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http://www.jiskha.com/display.cgi?id=1316888381
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math
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Posted by saranghae12 on Saturday, September 24, 2011 at 2:19pm.
what is 2 times pie times 2.5to the second power + 2 times pie times 2.5 times 5.5?
7th grade math - bobpursley, Saturday, September 24, 2011 at 2:41pm
put this in the google search window:
2*PI*2.5^2 + 2*PI*2.5*5.5=
7th grade math - Helen, Saturday, September 24, 2011 at 2:46pm
Can ayou nswer this? Good luck!!!!!!!!!.
Horses are $10, pigs are $3 and rabbits are $0.50. A farmer buys 100 animals for $100, How many of (each ) animal did he buy? Hint: there are 2 answers
7th grade math - bobpursley, Saturday, September 24, 2011 at 2:52pm
set them equal.
here is one answer:
7th grade math - saranghae12, Saturday, September 24, 2011 at 3:08pm
Answer This Question
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s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171758.35/warc/CC-MAIN-20170219104611-00227-ip-10-171-10-108.ec2.internal.warc.gz
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CC-MAIN-2017-09
| 1,597 | 24 |
http://mathnexus.wwu.edu/archive/statistic/detail.asp?ID=276
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math
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Lemon Pledge and M&M's
According to Vince Staten's book Can You trust a Tomato in January? (1994)....
Question: Find systematic ways to test the validity of these claims. Are they true?
- Lemon Pledge furniture polish contains more lemons than Country Time Lemonade.
- M&M's are mixed in these color ratios: 3 brown, 2 yellow, 2 red, 1 green, 1 orange, and 1 tan.
D.C. (Bellingham) offers these approaches....
- I would obtain some chemical process to determine the mixture ratio of the lemon juice versus the overall volume, and run several trials on each of the Country time lemonade and the furniture polish. The lemonade will be first strained for any pulp and the pulp will be weighed and incorporated into the total ratio. If necessary, different variations of the lemonade may be tested (pulp, no pulp...). After (for thoroughness) about 50 trials of determining the ratio, I would average and do a hypothesis test via regression on the furniture polish and each of the lemonade ratios to see if they are equal on average, or if the furniture polish, via a t-test, has a statistically significant greater size proportionally to the lemonade. I would then conclude to a certain confidence interval (likely 95%) whether the lemonade has less lemon in it than the polish.
- I would buy several bags (lets go with 100 this time) and count out the number of each respective color in each bag, and record them in a table. I would then test their probablity ratios as described in the problem via a test on a multinomial distribution with colors assigned as p's (e.g. pbrown=3/10). I would use the test to see if there is a statistical difference in the probabilities estimated and their estimations. Based on this I would conclude at a certain level of confidence (likely 95%) whether the actual mixture differs in its ratio from the specified mixture.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578605510.53/warc/CC-MAIN-20190423134850-20190423160850-00295.warc.gz
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CC-MAIN-2019-18
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https://dokumen.tips/documents/16-what-if-it-is-reflected-more-than-once-pg-23-rigid-transformations-translations.html
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math
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1.6What if it is Reflected More than Once?Pg. 23Rigid Transformations: Translations1.6 What if it is reflected more than Once?_____Rigid Transformations: Translations
In Lesson 1.5, you learned how to change a shape by reflecting it across a line, like the ice cream cones shown at right. Today you will learn more about reflections and learn about a new type of transformation: translations.
1.38 TWO REFLECTIONS As Amanda was finding reflections, she wondered, What if I reflect a shape twice over parallel lines? Investigate her question as you answer the questions below. a. Find ABC and lines n and p (shown below). What happens when ABC isreflected across line n to form and then is reflected across line p to form First visualize the reflections and then test your idea of the result by drawing both reflections.PredictionDrawing
b. Examine your result from part (a). Compare the original triangle ABC with the final result, What single motion would change ABC to
Moving it over, slidingGeogebra Reflectionsc. Amanda analyzed her results from part (a). It Just looks like I could have just slid ABC over! Sliding a shape from its original position to a new position is called translating. For example, the ice cream cone at right has been translated. Notice that the image of the ice cream cone has the same orientation as the original (that is, it is not turned or flipped). What words can you use to describe a translation?
Moving it over, slidingTranslationTransformationMoving the shape in some waySliding shape over
TranslationSlid over, not flipped
Right 7Down 3Motion Rule:
Rightor LeftUpor Down
Right 7Down 3
Left 4Up 1Right 3Down 7Down 5Right 8
(2, 3)(-1, 5)(2, -1)
(-2, -2)(2, -1)(4, -5)
f. Can you find the new point without counting on the graph? Use the motion rule to find if P is at (2, -1).
(2 3, -1 + 1)
(2 + 7, -1 3)
(2 + 5, -1)
1.40 NON-CONGRUENT RULES Use the following rules to find the new shape by plugging in each x and y value to find the new coordinate.
(-1, -4)(0, -2)(3, -4)
(-6, -4)(-4, -2)(2, -4)
c. What is the difference between (a) and (b)? Why do you think one is congruent to the original and one is not?
Multiplying changes the size of the shape1.41 WORKING BACKWARDS What if you are only given the location of the translated shape? Can you find the original shape?
Right 4Down 1Left 4Up 1
(-2, -2)(0, -4)(1, 2)
Left 3Right 3
(6, -1)(6, -4)(4, -4)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178360293.33/warc/CC-MAIN-20210228054509-20210228084509-00436.warc.gz
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CC-MAIN-2021-10
| 2,390 | 26 |
https://www.lessonplanet.com/teachers/stem-and-leaf-plots-9th-12th
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math
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Stem and Leaf Plots
Students organize statistical data using a stem and leaf plot. They complete examples where the stem is the greatest common place value of the data, and the leaves are the next greatest common place value.
9th - 12th Math 7 Views 32 Downloads
Equal Salaries for Equal Work?
Learners perform data analysis and draw conclusions bound to stir lively debate in a statistical activity. Starting with data comparing men's and women's wages, the class performs two different kinds of regressions to determine trends....
9th - 12th Math CCSS: Designed
New Review Statistics-Investigate Patterns of Association in Bivariate Data
Young mathematicians construct and analyze patterns of association in bivariate data using scatter plots and linear models. The sixth chapter of a 10-part eighth grade workbook series then prompts class members to construct and interpret...
7th - 10th Math CCSS: Designed
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720380.80/warc/CC-MAIN-20161020183840-00373-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 911 | 9 |
https://www.physicsforums.com/threads/general-solution-of-ordinary-differential-equation.285722/
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math
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1. The problem statement, all variables and given/known data Find the general solution of the differential equation, y' + y = be^(-λx) where b is a real number and λ is a positive constant. 2. Relevant equations y' + P(x)y = Q(x) Integrating factor: e^(∫P(x) dx) 3. The attempt at a solution Let P(x) = 1, Q(x) = be^(-λx) The equation is already in the form y' + P(x)y = Q(x). So, the integrating fator is I(x) = e^(∫1 dx) = e^(x) Multiplying both sides by the integrating factor. e^(x)y + e^(x)y = be^(-λx)e^(x) (e^(x)y)' = be^(-λx)e^(x) Now integrating the left hand side, e^(x)y = be^(-λx)e^(x) Here is my problem. I don't know where to go from here. How do I integrate the right hand side? That's my main problem. Any help will be greatly appreciated.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039745015.71/warc/CC-MAIN-20181119023120-20181119045120-00451.warc.gz
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CC-MAIN-2018-47
| 765 | 1 |
https://www.thestudentroom.co.uk/showthread.php?t=607367&page=2
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math
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find cos 165 no calc Watch
thats just stating a formula.....
noooooooooo lol... but they might ask you a question where someone says "Rachel says:
cos(this) + cos(that) is the same as cos(this + that), therefore cos(A) + cos(B) must always equal cos(A + B).
