466445. Since the solution to 41 from 2 chapter was answered, more than 233 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 9 chapters, and 1546 solutions.
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# A rectangilar safe is to be made of steel of uniform thickness, including the door the inside dimensions are 1.20 m ,1.20 m and 2.00 m if the volume of the
steel is 1.25m^3 find its thickness
1
by sweetysiri92
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https://discourse.pymc.io/t/hierarchical-model-for-outlier-detection-on-high-throughput-screening-assays/10567 | 1,669,766,653,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710712.51/warc/CC-MAIN-20221129232448-20221130022448-00016.warc.gz | 255,095,718 | 5,790 | # Hierarchical model for outlier detection on high-throughput screening assays
Hi everyone,
First post here. I’m a Bayesian noob, even though I’ve been aware of Bayesian stats for a long time and it’s always fascinated me. I’m making my way through my first book at the moment (“Think Bayes”), but I’m impatient and want to get my feet wet. I’ve got a problem that seems perfect for a hierarchical model, but I can’t quite figure out how to use it.
I really hope it’s not too basic for this forum, but I’m a biologist, not a statistician and literally have no one in real life that’s remotely interested in these methods to talk to.
A little bit of background, if anyone is curious. I’m a molecular biologist and I work in a synthetic biology company. Most of my work revolves around making bacteria produce some chemical. A very common approach is to mutate thousands of cells and screen them all. Most of the time nothing happens, but sometimes you get a mutation that makes the bacteria spit out more of the chemical.
We try to find the good ones by isolating thousands and growing them individually in well-plates with, then measuring the content of the chemical in each hole. We do this in multiple “experiments”, each with tens of plates with 96 holes each. Because it’s biology, there’s a lot of variability - between individual experiments/runs, plates, instrumental errors and other noise.
This is how a typical dataset looks like: https://i.imgur.com/6jiLLaX.png
x represents the different mutants or strains and y represents the different measurements that correspond to each strain.
I want to: 1. normalize the data while keeping the between-group uncertainty, 2. classify the outliers, if there are any.
The goal is to identify the “good” bacteria, or the ones where the mutations actually did something. Assuming mutations did absolutely nothing to the overwhelming majority of the population, we are looking for outliers.
Picking an outlier that ends up not being one wastes a ton of time. That’s why I think uncertainty is extremely important here, hence my desire to try a Bayesian approach. I tried making a simple hierarchical model taking only the between-experiment variability into account to keep it simple. Since the x is not really a variable, I fixed the slope to 0 and only fit the intercept and noise. I used normal distributions across the board, again to keep it simple for now.
And this is what I got https://i.imgur.com/BTXyPtR.png
Very close to what I get if I just calculate the mean and std of each group, so that’s good.
The problem is, I don’t really know what to do with it! I thought about normalizing the dataset to the same “Experiment” mean, but then there’s no point in the whole thing, because I’m not using the uncertainty.
Any tips welcome!
And again, I apologize for such a basic post. It’s probably extremely obvious and I’d not be asking this if I read more, but I really wanted to get something useful done before I manage to finish some books.
1 Like
Welcome!
Outlier detection can be handled implicitly or explicitly. It sounds like you want to model inlier/outlier explicitly a scenario that is typically done via a mixture model. You can take a look through this notebook or this one. You can also look at this notebook, which is perhaps a bit more involved that what you need, but might get you thinking about how this approach might (or might not) be appropriate for your scenario.
Regardless, if you want feedback on a particular model, it might be useful to generate some synthetic data that approximates the kind of thing displayed in the plot you shared. By generating the data yourself, you will have a much easier time knowing when your model is behaving “correctly”. And it will be easier for others to get a sense of the scenario you’re dealing with. | 811 | 3,831 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2022-49 | latest | en | 0.935573 |
https://www.stepbystep.com/Science-Activities-for-Elementary-and-Home-Economics-Teachers-151558/ | 1,597,478,929,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439740733.1/warc/CC-MAIN-20200815065105-20200815095105-00123.warc.gz | 816,263,827 | 11,515 | # Science Activities for Elementary and Home Economics Teachers
As more and more standards are expected to be mastered by today’s students, teachers today may find themselves looking for way to combine subjects while still being able to cover a variety of material. Elementary and Home Economics teachers can take advantage of the following activities which involve math, science, health and nutrition.
“Food Survey”
As part of a thematic unit on nutrition, I have discovered a math activity that incorporates graphing and the food pyramid. Starting on Monday, I have students write down what they eat at every meal for four days. On Friday, we go over the foods and put a tally in each category that they represent. Then, the students make a bar graph to see the quantities of each food group they are eating. I have a sample bar graph out that has the recommended daily allowances multiplied over a four day period. Most students are amazed how much their graph differs with the recommended daily allowances. The exercises are a great way to combine graphing and nutrition.
“Receipt Report”
To teach the concepts of budgeting, I like to use an activity that uses data analysis. I save my old grocery receipts and cut them into groups of approx. five to ten items each and have the students write their names on the top of the paper. Then on the back I have them copy: mean, median, mode, and range. Students find the answers to the corresponding term. I find it is easier for me to check the receipt if the students write on it as opposed to having them do it on a sheet of paper and stapling it. This way, it’s less weight for me to have to carry home and I am saving paper.
“Predictable Plants”
When it is time to do a unit on agriculture and botany, I have a favorite activity entitled, “Predictable Plants”. First, I give students a Styrofoam cup, soil, and six bean seeds. After they have been planted, watered, and labeled, I give them a blank calendar. We fill it out for the month and I ask students to predict how many of the seeds will grow on the given days. I explain how for the first few days they may not see anything but then they may start to see seedlings sprout by the end of the week. We talk about how some may not grow from that stage and how some may keep on growing. After the students predict the data, they check it every day and mark in the correct amount with another color pen. At the end of the month we examine the data to make fractions out of the responses. I find this activity works best if it can be started as close to the first of the month as possible to correspond with the calendar that the students create.
These examples were just a few that can be modified to suit students’ levels. If wanting to incorporate a writing activity into data analysis, students can write about the performance or interpretation of their data. A fun way to promote these activities is to offer an incentive, such as a no homework pass, to students who accurately predict or answer questions correctly. By utilizing as many subjects as possible, the activity can be stretched out over a two to three day project, depending on grade level. | 653 | 3,169 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2020-34 | latest | en | 0.95889 |
http://icpc.njust.edu.cn/Problem/Hdu/5550/ | 1,586,386,843,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371824409.86/warc/CC-MAIN-20200408202012-20200408232512-00198.warc.gz | 84,106,673 | 10,284 | # Game Rooms
Time Limit: 4000/4000 MS (Java/Others)
Memory Limit: 65535/65535 K (Java/Others)
## Description
Your company has just constructed a new skyscraper, but you just noticed a terrible problem: there is only space to put one game room on each floor! The game rooms have not been furnished yet, so you can still decide which ones should be for table tennis and which ones should be for pool. There must be at least one game room of each type in the building.
Luckily, you know who will work where in this building (everyone has picked out offices). You know that there will be $T_{i}$ table tennis players and $P_{i}$ pool players on each floor. Our goal is to minimize the sum of distances for each employee to their nearest game room. The distance is the difference in floor numbers: 0 if an employee is on the same floor as a game room of their desired type, 1 if the nearest game room of the desired type is exactly one floor above or below the employee, and so on.
## Input
The first line of the input gives the number of test cases, $T(1≤T≤100)$. $T$ test cases follow. Each test case begins with one line with an integer $N(2≤N≤4000)$, the number of floors in the building. $N$ lines follow, each consists of 2 integers, $T_{i}$ and $P_{i}(1≤T_{i},P_{i}≤10^{9})$, the number of table tennis and pool players on the $i_{th}$ floor. The lines are given in increasing order of floor number, starting with floor 1 and going upward.
## Output
For each test case, output one line containing Case #x: y, where $x$ is the test case number (starting from 1) and $y$ is the minimal sum of distances.
## Sample Input
1
2
10 5
4 3
## Sample Output
Case #1: 9
Hint
In the first case, you can build a table tennis game room on the first floor and a pool game room on the second floor.
In this case, the 5 pool players on the first floor will need to go one floor up, and the 4 table tennis players on the second floor will need to go one floor down. So the total distance is 9.
wange2014
## Source
The 2015 China Collegiate Programming Conte | 532 | 2,058 | {"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} | 2.859375 | 3 | CC-MAIN-2020-16 | longest | en | 0.924509 |
http://bestmaths.net/online/index.php/year-levels/year-10/year-10-topics/non-right-angled-triangles/summary/ | 1,721,565,269,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517701.96/warc/CC-MAIN-20240721121510-20240721151510-00708.warc.gz | 3,875,087 | 4,103 | ## Non-right-angled Triangles Summary
Non-right-angled Triangles
### Summary
the trigonometric methods given earlier apply only to triangles containing a right angle.
for triangles without a right angle, the sine rule, the cosine rule and the area formula can be used to solve triangles and find their areas.
### Key Skills
• use the sine rule to solve triangles where two sides and one opposite angle or two angles and one opposite sideare given.
• use the cosine rule to solve triangles where two sides and the included angle or three sides are given.
• find the area of a non-right-angled triangle using the area formula. | 138 | 630 | {"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-2024-30 | latest | en | 0.719939 |
https://exploreroots.com/2022/06/01/multiplication-division/ | 1,679,336,224,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943555.25/warc/CC-MAIN-20230320175948-20230320205948-00739.warc.gz | 304,044,655 | 15,525 | Categories
# MULTIPLICATION & DIVISION
We similarly can apply the procedures of addition or subtraction during multiplication and division and get the results for multiplication and division of different numbering systems
MULTIPLICATION:
Procedure of multiplication is same as that of decimal
Generalized multiplication of two 4-digit numbers is as follow:
Eg. 910 * 810
910= 10012
810 =10002
Similarly we can do it for fractional binary numbers; we just have to adjust binary point to the numbers of places equal to addition of numbers of places of the multiplicand and multiplier
If we implement the general multiplication method of two 4-bit numbers then we need 16 AND gates to calculate those 16 terms of multiplication and also full adders to add the terms and the carries flying from one column to another as shown below:
DIVISON: Similar to multiplication we can do division as shown below:
Q- Divide 4210 by 610 using binary division
4210 =1010102
610 =1102
Hence quotient is 1112 and remainder is 0002
Division and multiplication for octal and hexadecimal number system:
We can convert the octal and hexadecimal numbers to binary and perform the multiplication and division as it would be very cumbersome to do it by keeping the numbers in their given form
Q- Multiply F016with 4516
F016=1111 00002
4516=0100 01012
And we can perform the multiplication in binary form. | 319 | 1,400 | {"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} | 4.1875 | 4 | CC-MAIN-2023-14 | longest | en | 0.867763 |
https://www.doubtnut.com/qna/11041176 | 1,716,547,509,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058709.9/warc/CC-MAIN-20240524091115-20240524121115-00026.warc.gz | 665,855,881 | 38,372 | # The equilibrium constant for a reaction is 10. What will be the value of ΔGΘ? R=8.314JK−1mol−1,T=300K.
Video Solution
Text Solution
Verified by Experts
## ΔGΘ=−2.303RTlogK =−2.303×8.314JK−1mol−1×300K×log10 =−5744.1J
|
Updated on:21/07/2023
### Knowledge Check
• Question 1 - Select One
## The equilibrium constant for a reaction is 10. what will be the value of ΔG∘? Given, R=8.314JK−1mol−1,T=300K.
A574.414Jmol1
B5744.14Jmol1
C57.4414Jmol1
D57441.4Jmol1
• Question 1 - Select One
## The equilibrium constant for a reaction is 100 what will be the value of ΔG∘ ? R=8.314JK−1mol−1,T=300K :-
A11488KJ
B11.488KJ
C12KJ
D12000KJ
• Question 1 - Select One
## If the equilibrium constant for a reaction is 10, then the value of △G∘ will be: (Given: R=8JK−1mol−1T=300K)
A+5.527 kJ mol1
B5.527 kJ mol1
C+55.27 kJ mol1
D55.27 kJ mol1
• Question 1 - Select One
## A reaction is at equilibrium at 100∘C and the enthalpy change for the reaction is 42.6 kJ mol−1. What will be the value of ΔS in J K−1mol−1?
A120
B426.2
C373.1
D114.2
• Question 1 - Select One
## The equilibrium constant for the reaction A+B⇔C+D is 10. ΔG∘ for the reaction at 300 K is
A0.6 kcal
B116 kcal
C691 kcal
D1.382 kcal
• Question 1 - Select One
## If the standard electrode potential for a cell is at 300 K, the equilibrium constant (K) for the reaction Zn(s)+Cu2+(aq) at 300 k is approximately : (R=8JK−1mol−1,F=96000mol−1)
Ae160
Be320
Ce160
De80
### Similar Questions
Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc
NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS Aggarwal, Manohar Ray, Cengage books for boards and competitive exams.
Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. Get all the study material in Hindi medium and English medium for IIT JEE and NEET preparation | 810 | 2,440 | {"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} | 3.5625 | 4 | CC-MAIN-2024-22 | latest | en | 0.735187 |
https://stuffsure.com/what-size-winch-do-i-need/ | 1,709,481,019,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476396.49/warc/CC-MAIN-20240303142747-20240303172747-00165.warc.gz | 530,750,191 | 16,383 | # What Size Winch Do I Need?
If you’re looking for information on what size winch you need, you’ve come to the right place. In this blog post, we’ll cover the different factors you need to consider in order to determine the right size winch for your needs.
Checkout this video:
## Introduction
Winches come in a variety of sizes that are designed to suit different purposes. Choose the wrong size winch and you may find yourself struggling to complete a simple task, or worse, putting yourself and others in danger. So, how do you know what size winch you need?
The size of the winch you need will be determined by the weight of the load you intend to lift and the speed at which you need to lift it. If you only need to lift light loads slowly, then a smaller winch will suffice. If you need to lift heavy loads quickly, then you will need a larger, more powerful winch.
In general, the following formula can be used to determine the size of winch you need:
(Weight of load / 2) + (Speed of lifting in feet per minute / 60) = Winch size in tons
For example, if you need to lift a 3,000lb load at a rate of 10 feet per minute, then you would need a winch with a capacity of 1.5 tons ((3,000 / 2) + (10 / 60)).
## How to determine the size of winch you need
You need to consider the maximum weight of your vehicle, including any additional weight from accessories or cargo. You also need to factor in the terrain you’ll be using the winch on. If you’ll be winching on soft surfaces like sand, you’ll need a more powerful winch.
### The weight of your vehicle
One of the main factors to consider when purchasing a winch is the weight of your vehicle. A winch that is too small for your vehicle will not be able to pull it out of a ditch, and a winch that is too large for your vehicle will be more expensive and may damage your vehicle. A good rule of thumb is to purchase a winch that is 1.5 times the weight of your vehicle. For example, if your car weighs 4,000 pounds (1,814 kg), you will need a 6,000-pound (2,722 kg) winch.
### The terrain you’ll be using it in
When choosing a winch, it’s important to first consider the terrain you’ll be using it in most often. If you frequently off-road in muddy or sandy conditions, for example, you’ll want a winch with a higher weight capacity and more pulling power. If you live in an area with milder terrain or you only use your winch occasionally, however, you may be able to get by with a lighter-duty model.
### What type of winching you’ll be doing
The first thing you need to know is what type of winching you’ll be doing. There are three types of winching: pulling yourself out of a ditch, pulling a boat onto a trailer, or pulling a tree stump out of the ground. Each type of winch has different requirements.
For off-roading, you need a winch that is capable of pulling your vehicle out of tough spots. A good rule of thumb is to choose a winch with at least 1.5 times the maximum weight capacity of your vehicle. This will give you the power you need to get unstuck when you’re in a bind.
If you’re looking for a winch to pull your boat onto a trailer, you need to pick one that has enough power to do the job. The rule of thumb here is to choose a winch with at least double the maximum weight capacity of your boat. This will give you the power you need to get your boat where it needs to go.
Finally, if you’re looking for a winch to pull tree stumps out of the ground, you need one that has enough power to do the job without damaging the stump or your vehicle. The rule of thumb here is to choose a winch with at least triple the maximum weight capacity of the stump. This will give you the power you need to get the job done without any problems.
## Conclusion
In conclusion, when choosing a winch, it’s important to consider the weight of your vehicle, what type of terrain you’ll be using it on, and how often you’ll be using it. A heavier-duty winch will be more expensive, but it will also be more durable and have a longer lifespan. If you only need a winch for occasional use, a less expensive model may be a better choice. | 970 | 4,112 | {"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-2024-10 | latest | en | 0.926445 |
https://ncertmcq.com/ncert-solutions-for-class-9-science-chapter-8/ | 1,726,313,870,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651579.22/warc/CC-MAIN-20240914093425-20240914123425-00618.warc.gz | 395,035,642 | 17,785 | ## NCERT Solutions for Class 9 Science Chapter 8 Motion
These Solutions are part of NCERT Solutions for Class 9 Science. Here we have given NCERT Solutions for Class 9 Science Chapter 8 Motion. LearnInsta.com provides you the Free PDF download of NCERT Solutions for Class 9 Science (Biology) Chapter 8 – Motion solved by Expert Teachers as per NCERT (CBSE) Book guidelines. All Chapter 8 – Motion Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks.
More Resources
NCERT TEXT BOOK QUESTIONS
IN TEXT QUESTIONS
Question 1.
An object has moved through a distance. Can it have zero displacement ? If yes, support your answer with an example. (CBSE 2015)
Yes, The displacement of the object can be zero. Let a boy completes one round of a circular track in 5 minutes. The distance travelled by the boy = circumference of the circular track. However, displacement of the boy is zero because his initial and final positions are same.
Question 2.
A farmer moves along the boundary of a square field of side 10 m in 40 s.
What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds ? (CBSE 2010, 2015)
ABCD is a square field of side 10 m.
The farmer moves along the boundary of the field from the corner A via the corners B, C and D.
After every 40 s, the farmer is again at the corner A, so his displacement after every 40 s is zero.
At the end of 2 minutes 20 seconds = (2 x 60 + 20) = 140 s, the farmer will be at the corner C.
Question 3.
Distinguish between speed and velocity. (CBSE 2010, 2012, 2013, 2015)
Speed Velocity 1. Distance travelled by an object per unit time is known as its speed. The distance travelled by an object in a particular direction (i.e. displacement) per unit time is known as its velocity. 2. Average speed of a moving object cannot be zero. Average velocity of a moving object can be zero. 3. tells how fast an object moves. Velocity tells how fast an object moves and in which direction it moves. 4. Speed is a scalar quantity. Velocity is a vector quantity. 5. Speed of an object is always positive. Velocity of an object can be positive or negative.
Question 4.
Under what conditions) is the magnitude of the average velocity of an object equal to its average speed ? (CBSE 2012, 2013)
When an object moves in one direction along a straight line.
Question 5.
What does the odometer of an automobile measure ? (CBSE 2010, 2011, 2014, 2015)
Odometer of an automobile measures distance travelled by the automobile.
Question 6.
What does the path of an object look like when it is in uniform motion ? (CBSE 2012)
Straight path.
Question 7.
During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station ? The signal travels at the speed of light, that is, 3 x 108 m s-1
Question 8.
When will you say a body is in
1. uniform acceleration ?
2. non-uniform acceleration (CBSE 2012, 2013)
1. A body has uniform acceleration if its velocity changes by an equal amount in equal intervals of time. .
2. A body has non-uniform acceleration if its velocity changes by unequal amount in equal intervals of time.
Question 9.
A bus decreases its speed from 80 kmh-1 to 60 kmh-1 in 5 s. Find the acceleration of the bus.
(CBSE 2010, 2011, 2012, 2015)
Here,
Question 10.
A train starting from a railway station and moving with a uniform acceleration attains a speed of 40 km h-1 n 10 minutes. Find its acceleration.
Question 11.
What is the nature of the distance-time graphs for uniform and non-uniform motion of an object ?
(CBSE 2012)
1. For uniform motion, distance-time graph is a straight line having constant gradient or slope as shown in figure.
2. For non-uniform motion, distance-time graph is a curve having increasing gradient or slope or decreasing gradient as shown in figures.
Question 12.
What can you say about the motion of an object whose distance-time graph is a straight line parallel to
the time axis ? (CBSE 2010, 2012)
When distance-time graph is a straight line parallel to the time axis, it means, the distance of the object is not changing with time. Thus, the object is stationary.
Question 13.
What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time-axis ?
In this case, speed of the object is constant. That is, the object travels equal distances in equal intervals of time along a straight line. Hence, motion of the object is uniform motion.
Question 14.
What is the quantity which is measured by the area occupied below the velocity-time graph ?
(CBSE 2010, 2012)
Magnitude of the displacement of a body is measured by the area under the velocify-time graph.
Question 15.
A bus starting from rest moves with a uniform acceleration of 0.1 m s-2 for 2 minutes. Find
(a) the speed acquired,
(b) the distance travelled. (CBSE 2012)
Question 16.
A train is travelling at a speed of 90 km h-1. Brakes are applied so as to produce a uniform acceleration of – 0.5 m s-2 . Find how far the train will go before it is brought to rest ?
Question 17.
A trolley, while going down an inclined plane has an acceleration of 2 cm s-2. What will be its velocity 3 s after the start ?
Here, u = 0,v = ?, a = 2 cm s-2, t = 3 s
Using, v = u + at, we get
v = 0 + 2 x 3 = 6 cm s-2.
Question 18.
A racing car has a uniform acceleration of 4 m s-2. What distance will it cover in 10 s after start ?
Question 19.
A stone is thrown in a vertically upward direction with a velocity of 5 m s-1 If the acceleration of the stone during its motion is 10 m s-2 in the downward direction, what will be the height attained by the stone and how much time will it take to reach there ?
NCERT CHAPTER END EXERCISE
Question 1.
An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes and 20 s ?
(ii) After every 40 s, athlete reaches his starting point, so after 40 s, his displacement is zero. It means, the athlete completes the circular track 3 times in 120 s and in the next 20 s, he is just opposite to his starting point. Therefore, the magnitude of the displacement of the athlete at the end of the 140 s (or 2 minutes 20 s) = Diameter of the circular track = 200 m.
Question 2.
Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 50 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging
(a) from A to B and
(b) from A to C ? (CBSE 2010, Term I)
Distance from A to B – 300 m
Displacement from A to B = 300 m
Time taken to go from A to B =2 minutes 50 s = 170 s
Question 3.
Abdul, while driving to school, computes the average speed for his trip to be 20 km h-1. On his return trip along the same route, there is less traffic and the average speed is 40 km h-1. What is the average speed for Abdul’s trip ? (CBSE 2011)
Question 4.
A motor boat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m s-2 for 8.0 s. How far does the boat travel during this time ? (CBSE 2011, 2013)
Question 5.
A driver of a car travelling at 52 km h-1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km h-1 in another car applies his breaks slowly and stops in 10 s. On the same graph paper plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied ?
Question 6.
Figure shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions :
(a) Which of the three is travelling the fastest ?
(b) Are all three ever at the same point on the road ?
(c) How far has C travelled when B passes A ?
(d) How far has B travelled by the time it passes C ?
(a) Speed = Slope of distance-time graph.
Since slope of distance-time graph for object B is the greatest, so object B is travelling the fastest.
(b) All the three objects will be at the same point on the road if all the three distance-time graphs intersect each other at a time. Since, all the three distance-time graphs do not intersect each other at a time, so they are never at the same point on the road.
(c) When B passes A, distance travelled by C = 9.6 – 2 = 7.6 km.
(d) Distance travelled by B by the time it passes C = 6 km.
Question 7.
A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m s-2, with what velocity will it strike the ground ? After what time will it strike the ground ?
Question 8.
The speed time graph for a car as shown in figure
(a) Find how far does the car travel in the firdt four seconds.
Shade the area on the graph that represents the distance travelled by the car during the period.
(b) Which part of the graph represents uniform motion of the car?
(a)
(b) The straight part of the curve parallel to time axis represents the uniform motion of the car.
Question 9.
State which of the following situations are possible and give an example for each of these :
(a) an object with a constant acceleration but zero velocity.
(b) an object moving with an acceleration but with uniform speed.
(c) an object moving in a certain direction with an acceleration in the perpendicular direction.
(CBSE 2012) | 2,362 | 9,413 | {"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-2024-38 | latest | en | 0.891906 |
https://www.mrexcel.com/board/threads/macro-variable-defination-problem.121317/ | 1,726,685,619,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651931.60/warc/CC-MAIN-20240918165253-20240918195253-00041.warc.gz | 828,344,046 | 18,229 | Macro Variable defination problem
Board Regular
i have a problem... one that im sure th answer is easy im just not seeing it. i am a fairly novice coder, so i do go about things the long way until i can at least get that down befor i move to more advanced stuff.