Prove rachel is wrong in her assumption"
All you do is choose two numbers where that doesn't work.
Cos (45 + 120) = Cos 45 Cos 120 - Sin 45 Sin 120.
(If you think about it, Cos 90 = 0.
So if Cos 45 + Cos 45 = Cos 90
then you're saying that which isn't true. )
Whenever you're finding Cos (one number + another number)
or Sin (one number + another number)
then you have to use the formulae for Cos(A+B) etc.
A= 180 degrees, B = 60 degrees, so that A + B = 240 degrees, then
cos[A + B] = cosA + cosB.
In general it is not true that cos[A + B] = cosA + cosB, but there are occasions when it is true. Similarly for sin[A + B] etc.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987835748.66/warc/CC-MAIN-20191023173708-20191023201208-00149.warc.gz
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CC-MAIN-2019-43
| 884 | 16 |
http://forums.wolfram.com/mathgroup/archive/2001/Feb/msg00237.html
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math
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- To: mathgroup at smc.vnet.net
- Subject: [mg27267] Questions
- From: "Tony" <tony at magic101.freeserve.co.uk>
- Date: Fri, 16 Feb 2001 03:58:17 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Does mathematica do reflections rotations of a given shape.
I mean if I plot a triangle if I had a fuction such as
f: R2 --> R2
Would mathematica do this and would it carry out composite function such as
GoF and FoG etc
Oh so many questions to ask and so little time to .........
Prev by Date:
Re: Mathematica 4.1 How to.....
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s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320386.71/warc/CC-MAIN-20170625013851-20170625033851-00424.warc.gz
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CC-MAIN-2017-26
| 624 | 17 |
https://www.veryshortintroductions.com/view/10.1093/actrade/9780198811701.001.0001/actrade-9780198811701-chapter-15
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math
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‘Maybe it is true—but you can’t prove it!’ first considers David Hilbert’s Program in the Foundations of Mathematics, which was to prove that mathematics was consistent. Hilbert’s ambitious proposal required all of mathematics to be axiomatized. The existence of such an axiom-system was disproved by the Austrian mathematician Kurt Gödel (1906–78). What Gödel showed was that such an axiom system cannot be provided even for the fragment of mathematics that concerns natural numbers, let alone the rest of it. Gödel’s result has been held to have many other philosophical consequences, concerning the nature of numbers, our knowledge of them, and even the nature of the human mind.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999273.24/warc/CC-MAIN-20190620190041-20190620212041-00051.warc.gz
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CC-MAIN-2019-26
| 701 | 1 |
http://farrell2001.tripod.com/Chordsine/chordsine.html
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math
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CHORDS AND SINES
Lesson title : Chords and Sines
Subject and Grade Level : 10 - 12th grade Mathematics
Brief Description : To discover the mathematical relationships between chords of a circle and the sine of an angle in a right triangle.
Objectives —The students will be able to:
1. Explore required definitions through web based diagrams.
2. Discover the mathematical relationships between a chord and the sine of an angle cutting a portion of a circle.
3. Communicate mathematical concepts in writing.
Educational/Skills Goals (Include academic (standards) and Internet goals)
1. Reflect upon and clarify their thinking about mathematical ideas and relationships.
2. Express mathematical ideas orally and in writing.
3. Read written presentations of mathematics with understanding.
Internet resources involved (web addresses)
Go to the site for Definitions and read the first two paragraphs and note the new definition of the sine function.
Examine the first Java Applet - a diagram depicting this new definition.
Experiment with changing segment lengths and angle measures by clicking and dragging on any point on the diagram. Look carefully at the right triangles as you drag points. Make notes of your observations.
Continue reading the Definitions page and try to vizualize what the author is proving. Make notes if necessary. Record the major steps in the author's proof.
Write an explanation of this informal proof of the sine function by describing the relationship between the standard definition and the new definition. Include both the definitions in your writing in addition to the concepts of right angles and similarity. Include diagrams where appropriate.
Timeline: 1 - 3 days depending on availability of computers, Internet access and ability levels of students.
Non-Internet Activities: Class work reiterating trigonometric ratios, relationships in right triangles and properties of chords in a circle.
Internet Activities: See above under procedure.
- 3 Response is exemplary, detailed and clear.
- 2 Response is generally correct.
- 1 Response is partially correct, but lacks clarity.
- 0 No response or response is incorrect.
Follow-up Activities and Extensions: Go to the site for Trigonometry for a complete view of trigonometry from angle measure to identities. Use the calculator site as and when required. Minimize the window and keep it available on your desktop.
After the lesson is taught, review the following:
Set-Up Time Required
Class Time Required
Problems and Issues that were encountered
Recommendations for Improvement
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CC-MAIN-2019-09
| 2,559 | 31 |
http://www.geology.lu.se/
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math
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Patrik Vestin defends his PhD thesis in Physical Geography and Ecosystems Analysis" Effects of...
22 September kl 10:15
Ashley Gumsley defends his PhD thesis: "Validating the existence of the supercraton Vaalbara in...
22 September kl 13:00
Geologi Seminar: "Moving beyond the age-depth paradigm in deep sea palaeoclimate archives"...
28 September kl 12:15
Jon Harbor, Purdue University: "Warning: education research may change the way you teach"
9 October kl 15:15
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s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688158.27/warc/CC-MAIN-20170922022225-20170922042225-00456.warc.gz
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CC-MAIN-2017-39
| 465 | 8 |
https://thekooshy.com/G/Thulium-Granulat.html
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math
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Step by step derivatives
In addition, Step by step derivatives can also help you to check your homework. Keep reading to learn more!
The Best Step by step derivatives
We'll provide some tips to help you select the best Step by step derivatives for your needs. Solving integral equations is a way of finding a function that satisfies a certain equation. In other words, it involves finding a function that "integrates" to a given value. This can be done by using a variety of methods, including integration by parts, integration by substitution, and integration by partial fractions. Each method has its own strengths and weaknesses, and the best method to use will depend on the specific equation that needs to be solved. However, no matter which method is used, solving integral equations can be a challenging task. Fortunately, there are many resources available to help with this process. With a little patience and perseverance, anyone can learn how to solve integral equations.
Linear algebra is a critical tool for solving mathematical problems. Linear algebra solvers are specially designed to solve linear algebra problems. There are many different types of linear algebra solvers, each with its own advantages and disadvantages. The most popular type of linear algebra solver is the Gaussian elimination method. This method is very efficient for solving large systems of linear equations. However, it can be slow for smaller systems of equations. Another popular type of linear algebra solver is the LU decomposition method. This method is more versatile than the Gaussian elimination method and can be used to solve both large and small systems of linear equations. Linear algebra solvers are an essential tool for mathematicians and engineers alike.
Web math is a type of online math that helps students learn mathematics. Web math can help students learn mathematics by providing interactive tutorials, exercises, and calculators. Web math can also help students learn mathematics by providing online resources, such as video lessons and articles. Web math can also help students learn mathematics by providing online tools, such as graphing calculators and online quizzes. Web math can also help students learn mathematics by providing online tutors who can answer questions and provide feedback. By providing these resources, web math can help students learn mathematics more effectively.
Looking for a Triangle solver calculator? Look no further! Our Triangle solver calculator is designed to help you quickly and easily solve Triangle problems. Simply enter the values for three sides of the Triangle, and our calculator will do the rest. It's that easy! So why wait? Give our Triangle solver calculator a try today!
How to solve using substitution is best explained with an example. Let's say you have the equation 4x + 2y = 12. To solve this equation using substitution, you would first need to isolate one of the variables. In this case, let's isolate y by subtracting 4x from both sides of the equation. This gives us: y = (1/2)(12 - 4x). Now that we have isolated y, we can substitute it back into the original equation in place of y. This gives us: 4x + 2((1/2)(12 - 4x)) = 12. We can now solve for x by multiplying both sides of the equation by 2 and then simplifying. This gives us: 8x + 12 - 8x = 24, which simplifies to: 12 = 24, and therefore x = 2. Finally, we can substitute x = 2 back into our original equation to solve for y. This gives us: 4(2) + 2y = 12, which simplifies to 8 + 2y = 12 and therefore y = 2. So the solution to the equation 4x + 2y = 12 is x = 2 and y = 2.
We cover all types of math issues
The app's smart calculator is super helpful for example when you need to add, subtract, divide, or multiple fractions because other calculators don't have that feature, and the camera feature is also useful for when you are in a hurry and neon the answers quickly. Not only that but the camera feature allows you to modify the range of space the camera use up. And probably my favorite part of the app is how it show you the steps to your answer so you could know how to do it. Over all a useful app.
Normally rating for an app doesn't make sense, but rating for this the app app makes a whole lot sense because, this is capable of solving any type of math problem and give the result with a graph without wasting the user's time. Even the intention to learn math is raised by this app. Finally, I would like to thank for the producers of this app.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711064.71/warc/CC-MAIN-20221205232822-20221206022822-00310.warc.gz
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CC-MAIN-2022-49
| 4,489 | 11 |
https://v2.atlasoceanvoyages.com/request-a-quote/
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math
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TYPE OF QUOTE
Individual QuoteGroup Quote
Country Of Residence
QUOTE WITH AIR
I am a travel advisorI am working with a travel advisorI am a traveler without a travel advisor
Log into your account in just a few simple steps.
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| 223 | 6 |
https://electricdruid.net/investigations-into-what-a-bbd-chorus-unit-really-does/
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math
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I’ve been curious about Chorus for a while, since I’ve been working on and off with chorus design myself. There were a few things I didn’t understand, like what the relationshp is between the modulation LFO’s waveshape and the frequency modulation of signals going through the chorus. You’d think that if you use a sinewave to modulate the BBD clock, you’d get a sinewave modulation of frequency, right? Wrong! So what do you get? At this point, I realised that it was a bit more complicated than I was giving it credit for and I’d have to really think about it. This page is some of the results of those studies.
Simulation of BBD chorus
So what did I do? Well, I did what I always do when I don’t understand something. I wrote a simulation of it. If I can write a sim of a situation, then I know that I understand it. If the sim doesn’t work, there’s something I’m still missing. Often the process of thinking about how to simulate something, and seeing how and why the simulation doesn’t work gives me an insight into the real situation. If that doesn’t work, playing with the simulation gives me a useful way to perform repeatable experiments that would often be awkward to do in reality.
My simulated delayline has 1024 stages, just like the SAD1024, MN3007, or MN3207 chip. Of these, only the last one is still available, so it’s the chip likely to turn up in modern analog chorus designs.
My chorus has linear clock modulation like the typical chorus effects. More about the problems this causes later – for now, we’re just simulating a typical chorus. The clock frequency at any given moment is:
$clock_freq = $clock_centre_freq + ($lfo * $mod_depth * 10000); // 10KHz mod range
Here’s the LFO waveform (blue) and the Clock rate (green). The horizontal green line is the clock centre frequency with no modulation applied. You can see that with a modulation depth of 20KHz, the clock frequency goes up to 60KHz, and down to 20KHz. The LFO rate and Clock rate are just chosen to give a reasonable display. We can see 400msecs of signal here.
Ok, so far, so good. Let’s feed some audio into it and see if we can see anything happening. Remember this is just the signal through the BBD (the “Wet only” signal), so it’s not a full chorus. In fact, it’s just a vibrato unit. But mixing the dry and wet signals together is easy, and that’s not the bit I don’t understand, so I’m ignoring the dry signal. This next graph adds a low audio ramp wave (red). You can easily see the pitch change caused by the clock modulation. Notice the initial delay before any signal comes through the delay line is clearly visible on the left hand side of the graph.
Now this is where things start to get interesting. What do you think is happening to that audio frequency? It should be varying up and down, following the changes in the clock rate, right? Let’s have a look. The next graph uses the slope of the output ramp wave to give an estimate of the audio output frequency at each moment. This is only possible with ramp waves of fixed amplitude, but it’s handy for our demo. This is plotted in red. I’ve taken the LFO off to stop it getting too cluttered.
Interesting, don’t you think? The frequency modulation produced isn’t a simple sine wave – it’s distorted. Let’s have better look at that without the audio:
So what’s going on here? Think about how the BBD makes a pitch change. When the LFO output is rising, the clock frequency is increasing, and samples are being read out faster than they were read in – their pitch is shifted up. Likewise, when the LFO is falling, the clock frequency is decreasing, and samples are read out more slowly than they were read in – the pitch is decreased. The key here is that the pitch shift is not caused by a high clock frequency or a low clock frequency, but by an increasing or decreasing clock frequency. It’s the rate–of–change of clock frequency that’s important.
For a sine wave LFO input like we’ve been using, the point of maximum increase is the middle of the upwards slope, where our clock rate crosses the horizontal red line. Similarly, the maximum decrease is on the downwards slope where it crosses the red line. If we plot this rate of increase, we’re plotting the differential of sin(x), which is just cos(x) – the same thing shifted forwards a bit.
But hang on a minute! Our frequency modulation isn’t following cos(x) for our sin(x) LFO! That curve isn’t a cosine curve any more than it’s a sine curve. Where’s that distortion coming from?
Why does the modulation get distorted?
Let’s back up for a moment and consider the delay. How would we measure the delay at any moment in time? Well, the total amount of delay is just the amount of delay provided by each bucket, all added together, and how much delay you get depends on how fast the clock was going for each of the previous buckets. The delay for a single bucket is the length of time since the last clock pulse – e.g. the clock period. The total delay is the sum of all the last X clock periods, where X is the number of BBD stages. Put another way, we’re integrating the area under the clock period curve for the last X samples.
Let’s plot the clock period curve. Here it is, added to the graph in green:
The first thing to notice about this is that it’s already slightly distorted, since we’re now looking at 1/sin(x) rather than sin(x). But the distortion is all in the vertical direction, not in the time axis. To say that another way, the waveform is still symmetrical left-to-right. Ok, now let’s see what shape curve the delay makes if we add up the last X periods of that clock period graph. Here it is in blue:
Now we see where the rest of the distortion comes from. Although the clock frequency matches the LFO, the actual delay doesn’t directly, because it is the sum of all the clock periods for the whole length of the delay line. Incidentally, with the clock frequency we choose originally, the blue line goes from slightly below 10msecs to slighty above 20msecs, so we’re pretty much in chorus territory here.
But it still doesn’t look like the frequency modulation!
Well, no, true. It doesn’t. But you remember when we talked about it being the rate-of-change of delay that was important? We were thinking that for a sin(x) LFO, we’d see a cos(x) frequency modulation? It isn’t that simple, since as we’ve shown, the total delay follows a much more complicated curve than the clock frequency. But the point still stands – it’s the rate-of-change of delay that matters. Here’s the plot with the rate-of-change added in pale blue:
Now at last we’ve got a waveform that looks like our frequency modulation! The frequency modulation follows the rate-of-change of the total delay, and that waveform isn’t anything like the modulation LFO’s waveform.
Great! So what frequency modulation do I get with other LFO waveforms?
Ok, let’s have a look at a few in isolation. First we’ve got the sine wave LFO that we’ve just seen:
A triangle wave LFO is probably even more common, since they’re easy to build:
And square wave LFOs are even easier to build, but rarely used for chorus:
Now, there’s an interesting result! Although the LFO jumps between two levels, the output frequency jumps between three!