Code:
Sub copy_into_window()
'
' Macro7 Macro
' Macro recorded 18/01/2005 by Nick Kotila
'
'
Let x = 1
Let y = ""
Do Until x = 23
If x = 1 Then y = Windows("Hamilton Epicenter.xls").Activate
If x = 2 Then y = Windows("L'assomption Epicenter.xls").Activate
If x = 3 Then y = Windows("Laval Epicenter.xls").Activate
If x = 4 Then y = Windows("Longueuil Epicenter.xls").Activate
If x = 5 Then y = Windows("Mirabel Epicenter.xls").Activate
If x = 6 Then y = Windows("Montreal Epicenter.xls").Activate
If x = 7 Then y = Windows("Montreal-Nord Epicenter.xls").Activate
If x = 8 Then y = Windows("Montreal-West Epicenter.xls").Activate
If x = 9 Then y = Windows("Repentinguy-Le Gardeur Epicenter.xls").Activate
If x = 10 Then y = Windows("Saint-Jean-sur-Richelieu Epicenter.xls").Activate
If x = 11 Then y = Windows("Ste Dorthee Epicenter.xls").Activate
If x = 12 Then y = Windows("St-Eustache Epicenter.xls").Activate
If x = 13 Then y = Windows("St-Hubert Epicenter.xls").Activate
If x = 14 Then y = Windows("Stoney Creek Epicenter.xls").Activate
If x = 15 Then y = Windows("Terrebonne Epicenter.xls").Activate
If x = 16 Then y = Windows("Victoriaville Epicenter.xls").Activate
If x = 17 Then y = Windows("Granby Epicenter.xls").Activate
If x = 18 Then y = Windows("Cowansville Epicenter.xls").Activate
If x = 19 Then y = Windows("Chomedy Epicenter.xls").Activate
If x = 20 Then y = Windows("Boisbriand Epicenter.xls").Activate
If x = 21 Then y = Windows("Auteuil Epicenter.xls").Activate
If x = 22 Then y = Windows("Ancaster Waterdown Dundus Epicenter.xls").Activate
Windows("NEWSALESLIST.XLS").Activate
Cells.Select
Selection.copy
y
Sheets("Sheet2").Select
Cells.Select
ActiveSheet.Paste
Application.Run "PERSONAL.XLS!Copydata"
Let x = x + 1
Loop
The problem i am having.. is you see the y all the way at the bottom, i know that doesn't work.. just im not sure how to define it so that it displays the worksheet funtion i set it too.
any help would be much appreciated.
Excel Facts
How can you turn a range sideways?
Copy the range. Select a blank cell. Right-click, Paste Special, then choose Transpose.
The code runs through all this, but because it always ends with the last line of code, it will always return the last possible Y value. Perhaps if you explained what you inteded the code to do, we could help you some more. Consider revising your loop. HTH.
well... basically im trying to make a macro.. that takes a page, copies it over to every file i have in 1 folder on sheet 2.. than run a macro i ahve already built on each file.
See if this works at all. I'm not entirely familiar with this method you are using, but maybe this works?
Code:
Sub copy_data_window()
Dim x As Integer
For x = 1 To 22 Step 1
If x = 1 Then Windows("Hamilton Epicenter.xls").Activate
If x = 2 Then Windows("L'assomption Epicenter.xls").Activate
If x = 3 Then Windows("Laval Epicenter.xls").Activate
If x = 4 Then Windows("Longueuil Epicenter.xls").Activate
If x = 5 Then Windows("Mirabel Epicenter.xls").Activate
If x = 6 Then Windows("Montreal Epicenter.xls").Activate
If x = 7 Then Windows("Montreal-Nord Epicenter.xls").Activate
If x = 8 Then Windows("Montreal-West Epicenter.xls").Activate
If x = 9 Then Windows("Repentinguy-Le Gardeur Epicenter.xls").Activate
If x = 10 Then Windows("Saint-Jean-sur-Richelieu Epicenter.xls").Activate
If x = 11 Then Windows("Ste Dorthee Epicenter.xls").Activate
If x = 12 Then Windows("St-Eustache Epicenter.xls").Activate
If x = 13 Then Windows("St-Hubert Epicenter.xls").Activate
If x = 14 Then Windows("Stoney Creek Epicenter.xls").Activate
If x = 15 Then Windows("Terrebonne Epicenter.xls").Activate
If x = 16 Then Windows("Victoriaville Epicenter.xls").Activate
If x = 17 Then Windows("Granby Epicenter.xls").Activate
If x = 18 Then Windows("Cowansville Epicenter.xls").Activate
If x = 19 Then Windows("Chomedy Epicenter.xls").Activate
If x = 20 Then Windows("Boisbriand Epicenter.xls").Activate
If x = 21 Then Windows("Auteuil Epicenter.xls").Activate
If x = 22 Then Windows("Ancaster Waterdown Dundus Epicenter.xls").Activate
Windows("NEWSALESLIST.XLS").Cells.Copy _
ActiveWorkbook.Sheets("Sheet2").Range("A1")
Application.Run "PERSONAL.XLS!Copydata"
Next x
End Sub
HTH
you sir.. are my hero
well actually.. runtime error 438: object doesn't support this property or method
than hilighted in yellow
Code:
Windows("NEWSALESLIST.XLS").Cells.copy _
ActiveWorkbook.Sheets("Sheet2").Range("A1")
Try:
Code:
Thisworkbook.Cells.Copy ActiveWorkbook.Sheets("Sheet2").Range("A1")
HTH.
i have only 1 more question... is there a way to stop or pause the macro at teh end of the loop for like 2 seconds, to let the other macro run? i think im having a problem of the sheets being skipped because the other macro is still working.
I'm quite unsure of this, again, I am not familiar with this method as I don't use a personal.xls file. Perhaps somebody else does?
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# Poll: How much time did you spend on each essay?
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Thursday Poll: How much time did you spend on average on each essay (this is from start to finish) ?
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Poll: How much time did you spend on each essay? [#permalink] 11 Nov 2011, 08:30
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http://en.wikibooks.org/wiki/Nanotechnology/AFM/Overview_of_properties_of_various_cantilevers | 1,419,179,777,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1418802771716.117/warc/CC-MAIN-20141217075251-00050-ip-10-231-17-201.ec2.internal.warc.gz | 89,625,051 | 9,082 | # Examples of AFM cantilevers
## For a BS-75kHz
L=225 w=28 t=3 h=17+3/2 (is actually trapezoidal)}
$k_{N}=\frac{1}{4}Yw\left( \frac{t}{L}\right) ^{3}=\frac{1}{4}\left(160000\right) 28\left( \frac{3}{225}\right) ^{3}=2.\,654\,8$
$f[Hz]=\frac{t\beta_{i}^{2}}{4\pi L^{2}}\sqrt{\frac{Y}{3\rho}} =\frac{\left( 3\ast10^{-6}\right) \left( 1.875\right) ^{2}}{4\pi\left( 225\ast10^{-6}\right) ^{2}}\sqrt{\frac{\left( 160\ast10^{9}\right) } {3\ast2330}}=79318.Hz$
$2\left( \frac{wh}{tL}\right) ^{2}=2\left( \frac{28\ast18.5}{3\ast 225}\right) ^{2}=1.\,177\,8$ so $k_{lat}~k_{tor}.$
$k_{tor}=k_{N}\frac{1}{2}\left( \frac{L}{h}\right) ^{2}=2.65\frac{1} {2}\left( \frac{225}{18.5}\right) ^{2}=195.\,99$
$k_{lat}=\frac{1}{4}Y\frac{tw^{3}}{L^{3}}=\frac{1}{4}\left( 160000\right) 3\left( \frac{28}{225}\right) ^{3}=231.\,26$
## For a MPP311
Specs: 13 kHz, 0.45 N/m : L=440 w=30 t=4 h=17.5+2 (is it actually trapezoidal??)
$k_{N}=\frac{1}{4}Yw\left( \frac{t}{L}\right) ^{3}=\frac{1}{4}\left( 160000\right) 30\left( \frac{4}{440}\right) ^{3}=0.901\,58$
$f$ $[Hz]=\frac{t\beta_{i}^{2}}{4\pi L^{2}}\sqrt{\frac{Y}{3\rho}} =\frac{\left( 4\ast10^{-6}\right) \left( 1.875\right) ^{2}}{4\pi\left( 440\ast10^{-6}\right) ^{2}}\sqrt{\frac{\left( 160\ast10^{9}\right) } {3\ast2330}}=27655.Hz$
$2\left( \frac{wh}{tL}\right) ^{2}=2\left( \frac{30\ast19.5}{4\ast 440}\right) ^{2}=0.220\,96$ so $k_{lat}
$k_{tor}=k_{N}\frac{1}{2}\left( \frac{L}{h}\right) ^{2}=0.9\frac{1} {2}\left( \frac{440}{19.5}\right) ^{2}=229.\,11$
$k_{lat}=\frac{1}{4}Y\frac{tw^{3}}{L^{3}}=\frac{1}{4}\left( 160000\right) 4\left( \frac{30}{440}\right) ^{3}=50.\,714$
## For a MPP211
Specs: 50 kHz, 1.5 N/m : L=215 w=30 t=4 h=17.5+2 (is it actually trapezoidal??)
$k_{N}=\frac{1}{4}Yw\left( \frac{t}{L}\right) ^{3}=\frac{1}{4}\left( 160000\right) 30\left( \frac{4}{215}\right) ^{3}=7.\, 727\,6$
$f$ $[Hz]=\frac{t\beta_{i}^{2}}{4\pi L^{2}}\sqrt{\frac{Y}{3\rho}} =\frac{\left( 4\ast10^{-6}\right) \left( 1.875\right) ^{2}}{4\pi\left( 215\ast10^{-6}\right) ^{2}}\sqrt{\frac{\left( 160\ast10^{9}\right) } {3\ast2330}}=1.\,158\,2\times10^{5}Hz$
$2\left( \frac{wh}{tL}\right) ^{2}=2\left( \frac{30\ast19.5}{4\ast 215}\right) ^{2}=0.925\,43$
so $k_{lat}~k_{tor}.$
$k_{tor}=k_{N}\frac{1}{2}\left( \frac{L}{h}\right) ^{2}=7.7\frac{1} {2}\left( \frac{215}{19.5}\right) ^{2}=468.\,02$
$k_{lat}=\frac{1}{4}Y\frac{tw^{3}}{L^{3}}=\frac{1}{4}\left( 160000\right) 4\left( \frac{30}{215}\right) ^{3}=434.\,68$
## For a MPP111
Specs: 200 kHz, 20 N/m : L=115 w=30 t=4 h=17.5+2 (is it actually trapezoidal??)
$k_{N}=\frac{1}{4}Yw\left( \frac{t}{L}\right) ^{3}=\frac{1}{4}\left( 160000\right) 30\left( \frac{4}{115}\right) ^{3}= 50.\,497$
$f$ $[Hz]=\frac{t\beta_{i}^{2}}{4\pi L^{2}}\sqrt{\frac{Y}{3\rho}} =\frac{\left( 4\ast10^{-6}\right) \left( 1.875\right) ^{2}}{4\pi\left( 115\ast10^{-6}\right) ^{2}}\sqrt{\frac{\left( 160\ast10^{9}\right) } {3\ast2330}}=4.\,048\,4\times10^{5}Hz$
$2\left( \frac{wh}{tL}\right) ^{2}=2\left( \frac{30\ast19.5}{4\ast 115}\right) ^{2}=3.\,234\,6$ so $k_{lat}>k_{tor}.$
$k_{tor}=k_{N}\frac{1}{2}\left( \frac{L}{h}\right) ^{2}=50.4\frac{1} {2}\left( \frac{115}{19.5}\right) ^{2}=876.\,45$
$k_{lat}=\frac{1}{4}Y\frac{tw^{3}}{L^{3}}=\frac{1}{4}\left( 160000\right) 4\left( \frac{30}{115}\right) ^{3}=2840.\,5$ | 1,670 | 3,285 | {"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": 27, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2014-52 | latest | en | 0.227957 |
http://www.prestigeroofinginc.net/lib/additive-and-cancellative-interacting-particle-systems | 1,582,147,800,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875144167.31/warc/CC-MAIN-20200219184416-20200219214416-00016.warc.gz | 220,606,597 | 8,939 | Additive and cancellative interacting particle systems by David Griffeath PDF
By David Griffeath
ISBN-10: 354009508X
ISBN-13: 9783540095088
Griffeath D. Additive and Cancellative Interacting Particle structures (LNM0724, Springer, 1979)(ISBN 354009508X)(1s)_Mln_
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Proves that the basic contact system {(~A)} Harris (1978) satisfies a more general collection of correlation inequalities than those in Theorem (Z. 14) has a simple but consequence. Theorem. Let {(~A)} be a nonergodic basic contact system (d = I) . Then lim inf t~oD Proof. o P(O c ~ t ) > 0 . If the system is nonergodic, then s 0 = %,i(0 is infected) = P(T@ : co) > 0 , and Z P(O ~ ~ ) = Let Z + = {0,1,Z, • "" } • 0 P ( T ~ > t ) -> a Vt . 14) ; we get Z Z+ 0 Z+ s ~t ' ~ n /~)->--~-- P(O¢ Z+ N t (0) > 0 S i n c e p a t h s c a n n o t jump o v e r o n e a n o t h e r , 0 i m p l y N t (0) > 0 .
Now . (Z. 6). 'k In addition, let ~Z = z + ~Z (~B) in terms of ~I and Introduce m a k e a copy of ~L = m i n { t : d( ([%B U (z+C)) let ~l be the ~tz + C in terms of '~t ' by letting the flow A which starts from B use Thus, /~Z @i while the flow starting from z + C uses @Z until T L A and @i thereafter. ~[~(~B)~AZ(~t Z TL > t . ii) P Since is mixing, and the second term does not have influence from ~ [] A Theorem. Let lim t~ ~ Proof. s. 10)) D o ~ (0,1) n--~ vo C(l t 1 . if A(x) / A(x+l) . Birkhoff's theorem yields 1 h a s an e d g e at ~- ) Since V0 in [-n, n] } pt has a positive , Zn = C([t I {edges of It~0 ) = [P([t Z, I {clusters of A in [-n,n]} I by at most lira It f o l l o w s t h a t xe gO [{edges of It in [-n,n] }[ VO Zn = P(~t density of edges for 0 e (0, i) , in P-probability.
To define them. But n o w w e introduce a different representation of process interpretation. from (~zxtB-U C ) , by making use of the coalescing branching AB Namely, whenever a particle from (~t) collides with one AC (~t) ' the former survives and the latter dies. 19) In terms of our construction, Vt ~ T . Z0) Problems. 19) • [] S h o w by example that the correlation inequalities of the last theorem do not hold for all additive systems. For which additive {(~A)} other than proximity systems are the inequalities valid? | 985 | 3,435 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2020-10 | latest | en | 0.887598 |
https://topic.alibabacloud.com/a/font-classtopic-s-color00c1detopcoderfont-srm-144-div2-550-point_1_11_32507368.html | 1,675,720,570,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500365.52/warc/CC-MAIN-20230206212647-20230207002647-00429.warc.gz | 589,513,050 | 17,264 | # TopCoder SRM 144 DIV2 (550-point)
Source: Internet
Author: User
Problem Statement
Let's say you have a binary string such as the following:
011100011
One way to encrypt this string is to add to each digit the sum of its adjacent digits. For example, the above string wocould become:
123210122
In particle, ifPIs the original string, andQIs the encrypted string, thenQ [I] = P [I-1] + P [I] + P [I + 1]For all digit positionsI. Characters off the left and right edges of the string are treated as zeroes.
An encrypted string given to you in this format can be decoded as follows (using123210122As an example ):
Now we repeat the process, assuming the opposite aboutP [0]:
Note that this algorithm produces at most two decodings for any given encrypted string. There can never be more than one possible way to decode a string once the first binary digit is set.
Given a stringMessage, Containing the encrypted string, return a vector <string> with exactly two elements. the first element shoshould contain the decrypted string assuming the first character is '0'; the second element shoshould assume the first character is '1 '. if one of the tests fails, return the string "NONE" in its place. for the above example, you shoshould return{"011100011", "NONE "}.
Definition
Class: BinaryCode Method: Decode Parameters: String Returns: Vector Method signature: Vector decode (string message) (Be sure your method is public)
Limits
Time limit (s ): 2 Memory limit (MB ): 64
Constraints
- MessageWill contain between 1 and 50 characters, inclusive.
- Each character inMessageWill be either '0', '1', '2', or '3 '.
Examples
0)
`"123210122"`
`Returns: { "011100011", "NONE" }`
The example from above.
1)
`"11"`
`Returns: { "01", "10" }`
We know that one of the digits must be '1', and the other must be '0'. We return both cases.
2)
`"22111"`
`Returns: { "NONE", "11001" }`
Since the first digit of the encrypted string is '2', the first two digits of the original string must be '1'. Our test fails when we try to assume thatP [0] = 0.
3)
`"123210120"`
`Returns: { "NONE", "NONE" }`
This is the same as the first example, but the rightmost digit has been changed to something inconsistent with the rest of the original string. No solutions are possible.
4)
`"3"`
`Returns: { "NONE", "NONE" }`
5)
`"12221112222221112221111111112221111"`
`Returns: { "01101001101101001101001001001101001", "10110010110110010110010010010110010" }`
This problem statement is the exclusive and proprietary property of TopCoder, Inc. any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c) 2003, TopCoder, Inc. all rights reserved.
Analysis:
Including the string class and vector container, it took some time to understand these things, but it was still modeled on a blog method.
I found that there are still many things I don't understand, so I just want to figure them out ~~
Code:
`#include <cstdio>#include <cstdlib>#include <iostream>#include <string>#include <cstring>#include <vector>using namespace std;class BinaryCode{ public: vector <string> decode(string message){ vector <string> ret; string str1(message.size(), 0), str2(message.size(), 0); str1[0]='0'; str2[0]='1'; if(1==message.size()){ if(message[0]<'0'||message[0]>'1'){ str1="NONE"; str2="NONE"; } else if(message[0] == '0') str2 = "NONE"; else if(message[0] == '1') str1 = "NONE"; } else{ int i; for(i=0; i<message.size(); ++i){ if(0 == i){ if(str1!="NONE"){ str1[i+1] = message[i]-str1[i]+'0'; if(str1[i+1]<'0'||str1[i+1]>'1') str1 = "NONE"; } if(str2!="NONE"){ str2[i+1] = message[i]-str2[i]+'0'; if(str2[i+1]<'0'||str2[i+1]>'1') str2 = "NONE"; } } else{ if(str1!="NONE"){ str1[i+1] = message[i]-str1[i]+'0'-str1[i-1]+'0'; if(str1[i+1]<'0'||str1[i+1]>'1') str1 = "NONE"; } if(str2!="NONE"){ str2[i+1] = message[i]-str2[i]+'0'-str2[i-1]+'0'; if(str2[i+1]<'0'||str2[i+1]>'1') str2 = "NONE"; } } } if(str1!="NONE"&&message[i-1]!=str1[i-1]-'0'+str1[i-2]) str1 = "NONE"; if(str2!="NONE"&&message[i-1]!=str2[i-1]-'0'+str2[i-2]) str2 = "NONE"; } ret.push_back(str1); ret.push_back(str2); return ret; }};`
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• Alibaba Cloud offers highly flexible support services tailored to meet your exact needs. | 1,464 | 5,893 | {"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} | 3.234375 | 3 | CC-MAIN-2023-06 | longest | en | 0.798403 |
http://mathhelpforum.com/calculus/241630-volume-solid-revolution-integration.html | 1,547,877,503,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583662690.13/warc/CC-MAIN-20190119054606-20190119080606-00141.warc.gz | 149,555,461 | 10,469 | # Thread: Volume of Solid of Revolution by Integration
1. ## Volume of Solid of Revolution by Integration
i need help with the very last question with the graph, part c where it says find volume, i am very new to calculus and never came across this did my research and found volume of solid by revolution , found something called washer as well. so confused sigh
2. ## Re: Volume of Solid of Revolution by Integration
To find the volume of a region bounded above by y = f(x) and below by the x axis, rotated about the x axis, use \displaystyle \begin{align*} V= \pi \int_a^b{ \left[ f(x) \right] ^2 \, \mathrm{d}x } \end{align*}
3. ## Re: Volume of Solid of Revolution by Integration
that makes no sense to me. but okay thanks anyway
4. ## Re: Volume of Solid of Revolution by Integration
Originally Posted by JadaPsherman
that makes no sense to me. but okay thanks anyway
If you are not familiar with the general integral form for finding a volume of rotation using the method of disks, why were you assigned such a problem?
5. ## Re: Volume of Solid of Revolution by Integration
i cant answer that question skeeter. the lecturer is trying to cover a calculus course that usually runs for 2 years (4 semesters). in one semester. its an assignment for math. but from the looks of it il have to repeat this course anyway. cant drop the course because it mandatory for my degree | 328 | 1,386 | {"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} | 2.796875 | 3 | CC-MAIN-2019-04 | latest | en | 0.942867 |
https://physics.stackexchange.com/questions/362671/dimension-of-the-parameter-of-susy-transformation | 1,571,506,081,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986697439.41/warc/CC-MAIN-20191019164943-20191019192443-00227.warc.gz | 622,405,106 | 31,208 | # Dimension of the parameter of SUSY transformation
I'm trying to gain some intuition on the dimension on the parameter of the supersymmetric transformation.
Assume I'm creating SUSY from scratch. I am making a wrong choice and defining my supersymmetry transformation $\Delta$ as: $$\Delta\psi = \xi \phi \quad,\qquad$$ where the anticommuting parameter $\xi$ has the dimension: $$[\xi] = [\text{length}]^{-1/2} = [\text{mass}]^{1/2} \quad.$$ Here $\psi$ and $\phi$ are the fermion and boson, correspondingly. I would also define the following transformation of the dummy field $F = m \phi$: $$\Delta F = \xi \psi\quad.$$ Then I would have: $$\Delta (m \psi \bar{\psi}) = \ldots+m\dfrac{1}{m^2}\xi^2\phi^2\quad.$$ Through the $F$-term, I would also get $$\Delta (m^2 \phi^2) =\ldots+ m^2\dfrac{1}{m^2}\xi^2\psi^2\quad.$$ Both lines are fine from dimensional point of view. Not sure how to define the other transformations in my alt-SUSY so far.
Obviously, the construction built on the first two equations in this question should quickly fail. What it the easiest way to see this?
• Your transformation cannot be a symmetry of a Lagrangian containing dynamical bosonic and fermionic fields. A boson kinetic term contains two spacetime derivatives, while a fermion kinetic term contains one, and so without derivatives in your transformation law the changes in these two terms under the transformation cannot cancel. (I may have misunderstood your transformation however, as I am confused as to why you have not specified the transformation of $\phi$ explicitly.) – diracula Oct 14 '17 at 22:03 | 415 | 1,598 | {"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 | 3 | CC-MAIN-2019-43 | latest | en | 0.839761 |
https://www.physicsforums.com/threads/problem-help.107968/ | 1,545,145,255,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376829429.94/warc/CC-MAIN-20181218143757-20181218165757-00093.warc.gz | 991,033,930 | 12,331 | # Homework Help: Problem Help!
1. Jan 24, 2006
### jkd989
A bodybuilder is holding a 35-kg steel barbell above her head. How much force would she have to exert if the barbell were lifted underwater?
In the hydraulic press used in a trash compactor, the radii of the input piston and the output plunger are 6.1 10-3 m and 4.5 10-2, respectively. If the height difference between the input piston and the output plunger can be neglected, what force is applied to the trash when the input force is 300 N?
Please answer these questions for me, they are the last two problems on my 100 problem worksheet that is due tomorrow. I have literally spent the past two hours trying to find the answers for these and i really need a good grade....Thanks in advance!!!
2. Jan 25, 2006
### Staff: Mentor
We don't just give answers here. Tell us how you have started these problems. (hint: do you understand the concepts of buoyancy and levers?)
[multi-post....locking] | 238 | 962 | {"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-2018-51 | latest | en | 0.946092 |
https://www.medianigeria.com/category/science/ | 1,716,185,442,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058222.5/warc/CC-MAIN-20240520045803-20240520075803-00332.warc.gz | 804,482,102 | 14,432 | ## 120 Internet Slang and Acronyms You Must Know
Internet slags are becoming increasingly popular, The reason they are becoming so popular is not only these shortcuts looks cool to the youths but they also save lot of your time by typing short. M/F = Are You Male or Female? RT = retweet CC = carbon copy DM = direct message MT = modify […]
## Where To Sell Blood In Nigeria
Where to sell blood in Nigeria, where can I sell my blood in Nigeria? If you want to make a blood donation in Nigeria, you can easily do so by visiting any of the National Blood Transfusion Service (NBTS) approved centres I.e All Nigeria general hospitals and All teaching Hospitals plus some private health institutions. See How Much […]
## How Much Blood Is In One Pint?
A pint of blood is about 525 mL. Each pint of blood contains 16 fluid ounces in a pint. The human body can contain anywhere from 9 to 12 pints of blood. The usual blood donation consists of one pint either packed cell or whole blood. See How Much A Pint Of Blood Is Sold In […]
## How Many Cups In A Pint
2 cups=1 pint 8 ounces=1 cup 2 cups=1 pint 2 pints=1 quart 4 quarts=1 gallon
## How Many Miles Make 1 Kilometers
1 mile = 1.6 km 1/10 mile = 0.16 km 1/8 mile = 0.2 km 1/4 mile = 0.4 km 1/2 mile = 0.8 km 1 mile = 1.6 km 1.5 mile = 2.4 km 2 miles = 3.2 km 2.5 miles = 4 km 5 miles = 8 km 10 miles = 16.1 km […]
## How Many Kilometers Make 1 Mile
There are 1.60934 kilometers in a mile in both imperial system (UK) and US. For marine navigation, there are 1.852 km in a nautical mile. What is the difference between Kilometer and Miles? A mile and a kilometer are both units of length or distance. Kilometers are used in the metric system and each one […]
## How Many Oz In A Gallon
The US Gallon is 128 fluid ounces. The UK or imperial gallon contains 160 ounces. The Oz is an abbreviation for ounces. The ounce is a unit of mass, weight, or volume used in most British derived customary systems of measurement. | 540 | 1,977 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2024-22 | latest | en | 0.819362 |
https://gis.stackexchange.com/questions/315745/create-a-line-string-from-street-geometry/315898 | 1,560,726,420,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998325.55/warc/CC-MAIN-20190616222856-20190617004856-00324.warc.gz | 444,291,043 | 37,842 | # Create a line string from street geometry
I'm currently facing some hard times trying to create a simplified line from a street geometry.