Linear versus Exponential clock modulation for BBD chorus
One of the problems with a typical chorus unit is the pitch modulation gets deeper as the BBD clock rate is reduced (e.g. as the delay is made longer). This makes the pitch variation very obvious – “seasick” or “warbley” are words often used to describe the sound. A typical chorus unit uses an LFO to modify its clock frequency, and that clock modulation is linear, so a given modulation depth will give (for example) +/-25KHz of clock modulation. This is how our simulation has operated thus far. When I considered this, it seemed to me that must be the reason why the depth seems to go up. If you consider a high clock frequency of 200KHz, a modulation of +/-25KHz is about 12%, or about 2 semitones. If you then consider what happens at a low clock frequency of 50KHz, the same modulation of +/-25KHz now shifts the clock by about 50%, or roughly an octave (50-25 = 25, which is 50% of 50KHz, 50+25 = 75, which is 150% of 50KHz).
So what’s the solution? Use exponential frequency modulation like a synth VCO of course! Then the LFO mod depth would be specified as “an octave” or “4 semitones” and an octave shift at 50KHz is the same as an octave shift at 200KHz.
An Update – some further thoughts
A while after posting this article, I had an email discussion about it with Brian Neunaber of Neunaber Audio Effects. Brian was initially slightly sceptical about the effect I claimed to have found and thought it might be an effect of the simulation or the frequency measurement method. This challenge pushed me to ensure that the method and results were sound. Once I’d convinced him that the effect was real, he wrote out the equations for what I’ve stated above and modelled them in Wolfram Alpha. I’ll reproduce his working below.
Firstly, we know that the total delay is related to the number of stages and the clock frequency:
total_delay = 1024 / (2 * clock_freq)
Note that clock_freq doesn’t have to be a constant. It could vary.
We also know that the change in pitch is related to the rate-of-change of the total delay:
change_in_pitch = d/dt (1024 / (2*clock_freq) )
Now, how about we make our clock have a base frequency of 40KHz, and modulate by +/-20KHz:
clock_freq = (40000 + 20000 * sin(2*pi*2*t) )
Put that into the pitch change equation:
change in pitch = d/dt (1024 / (2 * (40000 + 20000 * sin(2*pi*2*t) ) ) )
We can plot that in Wolfram Alpha. This shows us our by-now-familiar distorted curve. Brian wondered how much actual pitch change that represents, so he also plotted log2(1+x) in Wolfram Alpha to see how much shift in octaves that is. The maximum pitch change is around 0.2 octaves, or approximately 2.4 semitones. That’s quite a lot for a chorus, and another plot shows that if we reduce the modulation depth, the distortion also decreases. It seems reasonable to me to suspect that slower LFO rates also decrease the distortion, since it usually reduces the waveform’s rate of change (though not for a sharp square wave). On this basis, the effect won’t show up on slow, shallow chorus waveforms like I initially thought, but will definitely be present on deep, fast flangers. Perhaps this article should have been titled “Investigations into what a BBD Flanger unit *really* does” instead!
My thanks to Brian for the discussion and his thoughts on the matter.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662515501.4/warc/CC-MAIN-20220517031843-20220517061843-00280.warc.gz
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CC-MAIN-2022-21
| 10,751 | 42 |
https://ilivetruth.com/014-getting-the-love-you-want/
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math
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014 – Getting The Love You Want
- Posted on
Why do people typically end up with partners that mirror their overbearing parents? A theory called Imago Theory claims to have the answer, and the answer is to heal childhood trauma. I explain how it seems to be true in my life, and elaborate on the theory and the 10 week program outlined in the book.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710974.36/warc/CC-MAIN-20221204140455-20221204170455-00299.warc.gz
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CC-MAIN-2022-49
| 349 | 3 |
https://doc.cinderella.de/tiki-index.php?page=Geometry+and+CindyLab
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math
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Geometry and CindyLab
In a sense this section is not much more than a reminder for the user of Cinderella. One should always be aware of the fact that in CindyLab all masses are still geometric points and all that springs, bouncers and floors are lines and segments. Thus it is always possible to enhance CindyLab experiments by geometric constructions. These geometric constructions can sometimes be extremely helpful in order to analyze the exact meaning of an experiment. We will illustrate this by three small examples.
Example 1: Equilibrium Condition for Forces
If a physical situation is in an equilibrium situation then none of the masses is accelerated. This however implies that in such a case at any mass there are no forces present. This in turn implies that if there are several sources of forces affecting at a particle, the all these forces have to sum up to zero. The experiment below exemplifies this situation for a simple network of rubber bands and springs. There a triangle of (blue) springs is constructed. All vertices of the triangle are joined to a central particle by rubber bands. In the start situation the lengths and directions of the rubber bands may be arbitrary. However, if one lets the System come to an equilibrium situation (by starting the simulation and adding some friction) then the forces caused by the rubber bands at the inner vertex have to cancel out. If all rubber bands have identical spring constants, then this implies that the three segments representing the rubber bands can be shifted parallel to form a triangle (sum of forces equals zero).
This can simply be tested by a small auxiliary construction that concatenates parallel shifts of the three segments (left part of picture). In the start situation one observes that this chain of three arrows does not necessarily have to meet. The second picture shows the equilibrium situation in which the three edges automatically form a perfect triangle.
Sometimes very surprising and interesting relations occur on equilibrium configurations. For instance, the next picture shows the situation of three springs that are surrounded by six rubber bands. The rubber bands may have arbitrary spring constants. In the equilibrium situation the six vertices of the construction will automatically lie on a conic.
Example 2: Planet Movement
There is an amazing and not very well known geometric property of planet movement in a two-body system. As already mentioned, a planet orbiting around a sun will describe the trace of an ellipse. If we consider the velocity of the planet it is fast whenever the planet is close to the sun and slow whenever it is far away. It also changes its direction all the time during the movement. In Cinderella it is easy to explicitly study the path of the velocity vector. For this one first adds a Sun and a particle with Velocity. If one starts the simulation the particle will move along a Kepler ellipse. Then one adds a free point and defines a Translation from the planet to this point. Now one can easily translate the velocity vector to this and obtain a picture of the isolated behavior of the velocity vector.
Viewing the trace of the velocity vector one might conjecture that the trace is circular. It is easy to at least visually verify this conjecture by simply adding a free circle to the drawing and moving it while the animation is running to a position in which it matches the trace of the velocity vector. The picture below shows how nicely it matches up.
Example 3: Forces at the Golden Gate Bridge
The picture below shows an example that was already considered in the section on Gravity. Here a background image of the Golden Gate Bridge is loaded. With the use of CindyLab a physics simulation is constructed that models the distribution of forces in the cables of the bridge. Cinderella is used to straighten out the perspective of the photograph. This can be done by using a Projective Transformation that maps the situation in the physics simulation to the situation in the picture. Adjusting the gravity to the correct value shows that this situation exactly resembles the situation on the supporting cables of the bridge.
The content on this page is licensed under the terms of the License.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571989.67/warc/CC-MAIN-20220813232744-20220814022744-00737.warc.gz
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CC-MAIN-2022-33
| 4,241 | 12 |
https://ojs.ictp.it/jnms/index.php/jnms/article/view/549
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math
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SECOND REFINEMENT OF GENERALIZED JACOBI ITERATIVE METHOD FOR SOLVING LINEAR SYSTEM OF EQUATIONS
AbstractThe Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. In this paper, we present the new method which is called secondrefinement of generalized Jacobi (SRGJ) method for solving linear system of equations. This new method is the fastest method to converge to the exact solution as compared with Jacobi (J), refinement of Jacobi (RJ), generalized of Jacobi and refinement of generalized Jacobi (RGJ) method by considering strictly diagonally dominant (SDD), symmetric positive definite (SPD) and M-matrices. It is verified by checking the number of iterations and rate of convergence. The SRGJ method can be applied to solve ODE and PDE problems when finite difference method results system of linear equations with its coefficient matrices are strictly diagonally dominant (SDD) or symmetric positive definite matrices (SPD) or M-matrices.