The data that I'm currently using comes from OpenStreetMap, using osm2pgsql.(Which means PostGIS, but I'm open to solutions that don't use it, or use external code, like C, JS, or whatever).
The problem: I need to create a simplified line string from given streets, however, most streets have multiple segments, such as:
In this example, the street is forked and segmented, the GeoJSON is available here.
Dumping the points of the street is useful which could be converted to a line string, however, their order is messed up, causing bizzare line formations. I could partially solve this issue ordering by lon/lat or lat/lon, but in several cases of points in the same axis or due geometry angle, it does not order them properly, and thus, does not work for all streets.
Few solutions I came up with:
• Using ST_Buffer on every segment, joining, and ST_ApproximateMedialAxis on the resulting geometry. It didn't work because some streets, even with a generous buffer have all it's segments touching each other and also ST_ApproximateMedialAxis doesn't always result in a line string (Not a function fault, it's the expected behavior).
• Ordering by LAT/LON ~ LON/LAT and creating a line from the result: Also didn't work as explained above.
• Using ST_LineMerge: Nope, in regular streets it does work, but on forked or segmented streets, it fails, as explained here.
• Iterating over points to create a line from every point nearest neighbor: Fails due the inability to find the real first and last points.
The hardest task so far is getting the farthest points from given set, to define the first and last point, getting this informations would solve the problem for me, but I'm clueless so far?
I thought about using ST_VoronoiPolygons, but I have no idea how to extract some result from that?
• `ST_DumpPoints` returns a geometry_dump type of set that holds a path along the geom. what kind of simplification do you need exactly? – ThingumaBob Mar 17 at 8:45
• @ThingumaBob A line string to be precise, keeping the overall street shape the most accurate possible. I've used ST_DumpPoints so I could attempt creating a line string from that points, however, as explained, they're not in order. – Nick LeBlanc Mar 17 at 12:34
• Perhaps you could add a justification for why you want to do this? For instance, if you're looking to create a routable road network there are ways to use this input without destoying it. – Richard Law Mar 17 at 20:23
• Sure thing @RichardLaw. Linear interpolation. – Nick LeBlanc Mar 17 at 21:45
I found a solution that fits my needs:
1. Dump all points from a street geometry.
2. Collect all points, create a Voronoi Diagram from the collection, then Dump the geometries to split them in individual, orderable polygons.
3. Finally, order the polygons from their area, limit the result to 2 (2 biggest polygons, the first and last points)
This is what it looks line in the end:
``````SELECT *
FROM
(SELECT (ST_DUMP(St_voronoipolygons(St_collect(dumpedpoints.geometry)))).geom AS polygons
FROM
(SELECT (St_dumppoints(geometry)).geom AS geometry
WHERE <your conditions> ) AS dumpedpoints) AS voronoid
ORDER BY ST_Area(voronoid.polygons) DESC
LIMIT 2
``````
With that in hand, I'm able to just query which point is inside the given polygons with ST_Within.
From that, having the first and last point, I wrote a JS that given a point, finds the nearest neighbor, store the data, go to the found neighbor, find his neighbor and repeat this until all points are iterated over.
``````/** Each point has a index inside, that's created sequentially, apart from the first OR last point, wich is always 0 so the code has the first iteration **/
const linePoints = [];
const copy = [...pointsCollection]; /** We create a iterable copy */
const points = copy.reduce(( Neighbor, Current, Index, Array ) => {
/** Avoid iterations over nulls */
if (Neighbor === null ) { return null }
/** If it's the last point, he doesn’t have any neighbors */
if(Neighbor.index + 1 === Array.length) { return null };
/** Remove itself from the points list, we do that so he doesn’t match with himself */
pointsCollection.splice(pointsCollection.findIndex(item => item.index === Neighbor.index), 1)
/** Your choice function of GeoLib */
let Nearest = nearestPoint(Neighbor, pointsCollection);
/** Push to the final list */
linePoints.push(Nearest);
/** Set the Neighbor varible of the next iteration as the Neighbor found in this */
return Nearest;
}, pointsCollection[0]); /** Set the initial value, in our case, the first or last point */
``````
The result of that operation is a sequential array that can be used to create a line string.
• What does the output look like? I'd imagine it's very jagged? Also, if the algorithm is "find start, find neighbour * n", then `ST_StartPoint` might be easier than calculating an entire voronoi and sorting by area? (I'm not sure how that works, actually.) Even on a split line, the line will almost certainly have a useful start and end. – Richard Law Mar 23 at 1:20
• @RichardLaw Most data from OSM(At least the parts I'm using) comes from community contributions(That are visually/graphically useful, but poor on precision), the line start can be exactly where we expect and at same time can be in the middle of the geometry, this was the first issue I faced with this problem, thus it's a problem when dealing with a generalist solution that needs to work on every street I'm working with. The line is in fact jagged, but simplification like Douglas-Peucker Algorithm(or your favorite/adequate one) does solve the problem with proper calculation :) – Nick LeBlanc Mar 23 at 1:54
• Maybe I'm just too thick to understand your solution, or I need some kind of visual explanation; I just don't understand how sorting your voronoi polygons by area achieves anything more advantageous than querying for the start/end vertices directly. But yes, perfectly generalised solutions for road networks are hard to come by, there is an extreme variety of edge cases. – Richard Law Mar 23 at 7:52
• @RichardLaw ST_StartPoint and ST_EndPoint only accepts LineStrings, almost all streets in OSM are MultiLineStrings, in the original example of this question, this approach would not work right away, even if i converted it to a LineString using several approaches, the ST_StartPoint and ST_EndPoint will lead to incorrect results. As i explained early, however drew the line be it person or algorithm, took arbitrary starting/ending points, in the original example, the starting point is on the middle of it, the same can be said to the ending point. – Nick LeBlanc Mar 23 at 16:28
• @RichardLaw Performance is in fact an issue(Not at all, 300ms the entire process above for each street, that can run in parallel on several cores and threads.), but i only need to calculate and store this data one single time, streets will hardly change their shapes, and if they do, i'll just recalculate it and store the changes :) – Nick LeBlanc Mar 23 at 16:31 | 1,665 | 7,143 | {"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-2019-26 | longest | en | 0.949597 |
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When a blank tile is played on a Double Word Score square or a Triple Word Score square, the value of the word is doubled or tripled even though the blank itself has a zero score value.
SCRABBLE® is a registered trademark. We do not cooperate with the owners of this trademark. All trademark rights are owned by their owners and are not relevant to the web site "scrabble-word.com". This site is intended for entertainment and training. We try to make a useful tool for all fans of SCRABBLE. "Scrabble Word" is the best method to improve your skills in the game. | 771 | 2,871 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2022-27 | latest | en | 0.756402 |
https://www.wiringscan.com/how-to-find-resistance-in-parallel-circuit/ | 1,701,762,511,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100550.40/warc/CC-MAIN-20231205073336-20231205103336-00203.warc.gz | 1,201,444,851 | 11,521 | # How To Find Resistance In Parallel Circuit
By | August 30, 2023
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Resistors In Series And Parallel Combination Determination Of The Equivalent Resistance Two Procedure Faqs
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4.5 | 687 | 3,369 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2023-50 | latest | en | 0.668959 |
https://www.jiskha.com/questions/1819614/the-wheel-of-fortune-a-contestant-gives-the-wheel-an-initial-angular-velocity-of-5-95 | 1,585,516,085,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370496227.25/warc/CC-MAIN-20200329201741-20200329231741-00431.warc.gz | 1,019,470,971 | 5,298 | # Physics
The wheel of Fortune. a contestant gives the wheel an initial angular velocity of -5.95 rad/s and the wheel stops after 5.8s of constant acceleration.
Determine the panel (e.g. \$600 or bankrupt) that the yellow pointer will be on when the wheel stops.
Angular Displacement(red)———-panel value and color———
I need help with this there is picture in the question but I couldn’t put it ? Any help please thanks
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3. 👁 75
1. Anyone???
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posted by Ama
2. the average angular velocity is half of the initial
the wheel will travel ... -5.95 rad/sec * 5.8 sec / 2 ... radians
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posted by R_scott
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https://gcse.wikia.org/wiki/Quadratic_factorisation | 1,623,899,373,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487626465.55/warc/CC-MAIN-20210617011001-20210617041001-00462.warc.gz | 253,793,291 | 30,452 | 490 Pages
Factorising quadratics is one of the three methods (completing the square and the quadratic formula being the other two) used to solve a quadratic equation, such as x2 + 4x + 4.
There is no simple method of factorising a quadratic expression, but with a little practice it becomes easier. One systematic method, however, is as follows:
### Example
Factorise
(here the 20y has been split up into two numbers whose multiple is 36. 36 was chosen because this is the product of 12 and 3, the other two numbers).
The first two terms, 12y2 and -18y both divide by 6y, so 'take out' this factor of 6y.
(we can do this because 6y(2y - 3) is the same as 12y² - 18y) (see factorisation and simplification)
Now, make the last two expressions look like the expression in the bracket: | 209 | 789 | {"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} | 3.734375 | 4 | CC-MAIN-2021-25 | latest | en | 0.948139 |
http://www.ccl.net/cca/documents/dyoung/topics-framed/gaussian.shtml | 1,659,951,973,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570793.14/warc/CC-MAIN-20220808092125-20220808122125-00692.warc.gz | 72,568,384 | 7,277 | http://www.ccl.net/cca/documents/dyoung/topics-framed/gaussian.shtml
CCL gaussian.html
The Absolute Beginners Guide to Gaussian
# The Absolute Beginners Guide to Gaussian
David Young
Cytoclonal Pharmaceutics Inc.
## Introduction:
This is to teach the beginner how to use the Gaussian XX series of programs. This guide is intended for use by someone who has never used the program before.
This guide is in no way intended to be a comprehensive or advanced guide to the Gaussian program. Also, this is not an explanation of the theory behind the types of calculations or their strengths, weaknesses, accuracy, etc.
The term "ab initio" in this guide refers to methods which calculate purely from the principle of quantum mechanics with no experimental data involved. The term "semiempirical" refers to methods which use the general process dictated by quantum mechanics, but simplify it to gain speed then correct for the simplification by the use of some experimental data.
The Gaussian programs are given version numbers according to which year they were released (i.e. Gaussian 90 is the 1990 version). Gaussian is a program for doing ab initio and semiempirical calculations on atoms and molecules. The program is operated by making an ASCII input file using any convenient text editor then running the program. The results of the calculation are put in one or more output file. Gaussian itself currently has no provisions for graphical or interactive inputs or outputs. However, such things do exist for use with Gaussian and can be obtained from other sources.
This guide gives the input description by showing three sample input files and describing what they mean. A section is provided on the calculation of vibrational frequencies followed by a brief description of outputs and lists of the input options.
## Input file for an atom:
Input files can have any name but often use the extension ".inp" or ".input" or ".com" depending on the system. Here is a sample input file for a single atom calculation.
\$ RunGauss
#n test rohf/sto-3g pop=full GFINPUT
O sto-3g triplet
0 3
O
Line 1: "\$ RunGauss" This line is always the same. Although optional on some machines it is a good practice to use it always.
Line 2: (blank) Line 2 is blank for many calculations. It can be used to specify a checkpoint file name or memory allocation.
Line 3: "#n test rohf/sto-3g pop=full GFINPUT" Line 3 is called the route card. It specifies what type of calculation to do and what to calculate and output. The line always starts with "#". The "n" suppresses printing of debugging messages. The "test" suppresses keeping a summary of the job in a central data bank called an archive. "rohf" is the ab initio keyword. It stands for "restricted open-shell Hartree Fock". Ab initio keywords must always be followed by a "/" and a basis set designation such as "sto-3g". The "pop=full" specifies the printing of a full Mulliken population analysis. The "GFINPUT" puts a copy of the basis set in the output file.
Line 4 is blank.
Line 5: "O sto-3g triplet" Line 5 is a comment for the users reference only.
Line 6 is blank.
Line 7: "0 3" Line 7 consists of two numbers. The first is the charge and the second is the spin multiplicity.
Line 8: "O" Line 8 specifies that oxygen is the atom to be calculated.
Line 9: Leave at least one extra blank line at the end of the input file.
## Input example for a diatomic molecule:
Here is a sample input for a diatomic molecule
\$ RunGauss
# test rhf/STO-3G opt
CO sto-3g
0 1
C
O 1 R
R 0.955
Only significant differences from the atom input file will be mentioned.
Line 3: "# test rhf/STO-3G opt" The "rhf" stands for "restricted Hartree Fock". The "opt" specifies that the program is to find the correct geometry for the molecule, as predicted by the specified ab initio method and basis set (in this case the bond distance).
Lines 8-11 are called the Z-matrix. These lines specify the geometry of the molecule and which parameters are to be optimized if an "opt" keyword is on the route card.
Line 8: "C" This specifies that the first atom is a carbon atom.
Line 9: "O 1 R" specifies that an oxygen atom is at a distance R from the first atom (the carbon). R is defined (in Angstroms) on line 11. If an optimization is being done, a new value for R representing the most stable geometry will be given in the output file.
## Input file for a polyatomic molecule:
Here is an input file for a formaldehyde molecule.
\$RunGauss
# test MNDO pop=reg
Formaldehyde single point w/ populations
0 1
C
O 1 OC
H 1 HC 2 A
H 1 HC 2 A 3 180.0
OC 1.2
HC 1.08
A 120.0
Line 3: "# test MNDO pop=reg" The ab initio method and basis have been replaced by a semiempirical method keyword "MNDO". The "pop=reg" specifies a Mulliken population analysis, but not as much information printed as with "pop=full".
Line 5: "Formaldehyde single point w/ populations" Note that a calculation, which is not a geometry optimization is referred to as a single point calculation.
Line 8: "C" The first atom is a carbon.
Line 9: "O 1 OC" The second atom is an oxygen with a distance to the first atom of OC.
Line 10: "H 1 HC 2 A" The third atom is a hydrogen with a distance to the first atom of HC and an angle between the third, first and second atoms of A (in degrees).
Line 11: "H 1 HC 2 A 3 180.0" The fourth atom is a hydrogen with a distance to the first atom of HC and an angle between the third, first and second atoms of A. The dihedral angle between the first, second, third and fourth atoms is 180 degrees (a planar molecule).
If an optimization were being done, the parameters OC, HC and A would be optimized, but the molecule would be kept planar. Note that parameters can be used more than once.
Additional atoms are added by adding lines like line 11 consisting of distance, angle and dihedral angle specifications.
Gaussian does have provisions for entering geometries as x, y, z Cartesian coordinates.
Geometry specifications sometimes uses points not on atomic centers out of convenience or necessity. These are called dummy atoms. These will not be covered in this guide.
## Calculating frequencies:
Gaussian can calculate vibrational modes along with their frequencies and force constants, using the "FREQ" keyword. These calculations are only meaningful if the molecule is at its equilibrium geometry for the given level of theory. Also, geometry optimizations and frequency calculations cannot be done in the same job. Therefore, to get a frequency calculation, first a geometry optimization should be done then the optimized geometry must be used to run a frequency calculation.
## The output file:
At least one output file is always produced. It can have any filename, but many systems are set up to use extensions ".lis" or ".out". This is an ASCII file which contains most of the results of the calculation, such as energies, geometries, frequencies and population analysis. Many things are put in this file that the user often ignores on any given calculation.
## Checkpoint files:
When a subsequent calculation is to use results from a previous calculation as its inputs, these results can be kept in a special file to avoid having to type them into the new input file. Many such result are put in a file called a checkpoint file. It is a binary file. The use of a checkpoint file can be specified using the correct options on line 2 and the route card.
## Cube files:
Properties, such as electron density or spin density can be calculated for a regular grid of points in space and saved as a cube file. This is a file with both binary and ASCII formats, which is often used as an input for other graphical visualization programs.
Cube file generation is prompted by usage of the "CubeDensity" keyword and specification of a grid of points.
## Other files:
Gaussian has many other optional input and output files. Often these are accessed as standard FORTRAN units according to the conventions of the specific operating system being used.
## List of ab initio keywords:
Note that an ab initio keyword must be accompanied by a basis set keyword in the format "ab_initio/basis". All of these can be prefaced by R for closed-shell restricted wave functions, U for unrestricted open-shell wavefunctions or RO for restricted open-shell wavefunctions. This list is provided for the sake of seeing what is available. Many of these have additional options describing how to control the calculation which are listed in the Gaussian User's Guide and Programmer's Reference.
HF - Hartree Fock (uses RHF for singlets and UHF for others)
RHF - restricted Hartree Fock
UHF - unrestricted Hartree Fock
ROHF - spin-restricted open-shell Hartree Fock
OSS - two open shell singlet wave function
GVB - generalized valence bond
CASSCF - complete active space MCSCF
MP2 - Moller-Plesset second order correlation energy correction
MP3 - Moller-Plesset third order correlation energy correction
MP4 - same as MP4SDTQ
MP4DQ - Moller-Plesset fourth order correlation energy correction with double and quadruple substitutions.
MP4SDQ - Moller-Plesset fourth order correlation energy correction with single, double and quadruple substitutions.
MP4SDTQ - Moller-Plesset fourth order correlation energy correction with single, double, triple and quaduple substitutions.
CI - same as CISD
CIS - configuration interaction with single excitations
CID - configuration interaction with double excitations
CISD - configuration interaction with single and double excitations
QCISD - quadratic configuration interaction with single and double excitations
QCISD(T) - quadratic configuration interaction with single and double excitations and triples contribution to the energy
## List of basis sets available:
Note that a basis set must accompany an ab initio keyword. The "*" and "**" indicate polarization functions (i.e. 6-31G**). The "+" and "++" indicate diffuse functions. For other options and how to use these options, see the Gaussian User's Guide and Programmer's Reference.
Basis sets available
basisoptionsatoms
STO-3G * H - Xe
3-21G * ** H - Cl
4-21G * **
4-31G * ** H - Ne
6-21G * **
6-31G + ++ * **H - Cl
LP-31G * **
LP-41G * **
6-311G + ++ * **H - Ar
MC-311G none H - Ar
D95 + ++ * **H - Cl
D95V + ++ * **H - Ne
SEC + ++ * **H - Cl
(same as SHC)
CEP-4G + ++ * **H - Cl
CEP-31G + ++ * **H - Cl
CEP-121G + ++ * **H - Cl
LANLIMB none H - Bi
(except lanthanides)
LANLIDZ none H - Bi
(except lanthanides)
The GEN keyword allows the basis set to be read from the input file.
## List of semiempirical keywords:
Note that semiempirical methods do not require a separate basis set. All of these can be prefaced by R for closed-shell restricted wavefunctions, U for unrestricted open-shell wavefunctions or RO for restricted open-shell wavefunctions. This list is provided for the sake of seeing what is available. Many of these have additional options describing how to control the calculation which are listed in the Gaussian User's Guide and Programmer's Reference.
AM1 - Austin method one
CNDO - complete neglect of differential overlap
INDO - intermediate neglect of differential overlap
MINDO3 - modified intermediate neglect of differential overlap third modification.
MNDO - modified neglect of differential overlap
## List of keywords:
This is the list of what to calculate and what to print and how to manage the calculation. This is not a comprehensive list. This list is provided for the sake of seeing what is available. For other options and how to use these options, see the Gaussian User's Guide and Programmer's Reference.
ANG - distances in Angstroms
AU - distances in bohrs
DEG - angles in degrees
CubeDensity - generate a cube file
Density - for cube file generation
direct - do integrals as needed (vice in a file on the disk)
InCore - do integrals in core memory
field - add a finite field to the calculation
freq - frequency determination
freq=noraman - frequency determination without Raman intensities
GFPRINT - put basis in output file
GFINPUT - put basis in output file in format for generalized input
IRC - follow a reaction path
LST - linear synchronous transit
NoFreeze - optimize all variables
opt - geometry optimization
Polar - calculate polarizability and hyperpolarizability, if possible
pop=none - no population analysis
pop=min - minimal printing of Mulliken population analysis
pop=reg - some printing of Mulliken population analysis
pop=full - full printing of Mulliken population analysis
pop=bonding - bonding population analysis
pop=no - natural orbital analysis
pop=noab - natural orbital analysis for separate alpha and beta spins
prop=grid - computes electrostatic potential
prop=field - computes electrostatic potential and field
prop=EFG - computes electrostatic potential, field and field gradients
punch - puts various information in a separate output file | 2,994 | 12,867 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2022-33 | latest | en | 0.890102 |
http://re-design.dimiter.eu/?cat=18 | 1,723,599,780,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641086966.85/warc/CC-MAIN-20240813235205-20240814025205-00691.warc.gz | 23,039,936 | 12,313 | # Category: Game theory
1) The number of first-year students in the Netherlands has soared from 105 000 in 2000 to 135 000 in 2011. The 30% increase is a direct result of government policy which links university funding with student numbers. In some programs in the country, student numbers have more than doubled during the last five years. Everyone is encouraged to enter the university system. 2) In the general case, there is no selection at the gate. Students cannot be refused to enter a program. 3) Now, the government’s objectives are to reduce the number of first-year drop-outs and slash the number of students who do not graduate within four years. Both objectives are being supported by financial incentives and penalties for the universities. Something’s gotta give. I wonder what… P.S. ‘Solve for the equilibrium’ is the title of a rubric from Marginal Revolution.
The Prisoner’s Dilemma (PD) is the paradigmatic scientific model to understand human cooperation. You would think that after several decennia of analyzing this deceivingly simple game, nothing new can be learned. Not quite. This new paper discovers a whole new class of strategies that provide a unilateral advantage to the players using them in playing the repeated version of the game. In effect, using these strategies one can force the opponent to any score one desires. The familiar tit-for-tat strategy, which so far had been assumed to be the optimal way of playing the repeated game, appears to be just the tip of an iceberg of ‘zero determinant’ strategies which ‘enforce a linear relationship between the two players’ scores’. This is huge and people have already started to discuss the implications. But what puzzles me is the following: The search for an optimal way to play the repeated PD has been going on at least since the 1980s. The best strategies have been sought analytically, and through simulation (see Robert Axelrod’s iterated PD tournaments). And yet nobody discovered or stumbled upon ‘zero determinant’ strategies for more than 30 years of dedicated research. So can we expect a rational but not omnipotent actor to use these strategies? I think the formal answer needs to be ‘yes’ – a rational actor plays the game in the most advantageous way for his/her interests and if zero determinant strategies provide en edge, then he/she needs to (and is expected and predicted to) play these. The alternative would be to impose some limitations to the…
The latest issue of Political Research Quarterly has an interesting and important exchange about the use of game theory to understand the effectiveness of torture for eliciting truthful information. In this post I summarize the discussion, which is quite instructive for illustrating the prejudices and misunderstandings people have about the role and utility of game theory as a tool to gain insights into the social world. In the original article, Schiemann builds a strategic incomplete-information game between a detainee (who can either posses valuable information or not, and be either ‘strong’ or ‘weak’) and a state which can be either ‘pragmatic’ (using torture only for valuable information) or ‘sadistic’ (torturing in all circumstances). There are two additional parameters capturing uncertainty about the value and completeness of the information provided by the detainee, and two styles of interrogation (providing leading evidence or not). The article then proceeds to identify the equilibria of the game, which turn out to be quite a few (six), and quite different – in some, truthful information is provided while in others, not; in some, torture is applied while in others, not; etc…. At this point you will be excused for wondering what’s the point of the formal modeling if it only shows that, depending on the parameters, different things are possible. Schiemann, however, makes a brilliant move by comparing each of these equilibria to some minimal normative standards that proponents of torture claim to uphold – namely, that torture should not be used on detainees who have provided all their information, that transmitted information should be generally reliable, and that in all cases only…
The plans for a referendum on Scottish independence offer a nice opportunity for applying spatial analysis. The latest point of contestation is whether a third option (enhanced devolution) should be offered to the voters in addition to the ‘Yes’ and ‘No’. The UK government is against including the third option, a Scottish movement is strongly in favor, and the major advocate of the independence camp Alex Salmond is undecided (as far as I can tell). Assuming that the government in London prefers Scotland to remain in the UK (and enhanced devolution to full independence), why do they oppose the inclusion of the third option in the referendum? That would only make sense if the UK government believes that more people would vote ‘No’ to independence when faced with the choice between the two extremes. At the same time, proponents of full independence will be better off including the third option only if they believe that they will lose a Yes/No referendum. Trying to check the current estimates of support for independence, however, does not lead to a straightforward answer. According to Wikipedia, the latest poll conducted in September 2011 places the two camps practically dead-even – 39% say they would vote ‘Yes’ and 38% say they would vote ‘No’. According to the betting markets on the other hand, Scottish independence in the near future doesn’t stand quite a chance. Obviously, London trusts the betting markets more than the polls. With the decision to oppose a third option in an eventual referendum, the UK…
Here is a puzzle: You meet a real estate agent for a property you are interested in. The house has an asking prize and you haven’t made any offers yet. The realtor mentions casually that she has just had an offer for the house which she has rejected. Would you ask what the offer was? Would the realtor tell you? Is it a fair question to ask? (obviously, the realtor is under no obligation to reveal the truth value of the rejected offer and there is no way for me to verify the answer).
Here is a formalized description of the problem: the Seller adn the Buyer can be each of two types – High or Low. High Buyers and Sellers prefer High Deal to No Deal no Low Deal, and Low Buyers and Sellers prefer High Deal to Low Deal to No Deal. First, the Seller announces whether she has rejected a Very low or a Moderate offer. If a Moderate offer has been (announced as) rejected, the Buyer can make either a High offer (which all Sellers accept) or No offer which ends the game. If a Very low offer has been (announced as) rejected, the Buyer can make a Low offer, No offer or a High offer (the latter two end the game). If a Low offer has been made, the Seller can either Accept or Reject it. In the case of rejection the Buyer can make a High offer or No offer – both actions end the game. Here is the game tree.