F. N. Dafchahi.,A New Refinement of Jacobi Method for Solution of Linear System Equations AX=b, Int. J. Contemp. Maths. science, 3 (17) 819-827,2008.
B. N. Datta, Numerical Linear Algebra and Application, Society for Industrial and Applied Mathematics, USA, 1995.
W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations, Springer International publishing, Switzerland, 2016.
C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, Society for Industrial and Applied Mathematics,USA, 1995.
A. H. Laskar and S. Behera, A New Refinement of Generalized Gauss-Seidel Method for Solving System of Linear Equations, International Journal of Mathematics Archive-5, 5 (6), 104-108, 2014.
A. H. Laskar and S. Behera, Refinement of Iterative Methods for the Solution of System of Linear Equations Ax = b, IOSR Journal of Mathematics (IOSR-JM), 10, (3), ver.IV, pp 70-73, 2014.
G. Meurant, Computer Solution of Large Linear Systems, Elsevier Ltd, USA, 1999.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335059.43/warc/CC-MAIN-20220928020513-20220928050513-00744.warc.gz
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CC-MAIN-2022-40
| 1,981 | 9 |
https://planetmath.org/hermitianmatrix
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math
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The diagonal elements of a Hermitian matrix are real.
The complex conjugate of a Hermitian matrix is a Hermitian matrix.
If is a Hermitian matrix, and is a complex matrix of same order as , then is a Hermitian matrix.
A matrix is symmetric if and only if it is real and Hermitian.
Hermitian, or self-adjoint operators on a Hilbert space play a fundamental role in quantum theories as their eigenvalues are observable, or measurable; such Hermitian operators can be represented by Hermitian matrices.
- 1 H. Eves, Elementary Matrix Theory, Dover publications, 1980.
- 2 The MacTutor History of Mathematics archive, http://www-gap.dcs.st-and.ac.uk/ history/Mathematicians/Hermite.htmlCharles Hermite
|Date of creation||2013-03-22 12:12:00|
|Last modified on||2013-03-22 12:12:00|
|Last modified by||matte (1858)|
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038083007.51/warc/CC-MAIN-20210415035637-20210415065637-00043.warc.gz
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CC-MAIN-2021-17
| 810 | 10 |
https://www.retailmenot.com/coupons/calculator
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math
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Details: 54% Off Retail Texas Instruments TI-83 Plus Graphing Calculator
Saved $50.00 on calculator (09/17/2017)
Details: $45 Off Texas Instruments TI-83 Plus Graphing Calculator - Used
FYI these are used calculators
Details: Get 10% off TI 84 calcuator
Details: $35 Off Texas Instruments TI-84 Plus Graphing Calculator
This is a scam
USED....not a new calculator
Should say used.
This is USED
This is not a coupon, this is marking up the price by 30% and then listing as a sale of 35% off. NOT A GOOD DEAL.
Details: Get $85 Off Texas Instruments TI-89 Graphing Calculator.
Hi! This offer is alerting you to a sale. No code is required to take advantage of the savings. All prices will be as marked. Thank you!
Where can this be utilized.
Details: Get 10% Off any TI calculator
Didn't work. Apparently it doesn't exist.
it didnt help at all:(
Details: Get 10% off
Details: $30 Off Texas Instruments Ti-84 Silver Edition Graphing Calculator - Used
This is for a used calculator.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823605.33/warc/CC-MAIN-20171020010834-20171020030834-00151.warc.gz
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CC-MAIN-2017-43
| 977 | 20 |
http://www.sparkpeople.com/mypage.asp?id=BLONDE_FL_CHIK
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math
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Everyday is a blessing and a new beginning
Shared Food & Fitness Trackers
I have dieting in many different ways over the years. But today, the title of my Bible Study was "No Pain, No Gain". I have always looked for a short cut, but, the reality of it is I need to take the long cut. As I allow God to direct my heart on this journey and put good things into His temple/my body, mixed with some good sweat/excercise/housework, etc.. I think I can do it. I want my body to be the best it can be. I believe I need to loose about 40 - 50 pounds. My first goal is 35 pounds by the end of Feb 2010. God help me!
Eat healthier for my body and excercise daily, this will help me reach my goal weight by Feb 2010 which is 155. This is my initial goal weight and may be changed in Feb.
By Nov 30 I will have lost 7 - 10 pounds.
I am working out almost everyday for an hour. Mostly cardio. Zumba, Spin, Step, Eliptical Machine.
Secrets of Success
This user doesn't have any secrets of success.
| Pounds lost: 0.0
Thanks for the add! Sorry it took me so long to get back to you. Best of luck with your goals ~ feel free to stop by any time should you need anything.
2702 days ago
(¸.•´ (¸.•´ (¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.
¸.•♥´ .•´¨¨ ¸´¸.•´¨Welcome to the EE team!!
I’ve belonged to a lot of teams here on spark-- i really do believe that the Emotional Eaters team is one of the very best, it’s a great group of people- very supportive and encouraging-- and it is very refreshing to talk with people who "get" what you're going through!! ¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.*¸.•´¸.•*¨¸.•*¨¸.•´¸.•*¨) ¸.•*¨)
Check out the main page of the EE team- there are “stickied” topics you may be interested in to get involved- a buddy thread, a place to introduce yourself, weigh-in challenge, a birthday post. ¸.•*¨¸.•´¸.•*¨(¸.•´ (¸.•´ (¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥. ¸.•♥´ .•´¨¨ ¸´¸.•´¸.•*¨)¸¸.•´ ..•-~'¸.•*¨)
Spark has a lot of great tools, and you will learn which ones work best for you. The best tools are the people tho, always willing to lend a hand, an ear, or a shoulder. I’ve been here for over a year now, and I still am overwhelmed, every day, by the kindness and goodness of others on this team!! That has made a world of difference for me. I hope you have the same success! ¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.*.•*¨¸.•´¸.•*
(¸.•´ (¸.•´ ♥¸.•´¸¸.• (¸.•´ (¸.•*¨ (¸.¸.•*´¨`*• .¸♥.
You are- WONDERFUL-cuz you’re you!!! BELIEVE IT!!! operationbeautiful-- END THE FAT TALK!!! ¸.•*¨¸.•´¸.•*¨(¸.•´ (¸.•´(¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.
(¸.¸.•*´¨`*• .¸♥. ~~best of luck to you on all of your goals!!! (¸.¸.•*´¨`*• .¸♥.
2710 days ago
Welcome to the Emotional Eaters team.
2710 days ago
Thanks for adding me to your page. Sounds like you are a Zumba fan too. I love it so much I became an instructor. Stay motivated & you'll reach your goals. Good luck to you & I'm sure we'll be in touch.
3143 days ago
Hey! Welcome to the BLF's team! You'll love to have a challenge on a daily basis!
Good luck in your journey. And if you are in need of help and support, you know where to find me!
3157 days ago
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218187690.11/warc/CC-MAIN-20170322212947-00426-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 3,365 | 27 |
https://www.answers.com/Q/Why_are_your_questions_answered_on_WikiAnswers
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math
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Why are your questions answered on WikiAnswers?
Your questions are answered on WikiAnswers because this is a question and answer site, and we feel like if you asked a question, you probably wanted an answer.
Not all questions are answered. Here are some reasons: The question may be something that is very easily answered by using a dictionary, a calculator, or some other simple search engine tool - people get bored answering questions like that The question may be too vague for a good answer - "What were they like?" or "Where did she grow up?" cannot be answered because we don't know who "they" or "she" are The question… Read More
Questions that do not have enough information are questions on Wikianswers that are most likely not to get answered.
As of August 13, 2013, there are 19,591,633 questions that have been answered on WikiAnswers.
If your Questions have been answered than wikianswers will send you an email.
No questions are too scary to be answered!