Essentially, by making an announcement that she has rejected a Moderate offer the Seller credibly commits to reject any Low offers. Importantly, Buyers suffer a cost from a rejected offer (which is realistic given the costs of the compulsory technical surveys one has to do before an offer). There is no penalty for a late deal (no time discounting). The game is of two-sided incomplete information – neither the Buyers nor the Sellers know the type of the opponent. So the questions:
1) Should you ask what the rejected offer was?
2) Should the realtor (the Seller) tell you?
3) Would the answer (announcement) of the Seller be informative?
4) Does the Seller do better under this game or a game with no signal (announcement)?
5) Does the Buyer do better under this game or a game with no signal?
6) Is this game Pareto-improving under any circumstances?
My answers are after the fold. | 1,686 | 7,906 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2024-33 | latest | en | 0.917008 |
https://fr.mathworks.com/matlabcentral/cody/problems/13-remove-all-the-consonants/solutions/1058578 | 1,590,763,204,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347404857.23/warc/CC-MAIN-20200529121120-20200529151120-00402.warc.gz | 354,342,773 | 15,729 | Cody
# Problem 13. Remove all the consonants
Solution 1058578
Submitted on 22 Nov 2016 by BluePoseidon1643
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
s1 = 'Jack and Jill went up the hill'; s2 = 'a a i e u e i'; assert(isequal(s2,refcn(s1)))
v = aeiou
2 Pass
s1 = 'I don''t want to work. I just want to bang on the drum all day.'; s2 = 'I o'' a o o. I u a o a o e u a a.'; assert(isequal(s2,refcn(s1)))
v = aeiou | 184 | 544 | {"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-2020-24 | latest | en | 0.761703 |
http://matrix.skku.ac.kr/Cal-Book1/Ch11/ | 1,685,574,424,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224647459.8/warc/CC-MAIN-20230531214247-20230601004247-00312.warc.gz | 32,096,450 | 56,223 |
Part II Multivariate Calculus
Chapter 11. Vectors and the Geometry of Space
Calculus
http://matrix.skku.ac.kr/Cal-Book1/Ch1/
http://matrix.skku.ac.kr/Cal-Book1/Ch2/
http://matrix.skku.ac.kr/Cal-Book1/Ch5/
Chapter 11. Vectors and the Geometry of Space
11.1 Three-Dimensional Coordinate Systems
문제풀이 by 김태현 http://youtu.be/_s_2T1VVob8
11.2 Vectors
문제풀이 by 오교혁 http://youtu.be/BFgh6irMqsc
11.3 The Dot Product
11.4 The Vector or Cross Product
11.5 Equations of Lines and Planes
문제풀이 by 구본우 http://youtu.be/lxuGE_Erthg
11.1 Three-Dimensional Coordinate Systems
In a two-dimensional plane any point can be represented as an ordered pair of real numbers, where is the -coordinate and is the -coordinate of the point. In three-dimensional space, a point is represented by three real numbers .
The coordinate axes labeled as the -axis, -axis and -axis are three directed lines that are perpendicular to each other and passing through a chosen fixed point (called the origin). This three-dimensional coordinate system (See Figure 1(a).) will enable us to represent a point in space. Normally, the -axis and -axis are taken as horizontal and the -axis as being vertical forming a Right-Handed Coordinate System, as in Figure 1(b). The three coordinate axes determine three coordinate planes. Thus the -plane contains the -axis and -axis; the -plane contains the -axis and -axis; the -plane contains the -axis and -axis. These three coordinate planes divide the space into eight parts, called octants. The positive axes determine the first octant, in the foreground. (See Figure 2.)
Figure 1 (a) Coordinate axes (b) Right-hand rule
Figure 2 Octants
Let be any point in space. Then, the real numbers are the (directed) distances from to the -plane, the -plane, and the -plane respectively. The point is denoted by this ordered triple and , and are known as the coordinates of ; is the -coordinate, is the -coordinate, and is the -coordinate. Thus starting at the origin , the point is located by moving units along the -axis, then units parallel to the -axis, and then units parallel to the -axis as shown in Figure 3.
Figure 3
The three-dimensional rectangular coordinate system (Cartesian coordinate system) is the set of ordered triples given by the Cartesian product
.
Recall that an equation of and in two dimension represents a curve. Similarly, an equation of , and in three dimension represents a surface. In general, if is a constant, then represents a plane parallel to the -plane, is a plane parallel to the -plane, and is a plane parallel to the -plane in .
Distance Formula in Three Dimensions
The distance between the points and is
.
Example 1
Determine the equation of a sphere with radius and center .
Solution. A sphere is the set of all points whose distance from the center is . (See Figure 4.) So, any point on the sphere satisfies or .
Figure 4
Thus, the equation of the required sphere is
. ■
If the center is the origin , then the equation of the sphere is
Example 2
Show that is the equation of a sphere, and find its center and radius.
Solution. We can rewrite the given equation in the form of an equation of a sphere if we complete the squares:
.
Comparing this equation with the standard form in the result of Example 1, we see that it is the equation of a sphere with center and radius . ■
Example 3
What region in is represented by the following inequalities?
, .
Solution. The inequalities can be rewritten as , so they represent the points whose distance from the origin is at least 2 and at most 3. But we are also given that , so the points lie on or above the -plane. Thus, the given inequalities represent the region that lies between (or on) the spheres and and above (or on) the -plane. (See Figure 5.)
var('x, y, z')
p1=implicit_plot3d(x^2 + y^2 + z^2 == 4, (x,-5, 5), (y,-5, 5), (z,-5, 5), opacity=0.2, color="red")
p2=implicit_plot3d(x^2 + y^2 + z^2 == 9, (x,-5, 5), (y,-5, 5), (z,-5, 5), opacity=0.4)
p3=implicit_plot3d(z==0, (x,-5, 5), (y,-5, 5), (z,-5, 5), opacity=0.4, color="green")
show(p1+p2+p3)
Figure 5
Example 4
Draw the surface in . (See Figure 6.)
Solution.
var('x, y, z')
implicit_plot3d(x+y-5==0, (x, -5, 5), (y, -5, 5), (z, -5, 5),
color='blue', opacity=0.5)
Figure 6
11.1 EXERCISES (Three-Dimensional Coordinate Systems)
http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-1-Sol.html
1. Draw the surface in .
Solution.
var('x, y, z')
implicit_plot3d(2*x-3*y+z==1, (x, -3, 2), (y,-3,2), (z,-3,3))
2. Draw the surface in .
Solution.
var('x, y, z')
s1=implicit_plot3d(x^2-y^2==3, (x,-3,3), (y,-3,3), (z,-2,0.5), color='red', opacity=0.3)
s1
3. Find the lengths of the sides of the triangle with vertices , and . Is a right triangle? Is it an isosceles triangle?
Solution. Isosceles triangle
3
3
3*sqrt(2)
4. Find the distance from to each of the following.
(a) The -axis (b) The -axis
(c) The -axis (d) The -plane
(e) The -plane (f) The -plane
Solution. Answer : (3, 4, 5, sqrt(41), sqrt(34), 5)
5. Find the equation of the sphere with center and radius 3. What is the intersection of this sphere with the -plane?
Solution. The equation of the sphere :
, and the intersection of this sphere with the -plane can be obtained by substituting in the equation. Hence
.
6. Find an equation of the sphere that passes through the point and has center .
Solution. The distance between and is the radius of the sphere.
Hence,
.
Thus, an equation of sphere is
.
7-8. Show that the equation represents a sphere, and find its center and radius.
7.
Solution.
8.
Solution. Completing squares in the equation gives :
, with the center
9. (a) Prove that the midpoint of the line segment from
to is , .
(b) Find the lengths of the medians of the triangle with vertices , and .
10-16. Determine the region of represented by the equation or inequality.
10. .
Solution. The equation represents a plane parallel to the -plane and 8 units in front of it.
11. .
12. .
Solution. The inequality represents all points on or between the horizontal planes (the -plane) and . So the answer is all points on or between the horizontal plane (the -plane) and .
13. , .
Solution.
var('x, y, z')
s1=implicit_plot3d(x^2+y^2==3, (x,-3,3), (y,-3,3), (z,-2,0.5), color='red', opacity=0.3)
s2=implicit_plot3d(z==-1, (x,-3,3), (y,-3,3), (z,-2,0.5), color='green', opacity=0.5)
s3=implicit_plot3d(x^2+y^2==3, (x,-3,3), (y,-3,3), (z,-0.99,-1.01), color='blue')
s1+s2+s3
14. .
Solution. The set of all points in whose distance from the -axis is . This is a cylinder of radius 3 and axis along -axis.
15. .
Solution. The inequality is equivalent to . So the region consists of those points whose distance from the point is greater than 1. This is the set of all points outside the sphere with radius 1 and center .
16. .
Solution.
var('x, y, z')
implicit_plot3d(x^2 + z^2 == 9 -2*z, (x, -5, 5), (y, -5, 5), (z, -5, 5), opacity=0.2, color="red")
17-18. Describe the given region by an inequality.
17. The half-space consisting of all points to the left of the -plane.
Solution. This describes all points with positive -coordinates, that is, .
18.The solid rectangular box in the first octant bounded by the planes , , and .
Solution.
var('x, y, z')
p1=implicit_plot3d(x == 1, (x, -5, 5), (y, -5, 5), (z, -5, 5), opacity=0.2, color="red")
p2=implicit_plot3d(y == 3, (x, -5, 5), (y, -5, 5), (z, -5, 5), opacity=0.2, color="blue")
p3=implicit_plot3d(z == 2, (x, -5, 5), (y, -5, 5), (z, -5, 5), opacity=0.2, color="green")
show(p1+p2+p3)
11.2 Vectors
Vectors are quantities that have both magnitude (or length) and direction. Recall that a scalar is a real number (with only magnitude).
For example, velocity, acceleration, displacement of an object moving in space and a force are all vector quantities.
Figure 1
A vector is denoted graphically by an arrow or by a directed line segment. A vector is printed as a boldface letter or by putting an arrow above the letter.
The magnitude of the vector is the length of the arrow and the arrow points in the direction of the vector.
For example in Figure 1, the displacement of a particle along a line segment from point to point is represented by . This displacement vector v, has initial point (the tail) and terminal point (the tip).
Equality of vectors: Two vectors u and v are equal (or equivalent) and write uv if they have the same length and same direction (or parallel) but not necessarily the same initial point. The zero vector, denoted by 0: it has length and no direction.
Addition of vectors: The sum of two vectors u and v denoted by uv is the vector from the initial point of to the terminal point of as shown in the triangle law in Figure 2.
Figure 2 The Triangle Law Figure 3 The Parallelogram Law
By placing v with the same initial point as u, we can construct a parallelogram with u and v as adjacent sides. Then, is the diagonal of the parallelogram starting at the same initial point. (This is called the Parallelogram Law: See Figure 3.) Note that uvvu. ( vector addition is commutative.) For instance, if several forces are acting on an object, the resultant force experienced by the object is the vector sum of these forces.
Scalar Multiplication: For any scalar and a vector v, the scalar multiple v is the vector whose length is times the length of v and whose direction is the same as v if and is opposite to v if . If , then (the zero vector). Scalar multiplication amounts to scaling the vectors, which can be elongation or contraction.
Figure 4
For example , known as negative of v, has the same length as v but points in the opposite direction. The difference of two vectors and is defined by .
Also if or .
Two non zero vectors are parallel if they are scalar multiples of one another.
Component Form of a Vector
Vectors can be treated algebraically by introducing a coordinate system. The position vector of a point is the vector with the initial point at the origin and terminal point at . The entries are called the components of and the vector was written as . The ordered triple refers to a vector while the ordered triple refers to a point in the space.
For any vector with the initial point and the terminal point , the vector representation of is by
.
For example, for the vector represented by the directed line segment with the initial point and terminal point , is
.
The magnitude (or length) of the vector v is denoted by the symbol or . (read as norm )
The length (or magnitude) of the position vector is .
A unit vector is a vector whose length is 1. In general, if , then the unit vector that has the same direction as is
.
The vector is the normalization of the vector , has the same direction as and
In component form, vectors are added by just adding their corresponding components. Similarly, we can subtract vectors by subtracting the corresponding components and multiple of a vector by a scalar is done by multiplying each component by the scalar . Thus,
,
,
.
We denote by the set of all three dimensional vectors. More generally, denotes the set of all -dimensional vectors. An -dimensional vector is an ordered -tuple: having components . For -dimensional vectors, addition and scalar multiplication is defined in terms of its components just as for the cases and .
Algebra of Vectors
If and are vectors in and and are scalars, then
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
Equality of Vectors: Two vectors u and v are equal if and only if their corresponding components are equal.
Let , and be unit vectors in the directions of the positive -, -, and -axes. Thus unit vectors are write as follow:
Figure 5 Standard basis vectors in and
Any vector in can be expressed in terms of the standard basis vectors (or unit vectors along axes) , and . For , we can write
.
The above representation is unique. For example, .
For example, if and , then .
For example, the unit vector in the direction of the vector is
Figure 6
. Note that the unit vector in the opposite direction of the vector is .
Application
Two forces and with magnitudes 10lb and 12lb act on an object at a point as shown in Figure 7. Find the resultant force acting at as well as its magnitude and direction. (Indicate the direction by finding the angle shown in Figure 7.)
Figure 7
We want to find . First we can find as
Hence,
Example 1
(a)Draw the vectors , and
(b) Show by means of a sketch, that there are scalars and such that
(c) Find the exact values of and .
Solution.
z=(0, 0); a=(-2, 3); b=(-2, -5); c=(7, 0)
s, t=var('s, t')
Ab = matrix(QQ, 2, 3, [a[0], b[0], c[0], a[1], b[1], c[1]])
T = Ab.echelon_form()
s=T[0, 2];t=T[1, 2]
A=arrow(z, a, color=(2, 1, 1))
A=A+text("a", (a[0]+0.3, a[1]+0.3))
A=A+arrow(z, (s*a[0], s*a[1]), color='blue')
A=A+text("sa", (s*a[0]+0.3, s*a[1]+0.3))
A=A+arrow(z, b, color=(3, 1, 0))
A=A+text("b", (b[0]+0.3, b[1]+0.3))
A=A+arrow(z, (t*b[0], t*b[1]), color='green')
A=A+arrow((t*b[0], t*b[1]), c, color='red')
A=A+text("tb", (t*b[0]+0.3, t*b[1]+0.3))
A=A+arrow((s*a[0], s*a[1]), c, color='red')
A=A+arrow(z, c, color='black')
A=A+text("c", (c[0]+0.3, c[1]+0.3))
A=A+point((a, b, c, (s*a[0], s*a[1]), (t*b[0], t*b[1])), rgbcolor='brown', size=30)
show(A)
Figure 8 ■
Example 2
For given vectors , , and . Find scalars and such that .
Solution.
z=vector([0, 0,0]); a=vector([1, -1, 2]); b=vector([3, -1, 2]); c=vector([0,1,2]); d=vector([2,1,4])
Ad= matrix(QQ, [a, b, c, d]).transpose()
print T
print -1/4*a + 3/4*b + 3/2*c
p=plot(a,color='red')+plot(b,color='green')+plot(c)+plot(d,color='goldenrod')
p
var('r,s,t')
n=3
eq=[r*a[i]+s*b[i]+t*c[i]==d[i] for i in range(3)]
solve(eq,r,s,t)
[ 1 3 0 2]
[ 1 3 0 2]
[-1 -1 1 1]
[ 2 2 2 4]
[ 1 0 0 -1/4]
[ 0 1 0 3/4]
[ 0 0 1 3/2]
(2, 1, 4) # vector
[[r == (-1/4), s == (3/4), t == (3/2)]]
d = -1/4*a + 3/4*b + 3/2*c. ■
11.2 EXERCISES (Vectors)
http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-2-Sol.html
1-2. Determine .
1. (a) ,
(b) ,
Solution. (a)
(b)
v1=vector([5, -3])
v2=vector([10, 7])
v2- v1
2. ,
Solution. .
3-4. Find the sum of the given vectors.
3. ,
Solution. .
4. ,
Solution.
v1=vector([0, 1, -4])
v2=vector([0, 2, 0])
v1+v2
5-8. Compute and .
5. ,
Solution. ,
,
.
6. , .
Solution.
a=vector([5, -1, 3])
b=vector([-1, 3, -2])
a.norm()
a+b
2*a-3*b
(a-b).norm()
7.
Solution. ,
,
,
.
8.
Solution.
a=vector([3, -4, 0])
b=vector([1, -1, 1])
print a.norm()
print a+b
print 2*a-3*b
print (a-b).norm()
(4, -5, 1)
(3, -5, -3)
sqrt(14)
9. Determine a unit vector that has the same direction as .
Solution. The vector has length
, so the unit vector with the same direction is
.
10. Find a vector that has the same direction as but has length 6.
Solution.
v1=vector([2,-4,-2])
v2=6/v1.norm()*v1
print v2
v2.norm()
6
11. A clothesline is tied between two poles, 6m apart. The line is quite taut and has negligible sag. When a wet shirt with a mass of 0.8kg is hung at the middle of the line, the midpoint is pulled down 6cm. Find the tension in each half of the clothesline.
Solution. Let and represent the tension vectors in each side of the clothe line as shown in the figure. Then and have equal vertical components and opposite horizontal components, so
and .
By similar triangles, .
The force due to gravity acting on the shirt has magnitude , hence we have . The resultant of the tensile forces counterbalances , so
and .
Thus, the tensions are
.
12.The tension at each end of the chain has magnitude 50N. What is the weight of the chain?
13. (a) Draw the vectors , and .
(b) Show, by means of a sketch, that there are scalars and such that .
(c) Find the exact values of and .
Solution. (a)
a=vector([2, -3])
b=vector([-2, -1])
c=vector([6, -5])
p=plot(a, color='red')+plot(b, color='green')+plot(c)
t=text("a", (a[0]+0.3,a[1]+0.3))+text("b",(b[0]-0.3,b[1]+0.3))+text("c",(c[0]+0.3,c[1]+0.3))
show(p+t, figsize=4)
(b)
j=2
k=-1
z=(0, 0)
a=(2, -3)
b=(-2, -1)
c=(6, -5)
A=arrow(z, a, color=(2, 1, 1))+arrow(z, b, color=(3, 1, 0))+arrow(z, c, color='black')
A=A+arrow(z, (j*a[0], j*a[1]), color='blue')+arrow(z, (k*b[0], k*b[1]), color='green')
A=A+arrow((k*b[0], k*b[1]), c, color='red')+arrow((j*a[0], j*a[1]), c, color='red')
A=A+text("a", (a[0]+0.3, a[1]+0.3))+text("ja", (j*a[0]+0.3, j*a[1]+0.3))+text("b", (b[0]+0.3, b[1]+0.3))
A=A+text("kb", (k*b[0]+0.3, k*b[1]+0.3))+text("c", (c[0]+0.3, c[1]+0.3))
A=A+point((a, b, c, (j*a[0], j*a[1]), (k*b[0], k*b[1])), rgbcolor='brown', size=30)
show(A)
var('s,t')
a=vector([2,-3])
b=vector([-2,-1])
c=vector([6,-5])
n=3
eq=[s*a[i]+t*b[i]==c[i] for i in range(2)]
solve(eq,s,t)
14. Let , , and in .
(i) Plot the vectors and .
(ii) Find scalars , and such that .
Solution.
a=vector([2,-3,1])
b=vector([-2,-2,1])
c=vector([6,-5,2])
d=vector([2,1,2])
p=plot(a,color='red')+plot(b,color='green')+plot(c)+plot(d,color='goldenrod')
p
var('r,s,t')
n=3
eq=[r*a[i]+s*b[i]+t*c[i]==d[i] for i in range(3)]
solve(eq,r,s,t)
Answer : [[r == (-28/3), s == (8/3), t == (13/3)]]
15. If and , describe the set of all points such that .
Solution.
Therefore the surface of a sphere with a center and a radius .
11.3 The Dot Product
The product of two vectors which is known as a scalar product or dot product or even as inner product, is defined as follows:
The dot product of and is the real number (scalar) given by .
The dot product of and is obtained by multiplying corresponding components and then adding the individual products.
For example,
,
.
Properties of the Dot Product
If , and are vectors in and is a scalar, then
(ⅰ)
(ⅱ)
(ⅲ)
(ⅳ)
(ⅴ)
Proof. Let , and . We shall prove few of them and remaining as exercise.
(ⅰ)
(ⅲ)
■
Geometric interpretation: The dot product enables us to find the angle between two nonzero vectors. Let be angle between and where in Figure 1.
Figure 1
Then the dot product of two nonzero vectors and is . Thus, the formula of the angle between two nonzero vectors and is given by
.
Figure 2
The dot product of two vectors is itself a scalar. Two special cases immediately arise:
(i) and are perpendicular if and only if .
(ii) and are parallel if and only if .
The zero vector 0 is perpendicular to all vectors.
Specially, for the unit vectors in ,
.
For example, consider the vectors and having lengths 5 and 8 with an angle between and .
As a result, we have the dot product of and is .
Example 1
Find .
Solution.
a=vector(QQ, [2, -3]);b=vector(QQ, [1, -7])
ab=a.dot_product(b)
Example 2
Find the angle between the vectors and .
Solution. Since,
and .
We have
That is, the angle between and is
def anglebetween(a,b)
return arccos(a.dot_product(b)/(a.norm()*b.norm()))
a=vector([2, 4, -4])
b=vector([2, 2, 0])
anglebetween(a, b)
Example 3
Show that is perpendicular to .
Solution. Since,
these vectors are perpendicular. ■
Since if and if , it follows that is positive for and negative for . The dot product measures the extent to which and point in the same direction.
If , then and point in the same general direction, if , then they are perpendicular, and if , then they point in generally opposite directions. (See Figure 3.) When and point in exactly the same direction, we have , so and .
If and point in exactly opposite directions, then and so and
.
Figure 3
Proposition: Let , and be vectors. If and are both perpendicular to , then every linear combination is perpendicular to .
Proof. Suppose that and are both perpendicular to . Then
and .
It follows that and therefore is perpendicular to . ■
Direction Angles and Direction Cosines
The angles , and which a nonzero vector a makes with the positive -axis, -axis and -axis are known as the direction angles of a. These angles lie in the interval .
Figure 4
The direction cosines of a vector a are the cosines of these direction angles and that are , and , respectively.
Thus we have
, , .
Consequently,
.
Also,
.
Therefore, dividing by both sides,
.
Thus, the direction cosines of are the components of the unit vector in the direction of .
Example 4
Find the direction angles of the vector
Solution. Since , gives
, , .
Hence
. ■
Projections and Components
Consider two vectors and with the same initial point and with as the angle between them, represented by and . Let be the foot of the perpendicular from to the line containing . Then is called the vector projection of onto and is denoted by .
Figure 5 Vector projections
The component of b along a (or the scalar projection of onto ) is the signed magnitude of the vector projection, which is the number . We denote this by . Observe that it is negative if . Since
the dot product of and is the product of the magnitude of and the scalar projection of b on to . Also
the component of along is obtained by the dot product of with the unit vector in the direction of . Thus, as a summary, the followings are true:
Scalar projection of onto : ,
Vector projection of onto :
The vector projection is the scalar projection times the unit vector in the direction of a.
(a) (b)
Figure 6
For each vector
,
This agrees with our previous use of the term “component” and gives the identity
.
The vector is orthogonal to the projection vector .
Hence the equation
.
Note that is orthogonal to the vector .
Example 5
Find the scalar projection and vector projection of onto .
Solution. Since , the scalar projection of onto is
.
The vector projection is this scalar projection times the unit vector in the direction of . That is,
.
a=vector([1,5,-3])
b=vector([2,3,-1])
(a.dot_product(b))/(a.norm()^2)*a
Answer : (4/7, 20/7, -12/7) ■
Some Applications
When a force is directed along the line of motion of the object, then the work done by in moving the object through a distance is . Suppose that the constant force , pointing in some other direction (See Figure 7.), moves the object from to , then the displacement vector is . Then, the work done by this force is defined to be the product of the component of the force along and the distance moved. If is the angle between and , then
.
If causes a displacement of a body, then the work done is
.
Figure 7
Example 6
A crate is hauled 10m up a ramp under a constant force of 160N applied at an angle of to the ramp. Find the work done.
Figure 8
If and are the force and displacement vectors, as pictured in Figure 8, then the work done is
. ■
A constant force with vector representation moves an object along a straight line from a point to anthor point. The work done when we find in this book the distance is measured in meters and the magnitude of the force is measured in newtons.
Example 7
Find a work done when a force and the displacement vector is
Solution.
def proj_ab(a,b):
return (a.dot_product(b))/(a.norm()^2)*a
a=vector([1,5,-3])
b=vector([2,3,-1])
proj_ab(a,b)
a=vector(QQ, [2, -3]);b=vector(QQ, [1, -7])
ab=a.dot_product(b)
show(ab)
11.3 EXERCISES (The Dot Product)
http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-3-Sol.html
1. Determine the dot product of two vectors if their lengths are 8 and and the angle between them is .
Solution. Let the vectors be and Then,
by definition of the dot product.
2-6. Find the dot product of and
2. , .
Solution.
a=vector([5, -3]);
b=vector([4, 6]);
a.dot_product(b);
3. .
Solution.
.
4. , .
Solution.
5. .
Solution.
6. and the angle between and is .
Solution. .
7-9. Compute the angle between the vectors.
7. , .
Solution. and
.
From the definition of the dot product, we have
.
Hence, the angle between and is
.
That is, and are orthogonal.
8. (a) ,
(b) ,
Solution. (a)
def anglebetween(a,b):
return arccos(a.dot_product(b)
/(a.norm()*b.norm()))
a=vector([6,3])
b=vector([4,2])
anglebetween(a,b)
(b)
a=vector([6, -3, 4]);
b=vector([2, 0, -3]);
anglebetween(a,b)
9. , .
http://matrix.skku.ac.kr/cal-lab/11-3-9.html
Solution. ,
, and .
From the definition of the dot product, we have
and
.
a=vector([2, -1, 3])
b=vector([3, 1, -5])
print "The angle between a and b is", anglebetween(a,b).n(), "radians"
print "The angle between a and b is", anglebetween(a,b).n()*180/pi.n(), "degrees"
The angle between a and b is 2.03952668853669 radians
The angle between a and b is 116.856271457445 degrees
10. Verify whether the given vectors are orthogonal, parallel, or neither.
(a) ,
(b) ,
(c) ,
Solution. (a) Since , and are orthogonal.
(b)
def anglebetween(a,b):
return
arccos(a.dot_product(b)/(a.norm()*b.norm()))
var('t')
a=vector([6, 3]);
b=vector([4, 2]);
solve(a.dot_product(b)/(a.norm()*b.norm())==cos(t), t)
anglebetween(a,b)
(c) Parallel.
11. Determine such that the vectors and are orthogonal.
Solution.
var('t')
a=vector([2, -6, t])
b=vector([t, t, t^2])
x=a.dot_product(b)
solve([x==0], t)
Answer : [t == -2, t == 2, t == 0]
12. Find a unit vector that is orthogonal to both and .
Solution. .
13-14. Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.)
13.
Solution. Since , the direction cosines of the vector are
.
Hence, .
14. .
Solution. direction cosine: ,
direction angle: , , .
15.Prove that the vector known as orthogonal projection of , is orthogonal to .
Solution.
This proves the result.
16-19. Find the scalar and vector projections of onto and orthogonal projection of , and .
16. , .
Solution. scalar projection: ,
vector projection: ,
orthogonal projection: .
17. , .
Solution.
a=vector(QQ, [2, -1, -2])
b=vector(QQ, [4, 3, 3])
ab=a.dot_product(b)
an=a.norm()
scal_proj=ab/an
scal_proj
vec_proj=scal_proj/an*a
vec_proj
orth_proj=b-vec_proj
orth_proj
vec_proj.dot_product(orth_proj)
18. ,
Solution. scalar projection: ,
vector projection: ,
orthogonal projection: .
19. ,
Solution. ,
so
and .
And .
20.Prove that the distance from a point to the line is
.
Find the distance from the point to the line .
21. Prove the Cauchy-Schwarz Inequality: .
Solution. Since ,
.
22. Prove the Triangle Inequality: .
Solution. Note that it is enough to prove .
Consider the L․H․S ,
Hence we have
23. Prove that
.
Solution.
and .
.
24.Show that vectors a and b are orthogonal if and only if .
25.Show that if and only if is orthogonal to .
26.Give geometric interpretation of the above two problems.
11.4 Cross Product
The cross product is only defined for vectors in and results in another vector in .
Component Form of the Cross Product
We define the cross product of two vectors and in the terms of the components of the vector.
THEOREM 1 Cross Product of Two Vectors
The cross product of two vectors and is the vector
.
The cross product of the vectors and can also be obtained as follows
or in the determinant form
.
For example, we consider two vectors and . Then
.
Example 1
Find a vector perpendicular to the plane that passes through the points , and .
Solution. The vector is perpendicular to both and and is therefore perpendicular to the plane through and . We know that
We compute the cross product of these vectors:
Hence, the vector is perpendicular to the given plane. Any nonzero scalar multiple of this vector, such as is also perpendicular to the Plane Equation.
Solution. 1. Note that and . (use determinant form for simplicity) Thus is a vector which is orthogonal to both and .
2. Suppose be a vector which is orthogonal to vectors and . Then components of can be obtained by solving two equations and .
3. , that is the vector product is not commutative. (In fact, )
Right-Hand Rule
An alternative characterization of the cross product uses the right-hand rule. As seen in Figure 1, if the fingers of the right hand point along the vector and then curl toward the vector , the thumb will give the direction of . In Figure 1, the right-hand rule shows the direction of .
Figure 1
THEOREM 2
Let and be two vectors in . Then the cross product is a vector with magnitude
where is the angle between and . The direction of is the direction given by the right-hand rule. (See Figure 1.) When , the direction of is undefined.
Proof. If and , then .
It is easy to see that
Taking square root both sides and observing that
for ,
we get the result.
Area
Let two nonzero vectors and be two sides of a parallelogram, then the area of the parallelogram is
.
Likewise, we see that the area of a triangle with sides and is
.
Thus, the length of the cross product is equal to the area of the parallelogram (See Figure 2.) determined by and .
Figure 2
Example 2
Find the area of the triangle with vertices , and .
Solution. In Example 1, we computed . The area of the parallelogram with adjacent sides and is the length of this cross product:
The area of the triangle is half the area of this parallelogram. Hence the required area of its triangle is . ■
The following theorem is a consequence of the definition of the cross product.
THEOREM 3 Parallel Vector
Two nonzero vectors and are parallel ( or ) if and only if .
Using , then it follows that for the standard basis vectors , , and , we have
, , ,
, , .
Observe that .
In general, . Hence, the associative law for multiplication usually does not hold. For example whereas .
For vector products, the following usual laws of algebra hold.
THEOREM 4 Properties of the Cross Product
If , and are vectors and is a scalar, then
(ⅰ)
(ⅱ)
(ⅲ)
(iv) or
(v)
(vi)
(vii)
Readers are encouraged to verify the above properties by using components of vectors.
Triple Scalar Product or Box Product
If , and , then
.
The product is called the triple scalar product of , and .
Note that follows from the properties of determinants.
http://matrix.skku.ac.kr/2012-LAwithSage/interact/1.html
Volume of a Parallelepiped
Consider a parallelepiped with coterminous edges determined by the vectors , , and . (See Figure 3.)
Figure 3
The area of the base parallelogram is . If is the angle between a and , then the height of the parallelepiped is . Therefore, the volume of the parallelepiped determined by the coterminous edge vectors , and is
the magnitude of the scalar triple product.
Example 3
Find the volume of the box (parallelepiped) determined by , and .
Solution. The volume of the parallelepiped is given by
.
Therefore, the volume is units cubed.
a=vector([3, 1, 1])
b=vector([1, 4, 1])
c=vector([1, 1, 5])
a.dot_product(b.cross_product(c))
THEOREM 5
The three vectors , , are coplanar (lie in the same plane) if and only if the volume of the parallelepiped is zero, and consequently .
Example 4
Use the scalar triple product to show that the vectors , and are coplanar.
Solution. We use to compute their scalar triple product:
.
Therefore, by Theorem 5 the volume of the parallelepiped determined by , and is 0. This means that , and are coplanar. ■
Torque
Suppose a force is acting on a rigid body at a point given by a position vector . Let be the angle between the position and force vectors. The torque vector with reference to the origin is .
It measures the tendency of the body to rotate about the origin. Its direction indicates the axis of rotation. Its magnitude is equal to the area of the parallelogram determined by and .
For example, if a bolt is tightened by applying a force to a wrench (See Figure 4.), it produces, a turning effect. Note that the only component of that can cause a rotation is the one perpendicular to , that is, .
Figure 4
Example 5
A bicycle pedal is pushed by a foot with a 40N force as shown in Figure 5. The shaft of the pedal is 20cm long. Find the magnitude of the torque about .
Figure
Solution.
. ■
Example 6
Find the cross product and verify that it is orthogonal to both and :
and
Solution.
a=vector(QQ, [1, 1, -2]);b=vector(QQ, [1, 0, -1])
c=a.cross_product(b)
show(c)
show(e.dot_product(a))
show(e.dot_product(b))
Answer : (-1, -1, -1) # a.cross_product(b)
0 # (e.dot_product(a))
0 # (e.dot_product(b)) ■
11.4 EXERCISES (The Cross Product)
http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-4-Sol.html
1-5. Find the cross product and verify that it is orthogonal to both and .
1. , .
Solution.
a=vector(QQ, [1, -1, 1])
b=vector(QQ, [2, 0, 3])
c=a.cross_product(b)
show(c)
show(e.dot_product(a))
show(e.dot_product(b))
0
0
2. , .
Solution.
Now, and
So, is orthogonal to both and .
3. , .
Solution. .
4. .
Solution. .
5. .
Solution. .
6. If and , find and .
Solution. , .
7.If , and ,
show that .
Solution.
(i)
(ii)
Hence, .
8. Find two unit vectors orthogonal to both and .
Solution.
a=vector(QQ, [1, -1, 2])
b=vector(QQ, [3, 0, 1])
c=a.cross_product(b)
cn=c.norm()
e=c/cn
show(e)
show(-e)
(1/35*sqrt(35), −1/7*sqrt(35), −3/35*sqrt(35))
. Thus, two unit vectors orthogonal to both are
,
that is, and .
9. Find two unit vectors orthogonal to both and .
Solution. .
Thus, two unit vectors orthogonal to both are , that is, and .
10. Find the area of the parallelogram with vertices , , and
.
Solution. We may think of these points in -plane in the space.
A=vector([0, 1, 0])
B=vector([2, 1, 0])
C=vector([1, 4, 0])
D=vector([1, -2, 0])
AB=B-A; AC=C-A
Area= abs(AB.cross_product(AC))
show(Area)
11.Find the area of the parallelogram with vertices , , and .
Solution. The parallelogram is determined by the vectors and , so the area of parallelogram is
Then .
12-13. Find a vector perpendicular to the plane through the points , and .
12. , ,
Solution.
P=vector([1, 0, 0]);
Q=vector([4, 1, -1]);
R=vector([2, -1, -2]);
PQ=Q-P;
PR=R-P;
PQ.cross_product(PR)
13. , ,
Solution. and , so a vector orthogonal to the plane through and is
.
That is, is orthogonal to the plane through and .
14-15. Find the area of triangle .
14. , ,
Solution.
P=vector([1, 0, 0]);
Q=vector([4, 1, -1]);
R=vector([2, -1, -2]);
PQ=Q-P;
PR=R-P;
CP=PQ.cross_product(PR);
1/2*CP.norm()
15. , , .
Solution. .
16-17. Find the volume of the parallelepiped with adjacent edges , , and .
16. , , ,
Solution.
P=vector([2, 0, 1]);
Q=vector([4, 2, 0]);
R=vector([3, 1, -1]);
S=vector([1, 1, 0]);
PQ=Q-P;
PR=R-P;
PS=S-P;
CP=PQ.cross_product(PR);
PS.inner_product(CP).abs()
17.,,,.
Solution. and .
.
So, the volume of the parallelepiped is cubic units.
8.Show that the vectors , and are not coplanar.
Solution. Not coplanar.
a=vector(QQ, [1, 1, 0])
b=vector(QQ, [2, -1, 4])
c=vector(QQ, [2, 1, 4])
M=matrix(QQ, [a, b, c]);M
print M
print M.det()
Answer : [ 1 1 0]
[ 2 -1 4]
[ 2 1 4]
-8
19.Determine whether the points , , and lie in the same plane.
Solution. and .
.
Thus, the volume of the parallelepiped determined by and is . This says that these vectors lie in the same plane. Therefore, their initial and terminal points and also lie in the same plane.
20. A wrench 40cm long lies along the positive -axis and grips a bolt at the origin. A force is applied in the direction at the end of the wrench. Find the magnitude of the force needed to supply of torque to the bolt.
21.Suppose that . Prove or disprove the following statements.
(a) If , then
(b) If , then
(c) If and , then
Solution. (a) False.
If , then , hence is perpendicular to . This can happen if .
For example, let and , then .
(b) False.
If , then , which implies that is parallel to , which of course can happen if .
(c) True.
Since , is perpendicular to , by part (a). From part (b), is parallel to . Since , and is both parallel and perpendicular to , we have . Hence .
22. Show that .
23. If and , then find .
11.5 Equations of Lines and Planes
In this section, we will derive vector equations of lines and planes in and , and we will deal with shortest distance problems related to these equations.
Lines
In the plane , the equation of the line can be uniquely determined when a slope and a specified point on the line are given. In general it can be generally written as follows:
where , and are real numbers and and are not both zero.
Let's find the equation of a line in . If a line passes through the point and is parallel to , then the vector is parallel to (See Figure 1.), where is any point on the line.
Figure 1
That is, the line is a set of all points that satisfies the following equation :
Thus, if is any point on the line through that is parallel to , then the vector is parallel to , so for some . This line can be represented as the equation .
We call this a vector equation of the line through that is parallel to .
A vector equation of a line can be split into a set of scalar equations by equating corresponding components; these are called parametric equations of the line. Thus we have vectors
,
which implies
From , symmetric equations of the line can be written defined as the following:
where , and are nonzero constants.
If and are distinct points with position vectors and in or , then the line determined by these points is parallel to the vector , so it follows from that the line can be expressed in vector form as
, .
Equation is called the two-point vector equation of the line through and .
Example 1
(a) Find a vector, parametric and symmetric equations of the line that pass through the point and is parallel to the vector .
(b) Find two other points on the line.
Solution. (a)Here and .
The vector equation is
.
Parametric equations are , , .
The symmetric equation is
.
(b)Choosing the parameter value gives , , and , so is a point on the line. Similarly, gives the point . ■
Example 2
Find a vector, parametric and symmetric equations for the line that pass through the points and .
Solution. Two points and with position vectors and forms a vector
and the vector equation can be written as
, .
Thus, the parametric equations are , , and symmetric equations of the line are .
Point-Normal Equation of Planes
A plane in can be uniquely obtained by specifying a point in the plane and a nonzero vector that is perpendicular to the plane. (See Figure 2)
Figure 2
The vector is called the normal vector to the plane. If is any point in this plane, then the is orthogonal to (See Figure 2). By the property of the dot (inner) product
From ,
or
where , and are not all zero.
We call a point-normal equation of the plane through with normal
.
For convenience, we simplify the left terms of as follows
where , and are not all zero and .
We call the general equation of the plane.
Example 3
Find a point-normal equation and a general equation of the plane that passes through with normal .
Solution. From , a point-normal equation of the plane is
.
Multiplying out and taking the constants to the right side yields the general equation
. ■
Vector and Parametric Equations of Planes
A plane can be uniquely obtained by passing through a point in and two nonzero vectors and that are parallel to and are not scalar multiples of one another. (See Figure 3.) That is, if is any point in the plane and and are positioned with their initial points at , then is expressed as a linear combination of and ;
or
where and and and , called parameters, are in . We call a vector equation of the plane through that is parallel to and .
Let be any point in the plane through that is parallel to the vectors and . Then can be expressed in the component form as
or
We call parametric equations of the plane.
Figure 3
Example 4
Find vector and parametric equations of the plane that passes through three points: , , .
Solution. Let , , and . Then we have two vectors that parallel to the plane as
, .
From , a vector equation of the plane is
.
Also we have parametric equations as
. ■
Perpendicular and Parallel Lines
Two lines and with direction vectors and , respectively, are
(i) intersect,
(ii) parallel if for some nonzero scalar ,
(iii) skew if neither (i) nor (ii).
Example 5
Show that the lines
: , , ,
: , ,
are perpendicular.
Solution. By taking the value for the parameters and , we get two vectors
and
are parallel to and , respectively. We can verify that two lines are perpendicular to each other by
. ■
Example 6
Show that the lines
,
are parallel.
Solution. The coefficient of the parameters and , we see that
and
are the direction vectors for and , respectively. Since , the two lines are parallel. ■
Example 7
Show that the lines and with parametric equations
: ,
:
are skew lines; that is, they do not intersect and are not parallel (and therefore do not lie in the same plane).
Figure 4
Solution. The lines are not parallel because the corresponding direction vectors and are not parallel. (Their components are not proportional.) If and have a point of intersection, there would be values of and such that
,
,
.
If we solve the first two equations, we get and , and these values do not satisfy the third equation. Therefore, no values of and satisfy all three equations. Thus and do not intersect. Hence, and are skew lines.
var ('t, s')
L1=parametric_plot3d([t,2*t+1,3*t +2], (t,-3.5,3.5), color='blue', thickness=5)
L2=parametric_plot3d([3-4*s,2-3*s,1+2*s], (s,-3.5,3.5), color='red', thickness=3)
show(L1+L2)
The Distance from a Point to a Line in Space
To find the distance from a point to a line that passes through a point parallel to a vector , we can find the relationship of the distance and the length as follows: (See Figure 5.)
Figure 5
where is the angle between and .
From Theorem 2 in Section 11.4,
which implies .
Then the distance from a point to a line is .
Example 8
Find the distance from the point to the line
: .
Solution. We see from the equations for that it passes through and is parallel to . We obtain
and
.
. ■
Projection of Vectors
To find the distance from a point to a plane in , we introduce the concept of the orthogonal projection of vectors.
(a) (b)
Figure 6
Figure 7
Let be the foot of the perpendicular from to and be vectors in with . Then is called an orthogonal projection of onto . The vector can be expressed as . Here is called a vector component of that is perpendicular to . In Figure 7, a vector is sum of and ; .
The following theorem give expression for the orthogonal projection .
THEOREM 1
If and are in , then we have the following:
(a) (b)
Proof. (a) Since is parallel to , we have .
Since and because is perpendicular to (See Figure 6), we can get the value as that satisfies
.
Therefore .
(b) .
Example 9
Find the projection of onto and a vector component of perpendicular to for and .
Solution. Since and , the projection of onto is
and a vector component of perpendicular to is
. ■
The Distance from a Point to a Plane in Space
We find a way to determine the distance from a point to the plane . Note that is the normal to the plane.
Figure 8
Let be any point in the given plane and let . Then, .
The distance from to the plane is equal to the absolute value of the scalar projection of onto the normal vector . (See Figure 8.) Thus,
.
Since lies in the plane, its coordinates satisfy the equation of the plane, so we have . Thus,
.
Example 10
Find the distance from a point to the plane .
Solution. Since a normal vector is ,
. ■
Similarly, in the distance from to a line is
.
Example 11
Find the distance from a point to the plane .
Solution. Since a normal vector is ,
.
Now we have some examples for properties of lines and planes in .
Example 12
Find an equation of the plane through the point with the normal vector .
Solution. Putting , , , , and , from , we see that an equation of the plane is
or . ■
Example 13
Find an equation of the plane that passes through the points , and .
Solution. The vectors and corresponding to and are
.
Since both and lie in the plane, their cross product is orthogonal to the plane and can be taken as the normal vector. Thus,
With the point and the normal vector , the equation of the plane is
or . ■
Example 14
Find the point at which the line , , intersects the plane .
Solution. We substitute the expressions for , and from the parametric equations into the equation of the plane:
This simplifies to , so . Therefore, the point of intersection occurs when the parameter value is .
Thus, , , .
Hence the point of intersection is . ■
Example 15
(a) Find the angle between the planes and .
(b) Find symmetric equations for the line of intersection of these two planes.
Solution. (a)The normal vectors of these planes are and , respectively.
Let be the angle between the two planes, which is called a dihedral angle. This dihedral angle is equal to the angle between two normal vectors , . By the property of the dot product,
,
and . Therefore two planes are orthogonal to each other.
(b) We first need to find a point on . For instance, we can find the point where the line intersects the -plane by setting in the equations of both planes. This gives the equations and , whose solution is , . Hence, the point lies on .
Now, we observe that, since lies in both planes, it is perpendicular to both of the normal vectors. Thus, a vector v parallel to is given by the cross product
.
Hence, the symmetric equations of can be written as
.
The line of intersection can also be obtained by solving the equations of the planes for two of the variables in terms of the third, which can be taken as the parameter.
For instance, the line was given as the line of intersection of the planes and . The symmetric equations that we found for could be written as
Figure 9 Shows how the line in Example 17 can also be regarded as the line of intersection of planes derived from its symmetric equations (Sage).
and
which is again a pair of linear equations. They exhibit as the line of intersection of the planes and . (See Figure 9.)
var ('x, y, z')
P1=implicit_plot3d(x + y + z == 1,(x,-7,7),(y,-7,7),(z,-7,7),color='blue',opacity=0.3)
P2=implicit_plot3d(x - 2*y + 3*z == 1,(x,-7,7),(y,-7,7),(z,-7,7),color='red',opacity=0.3)
show(P1+P2)
Perpendicular and Parallel Planes
Two planes and with normal vectors and , respectively, are
(i) perpendicular : if , and
(ii) parallel if for some nonzero scalar .
Example 16
Show that the planes are parallel and find the distance between the parallel planes and .
Solution. First, we note that the planes are parallel because their normal vectors and are parallel. To find the distance between the planes, we choose any point on one plane and calculate its distance to the other plane. In particular, if we put in the equation of the first plane, we get , so is a point in this plane. Then, the distance between and the plane is
.
Hence, the distance between the planes is . ■
Example 17
In Example 7, we showed that the lines
: ,
: .
are skew. Find the distance between them.
Solution. Since the two lines and are skew, they can be viewed as lying on two parallel planes and . The distance between and is the same as the distance between and which can be computed as in Example 16. The common normal vector to both planes must be orthogonal to both (the direction of ) and (the direction of ). Hence, a normal vector is
.
If we put in the equations of we get the point on , so, an equation for is
or .
If we now set in the equations for , we get the point on . So the distance between and is the same as the distance from to . Then, this distance is
. ■
Example 18
Find the distance from the point to the plane .
Solution. Use to get the distance.
a=vector(QQ, [2, -4, 3]);
d= -2
p=vector(QQ, [-3, 1, 5])
dis=abs(a.dot_product(p)+d)/a.norm()
show(dis)
Example 19
Plot the two planes and . Find the line of intersection of the two planes and plot it along with the two planes. (See Figure 10.)
http://matrix.skku.ac.kr/cal-lab/cal-11-5-19.html
Figure 10
Solution.
var ('x,y,z')
P1=implicit_plot3d(x + y + z == 1,(x,-2,3),(y,-2,3),(z,-2,3),color='orange',opacity=0.3)
P2=implicit_plot3d(2*x - y + z == 2,(x,-2,3),(y,-2,3),(z,-2,3),color='green',opacity=0.3)
show(P1+P2)
We may also get the parametric equation of the line of intersection of the two planes in Sage.
var('x, y, z')
solve([x+y+z==1, 2*x-y+z==2], [x, y, z])
11.5 EXERCISES (Equations of Lines and Planes)
http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-5-Sol.html
1-7. Find a vector equation, parametric equations and symmetric equations for the line.
1. Through the point and parallel to the vector .
Solution. For this line, we have and . Hence a vector equation is and parametric equations are . The symmetric equations are .
2. Through the point and parallel to the vector .
Solution.
var('t')
r0=vector([3, 5, 1])
pv=vector([4, 1, -1])
r0+t*pv
Answer : (4*t + 3, t + 5, -t + 1)
parametric equation: , , ,
symmetric equation: .
3. Through the origin and parallel to the line , , .
Solution. This line has the same direction as the vector, .
Here , so a vector equation is and parametric equations are . The symmetric equations are .
4. Through the point and perpendicular to the plane .
Solution. This line is passing through and along the normal vector to the given plane.
(ℝ)
⇒ vector equation: ,
parametric equation: , , ,
symmetric equation: .
5. Through the origin and the point .
Solution. For this line, we have and . Hence a vector equation is and parametric equations are .
The symmetric equations are .
6.Through the points and .
Solution. parametric equation: , , ,
symmetric equation: .
var('t')
A=vector([3, 5, -3])
B=vector([-1, 0, 5])
v=B-A
A+t*v
Answer : (-4*t + 3, -5*t + 5, 8*t - 3)
7. Through and perpendicular to both and .
Solution. A line perpendicular to the given two vectors has the same direction as a cross product of the two vectors. That is,
.
Here, , so a vector equation is and parametric equations are . The symmetric equations are .
8. Is the line through and parallel to the line through and ?
Solution. The lines are not parallel because the corresponding vectors , are not parallel.
var('t, s')
A=vector([3, 4, 5])
B=vector([-2, 0, 1])
v=B-A
print A+t*v
C=vector([2, 1, 4])
D=vector([-3, -3, -3])
w=D-C
print C+s*w
A=vector([3,4,5])
B=vector([-2,0,1])
C=vector([2,1,4])
D=vector([-3,-3,-3])
L1=line3d([A,B])
L2=line3d([C,D],color='red')
show(L1+L2)
Answer : (-5*t + 3, -4*t + 4, -4*t + 5)
(-5*s + 2, -4*s + 1, -7*s + 4)
9. Is the line through and perpendicular to the line through and ?
Solution. Direction vectors of the lines are and .
Since , the vectors and the lines are not perpendicular.
10-13. Determine whether the lines and are parallel, skew, or intersecting. If they intersect, find the point of intersection.
10. : , , : , , .
Solution. It is apparent that the lines are skew in the following figure.
var('t, s');
L1=parametric_plot3d((25, 1+3*t, -4*t), (t, -50, 50))
L2=parametric_plot3d((3+s, 4-2*s, s), (s, -50, 50), color="red")
show(L1+L2)
11.: , , , ℝ.
: , , , ℝ.
Solution. Since the direction vectors are and , we have . Hence the lines are parallel.
12. : : .
Solution. The lines are not parallel because the corresponding vectors , are not parallel. If and have a point of intersection, there would be values of and such that
, , .
and are skew.
13. : : .
Solution. From the figure it is clear that the lines are intersecting.
var('x');
diff(x^(15/14)+5*e^x,x)
var('s, t')
A=vector([3,1,4])
B=vector([-2,2,1])
C=vector([4,3,7])
D=vector([3,0,2])
Lt=A+t*B
Ls=C+s*D
print "Clearly the two lines are intersecting"
parametric_plot3d(Lt,(t,-3,3))+parametric_plot3d(Ls,(s,-3,3),color='red')
sol=solve([Lt[0]==Ls[0], Lt[1]==Lt[1],Lt[2]==Ls[2]], s, t, solution_dict=True)
show(sol)
14-15. Find an equation of the plane.