The majority of questions on WikiAnswers are actually unanswered.
WikiAnswers does not necessarily provide answers to all questions submitted. WikiAnswers questions are answered mainly by contributors from the community, so the number of questions answered relies greatly on the users of WikiAnswers, and the amount that they are able and prepared to contribute.
over 20,000 questions were answered in 2009.
Wikianswers is not an automated service, it is Wikianswers' users that answer the questions. There's absolutely no guarantee a question will be answered fast or even at all.
Questions on WikiAnswers are answered by humans who come to the site.
No. The questions on WikiAnswers are answered by humans, visitors to the site.
You cannot demand answers from WikiAnswers on your questions. WikiAnswers does not answer your questions, it is the members of this community that answer your questions. You can request for your question to be answered but not demand for the same.
Yes and no. Questions on WikiAnswers are answered by members of the WikiAnswers Community. There are not people sitting in an office answering the questions asked. However, there are many professionals who answer questions on WikiAnswers. Many of the supervisors are professionals in the category they supervise. So you are very liekly to get a good professional answer to your question.
Since WikiAnswers is fueled by anonymous and registered contributors worldwide, there is a chance that your question may not get answered. There is a possibility that your question will not be answered by WikiAnswers for a number of reasons, anyway. However, there is also the possibility that all of your questions will get answered.
Yes, questions can be answered by anyone, whether you have an account or not. We encourage you to share your knowledge here on WikiAnswers!
Yes, WikiAnswers is a good place for questions (mostly that are not needed to be answered immediately).
WikiAnswers cannot answer many types of questions. Here are some questions that cannot be answered, and will be dropped from the site: Chatting - questions like "What are you doing?" and "What is the homework?" cannot be answered because this is not a chat room. Vague Questions - questions that are too vague, like "What is the meaning of life?" or "Why?" cannot be answered. Incomplete questions - sentence fragments, or partial questions, cannot be… Read More
unfortunately, all of the questions in the whole world cannot be answered. you can answer them yourself, if you know what the answer is to them, if you become a member of wikianswers. Many questions are also repeats of older answered questions, if you find these you should request a question merge.
Yes, there are tons of unanswered questions on WikiAnswers.
over three questions.
On WikiAnswers, yes, mathematical questions can also be answered. There is a whole category dedicated to math.
Thousands of questions are posted on WikiAnswers every day. As WikiAnswers relies mainly on volunteers to answer questions, it is not always possible for every question to be answered.
Not all questions submitted to WikiAnswers are answered. This is because answers on WikiAnswers are given by users on a completely volunteer basis. For information on how to increase your chances of getting your questions answered, check out the related questions below.
There are many thousands of unanswered questions, on hundreds of topics on WikiAnswers - fortunately this is no longer one of them !
Some common problems with WikiAnswers are that new questions take a long time to get answered, and answers are sometimes short and unhelpful. WikiAnswers tries to solve these problems by holding contests and Answerthons, but there are still many unanswered questions. Check out the related questions below for some tips on getting your questions answered on WikiAnswers.
What is the point of using WikiAnswers if your questions are never answered and there might be weirdos just waiting for people on here explain your answer?
There is a point to using WikiAnswers because questions do get answered. I know it might not always seem that way, but questions do get answered by other users that care. Do you need proof? You have this question. It just got answered. yeah but when you send questions to yhe community they don't get answered!
WikiAnswers is a Q&A wiki; it relies mainly on contributions from the community to answer questions. Therefore, questions submitted may not always be answered.
I hope so. I just answered your question in English. ;-) Yes, they can be answered here.
Because those questions have yet to be answered.
WikiAnswers is a large site and there are more than 16 million questions. Your question gets answered if a contributor notices it and answers it.
Click on the "Browse questions" link on the top of the page (in the middle). This allows you to see all the different categories on WikiAnswers, and the questions in each of them.
Just click on "Unanswered questions" in the green bar at the top.
WikiAnswers can answer all questions that abide by the TOS and Community Guidelines. Anything above a PG-13 standard, illegal etc cannot be answered and is subjected to being taken down.
Number of Questions Answered on WikiAnswers According to the latest available data, the WikiAnswers community answers about 15,000 questions per day. Other statistics In October 2010 the site received its 10 millionth answer. As of January 2011, there are more than 11 million answers.
How do you search all ready answered questions posted in WikiAnswers related to the field of computer science?
Follow the related link to the answered questions on Computer Science.
no, I answered this and I'm not part of it
you dont this an online site specically for questions to be answered not for relationships
You have just answered your own question - by posting this one !
Because you can ask Wikipedia questions and have them answered and WikiAnswers tells you anything but Wikipedia can be limiting.
no just click on answer thing (which was on the left side of the answer box and you can answer questions, on wikianswers if you have an wikianswer address you have it so people can see who answered or cahnged it
Yes, WikiAnswers is a website where you can ask questions and get answers to them. If you ask a question that has already been answered, you will be redirected to the answer. You can also answer questions on the website.
The questions are answered by REAL people - from all over the planet !
Any member can edit an answer.
YES! IT HELPS WITH ALL HARD AND BASIC QUESTIONS THAT NEED TO BE ANSWERED
What question did you want answers to. Try again.
There are a lot of questions to be answered and only so many contributors.
no , because there is always new question's to answer.
Anywhere from a couple of seconds, to never.
As a Supervisor, if you merge two answered questions on WikiAnswers, the answers will be placed one below the other on the merged question. Usually a minor edit needs to be done to remove any duplicated information.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000610.35/warc/CC-MAIN-20190627015143-20190627041143-00007.warc.gz
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CC-MAIN-2019-26
| 8,024 | 53 |
https://www3.labri.fr/public/groupes/infos_evt.php?id_agenda=14917&id=12238&cat=groupe_details&id_gp=131&rp_id=0
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math
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|Résumé||The Hydra game was introduced in 1982 by the mathematicians L. Kirby and J. Paris in their article: "Accessible Independence Results for Peano Arithmetic".
This article contains two theorems:
1. Whichever the strategy of Hercules and the Hydra, any battle eventually terminates with Hercules' victory.
2. The previous result cannot be proved in Peano Arithmetic.
We present a formal, self-contained (axiom-free) proof of a variant of both theorems, with the help of the Coq proof assistant.
Since Coq's logic is higher-order intuitionnistic logic, the reference to Peano Arithmetic is replaced with a study of a class of proofs of termination indexed by ordinal numbers less or equal than epsilon_0.
We present the main parts of this proof, as well as the main features of Coq that made its construction possible. |
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s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250601040.47/warc/CC-MAIN-20200120224950-20200121013950-00048.warc.gz
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CC-MAIN-2020-05
| 826 | 7 |
https://www.shaalaa.com/question-bank-solutions/terms-related-curved-mirrors-focus-principal-axis-centre-curvature-radius-curvature-explain-following-a-coin-placed-bottom-vessel-appears-be-raised-when-water-poured-vessel-b-straight-stick-partly-dipped-water-obliquely-appears-be-bent-surface-water-c-sun-seen-sunrise-after-sunset_30885
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math
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Explain the following :
A coin placed at the bottom of a vessel appears to be raised when water is poured in the vessel.
The coin at a appears to be at B i. e. depth of coin observed is less than the actual depth at A.
The ray of light starting from A (denser) medium bends away from the normal. Due to the Refraction of light, the coin appears at B at a lower depth. Hence, in the same way, the depth of water appears to be less deep.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401583556.73/warc/CC-MAIN-20200928010415-20200928040415-00772.warc.gz
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CC-MAIN-2020-40
| 435 | 4 |
https://mr-mathematics.com/solving-and-setting-up-equations/
|
math
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Students learn how to solve an equation using the balance method and trial and improvement. As learning progress they are taught how to form equations from known geometrical facts and real life problems.
Year 13 Further Mathematics: Statistics 1: Geometric and Negative Binomial Distributions
Scheme of Work: A-Level Applied Mathematics: Statistics 2: Conditional Probability
A-Level Applied Mathematics Scheme of Work: Normal Distribution
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571536.89/warc/CC-MAIN-20220811224716-20220812014716-00280.warc.gz
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CC-MAIN-2022-33
| 439 | 4 |
https://online.2iim.com/CAT-question-paper/CAT-2020-Question-Paper-Slot-2-Quant/quants-question-26.shtml
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math
|
The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. In CAT 2019 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank
Question 26 : How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?
_ _ _ _ on the 4 digit 7 has to come before 3
So, 4C2 possibilities for 7 coming before 3 into the spaces
7 ___ 3 ____, 2 numbers are already there and 2 remaining spots we have to fill in
From 8 digits available (Excluding 7 and 3)
So, 8C2 ways of choosing
After choosing two from 8, that two can be placed in any way
For example : 1 and 2 can be arranged as 12 and 21
So, 4C2 × 8C2 × 2
Now we need to subtract the possibility where 0 comes in the first position
0753, So these are in the form 0__ __ __
In this 3 places 7 before 3 can be placed in 3C2 ways and remaining 1 digit
Can be chosen from 7 (Excluding 0,3,7) digits.
3C2 × 7 = 21 numbers
Should subtract 21 from 4C2 × 8C2 × 2
= (6 × 28 × 2) – 21
The question is "How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?"
CAT® (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.
2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056476.66/warc/CC-MAIN-20210918123546-20210918153546-00713.warc.gz
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CC-MAIN-2021-39
| 1,846 | 23 |
https://community.ptc.com/t5/PTC-Mathcad/bd-p/PTCMathcad/page/7
|
math
|
Hello, In the attached sheet: For each load value for P, i 'd like to compute von Mises stress when ...
1 Reply 229 Views
Hello. I'm currently doing some basic unbalanced 3 phase load calculation with complex numbers. I de...
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Habe mir auf einem neuen Computer MathCAD Prime 6 heruntergeladen über Ihre Webseite, eine neue Liz...
Hello Everyone.From : How to plot a cup ? Thanks in advance for your time and help.Regards.
Does anyone know how to get Mathcad Prime 6 to return the Date and Time? (I know about the time(z) f...
3 Replies 276 Views
I bought PTC Mathcad Prime 6.0 Student Edition – One Year Term License and I am trying to download...
Bonjour, j'aurais besoin de mathcad 15. J'ai utilisé l'essai de 30 jours, maintenant j'aimerais sav...
I am trying to build circle Involvents. I built five involutes, and the sixth, the seventh, etc. the...
Lets say I have 55kg I want to get the equivalent in Stones. How can I set this up?
Can anyone look at this and tell me what I'm doing wrong?
ich habe bereits Mathcad Prime 4.0 Express auf meinem PC installiert. Nun habe ich eine Lizenz für ...
I have troubles in simplfying this equation normally in Mathcad15 it can be simplfied as following e...
I need to rant about how rubbish Prime is, so I am looking at the support renewals and its coming in...
I installed Mathcad and got to the Mathcad License Setup window, but when it tries to acquire a Math...
Is it possible to assign the subject of the matrix on top (as Mathcad 15, first picture) instead of ...
1 Reply 148 Views
What does this [9x1] matrix element imply, and how do I change it to numerical results? Thank you fo...
Hello Where can I find the documentation of examples of OLE Automation interface and expecially an e...
1 Reply 90 Views
I restored my computer and now I can't download Mathcad from your website. What can I do? I still ha...
I have a problem with matrix calculation, the answer of my assigned variable nkr do not want to disp...
Hello Everyone.From : To : How to eliminate 4 segments that are NOT a side of pentagonal prism ?Than...
Hi, i need this operator in mathcad (ll) ll Represents a logical OR operation that employs short-cir...
2 Replies 191 Views
Hello Everybody, I have a fairly complicated equation set to compute speed up factors vs divergence ...
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1 Reply 123 Views
I have two complex number variables. The results of the sum of the inverse of the two complex variab...
Continuing from Part 3B. Part 3C is the solved examples and solved problems for the RLC Higher Order...
Hello, I am currently doing my homework in Mathcad. I woould like to know if I can do more than one ...
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First time poster, casual user of MathCAD Prime 6.0, and have a question regarding setting up an equ...
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https://engineering.stackexchange.com/questions/7172/practical-examples-of-lti-transfer-function/7173
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math
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My question is pretty simple. The transfer function of an LTI system seems rather limited in use since the initial conditions must be zero. What are some practical engineering uses of it, and examples? I understand it's mathematical use, but fail to see where it's utility would really come in handy except in very simple mathematical models.
Why would a linear, time-invariant system require initial conditions to be zero? This is completely incorrect.
A linear, time-invariant system is any system that is linear (no state terms multiplying one another or themselves) and time-invariant, meaning that the coefficients don't change with respect to time.
A simple system would be an RLC circuit. Resistance in a circuit doesn't affect its capacitance or inductance, and the same is true for the other terms. The circuit is linear, and, provided you're not actively tuning the circuit (changing any of those values), the system is time-invariant.
An RLC circuit can be tuned by variable capacitors or variable inductors, and such a tunable circuit is commonly referred to as a "radio".
OR, you could have an RLC circuit that features a voltage proportional to, say, a shaft spinning. If you called the voltage "back EMF", then this RLC circuit is referred to as a "motor".
The motor circuit is probably one of the most-used LTI systems, at least for instruction. You can do all kinds of control theory with motors (see also: robots), but heat transfer, fluid dynamics... a lot of systems can be adequately represented by LTI systems. Those systems that don't exactly meet the LTI criteria can typically be linearized and used as an LTI system. See also: Inverted pendulum control, a.k.a. the Segway or Hoverboard.
Imagine hitting a pendulum by a hammer with same force and same direction. The pendulum's response will be always same, yesterday, today, tommorow, and 1 year after. It means, between your impact force by hammer and pendulum's respone, there will be an unchanged relation independent on time. Here, you can model this system as LTI system. Hammer impact and pendulum's response will be system input and output, respectively. And, the relation between input and output will be a transfer function.
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CC-MAIN-2021-49
| 2,209 | 8 |
https://www.briarcliff.edu/academics/departments/mathematics/mathematics/
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math
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Degree Type: Bachelor of Science, Bachelor of Arts
Program(s) Offered: Major, Minor, Teaching Endorsement
Do you have a knack for solving problems, finding patterns and figuring out how things work? If so, majoring in mathematics might be for you!
In today’s world, mathematicians are in high demand, which equals a job for you — and not the boring desk job most people imagine! Today’s mathematicians are making and breaking secret codes for the military, designing the world’s most efficient bridges and skyscrapers, and advising non-profit organizations to be more sustainable.
Choose one of two mathematics tracks, and we’ll help make sure your degree is tailor-made to fit your career goals:
Math classes are small in size at Briar Cliff, so your professors will you know you by name — not a number (you have enough numbers to worry about!). You might even have the chance to help a faculty member with research, with the latest in computing technology at your fingertips.