14. Through the point and perpendicular to the vector .
Solution. .
15.Through the point and with normal vector
Solution. is a normal vector to the plane and is a point of the plane. Then or to be the equation of the plane.
16. Which of the following four planes are parallel?
, ,
.
Solution. and are parallel.
17. Which of the following four lines are parallel?
, ,
, .
Solution. and are parallel.
18-19. Find an equation of the plane through the given point with the normal vector which is the direction of the line with the given parametric equations.
18. , , .
Solution. is a normal vector to the plane and is a point of the plane. Then or to be the equation of the plane.
19. , , .
Solution. is a normal vector to the plane and is a point of the plane. Then or is the equation of the plane.
20-21. Find the distance from the point to the given plane.
20. .
Solution. The normal vector to the plane is
n=vector(QQ, [2, -1, 3])
d= -4
p=vector(QQ, [3, 1, 5])
dis=abs(n.dot_product(p)+d)/a.norm()
dis
21. .
Solution. The distance .
22-23. Find the distance between the given parallel planes.
22. .
Solution. : , : . Note that is a point of the first plane. Since the planes are parallel, the distance between the two planes is the distance from to the second plane. Then, the distance between and the plane is
.
23. .
Solution. Put in the equation of the first plane to get the point on the plane. Since the planes are parallel, the distance between the two planes is the distance from to the second plane. Hence
.
24.Find the distance between the two skew lines
and .
25. Prove that the distance between the parallel planes and is .
26. (Line of intersection of two planes) Plot the two planes and . Find the line of intersection of two planes and hence plot this.
http://matrix.skku.ac.kr/cal-lab/cal-11-5-26.html
Solution.
var('x,y,z,t')
solve([x + y + z == 1,2*x - y + z == 2],x,y,z)
Answer : x == -2/3*r1 + 1, y == -1/3*r1, z == r1
Clearly the line of intersection of the is .
P1=implicit_plot3d(x + y + z == 1, (x,-3,3), (y,-3,3), (z,-3,3), color='blue', opacity=0.3)
P2=implicit_plot3d(2*x - y + z == 2, (x,-3,3), (y,-3,3), (z,-3,3), color='red', opacity=0.3)
L=parametric_plot3d([1-2/3*t,-1/3*t,t], (t,-3.5,3.5), color='green',thickness=3)
show(P1+P2+L)
27. (Line of intersection of two planes) If the two lines have a point in common then there exists and such that . The above system must have a unique solution. Let is verify this and find a common point.
Solution.
var('s, t')
Lt=(4+3*t, 3+t, 7+4*t)
Ls=(3-2*s, 2*s, 2+s)
sol=solve([Lt[0]==Ls[0],Lt[1]==Ls[1],Lt[2]==Ls[2]], s, t, solution_dict=True)
show(sol)
Clearly, gives a unique solution and point is the common point.
def axes(xmin=-1,xmax=1,ymin=-1, ymax=1, zmin=-1,zmax=1,**kwds):
ex = vector((1,0,0))
ey = vector((0,1,0))
ez = vector((0,0,1))
labels=text3d('x', (xmax+0.2,0,0)) + text3d("y", (0, ymax+0.20, 0)) + text3d("z", (0, 0, zmax+0.2))
return G+labels
A=axes(xmin=-3, xmax=3, ymin=-3, ymax=3, zmin=-3, zmax=3, color='red', thickness=2)
A
Cylinder and Traces
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity.
The cylinder is parallel to one of the coordinate axes.
DEFINITION 1 Cylinder
Given a curve in a plane and a line not in , a cylinder is the surface consisting of all lines parallel to given line that passes through a given plane curve .
DEFINITION 2 Trace
A trace of a surface is the set of points at which the surface intersects a plane that is parallel to one of the coordinate planes. The traces in the coordinate planes are called -trace, -trace and -trace.
Example 1
Draw a graph of the surface .
Figure 1 The surface is a parabolic cylinder.
Solution. Since there are no ’s in the equation, the trace of the graph in the plane is the same for every . The trace of the cylinder in every plane parallel to the -plane is parabola in the -plane and moving it in the direction of the -axis. The graph is a surface, called a parabolic cylinder and it is made up of infinitely many shifted copies of the same parabola. Here the rulings of the cylinder are parallel to the -axis.
var('x, y, z, v, u')
S=implicit_plot3d(x==z^2, (x,-2,2), (y,-2,2), (z,-2,2), plot_points=100, smooth=True, color='goldenrod', opacity=0.3)
p1=sum([parametric_plot3d((i^2 , v, i), (v,-2,2), color='red') for i in srange(-sqrt(2), sqrt(2), 0.5)])
p2=sum([parametric_plot3d((u^2 ,i, u), (u,- sqrt(2) , sqrt(2)), color='red') for i in srange(-2,2,0.5)])
show(S+p1+p2, frame=False)
■
Example 2
Sketch the graph of the surfaces in .
Solution. An equation in , is missing the variable . For all real values , the graph is a cylinder consisting of lies parallel to the -axis passing through the curve in the -plane.
Graph the curve in the -plane, which in the -trace of the surface.
Draw a second trace in a plane parallel to the -plane.
Draw lines parallel to the -axis passing through the two traces.
The result is a cylinder, running parallel to the -axis, consisting of copies of the curve .
Figure 2 Figure 3
var('i,u,x,y,z')
p1=parametric_plot3d((i, 0, sin(i)), (i, -5, 5), opacity=0.5) + parametric_ plot3d((i, -5, sin(i)), (i, -5, 5), opacity=0.5)+parametric_plot3d((i, 5, sin(i)), (i, -5, 5), opacity=0.5)
p2=sum([parametric_plot3d((i, u, sin(i)), (u, - 5 , 5), color=' red ') for i in srange(-5, 5, 0.5)])
show(p1+p2, frame=False)
var('x,y,z')
p =implicit_plot3d(z==cos(x), (x, -5, 5), (y, -5, 5), (z, -5, 5),opacity=0.5, smooth=True, axes=True) + text3d('z', (0,0,5), color=(0.5,0,0))+text3d("y", (0,5,0), color=(0,0.5,0))+text3d('x', (5,0,0), color=(0,0.5,0))
show(p, frame=False)
The general second-degree equation in ,
is a quadric surface. Here are constants. This equation can be brought into one of the two standard forms
or .
Quadric surfaces are the three dimensional counterparts of the conic sections in the plane.
Example 3
Sketch the quadric surface defined by the equation
.
This is an ellipsoid.
Solution. By substituting , we find that the trace in the -plane is which we recognize as an equation of an ellipse. In general, the horizontal trace in the plane is
which is an ellipse, provided that ＜9 that is, . The largest ellipse parallel to the -plane occurs with ; it is the -plane, which the ellipse
with axes of length and .
Similarly, the vertical traces are also ellipses:
, , (if )
, , (if ).
Figure 4 The ellipsoid
Figure 4 shows how drawing some traces indicates the shape of the surface. It’s called an ellipsoid because all of its traces are ellipses. Notice that it is symmetric with respect to each coordinate plane; this is a reflection of the fact that its equation involves only even powers of , and .
var('x,y,z')
p = implicit_plot3d((x^2)/25+(y^2)/16+(z^2)/9==1, (x, -10, 10), (y, -10, 10), (z, -10, 10), opacity=0.5, smooth=True, axes=True)+text3d("(0, 0, 3)", (0,0,3), color=(0.5,0,0)) + t ext3d("(0, 4, 0)", (0,4,0), color=(0,0.5,0)) + text3d('z', (0,0,10), color=(0.5,0,0)) + text3d("y", (0,10,0), color = (0,0.5,0)) + text3d('x', (10, 0, 0), color=(0, 0.5, 0))
show(p, frame=False)
Example 4
Sketch the quadric surface defined by the equation
.
This is an ellipsoid paraboloid.
Figure 5
Solution. If we put , we get , so the -plane intersects the surface in a parabola. If we put (a constant), we get . This means that if we slice the graph with any plane parallel to the -plane, we obtain a parabola that opens leftward. Similarly, if , the trace is, which is again a parabola that opens leftward. If we put , we get the horizontal traces , which we recognize as a family of ellipses. Knowing the shapes of the traces, we can sketch the graph in Figure 5. Because of the elliptical and parabolic traces, the quadric surface is called an elliptic paraboloid.
var('x,y,z')
p =implicit_plot3d((x^2)*5+y^2==z, (x, -5, 5), (y, -5, 5),(z, -5, 5),opacity=0.5,smooth=True, axes=True)+text3d('z', (0,0,5), color=(0.5,0,0))+text3d("y", (0,5,0), color=(0,0.5,0))+text3d('x', (5,0,0), color=(0,0.5,0))
show(p,frame=False)
Example 5
Sketch the surface .
Solution. The traces in the vertical planes are the parabolas which open upward. The traces in are the parabolas , which open downward. The horizontal traces are , a family of hyperbolas. We draw the families of traces in Figure 6, and we show how the traces appear when placed in their correct planes in Figure 7.
Figure 6 Vertical traces are parabolas; horizontal traces are hyperbolas. All traces are labeled with the value of .
Figure 7 Traces moved to their correct planes.
In Figure 8, we fit together the traces from Figure 7 to form the surface a hyperbolic paraboloid. Notice that the shape of the surface near the origin resembles that of a saddle.
Figure 8 The surface is a hyperbolic paraboloid.
Example 6
Sketch the surface .
Solution. The trace in any horizontal plane is the ellipse
but the traces in the - and -planes are the hyperbolas
and .
This surface is called a hyperboloid of one sheet and is sketched in Figure 9.
Figure 9
var('x,y,z')
p =implicit_plot3d((x^2)/9-y^2+(z^2)/9==1, (x, -10, 10), (y, -10, 10),(z, -10, 10),opacity=0.5,smooth=True, axes=True)+text3d('z', (0,0,10), color=(0.5,0,0))+ text3d("y", (0,10,0), color=(0,0.5,0))+text3d('x', (10,0,0), color=(0,0.5,0))
show(p,frame=False)
Table 1 contains graphs of the six basic types of quadric surfaces in standard form. All surfaces are symmetric with respect to the -axis. If a quadric surface is symmetric about a different axis, its equation changes accordingly.
Example 7
Draw a graph of the surface .
Solution. Dividing by , we first put the equation in standard form:
.
Comparing this equation with Table 1, we see that it represents a hyperboloid of two sheets, the only difference being that in this case the axis of the hyperboloid is the -axis. The traces in the - and -planes are the hyperbolas
and .
The surface has no trace in the -plane, but traces in the vertical planes for are the ellipses
, .
which can be written as
, .
These traces are used to make the sketch in Figure 10.
Figure 10
var('x,y,z')
p =implicit_plot3d((x^2)*5-y^2+2*z^2+5==0, (x, -5, 5), (y, -5, 5), (z, -5, 5), opacity=0.5, smooth=True, axes = True) + text3d('z', (0,0,5), color = (0.5,0,0)) + text3d("y", (0,5,0), color=(0,0.5,0)) + text3d('x', (5,0,0), color=(0, 0.5, 0)) + text3d("(0, -2, 0)", (0,-2,0), color = (0.5,0,0)) + text3d("(0, 2, 0)", (0, 2, 0), color=(0, 0.5, 0))
show(p,frame=False)
Surface Equation & Traces Surface Equation & Traces Ellipsoid All traces are ellipses. If , the ellipsoid is a sphere. Cone Horizontal traces are ellip-ses. Vertical traces in the planes and are hyper-bolas if but are pairs of lines if . Elliptic Paraboloid Horizontal traces are ellip-ses. Vertical traces are para-bolas. The variable raised to the first power indicates the axis of the paraboloid. Hyperboloid of One Sheet Horizontal traces are ellip-ses. Vertical traces are hyper-bolas. The axis of symmetry cor-responds to the variable whose coefficient is nega-tive. Hyperbolic Paraboloid Horizontal traces are hy-per-bolas. Vertical traces are para-bolas. The case where is illustrated. Hyperboloid of Two Sheets Horizontal traces in are ellipses if or . Vertical traces are hyper-bolas. The two minus signs indicate two sheets.
TABLE 1 Graphs of quadric surfaces
Example 8
Solution. By completing the square we rewrite the equation as
Comparing this equation with Table 1, we see that it represents an elliptic paraboloid. Here, however, the axis of the paraboloid is parallel to the -axis, and it has been shifted so that its vertex is the point . The traces in the plane are the ellipses
, .
The trace in the -plane is the parabola with equation , . The paraboloid is sketched in Figure 11.
Figure 11
var('x,y,z')
p = implicit_plot3d(x^2+2*y^2-2*x-z+4 ==0, (x, -5, 5), (y, -5, 5), (z, -5, 5), opacity=0.5, axes=True) + text3d('z', (0, 0, 5), color=(0.5, 0, 0)) + text3d("y", (0, 5, 0), color=(0, 0.5, 0)) + text3d('x', (5, 0, 0), color=(0, 0.5, 0)) + text3d("(1, 0, 3)", (1, 0, 3), color=(0, 0.5, 0))
show(p, frame=False)
Example 9
Sketch the equation
.
Figure 12
Solution.
var('x, y, z')
implicit_plot3d(x^2-3*y^2-2*z^2==0, (x, -1.5, 1.5), (y, -1.5, 1.5), (z, -1.5, 1.5), color='red', plot_points=80, smooth=True)
11.6 EXERCISES (Cylinders and Quadric Surfaces)
http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-6-Sol.html
1.(a) What does the equation represent as a curve in ?
(b) What does it represent as a surface in ?
(c) What does the equation represent?
http://matrix.skku.ac.kr/cal-lab/cal-11-6-Exs-1.html
Solution. (a) Equation represents a parabola of slope passing through origin in .
(b) The equation of the graph is , which doesn't involve in . This means that any vertical plane with equation (parallel to the -plane) intersects the graph in a curve with , that is, a parabola. Below figure shows how the graph is formed by taking the parabola in the -plane and moving it in the direction of the -axis. So the graph is a surface, called a parabolic cylinder, made up of infinitely many shifted copies of the same parabola.
S=implicit_plot3d(z==y^2,(x,-2,2),(y,-2,2),(z,-2,2),plot_points=100,smooth=True,color='goldenrod', opacity=0.3)
p1=sum([parametric_plot3d([i,y,y^2],(y,-sqrt(2),sqrt(2)),color='red') for i in srange(-2,2,0.5)])
show(S+A+p1,frame=False)
(c) also represents a parabolic cylinder, this time with axis the -axis in .
2.(a) Sketch the graph of as a curve in .
(b) Sketch the graph of as a surface in .
(c) Describe and sketch the surface .
Solution. (a)
plot(exp(2*x), (x, -1, 1))
(b)
var('x, y, z')
implicit_plot3d(y==exp(2*x), (x, -1, 1), (y, -1, 1), (z, -1, 1))
(c)
var('x, y, z')
implicit_plot3d(z==exp(2*y), (x, -1, 1), (y, -1, 1), (z, -1, 1))
3-5. Describe and sketch the surface.
3.
Solution.
var('x, y, z')
implicit_plot3d(y^2+5*z^2-5==0, (x, -3, 3), (y, -3, 3), (z, -3, 3), opacity=0.5)
4.
Solution.
var('x, y')
z=cos(y)
plot3d(z, (x, -2, 2), (y, -pi, pi))
5.
Solution.
var('x, y, z')
implicit_plot3d(y*z==3, (x, -3, 3), (y, -10, 10), (z, -10, 10), opacity=0.5)
6-10. Find the traces of the given surface in , , . Then, identify the surface and sketch it.
6.
Solution.
var('x, y, z')
implicit_plot3d(x^2+9*y^2+9*z^2==9, (x, -3, 3), (y, -3, 3), (z, -3, 3), opacity=0.5)
7.
Solution. The trace in are ellipses of the form , , the trace in are parabolas of the form , and the trace in are parabolas of the form .
Combining these traces we form the graph.
8.
Solution.
var('x, y, z')
implicit_plot3d(25*x^2+z^2==100+4*y^2, (x, -3, 3), (y, -3, 3), (z, -3, 3), opacity=0.5)
9.
Solution. The trace in are hyperbolas of the form , the trace in are circles of the form , , and the trace in are hyperbolas of the form .
Combining these traces we form the graph.
10.
Solution.
var('x, y, z')
implicit_plot3d(y^2+4*z^2-x==0, (x, -3, 3), (y, -3, 3), (z, -3, 3), opacity=0.5)
11-14. Reduce the equation to one of the standard forms, classify the surface, and sketch it.
11.
Solution. Dividing both sides by 15 gives , an elliptic paraboloid with vertex and axis the horizontal line .
12.
Solution.
var('x, y, z')
implicit_plot3d(z^2 == 9*x^2+4*y^2-5, (x, -3, 3), (y, -3, 3), (z, -3, 3), opacity=0.5)
13.
Solution. Completing squares in and gives
or ,
a hyperboloid of one sheet.
14.
Solution.
var('x, y, z')
implicit_plot3d(x^2 == 3*y^2+2*z^2, (x, -3, 3), (y, -3, 3), (z, -3, 3), opacity=0.5)
15.
Solution.
var('x, y, z')
implicit_plot3d((x^2+9/4*y^2+z^2-1)^3-x^2*z^3-9/80 *y^2*z^3==0, (x, -1.5, 1.5), (y, -1.5, 1.5), (z, -1.5, 1.5), color='red', plot_points=80, smooth=True).show()
16.Sketch the region bounded by the surfaces and for .
Solution.
var('x, y, z')
z=(x^2+y^2)^(1/2)
plot3d(z, (x, -2, 2), (y, -2, 2), (z, 2, 4))
17. Find an equation for the surface obtained by rotating the parabola about the -axis. (Use revolution_plot3d to get the plot of this surface.)
18. Find an equation for the surface consisting of all points for which the distance from to the -axis is twice the distance from to the -plane. Identify the surface.
Solution. Let be an arbitrary point whose distance from th -axis is twice its distance from the -plane. The distance from to the -axis is and the distance from to the -plane() is .
Thus .
So, the surface is a right circular cone with vertex the origin and axis the -axis.
19. Find an equation for the surface consisting of all points that are equidistant from the point and the plane
Calculus | 19,937 | 68,961 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2023-23 | latest | en | 0.848161 |
https://www.askthebuilder.com/extension-cords-size-chart/?awt_l=BT9hy&awt_m=JYsPC4VRT5NiL5 | 1,723,024,106,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640690787.34/warc/CC-MAIN-20240807080717-20240807110717-00735.warc.gz | 520,970,662 | 23,386 | Q&A /
# Extension Cords Size Chart
Extension cord sizing is not a guessing game. This is a beefy 12-gauge extension cord. This is the male end in my hand and the female end has a small glowing light in it when energized. Copyright 2018 Tim Carter
"Electricity encounters friction as it travels through electrical wires. Knowing this, use only as much extension cord as you really need. I can call you on the phone to answer your extension cord questions so you don't get KILLED or BURN DOWN YOUR HOME. The call is FREE if you're not satisfied with my answers. CLICK HERE to set up the call."
## Extension Cord Sizing Checklist
The size of your extension cord is very important. If you under-size one, you can start a fire or ruin an expensive tool.
CLICK on my face to ensure you get the CORRECT extension cord so you or your family doesn't DIE IN A FIRE.
Fortunately, many common small hand-held electrical tools can operate without danger of motor damage when powered by a 16 gauge cord that is 100 feet long. To make sure you're properly protected, use the following sizing guidelines below.
### How Do You Start to Size an Extension Cord?
You start to size an extension cord by obtaining the motor amperage from the plate on the tool. You'll find this information on the small metal plate where the serial number and model number is listed.
The green arrow points to the amperage of this professional circular saw. It shows 15A. That means 15 amps. Copyright 2018 Tim Carter
Usually, you will see an amperage rating. A tool may say it's rated for 8 amps. That's amperage.
### What is Ohms Law?
Ohm's law is a physics principle that helps keep you safe with electricity. In its simplest form Ohm's law is:
Volts X Amps = Watts
This simple formula helps you to understand the sizing of extension cords because you may be required to convert an amp rating on a tool or appliance to watts.
Think about a light bulb. They're often sized by watts. The voltage in most circuits in USA homes is 120 volts. You may have a circuit breaker panel in your garage that has 15 or 20-amp breakers. All of these things concern Ohm's Law.
If for some odd reason, you see watts listed instead of amps, you can convert watts to amps easily!
Here is how you do that: The formula for the conversion is:
Voltage x Amps = Watts
120 x 20 = 2,400
120 x 15 = 1,800
Because we use 120 volts as an electrical standard here in the USA, that means that every 600 watts equal 5 amps (120 x 5 = 600).
### What is Voltage Drop?
Voltage drop is the loss of voltage as it travels down a long wire.
Voltage drop is real. Electricity encounters resistance as it travels through electrical wires. Knowing this, use only as much extension cord as you really need. Resistance in the real world often creates friction which in turn almost always creates heat.
You can do your own simple experiment to demonstrate somewhat how this works. Use your one hand to rub your forearm back and forth. Go slowly at first and you may not feel much. Increase the speed of going back and forth and press down harder as you rub. That increased resistance will make your skin feel HOT for sure!
In other words, don't use a 100-foot cord for a project that is only 20 feet away. Purchase and maintain an assortment of different length cords.
### Can I Have Multiple Tools On 1 Cord?
Yes, you can have multiple tools operating on one extension cord. You just have to be sure the cord is large enough to handle the loads.
I was guilty of this infraction many years ago before I fully understood all that was involved.
On construction sites, we'd commonly feed multiple saws and drills from one cord. If the circuit breaker at the panel is working fine, then you'll pop the breaker if there's a current overload.
But, if you've got a smaller-gauge extension cord, it's possible to overheat the cord and melt the insulation before the circuit breaker would trip!
However, if the breaker is bad you can either burn up the cord or damage tools from voltage drops. Use common sense.
### How Do You Size an Extension Cord?
You size an extension cord by first determining the appliance or tool that will be plugged into the cord.
Determine the amperage of the tool(s) being used. Here is a handy list of some common electric power tools. The average amperage is listed below the tool. Always check on your tool label for its specific amperage.
Here are some COMMON amperage ratings of tools around your home:
• Circular saw: 12-15 amps
• Power drill: 3-7 amps
• Hedge Trimmer: 2-3 amps
• Weed Wacker: 2-4 amps
• Electric Chain Saw: 7-12 amps
• Leaf Blower: 6-12 amps
• Electric Lawn Mower: 6-12 amps
• Table Saw: 14-20 amps!
• Reciprocating Saw: 6-8 amps
• Router: 4-6 amps
### Is the Length of the Cord Important?
Yes, the longer the cord is the greater the voltage drop will be. If you must go a distance greater than 100 feet, then upsize the extension cord.
Calculate the length of the cord you will need. Of course, you want to determine the maximum distance you think you will be from a permanent electrical outlet.
### What Does Wire Gauge Mean?
Wire gauge is the measure of the diameter of the metal conductors in the extension cord. Common extension cord wire gauges are:
• 18
• 16
• 14
• 12
• 10
Use the following list to select the proper gauge extension cord. Remember, wire gauge refers to the thickness of the actual copper wire. As a wire gets thicker it can carry more electricity (amps). To confuse us, some idiot decided that as a wire gets thicker (bigger) the gauge number should get smaller!
The orange cord is only 18 gauge. Look how thin it is compared to the yellow cord that's 12-gauge. NOTE the 18-2 before the word TYPE in the red oval. That's how you know it's 18-gauge wire. Copyright 2018 Tim Carter
Here's what I mean. A 14-gauge wire can handle LESS current than a 12-gauge wire. The number 14 is bigger than 12. Confused? You should be!
### What Load Can Each Gauge Wire Handle?
16-Gauge Cords: Any 16-gauge cord between 0 and 100 feet long will adequately handle tool loads up to 10 amps.
14-Gauge Cords: Any 14-gauge cord between 0 and 50 feet long will adequately handle loads between 10 and 15 amps.
12-Gauge Cords: If your tool load is between 10 and 15 amps and the length of the cord is 50 to 100 feet, you need a 12-gauge cord to safely power any tool.
This is a great extension cord for many purposes. CLICK THE IMAGE NOW to have it delivered to your home.
### Why Does my Circuit Breaker Trip With the Right Cord?
Your circuit breaker may trip because the tool you're trying to power draws too much current. This is very common if you're trying to operate a large table saw cutting thick wood.
CAUTION: Most circuits in ordinary houses are wired with 14-gauge solid copper wire. This means you'll see a 15-amp breaker on the circuit breaker panel.
You may purchase a 12-gauge extension cord thinking that you'll be able to operate a powerful table saw but the breaker will probably trip when you load the saw. Remember, the circuit is rated for the SMALLEST SIZED cable or wire in the circuit.
### Do Other Things on a Circuit Add to the Load?
Yes, other things, like a garage light or some other appliance, could be on the same circuit you've plugged the extension cord into. This adds to the total load on the circuit! You may think you have 15 amps available going to your extension cord, but several of those amps might be in use from something else.
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Extension Cord Sizing | How to Get the Right Cord | AsktheBuilder.com
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Extension cord sizing is very important. A cord that's too small can cause a fire or ruin an expensive tool.
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SPONSORS / | 1,821 | 7,777 | {"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-2024-33 | latest | en | 0.931721 |
http://blog.philbirnbaum.com/2016/08/log5-isnt-necessarily-biased-if-you.html | 1,534,373,737,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221210362.19/warc/CC-MAIN-20180815220136-20180816000136-00286.warc.gz | 59,764,039 | 10,286 | Friday, August 26, 2016
"Bias" in log5 estimates -- a clarification
Last post, I argued that the log5 method has a bias. When you estimate a team's talent, in the sense of how well it would do playing a normal season against a league's worth of teams, you wind up being too conservative, giving the underdog too much of a chance to win.
Why does that happen? Because for the log5 formula to work, you need to use a team's expectation against a .500 team, not a team's expectation averaged out among all teams. The two aren't the same. You could come up with a method to figure out how big the difference is; it varies by the empirical spread of talent in the league.
It's easy to see why this is the case with a simple example. Suppose I know more statistics than 90 percent of the population with a degree. If I played a season's worth of stats exams against all of them, I'd finish with an .900 record. But, consider someone with an average amount of stats knowledge, a .500 graduate. That person probably took one or two stats courses, at most. So, I'd beat him or her almost 100 percent of the time, not just 90 percent.
The differences aren't that big in pro sports. By my estimate, an NFL or NBA team that has a .686 talent over an average season actually has a .700 talent against an average team. In the normal range of MLB team talent, the difference is negligible. A team with .565 talent -- that's 91.5 wins out of 162 -- would probably play only .566 against an average team, a discrepancy of only one point.
-------
Anyway, after I posted that, Ted Turocy wrote me, disagreeing with how I described the problem. Ted agreed with my argument itself, but felt strongly that it doesn't show that log5 is "biased."
Here's how I understand his objections:
1. The log5 (or odds ratio) method has been used successfully for years. In the academic literature, it's called the "Bradley-Terry" method, named after two academic researchers who introduced it in 1952. In one of the fields Ted studies, Contest Theory, it's been the standard for decades. In the academic world, researchers don't make the mistake I described -- it's understood completely that talent estimates relate to performance against a .500 team. In fact, the algorithms used to estimate talent don't usually even mention season-against-league performance.
2. The log5 formula (or the odds ratio formula, which is algebraically identical) has been formally proven to provide unbiased estimates under certain assumptions (which I'll talk about in a future post).
3. My objection, that log5 is biased if you use "against league" estimates of talent instead of "against .500" estimates of talent, applies to ANY estimator, not just log5. That's because for "average talent against all teams" to always equal "talent against an average team", the formula would have to be linear. But linearity won't work for a correct formula, since all estimates have to be between .000 and 1.000, and linear formulas would routinely exceed those limits.
I agree with all three of these objections, with one minor nitpick: the academic literature rarely uses the term "log5." It mostly uses "Bradley-Terry," or "odds ratio." While the formula is the same, the application is different.
In "normal" sabermetrics, "log5" just uses a season's record as an estimate of talent -- I have *never* seen a mainstream sabermetric study acknowledge that the "against .500" talent should be used instead. In my experience, it's just been commonly assumed that "talent against league" and "talent against .500" were exactly the same number -- and, sometimes that's been stated explicitly. (In fairness, while the two aren't the same, it turns out that in baseball, they're close enough for most purposes.)
So, I was prepared to say, OK, maybe we can say that "log5" is biased the way it's used in the sabermetric literature, but Bradley-Terry isn't biased in the way it's used in the academic literature. But, Ted let me know that, no, that won't work -- the term "log5" actually *is* used in the academic literature to mean "odds ratio formula," and it's used properly. So my description of it as "biased" is still wrong.
OK, fair enough. Ted has convinced me that my title is misleading, that it implies that the log5 formula *itself* is biased, even when used properly and talent is assumed to mean "against a .500 team." I had considered "log5" to implicitly mean "using talent against league," which I shouldn't have.
I should have said something like: "A log5 estimate is biased against the favorite when "record against league" is used as the measure of team talent instead of "record against .500.""
Having said that, I say again that both Ted and I agree that the bias is there, the explanation is correct, and it's just the characterization of "log5 is biased" that's in dispute.
I'll soon update the previous post to make that clear.
------
BTW, during our e-mail exchange, Ted educated me about other aspects of the issue, for which I thank him. My current understanding of log5, as I will describe it in future posts, is much clearer because of his help. However, I think Ted still disagrees with me on a few of the things I will be posting. I may wind up being wrong, but probably less wrong than if Ted hadn't helped me out. | 1,219 | 5,308 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2018-34 | longest | en | 0.975415 |
http://www.conservapedia.com/Talk:Pi | 1,513,484,708,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948592972.60/warc/CC-MAIN-20171217035328-20171217061328-00321.warc.gz | 326,569,466 | 14,085 | Talk:Pi
Answering the question posed in the article, "As of 2002, the record is held by Yasumasa Kanada of Tokyo University at 1,241,100,000,000 digits. That result was never printed out: can you figure out why not?"
An ordinary printed page can hold about 5,000 digits.
To print 1,241,100,000,000 digits would require 248,220,000 pages, or 496,440 reams of paper. A ream of paper is the size of a large book. It would take a building the size of a city library to hold the printed output. Dpbsmith 23:08, 13 January 2007 (EST)
Counting the letters in the phrase "Now I wish I had a drink—alcoholic, of course" Does not help because it gives a wrong answer. it gives 3(.)141315926, it should be 3.1415926... --TimSvendsen 23:54, 15 January 2007 (EST)
• Yikes! I'm going to have to turn in my geek badge. It should be "How I want a drink--alcoholic of course." I was mixing it with "How I wish I could recollect pi easily today." Sorry. Dpbsmith 13:16, 16 January 2007 (EST)
So I'm assuming by the change back to the old version, my revision was no good. An explanation why would be nice, though. ColinR 21:09, 12 March 2007 (EDT)
Groan
What was I thinking here? [1]
113 divided into 355 like this:
3.14156.....
---------
113|355.00000
I had 1/pi by mistake - not even an approximation, more like an abomination. --Ed Poor 23:44, 28 March 2007 (EDT)
I like Pi
Pi R Squared? No they're not, Pie are round. Brownies are square. Human 22:07, 20 April 2007 (EDT)
LOL. --Ed Poor Talk 09:08, 11 March 2008 (EDT)
22/7
Besides the fact that "Pi is exactly 3!", 22/7 is also a repeating decimal. Pi is also known as Archimedes' constant, Ludolphine, and Ludolph's Number. Ludolph van Ceulen (Germany) spent a great deal of time calculating digits of pi. The number is engraved on his tombstone. If I were to get buried, I would have all the digits I memorized engraved on it, but I want to get cremated instead. Fuzzy 10:16, 11 March 2008 (EDT)
It is not true that Pi is exactly 3. What is your suggestion to improve the article? --Ed Poor Talk 10:31, 11 March 2008 (EDT)
I haven't said anything about my beliefs, let's just leave my life out of this, eh? And, with you saying that pi=3, are you suggesting CP completely rewrites this article? Fuzzy 10:39, 11 March 2008 (EDT)
If you are not claiming that pi = 3, then that makes two of us. :-)
I've made a few updates to the article, primarily about scriptural references and historical estimates. --Ed Poor Talk 12:41, 11 March 2008 (EDT)
Is the Bible wrong about pi?
In the ancient world, measurements were not given as exact as they are today, and that was generally considered acceptable. http://www.tektonics.org/lp/piwrong.html DanH 01:22, 10 March 2008 (EDT)
Who said it was wrong? Sloppy ancients aren't nessecarily wrong ancients. Barikada 01:25, 10 March 2008 (EDT)
So, can I reinsert the Bibical perspective? Barikada 17:15, 10 March 2008 (EDT)
It's not relevant simply to note that the Bible happens to approximate it in passing. However, many use it as an argument to show that the Bible is errant, and that's what I surmise may have been the purpose for its inclusion DanH 17:35, 10 March 2008 (EDT)
Wait. The Bible's interpretation of Pi is not relevant to Pi? What? Look, friend, the Bible is always relevant. Barikada 18:14, 10 March 2008 (EDT)
You admit you're an atheist on your user page. Why are you so interested in inserting this in there? DanH 18:15, 10 March 2008 (EDT)
I admit I'm an atheist-- You say it like it's a bad thing. I'm not trying to stat a fight, Dan, I just figure that, as a wiki with a majority of users that are Christian, it would be good to include the Biblical perspective on matters where it has spoken, as is done in shrimp. Barikada 18:18, 10 March 2008 (EDT)
I didn't realize that was still in shrimp. Anyways, as the article posted above explains, the numbers were not meant to be exact, and the circumference and diameter may have been given as approximate estimates, but pi wasn't a concept that most people knew about or cared about. The Bible wasn't meaning to comment on pi at that point, only at the relevant calculations. DanH 18:24, 10 March 2008 (EDT)
That's great, Dan. You seem pretty hostile to the Bible. Barikada 20:16, 10 March 2008 (EDT)
I don't see how Dan seems to be "pretty hostile to the Bible". Your insertion was simply wrong, as the Bible is not trying to give a value for pi at all. Besides, the Bible reference which is frequently quoted by bibliosceptics as supposedly representing pi is already in the article, and even that warrants being removed (in that form) in my opinion. Philip J. Rayment 20:47, 10 March 2008 (EDT)
Oh... So anything a skeptic quotes must be purged, then? What is the purpose of the verse if not to show the value of pi? Furthermore, how do you know what the Bible is and is not trying to say, Philip? Barikada 20:48, 10 March 2008 (EDT)
Also, bibliosceptics is A: Spelled wrong and B: a word which would translate as "Skeptical of books." Barikada 20:49, 10 March 2008 (EDT)
Oh, bugger. It seems I didn't notice that the verse was already quoted in the History section. Barikada 20:51, 10 March 2008 (EDT)
I didn't say that anything a sceptic quotes should be purged.
What's the purpose if not to show the value of pi? To describe the object's size, genius!
What is incorrect about the spelling of "bibliosceptics"? Yes, the word could mean "sceptical of books", but as "Bible" means "book", it's appropriate to use it to mean "sceptical of the Bible".
Philip J. Rayment 21:03, 10 March 2008 (EDT)
"Besides, the Bible reference which is frequently quoted by bibliosceptics as supposedly representing pi is already in the article, and even that warrants being removed (in that form) in my opinion." That's exactly what you said, Philip!
Then why not describe it correctly?
Skeptics. With a K. Also: Yes. I know it means book. Your use of faux Latin does not make you smarter. Barikada 21:13, 10 March 2008 (EDT)
That quote of mine does not indicate that anything a sceptic quotes should be purged, and neither does it say that that bit should be removed because it's something a sceptic quotes.
Aussies traditionally spell "sceptic" with a "c", hence my use of "bibliosceptic" rather than "biblioskeptic".
Philip J. Rayment 22:12, 10 March 2008 (EDT)
A fourth consecutive edit, because a thought occurs. How can we be sure that man's measurements are correct in this case but the Bible is not? Furthermore, if the Bible is wrong here, how can we logically accept that everything else is exact-- IE, the age of the Earth? Barikada 20:56, 10 March 2008 (EDT)
What reason is there to think that the Bible's measurements are incorrect? The logic of your question is valid, but the premise (that the Bible is incorrect) is not. Philip J. Rayment 21:05, 10 March 2008 (EDT)
Well, if it's ten cubits from one side to the other, it should be 31 all around, if we're rounding. Barikada 21:13, 10 March 2008 (EDT)
What if it was actually 9.7 cubits (rounded to 10) from one side to the other? Philip J. Rayment 22:12, 10 March 2008 (EDT)
Then the measurement given is, quite simply, wrong. Barikada 23:44, 11 March 2008 (EDT)
Huh? Okay, I'll have to spell it out for you. If (and this is not the only possible explanation) the actual diameter was 9.7 cubits, then the actual radius would be 30.47 cubits. If both of those figures are rounded to the nearest cubit, then the diameter would be listed as 10 cubits and the circumference would be listed as 30 cubits. And guess what! That's what the Bible lists them as! So if this is correct (and it doesn't have to be exactly that: it could be 9.6 cubits for example), then the Bible is perfectly accurate! ("Accurate" is a different thing to "precise", as Ed mentions below.) If you still aren't convinced, have a look at the links in the External Links section of the article, particularly the Math Forum one. In fact, don't reply here unless you first read the three links. Philip J. Rayment 02:03, 12 March 2008 (EDT)
Yes. Rounding. I get it. It's impercise. If I say Ed is six feet tall, I'm wrong because he's not. If I say he's about six feet tall, I'm right, because he's just over six feet tall. Is that so hard to understand, Philip? Barikada 10:06, 12 March 2008 (EDT)
Alright. Scanned through the links. I get it-- God couldn't be arsed to tell the lowly Earthers a more prescise number. Barikada 17:51, 12 March 2008 (EDT)
You've earned yourself another block for that arrogant response.
If Ed is 6 feet, 3.02 inches tall, would you refer to him as "about 6'3" tall"? The articles said nothing about God not telling us a more precise number. The first link points out that their measurements would not be that precise to start with. In this case, they are not rounding, but simply measuring with a course measuring device. The second reference pointed out that it was common to round numbers in those times. Insisting on using the word "about" is really a case of you expecting people from 3000 years ago to follow your conventions. It doesn't mean that they got anything wrong. The third reference pointed out the following:
• "...in the absence of an explicit indication of precision, the absence of a tenths digit implies that the figure is accurate to the nearest 1 cubit...". So the measurements were accurate to within the implied level of precision!
• "Every measurement we ever make is an approximation.". So do you preface every measurement with "about"? (That's the point of my question above about Ed being 6'3.02" tall.) Absence of the word "about" does not mean that the measurement is "wrong".
You acknowledged none of those points in your response, instead making a silly comment about God. It's clear that you simply want to argue a point that has been thoroughly refuted, and you've stopped doing so civilly. Hence your block. Learn from it.
Philip J. Rayment 21:55, 12 March 2008 (EDT)
You're not wrong to call me six feet tall; I don't mind losing 3 inches in the interest of smooth prose. Just don't call me two meters tall! --Ed Poor Talk 18:50, 12 March 2008 (EDT)
That's what the "about" is for-- it indicates impercision. Most useful article ever, by the way. Barikada 18:59, 12 March 2008 (EDT)
I took a few science courses in high school and college. You might be interested to learn about the difference between "accuracy" and "precision". (I probably should compare and contrast the two ideas in a proposed new article: accuracy and precision.)
Here's how it's relevant to Pi. When the Bible says ten cubits, that is an approximation. Scientists would say the measurement is being given to "one significant figure". It really could be anything between 9 and 11 cubits, and it still wouldn't be wrong, because it's only an approximation, like saying that Ed Poor is six feet tall (I'm 6'3" in bare feet).
The ratio between the diameter of a wheel and its circumference is, roughly, three. And if you drew a circle on the ground, with a diameter of 10 cubits, you would pace off 30 cubits when you walked around the circle. Pacing is not a very precise measurement, but it's good enough for some cases. --Ed Poor Talk 09:01, 11 March 2008 (EDT)
"It really could be anything between 9 and 11 cubits...": 9.5 and 10.5 actually. Philip J. Rayment 09:06, 11 March 2008 (EDT)
Anyway, you're being too patient with a time-waster. Liberals l-o-v-e to change the subject, with distractions like the supposedly preferable spelling of sceptic. I'm sceptical of this fella's motives, and I've left a note at his talk page. --Ed Poor Talk 09:13, 11 March 2008 (EDT)
I would actually like him to answer my last question above, though. Philip J. Rayment 09:43, 11 March 2008 (EDT)
Ed: You'll get a response in the appropriate place momentarily, don't worry.
Philip J. Rayment: So you have wished it, so it shall be. Response is above. Barikada 23:44, 11 March 2008 (EDT)
The Bible does not provide a value for pi, so the following statement is misleading at best:
The Qur'an also defines Pi as 3.(al-Sûra aleph bei).
Use of the word "also" implies that the Bible has provided a definition. The story about the ten cubits does not define pi. It merely gives a diameter and a radius of something presumed to be circular. (A circumference of thirty is consistent with a diameter of ten, with a precision of one significant digit.)
In any case, I'd like to see the exact words of an English translation of any Koran passage related to circle math before approving any claim as damaging as "defines Pi as 3." --Ed Poor Talk 11:53, 11 March 2008 (EDT)
Over the years, I've found this to be one of the sillier arguments against the Bible. I've found that those who push it don't believe it, but only do so to try to force in a 'gotcha' that they themselves know isn't the case, but nevertheless they draw enjoyment from trying to act like it is anyway. Learn together 18:48, 28 March 2008 (EDT)
I do not like the "Pi in the Bible" section...
...for many reasons. First, the title is misleading, as the text points out. There is no pi in the Bible (only unleaven bread--just kidding!), nor does the Bible make any attempt to define pi or e or or any other mathematical or physical constant. Second, I think the subject is out of place in an article about mathematics. Perhaps it should be a minor section in an apologetics-related article. Or be omitted entirely, as it is not really a serious criticism, but more a "baby apologetics" thing that appeals to unsophisticated Bible skeptics.
Thirdly, while I appreciate that someone has done the work of gathering the arguments in one place, the wording could be better. It says "Critics claim this, but they are making the following assumptions". Better to say "Critics say this but they are wrong for these reasons." You do not know what someone else's assumptions are.
Fourthly, a minor point. If you opt to keep this section, you might point out that when critics complain that the Bible rounds the circumference to a multiple of ten instead of something more precise (say, 31.4 cubits), they are being inconsistent, because that number is also imprecise. Because pi is irrational, there is no number that could be contained (in a finite Bible) that could give the measurement exactly. What the baby skeptics are doing here is setting an impossible condition for precision, then saying that if the Bible is imprecise it is not inerrant (another big leap in logic), and hoping that no one will notice the flaws in their reasoning.
—The preceding unsigned comment was added by Ga ohoyt (talk)
I wasn't happy with the title either (and I wrote it!), but I wasn't sure what else to have. The next best think I could think of was to put pi in quote marks: "Pi" in the Bible.
I don't think the article is particularly out of place. The article is about pi specifically (not just "mathematics"), and this section is about pi, or at least about a claim made about pi. It is not a serious criticism in the sense of having even a shred of validity, but it is something that is often claimed by bible critics. The Skeptics Annotated Bible mentions it, for example.
As for the mention of assumptions, no, you don't need to know what assumptions they are consciously making; there are certain assumptions inherent in the argument, which is all that the comment is saying. That is, they must be making these assumptions, even if subconsciously. That's not to say that the wording can't be altered to something better, but I do think it's acceptable as it is.
There were a couple of other problems with the claim that I thought of mentioning, but the section was large enough already and the others were in a sense variations on the ones already mentioned, so I thought that was enough. Yes, they often claim that the value is "incorrect", but then are unable to give the "correct" value themselves (because it has an infinite number of digits). And that would be a good thing to point out if the Bible was actually claiming to give a value for pi, but as it's not, it seemed a little bit unnecessary.
Philip J. Rayment 21:48, 13 March 2008 (EDT)
Better now? Ga ohoyt 20:49, 14 March 2008 (EDT)
I'm not sure (but I don't think it's worse). I don't think it's appropriate to have a question for a heading, and neither do I think it's appropriate for the heading to be part of the flow of the text, as is now the case, because the first sentence of the section doesn't make sense without the heading. A heading should give an idea of what the section is about, not be part of the section, if you're following me. Also, the claim is not (normally) explicitly made that the Bible defines pi, as indicated by the heading. Rather, that claim is implicit in the explicit claim that the Bible has an incorrect value for pi. Philip J. Rayment 01:19, 15 March 2008 (EDT)
I think the section is necessary because we do periodically hear this canard about Pi, and the encyclopedia should give the reader the information he needs to respond to it. However, I think the article's response is insufficiently dismissive.
I would simply say that the numbers in the Biblical passage are correct, to their given precision. Hence there is no controversy. Likewise, if an encyclopedia gives the radius and circumference of the Earth to the nearest thousand feet, the encyclopedia is not "wrong about Pi," and nobody would seriously say it was. It seems that only in the case of the Bible are critics so impassioned as to buy such a dopey argument.
Also, I think it is too weak to say it was "common at the time to round numbers." It is common all the time to give measurements like this, and to do so without any conscious or explicit rounding. The way these bullet points are worded, they give the impression that the values D=10 and C=30 need to be explained by some hypothetical act: maybe someone rounded a measurement, maybe they measured different parts of the rim, etc. But D=10 and C=30 does not need any of these explanations because, as I said, they are correct to their given precision, and there is no discrepancy that needs to be explained. I'd just remove them, lest they contribute to the sense of false controversy.--NgSmith
Question on the Bible reference
Were decimals and fractions even in use in the Holy Land at the time 1 Kings was written? Jinxmchue 23:26, 4 April 2008 (EDT)
Decimals, no, I think. Fractions, yes, to some extent, I think. Philip J. Rayment 04:39, 5 April 2008 (EDT) | 4,753 | 18,469 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2017-51 | longest | en | 0.964697 |
https://www.studypool.com/discuss/1161499/can-someone-please-help-me-understand-8?free | 1,495,579,742,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463607704.68/warc/CC-MAIN-20170523221821-20170524001821-00393.warc.gz | 924,933,570 | 14,512 | Mathematics Tutor: None Selected Time limit: 1 Day
The distance d, in miles, that a car travels on a 3-hour trip is proportional to its speed s (which we assume remains the same throughout the trip), in miles per hour.
(a) What is the constant of proportionality in this case?
(b) Write a formula that expresses d as a function of s.
d =
Sep 10th, 2015
speed = s
b.
d= s*time
d=s*3hrs
Sep 10th, 2015
...
Sep 10th, 2015
...
Sep 10th, 2015
May 23rd, 2017
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http://www.overclock.net/t/1612870/steam-steam-hardware-and-software-survey-september-2016/50 | 1,516,161,245,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886794.24/warc/CC-MAIN-20180117023532-20180117043532-00490.warc.gz | 538,732,942 | 31,729 | Overclock.net › Forums › Industry News › Hardware News › [Steam] Steam Hardware and Software Survey September 2016
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# [Steam] Steam Hardware and Software Survey September 2016 - Page 6
Quote:
Originally Posted by lombardsoup
10,000 in a population of close to 13 million concurrent users per day (at least Valve reports the latter number). Are you serious? That's representative of very little. Furthermore, we don't actually know how many people are being surveyed.
'murican political pollsters try to justify their polling in the same manner. Sample sizes of 10,000+ in a nation of 320,000,000, with a third of this actively voting. That's representative of absolutely nobody.
It's not super intuitive. Once you get over a certain sample size, you can get accurate estimates of a population with seemingly very few people being sampled.
A sample size of 10,000 for a population of 13,000,000 has a confidence level of over 95% and a confidence interval of +/- 1%.
For example, If you wanted to just be within +/- 5% for the entire Steam population (125 Million), you would only need to survey 400 people.
Edited by AmericanLoco - 10/3/16 at 5:08pm
Quote:
Originally Posted by AmericanLoco
It's not super intuitive. Once you get over a certain sample size, you can get accurate estimates of a population with seemingly very few people being sampled.
A sample size of 10,000 for a population of 13,000,000 has a confidence level of over 95% and a confidence interval of +/- 1%.
For example, If you wanted to just be within +/- 5% for the entire Steam population (125 Million), you would only need to survey 400 people.
Once again, this is the problem: we don't actually know how many people are being sampled. For whatever reason, Valve refuses to publish that number.
Don't have time to have a detailed look right now, but you can get a very rough lower limit of their sample size from the data.
Pick the smallest percentage reported
Calculate minimum sample require to give a single sample with this data.
For one person in the sample to have a DK2 means 1/0.0003 = 3,333
So they surveyed at least 3,333 people.
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Quote:
Originally Posted by GingerJohn
Don't have time to have a detailed look right now, but you can get a very rough lower limit of their sample size from the data.
Pick the smallest percentage reported
Calculate minimum sample require to give a single sample with this data.
For one person in the sample to have a DK2 means 1/0.0003 = 3,333
So they surveyed at least 3,333 people.
At least that's something to work with. Fairly low margin of error. Its tough not to be a skeptic when the company in question purposefully leaves out relevant data.
Quote:
Originally Posted by TheLAWNOOB
Miners buy up the 480s. Prices are higher than MSRP. Gamer cant get reasonably priced cards.
If you compare 480 to 1060, 1060 has much more marketshare even though its released later.
That mining garbage again? That explains the prices. I thought they moved on to specialized ASIC processors.
Quote:
Originally Posted by Omega X
That mining garbage again? That explains the prices. I thought they moved on to specialized ASIC processors.
Even though the time where one could have made money on mining has been over for a while now, there are still a few diehard true believers. I uh...tend to take advantage of them on ebay. I don't mind the bulk orders of 480's, not at all.
If you want someone to blame for price increases, you're looking at him!
Quote:
Originally Posted by AmericanLoco
If video card X has 0.05% market share last month with 10,000 randomly sampled people, then the next month it also has 0.05% market share with a different 10,000 randomly sampled population - then it starts to become quite evident that video card is only in 5 out of every 10,000 people's computers.
That's actually a very good point - the fact that you don't see big swings month to month lends credence to their results.
Edited by Forceman - 10/3/16 at 6:21pm
Quote:
Originally Posted by GingerJohn
Don't have time to have a detailed look right now, but you can get a very rough lower limit of their sample size from the data.
Pick the smallest percentage reported
Calculate minimum sample require to give a single sample with this data.
For one person in the sample to have a DK2 means 1/0.0003 = 3,333
So they surveyed at least 3,333 people.
In the CPU section it goes as low as 0.01% for 5 core (probably someone who didn't get 100% lucky in unlocking a 4 Core Thuban to a 6 core), 10 core and 16 core CPUs being used (with 12 cores at 0.02%), and in the Total Hard Drive space - Less than 10 GB, also at 0.01%, so they surveyed at least three times that.
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Cooler Master Octane
Steam Hardware Survey is only indicative of Steam users.
This website proves how reliable Steam is:
https://www.netmarketshare.com/operating-system-market-share.aspx?qprid=10&qpcustomd=0
As for those claiming you need Steam to run DOTA: in China it does not use the Steam client. Thus there are millions upon millions of PC's that will never get surveyed because they aren't running Steam. But according to you guys because they aren't running Steam they are irrelevant. Another extremely narrow minded thread.
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Quote:
Originally Posted by Liranan
Steam Hardware Survey is only indicative of Steam users.
This website proves how reliable Steam is:
https://www.netmarketshare.com/operating-system-market-share.aspx?qprid=10&qpcustomd=0
As for those claiming you need Steam to run DOTA: in China it does not use the Steam client. Thus there are millions upon millions of PC's that will never get surveyed because they aren't running Steam. But according to you guys because they aren't running Steam they are irrelevant. Another extremely narrow minded thread.
I didn't think of that angle, good point. Many other types of polling are plagued by bias: they don't go outside of a certain group.
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• [Steam] Steam Hardware and Software Survey September 2016
Overclock.net › Forums › Industry News › Hardware News › [Steam] Steam Hardware and Software Survey September 2016 | 2,717 | 9,726 | {"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-2018-05 | latest | en | 0.944667 |
https://brainmass.com/chemistry/stoichiometry/26770 | 1,713,045,584,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816853.44/warc/CC-MAIN-20240413211215-20240414001215-00177.warc.gz | 136,011,108 | 6,877 | Purchase Solution
# Mole and Weight Percent Composition
Not what you're looking for?
Gas chromatographic analysis of a mixture of organic compounds gave the following peak areas (sq cm): hexane = 2.7; heptane = 1.6; hexanol = 1.8; toluene = 0.5.
(a) Calculate the mole percent composition of the mixture. Assume that the response of the detector (area per mole) is the same for each component.
(b) Calculate the weight percent composition of the mixture, using the same assumptions as in part A.
##### Solution Summary
This solution is provided in 218 words. It calculates moles and molar mass to find the mass percentage of the gases.
##### Solution Preview
(a) Total moles = 2.7 + 1.6 + 1.8 + 0.5 = 6.6 moles
mole percent of hexane = (2.7/6.6)*100 = 40.91%
mole percent of heptane = (1.6/6.6)*100 = 24.24%
mole percent of hexanol = (1.8/6.6)*100 = 27.27%
mole percent of ...
##### Match Elements with their Symbols
Elements are provided: choose the matching one- or two-letter symbol for each element.
##### General Chemistry - Classification of Matter
This test will assess your knowledge on the classification of matter which includes elements, compounds and mixtures.
##### Thermochemistry
The quiz helps in revising basic concepts about thermochemistry.
##### Functional groups in Organic Chemistry
You will be tested on the names of functional groups in Organic Chemistry. It is very important to know the functional groups to understand Organic reactions.
##### Organic Chemistry Naming: Alkanes
This is a quiz which is designed to assist students with learning the nomenclature used to identify organic compounds. This quiz focuses on the organic compounds called Alkanes. | 411 | 1,704 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-18 | latest | en | 0.897037 |
https://education.seattlepi.com/mini-science-projects-specific-heat-capacity-6982.html | 1,660,041,779,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570921.9/warc/CC-MAIN-20220809094531-20220809124531-00144.warc.gz | 216,002,727 | 87,151 | # Mini Science Projects About Specific Heat Capacity
Specific heat refers to the amount of heat per unit needed to raise the temperature by 1 degree Celsius. Specific heat is a constant -- the equation for the specific heat of water is 1 calorie gram degree Celsius of water equals 4.186 joules/gram Celsius, which is one of the highest specific heats of any substance. You can develop many small science fair projects on specific heat in less than a day.
## Elementary School Science Fair Projects
While most elementary school classroom teachers frown on using an open flame in their classrooms because of safety concerns, many experiments can be done without an open flame, either at home or in a classroom. For example, students can compare the specific heat of water and the specific heat of other objects such as sand, metal or glass. Students can also compare the specific heat of water and ice and discover that both of those specific heats are the same.
## Middle School Experiments
Middle school students can measure specific cooling temperatures of water and other objects over a period of time and record their observations. Middle-schoolers can also compare the specific heat of objects to heat conservation. This allows them to discover what they can do during an experiment to maintain the heat of an object -- such as covering a hot cup of water with a lid or a piece of foil -- and what reduces specific heat more quickly, such as putting a cup of water in the shade rather than sunlight.
## High School Specific Heat Projects
High school students have moved beyond the comparison of specific heat in objects, and can concentrate on the identification of objects based on their specific heat. Students may want to try identifying metals using their specific heat. Students can heat metals using a burner or a device that can heat a metal to a specific temperature and then measure the specific heat of the metal using a calorimeter. The metals must first be cooled to a specific temperature, which can be accomplished with ice. | 390 | 2,050 | {"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-2022-33 | longest | en | 0.936655 |
http://www.lofoya.com/Solved/30/how-many-litres-of-water-should-be-added-to-a-30-litre-mixture-of | 1,519,064,138,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812758.43/warc/CC-MAIN-20180219171550-20180219191550-00567.warc.gz | 483,551,446 | 15,330 | # Difficult Alligations or Mixtures Solved QuestionAptitude Discussion
Q. How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?
✔ A. 5 litres ✖ B. 7 litres ✖ C. 10 litres ✖ D. None of these
Solution:
Option(A) is correct
30 litres of the mixture has milk and water in the ratio 7 : 3. i.e. the solution has 21 litres of milk and 9 litres of water.
When you add more water, the amount of milk in the mixture remains constant at 21 litres. In the first case, before addition of further water, 21 litres of milk accounts for 70% by volume. After water is added, the new mixture contains 60% milk and 40% water.
Therefore, the 21 litres of milk accounts for 60% by volume.
Hence, 100% volume $=\dfrac{21}{0.6} =35$ litres.
We started with 30 litres and ended up with 35 litres.
Therefore, 5 litres of water was added.
Edit: For an alternative solution, check comment by Vaibhav Gupta.
Edit 2: For yet another alternative solution, check comment by K Sainath.
## (7) Comment(s)
Jitendra
()
suppose x litres of water mixed. Now take the ratio of water with mixture
: (30*(3/10)+x)/(30+x)=40/100
by solving this you will get x=5.
K Sainath
()
As 30 litre of mix having $\text{milk:water}=21:9$
Let, new water be $x$
Then $\dfrac{(x+9)}{21}=\dfrac{40}{60}$
By solving we get $x= \textbf{5 litre}$ that is to be added.
Vaibhav Gupta
()
Alternate solution:
$7:3$ means it has 21l milk and 9l water
Let $x$ litre water is added then total mixture $= 30+x$
As 40% must be water so 60 % must be milk
Therefore,
$\text{60% of } (30+x) = 21 \text{ litre}$
By solving it we get,
$x=5$
Thus, 5 litres of water must be added
Dhondu
()
Good question. Keep doing the good job.
Hassini
()
i cant understand tell clearly
Wsedrftgyh
()
awsedrftghjnm
Vaibhav Gupta
()
See my solution that would be helpful
if (defined ( 'LF_SITECTRL' )) echo LF_SITECTRL; ?> | 610 | 2,003 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2018-09 | latest | en | 0.85651 |
https://math.stackexchange.com/questions/4105946/how-to-find-this-line-length-and-targeted-point-coordinates-based-on-other-point | 1,716,333,295,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058522.2/warc/CC-MAIN-20240521214515-20240522004515-00206.warc.gz | 325,145,783 | 36,077 | # How to find this line length and targeted point coordinates based on other points?
First of all I'm beginner in "advanced" math. For this reason I don't know how to compute this problem.
Consider we have a generic rectangle with width W and height H. Also, consider that inside the bounds of that rectangle exists a point B and a point M, in any coordinates inside the rectangle. Knowing this, how can we find the coordinates of a point T which lies in a line MBT and that also stays on the edge of that rectangle? The reason to find the coordinates of T is that I will can draw a line between B and T.
To help understand the problem, see this figure: example
To try to solve this, I attempted some stuff:
1. I imagined that the rectangle is living inside a circle;
2. the center of the circle coincides with the center of the rectangle, then we have the radius of the circle dividing the diagonal of the rectangle by 2;
3. Using the center point C, we can create a triangle MCB, which also have all it's sides known from distance of points formula;
4. By using it's sides is possible to find the angle at the vertice B using the cosine's law;
5. From the angle X above, we can get it's adjacent X' by subtracting it from 180 degree;
6. With the angle X', then, is possible to find the length of the line from B to a point T2 formed by the triangle CBT2 (as illustrated below), again using cosine's law;
7. After getting the length of the line BT2 called L, is possible to find the coordinates of the point T2 using the way described here: Finding a point along a line a certain distance away from another point! (being L, the related distance).
illustration
Those steps are really messy and I was only about to get the coordinate of T2 instead of T. I could go further to find T taking the fact that T is between B and T2 or even creating more triangles and so on.
Then, as I have to use those calculations in programming, are those worth it? If not (and probably not) what a fine way to find the coordinates of the point T in this scenario?
First assume that the vertices of the rectangle are $$(0,0)$$, $$(W,0)$$, $$(W,H)$$ and $$(0,H)$$. If $$B=(b_1,b_2)$$ and $$M=(m_1,m_2)$$, then the ray $$MB$$ (you need the ray in order to ensure that the points are in the order $$M,B,T$$ and not $$T,M,B$$) has parametric equation $$M+\lambda (B-M)$$, where $$\lambda \in \mathbb{R}^+$$, that is, the points of the ray are the ones of the form $$(m_1+\lambda (b_1-m_1),m_2+\lambda (b_2-m_1))$$.
Now you can find the intersection of the ray with each of the lines that contain the sides of the rectangle, if the point of intersection $$S=(s_1,s_2)$$ verifies $$0\leq s_1\leq W$$ and $$0\leq s_2\leq H$$, then you can take $$T=S$$, else, you just compute the other intersections (one of them will give you the point). For example, the point of intersection of the ray $$MB$$ with the line $$y=0$$ (if it exists) has $$m_2+\lambda (b_2-m_2)=0$$, so $$\lambda =\frac{m_2}{m_2-b_2}$$, it doesn't exists if $$m_2=b_2$$ (in that case the line $$BM$$ is parallel to the $$x$$-axis) or $$m_2 (in that case the ray "goes upwards").
If the vertices of the rectangle have given coordinates (the sides are not necessarily parallel to the coordinate axes), you can use the same idea intersecting ray $$MB$$ with each of the lines containing the sides (the equations won't be that nice, but it still works). | 903 | 3,398 | {"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": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 25, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2024-22 | latest | en | 0.944919 |
https://www.knowpia.com/knowpedia/Photo-Carnot_engine | 1,679,948,066,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00366.warc.gz | 927,346,701 | 17,283 | BREAKING NEWS
Photo-Carnot engine
## Summary
(Learn how and when to remove this template message)
A photo-Carnot engine is a Carnot cycle engine in which the working medium is a photon inside a cavity with perfectly reflecting walls. Radiation is the working fluid, and the piston is driven by radiation pressure.
A quantum Carnot engine is one in which the atoms in the heat bath are given a small bit of quantum coherence. The phase of the atomic coherence provides a new control parameter.[1]
The deep physics behind the second law of thermodynamics is not violated; nevertheless, the quantum Carnot engine has certain features that are not possible in a classical engine.
## Derivation
The internal energy of the photo-Carnot engine is proportional to the volume (unlike the ideal-gas equivalent) as well as the 4th power of the temperature (see Stefan–Boltzmann law) using ${\displaystyle a={\frac {4\sigma }{c}}}$ :
${\displaystyle U=V\varepsilon aT^{4}\,.}$
The radiation pressure is only proportional to this 4th power of temperature but no other variables, meaning that for this photo-Carnot engine an isotherm is equivalent to an isobar:
${\displaystyle P={\frac {U}{3V}}={\frac {\varepsilon aT^{4}}{3}}\,.}$
Using the first law of thermodynamics (${\displaystyle dU=dW+dQ}$ ) we can determine the work done through an adiabatic (${\displaystyle dQ=0}$ ) expansion by using the chain rule (${\displaystyle dU=\varepsilon aT^{4}dV+4\varepsilon aVT^{3}dT}$ ) and setting it equal to ${\displaystyle dW_{V}=-PdV=-{\frac {1}{3}}\varepsilon aT^{4}dV\,.}$
Combining these ${\displaystyle dW_{V}=dU}$ gives us ${\displaystyle -{\frac {1}{3}}TdV=VdT}$ which we can solve to find ${\displaystyle T^{3}V={\text{const}}\,}$ , or equivalently ${\displaystyle PV^{4/3}={\text{const}}\,.}$
Since the photo-Carnot engine needs a quantum coherence in the gas which is lost during the process, the rebuild of coherency takes more energy than is produced with the machine.
The efficiency of this reversible engine including the coherency must at most be the Carnot efficiency, regardless of the mechanism and so ${\displaystyle \eta \leq {\frac {T_{H}-T_{C}}{T_{H}}}=1-{\frac {T_{C}}{T_{H}}}\,.}$
• Marlan O. Scully, M. Suhail Zubairy, G. S. Agarwal, Herbert Walther (2003-02-07). "Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence". Science. 299 (5608): 862–864. Bibcode:2003Sci...299..862S. doi:10.1126/science.1078955. PMID 12511655. S2CID 120884236.{{cite journal}}: CS1 maint: uses authors parameter (link) | 731 | 2,543 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 12, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2023-14 | latest | en | 0.86258 |
http://www.absoluteastronomy.com/topics/No-win_situation | 1,386,412,257,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163053923/warc/CC-MAIN-20131204131733-00099-ip-10-33-133-15.ec2.internal.warc.gz | 274,212,285 | 7,561 | No-win situation
# No-win situation
Discussion
Encyclopedia
A no-win situation, also called a "lose-lose" situation, is one where a person has choices, but no choice leads to a net gain. For example, if an executioner offers the condemned the choice of dying by being hanged, shot, or poisoned, since all choices lead to death, the condemned is in a no-win situation. This bleak situation gives the chooser little room: whatever choice is made, the person making it will lose their life.
Less drastic situations might also be considered no-win situations: if one has a choice for lunch between a ham sandwich and a roast beef sandwich, but is a vegetarian or has a wheat allergy
Wheat allergy
Wheat allergy is a food allergy, but can also be a contact allergy resulting from occupational exposure. Like all allergies wheat allergy involves IgE and mast cell response. Typically the allergy is limited to the seed storage proteins of wheat, some reactions are restricted to wheat proteins,...
, that might be considered a no-win situation.
## In game theory
In game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, a "no-win" situation is one in which no player benefits from any outcome. This may be because of any or all of the following:
• Unavoidable or unforeseeable circumstances causing the situation to change after decisions have been made. This is common in Text adventures.
• Zugzwang
Zugzwang
Zugzwang is a term usually used in chess which also applies to various other games. The term finds its formal definition in combinatorial game theory, and it describes a situation where one player is put at a disadvantage because he has to make a move when he would prefer to pass and make no move...
, as in chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
, when any move a player chooses makes him worse off than before
• A situation in which the player has to accomplish two mutually dependent tasks each of which must be completed before the other or that are mutually exclusive (a Catch-22
Catch-22 (logic)
A Catch-22, coined by Joseph Heller in his novel Catch-22, is a logical paradox arising from a situation in which an individual needs something that can only be acquired with an action that will lead him to that very situation he is already in; therefore, the acquisition of this thing becomes...
)
• Ignorance of other players' actions, meaning the best decision for all differs from that for any one player (as in the Prisoner's Dilemma
Prisoner's dilemma
The prisoner’s dilemma is a canonical example of a game, analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W...
).
## In history
Carl von Clausewitz
Carl von Clausewitz
Carl Philipp Gottfried von Clausewitz was a Prussian soldier and German military theorist who stressed the moral and political aspects of war...
's advice (never to launch a war that one has not already won) characterizes war as a no-win situation. A similar example is the Pyrrhic victory
Pyrrhic victory
A Pyrrhic victory is a victory with such a devastating cost to the victor that it carries the implication that another such victory will ultimately cause defeat.-Origin:...
, in which a military victory is so costly that the winning side actually ends up worse off than before it started. Looking at the victory as a part of a larger situation, the situation could either be no-win or a win for the other side than the one that won the "victory". For example, the "victorious" side may have accomplished their objective, but the objective may have been worthless, or they may lose a strategic advantage in manpower or positioning.
In Europe before the Reformation
Protestant Reformation
The Protestant Reformation was a 16th-century split within Western Christianity initiated by Martin Luther, John Calvin and other early Protestants. The efforts of the self-described "reformers", who objected to the doctrines, rituals and ecclesiastical structure of the Roman Catholic Church, led...
those accused of being witches were sometimes bound and then thrown or dunked in water to test their innocence. A witch would float (by calling upon the Devil to save her from drowning), and then be executed; but a woman not a witch would drown (proving her innocence but causing her death).
## Video games
An adventure game is a video game in which the player assumes the role of protagonist in an interactive story driven by exploration and puzzle-solving instead of physical challenge. The genre's focus on story allows it to draw heavily from other narrative-based media such as literature and film,...
s and role-playing video game
Role-playing video game
Role-playing video games are a video game genre with origins in pen-and-paper role-playing games such as Dungeons & Dragons, using much of the same terminology, settings and game mechanics. The player in RPGs controls one character, or several adventuring party members, fulfilling one or many quests...
s where it is impossible for the player to win the game (not due to a bug
Software bug
A software bug is the common term used to describe an error, flaw, mistake, failure, or fault in a computer program or system that produces an incorrect or unexpected result, or causes it to behave in unintended ways. Most bugs arise from mistakes and errors made by people in either a program's...
but by design), and where the only other options are restarting the game, loading a previously saved game, wandering indefinitely, or a game over
Game over
Game Over is a message in video games which signals that the game has ended, often due to a negative outcome - although the phrase sometimes follows the end credits after successful completion of a game...
(negative game end, such as death). It is also known as a walking dead, dead end or zombie situation.
Unwinnable should not be confused with "unbeatable," which is used to describe a character, monster, or puzzle that is too powerful or difficult to be overcome by the player or character at a lower standing, and is normally found in role-playing video game
Role-playing video game
Role-playing video games are a video game genre with origins in pen-and-paper role-playing games such as Dungeons & Dragons, using much of the same terminology, settings and game mechanics. The player in RPGs controls one character, or several adventuring party members, fulfilling one or many quests...
s.
• Cornelian dilemma
Cornelian dilemma
A Cornelian dilemma is a dilemma in which someone is obliged to choose between two courses of action either of which will have a detrimental effect on himself or herself or on someone near to him or her...
• Winner's curse
Winner's curse
The winner's curse is a phenomenon akin to a Pyrrhic victory that occurs in common value auctions with incomplete information. In short, the winner's curse says that in such an auction, the winner will tend to overpay...
• Catch-22 (logic)
Catch-22 (logic)
A Catch-22, coined by Joseph Heller in his novel Catch-22, is a logical paradox arising from a situation in which an individual needs something that can only be acquired with an action that will lead him to that very situation he is already in; therefore, the acquisition of this thing becomes...
• Double bind
Double bind
A double bind is an emotionally distressing dilemma in communication in which an individual receives two or more conflicting messages, in which one message negates the other. This creates a situation in which a successful response to one message results in a failed response to the other , so that...
• Win-win game
Win-win game
A win-win game is a game which is designed in a way that all participants can profit from it in one way or the other. In conflict resolution, a win-win strategy is a conflict resolution process that aims to accommodate all disputants.-Types:...
• Morton's fork
Morton's Fork
A Morton's Fork is a choice between two equally unpleasant alternatives , or two lines of reasoning that lead to the same unpleasant conclusion...
• Kobayashi Maru
Kobayashi Maru
The Kobayashi Maru is a test in the fictional universe of Star Trek. It is a Starfleet training exercise designed to test the character of cadets in the command track at Starfleet Academy. The Kobayashi Maru test was first depicted in the opening scene of the film Star Trek II: The Wrath of Khan... | 1,866 | 8,890 | {"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-2013-48 | latest | en | 0.961178 |
https://www.solutioninn.com/a-cubical-box-of-widths-lx--ly--lz | 1,603,540,232,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107882581.13/warc/CC-MAIN-20201024110118-20201024140118-00058.warc.gz | 906,022,551 | 8,656 | # A cubical box of widths Lx = Ly = Lz
A cubical box of widths Lx = Ly = Lz = L contains an electron. What multiple of h2l8mL2, where m is the electron mass, is?
(a) The energy of the electron's ground state,
(b) The energy of its second excited state, and
(c) The difference between the energies of its second and third excited states? How many degenerate states have the energy of?
(d) The first excited state and
(e) The fifth excited state?
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Best for online homework instance. | 181 | 714 | {"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-2020-45 | latest | en | 0.899171 |
http://www.dummies.com/how-to/content/how-to-round-off-numbers-in-r.navId-812015.html | 1,469,655,165,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257827079.61/warc/CC-MAIN-20160723071027-00157-ip-10-185-27-174.ec2.internal.warc.gz | 419,662,677 | 15,283 | Although R can calculate accurately to up to 16 digits, you don’t always want to use that many digits. In this case, you can use a couple functions in R to round numbers. To round a number to two digits after the decimal point, for example, use the round() function as follows:
```> round(123.456,digits=2)
[1] 123.46```
You also can use the round() function to round numbers to multiples of 10, 100, and so on. For that, you just add a negative number as the digits argument:
```> round(-123.456,digits=-2)
[1] -100```
If you want to specify the number of significant digits to be retained, regardless of the size of the number, you use the signif() function instead:
```> signif(-123.456,digits=4)
[1] -123.5```
Both round() and signif() round numbers to the nearest possibility. So, if the first digit that’s dropped is smaller than 5, the number is rounded down. If it’s bigger than 5, the number is rounded up.
If the first digit that is dropped is exactly 5, R uses a rule that’s common in programming languages: Always round to the nearest even number. round(1.5) and round(2.5) both return 2, for example, and round(-4.5) returns -4.
Contrary to round(), three other functions always round in the same direction:
• floor(x) rounds to the nearest integer that’s smaller than x. So floor(123.45) becomes 123 and floor(-123.45) becomes –124.
• ceiling(x) rounds to the nearest integer that’s larger than x. This means ceiling (123.45) becomes 124 and ceiling(123.45) becomes –123.
• trunc(x) rounds to the nearest integer in the direction of 0. So trunc(123.65) becomes 123 and trunc(-123.65) becomes –123. | 431 | 1,622 | {"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} | 3.96875 | 4 | CC-MAIN-2016-30 | latest | en | 0.863516 |
https://stats.stackexchange.com/questions/296268/understanding-expected-risk-for-binary-classification | 1,627,814,732,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154175.76/warc/CC-MAIN-20210801092716-20210801122716-00516.warc.gz | 536,317,797 | 36,257 | # Understanding expected risk for binary classification
We have defined expected loss as follows:
$\mathbb{E}_y[C(y,a)|x] = \int C(y,a)P(y|x)dy$
"C(.)" being the cost-function, "y" the class, "a" a taken action. In the case that y can only have two possible values, say y $\in \{0,1\}$, isn't it then the case that if $P(y=1|x) = p$ it follows that $P(y=-1|x) = 1-p$? And hence if two actions are possible, expected loss could be written (in the discrete case) as:
$C(y=1,a=-1)*P(y=1|x)+C(y=-1,a=1)*1-P(y=-1|x)$?
Is this correct? I see that even in cases where there are only two classes, the posteriors P(y=1|x) and P(y=-1|x) would be used, without expressing one in the terms of the other.
• What is your question? – Tim Aug 4 '17 at 19:53
• Edited: Included my question. Particularly I was told here that this is not always the case, and I do not understand why: stats.stackexchange.com/questions/296230/… – user24544 Aug 4 '17 at 19:56 | 293 | 945 | {"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} | 2.796875 | 3 | CC-MAIN-2021-31 | latest | en | 0.900575 |
http://www.chegg.com/homework-help/electrical-power-and-controls-2nd-edition-chapter-14-solutions-9780131130456 | 1,472,146,877,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982293692.32/warc/CC-MAIN-20160823195813-00130-ip-10-153-172-175.ec2.internal.warc.gz | 372,561,037 | 15,827 | View more editions
# Electrical Power and Controls (2nd Edition)Solutions for Chapter 14
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Chapter: Problem:
SAMPLE SOLUTION
Chapter: Problem:
• Step 1 of 4
The following is the given ladder diagram for a system with manual controls:
Figure 1
• Step 2 of 4
(a) It is given that 8-point I/O cards are used. Here, use one-slot addressing; it means there are only 8 points for input in group 0 and 8 points for output in group 1.
Therefore, the addressing bits will vary from 00-07 for both input and output devices.
The following ladder indicate the required inputs:
Figure 2
• Step 3 of 4
The following ladder indicate the required outputs:
Figure 3
(b) In figure 1, when the power supply is provided, the green on the third will be on as it is connected to a normally closed switch. When start-1 button is pushed, the coil relay (CR1) will get energized and the switches CR1-1, CR1-2 and CR1-3 will change their state. CR1-1 and CR1-3 will be closed and CR1-2 will be opened due to which green light will be off.
When CR1-3 and float switch closed simultaneously, CR2 will get energized and CR2-1 and CR2-2 will be closed. CR2-1 will start the motor A and CR2-2 will switch on the red light on rung 10.
When start-2 is pressed, CR3 will get energized, which in turn will close CR3-1, CR3-2 and CR3-3. CR3-2 and CR3-3 will turn on the motor B and red on rung 11, respectively.
• Step 4 of 4
The following is the PLC ladder diagram showing the addresses for all devices:
Figure 4
Corresponding Textbook
Electrical Power and Controls | 2nd Edition
9780131130456ISBN-13: 0131130455ISBN: | 499 | 1,822 | {"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-2016-36 | latest | en | 0.884144 |
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