An introduction to problem solving and structured programming using C# and XNA. Students will learn the basic concepts of programming by designing game programs for the Xbox. Topics covered include basic data types, control structures and subprograms. Students will learn how to design, code, debug, document, and execute programs using techniques of good programming style. Lab included. Read more »
A continuation of CSCI 201 with C# and XNA. Topics to be covered include arrays, structures, strings, files, classes, and objects. Students will be expected to write and run a number of larger programs. Lab included. Read more »
A study of database concepts and database management systems. Topics covered include database design, relational models, normalization and queries. Hands-on experience with database management system is provided. Read more »
Functions, mathematical models, limits, continuity, slope and instantaneous velocity, derivatives, techniques of differentiation, related rates, linearization, exponential and logarithmic models, indeterminate forms, graphical analysis, optimization problems, antiderivatives, definite integrals, Fundamental Theorem of Calculus Prerequisite: Recommendation of the department chairperson based on mathematics assessment Read more »
Techniques of integration, applications of definite integrals, numerical integration, improper integrals, differential equations, infinite series, convergence tests, power series, Taylor polynomials, parametric curves, polar curves, vectors, dot and cross products, lines and planes in space. Prerequisite: MATH 217 Read more »
Vector-valued functions, curvilinear motion, functions of several variables, partial derivatives, linear approximations, directional derivatives and gradients, optimization, multiple integrals and applications, vector fields, line integrals. Prerequisite: MATH 218 Read more »
Set theory, sequences, counting principles, probability, matrix algebra, relations, functions, algorithms, ordering and binary operations, Boolean algebras, graphs and trees. Prerequisite: MATH 111 or recommendation of the department chairperson based on mathematics assessment Read more »
Topics include probability, principles of statistical inference, inferences on a single population, and inferences on two populations. Emphasis is placed on the understanding of basic concepts and the solutions of problems using computer output from realistic data similar to that occurring in common applications. Prerequisite: MATH 111 or consent of instructor Read more »
Topics include analysis of variance, various types of regression, and other statistical techniques including t-tests and design of experiments. Emphasis is placed on the understanding of basic concepts and the solutions of problems using computer output from realistic data similar to that occurring in common applications. Prerequisite: MATH 324 Read more »
Systems of linear equations, matrix algebra, determinants, vector spaces, subspaces, basis and dimension, eigenvalues and eigenvectors, linear transformations and applications. Prerequisite: MATH 218 Read more »
Topics include probability, calculation of moments (mean and variance), calculation of moment generating functions, principles of statistical inference, distributions of random variables, and the derivation of tests of statistical hypotheses. Emphasis is placed on the understanding of basic concepts, maximum likelihood estimators, minimum variance estimators, sufficient statistics, the derivation of best tests, and the solutions of problems using computer output from realistic data similar to that occurring in common applications. Prerequisite: MATH 218 Read more »
Intensive study of an advanced topic in mathematics. Open to junior and senior mathematics majors. Prerequisite: consent of instructor Read more »
An introductory physics course for students who know calculus. Topics include vectors, motion, A force, energy, momentum, mechanical waves and fluids. Highly recommended for all secondary science teachers, mathematics majors, chemistry majors, pre-engineers and science students who plan graduate study. Three lectures, one lab. Prerequisite: MATH 218 Read more »
Newspaper headlines and bestseller titles continue to emphasize the importance in business of effective communication. Read more »
All incoming students will take a mathematical skills assessment to determine where in the curriculum you will start.
First-year students intending to major in mathematics should have successfully completed four years of high school mathematics including some trigonometry. If you're uncertain about your preparation, contact the department of mathematics.
For additional requirements and curriculum information, download the latest University academic catalog.
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| 5,807 | 23 |
https://www.zeromillion.com/business/business-loan-calculators/
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math
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The reading level for this article is All Levels
If you have ever gotten a mortgage, you have probably wondered just how exactly the monthly payment is determined, and what the formula is for it. It is a common misconception among those new to financing that the formula for deriving these calculations is a simple matter of identifying a percentage of the loan, and charging it, in addition to the monthly fraction of the principal, to the borrower. While this is the most intuitive way of understanding amortization, it is thankfully incorrect, as we would all be paying quite a lot more than we actually do if it were true!
The actual formula, which will look a bit more confusing, looks something like this. In this equation, P is the principal amount borrowed, A the periodic investment, and n is the total number of monthly payments (in the case of a conventional 30 year mortgage, this would be 360), and r is the interest rate. A more detailed explanation of the detail of the formula can be found here.
The reason for the complexity is a matter of banking profit; because it is more likely that a loan will be paid off in full sooner rather than later, it makes logical sense to prioritize high amounts of interest at the start of the loan term. This allows banks to maximize profit while being able to loan at highly competitive interest rates; the amortization equation is simply the equilibrium point of many centuries’ worth of competitive lending, so as to maximize benefit to the customers and the bank.
However, it does nonetheless provide a bit of confusion to those who are trying to figure it out intuitively, so to them I would recommend, simply make use of business loan calculators. It’s a lot easier, and you will be a lot happier that way.
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http://thegophysics.com/the-beginning-of-physics-newtons-work/?utm_source=rss&utm_medium=rss&utm_campaign=the-beginning-of-physics-newtons-work
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math
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In this article we will once again dive in the work of Sir Isaac Newton. I already wrote an article about this one (The Beginning of Physics: Newton) but, he does deserve something more. This time we’ll explore his work in more detail than his life.
This is the eleventh article in the Beginning of Physics series. If you didn’t read the previous part you should definitely do so, specially because Newton’s life is in there:
So where do we start? Good question, and the answer is optics (because I want so)
Newton on Optics
In 1666 Newton discovered some important stuff about light. Like its nature and composition, you know, basic stuff.
This year, as previously said in the last article, was his miraculus year, where he wrote his theory of light and colors.
He observed that when light passes through a prism, different colors are refracted in different angles. This lead Newton to the conclusion that color is a property intrinsic to light itself. This might not seem such a huge deal today (because it’s obvious), but back then this was a serious debate, and Newton ended it!
He also showed that colored-light doesn’t change its properties. At all. Try it yourself: You may reflect it, scatter it or even transmit it. The light remains the same color. From this Newton came to the brilliant conclusion that color is a result of objects interacting with already-colored-light, rather than being generated by the object themselves. And this is true!!
It should be pretty obvious be now that Newton believed that light was a particle. In fact, people who later believed light was a particle showed Newton’s theories as a proof. This caused a lot of debate on Newton’s theories (like Robert Hooke) but also caused Newton’s entrance on the Royal Academy in 1672.
Newton on Math
Newton’s work has been said to “distinctly advance every branch of mathematics then studied“. His most known work is calculus. Yes, the stuff which is being way too hard for you to learn.
Newton wrote some brief stuff on calculus in 1666 and later worked it hard while on planetary motion (more on that later). He used integrals and derivatives to calculate the motion of planets (because these can be described by the change in velocity, acceleration and other properties).
But now comes the big Revelation: Newton wasn’t the first one to use calculus. I know right, didn’t expect this one… Newton’s Rival was Gotfried Wilbelm Leibniz, born in Leipzig, former Holy Roman Empire, in 1646. He, kind of like Newton, worked basically in every branch of science. Inventor of the two wheeled mechanical calculator, the binary notation (later used on computers) and a major figure in philosophy, Leibniz was quite a badass as well.
Gotfried worked out elements of calculus as far back as 1675, a decade before Newton’s Principia. In this year, Leibniz did what no human being had ever done before: he calculated the area under the graph of a function using integrals! You might not think this is something amazingly awesome, but it really is.
While in is work on calculus, Leibniz made up the symbols of differentials (δ) and the integral symbol, summa (∫). We still use this symbols, because we use Leibniz system of calculus, not Newton’s! You also didn’t know this one, did you?
So, why is this dispute still a thing really? Because Leibniz would only publish his full version in 1693 in the “Fundamental Theorem of Calculus”. For the rest of Leibniz life, he would fight to prove that he invented calculus first and independently of Newton. Only on more recent years can we give the credits he deserved.
Now, we may all love a good fight such as this one but, we’re forgetting the most important thing: two persons independently came to calculus! What other proof do you need to believe math is the language of the universe?
Now, back to Newton.
Newton on Gravity
As already wrote in the last article (), Newton was talking to Edmund Halley when asked “Why do planets move in ellipsis?”. Newton thought for a second and said “Hold my bear please” and 18 months later came back with the answer: Universal Theory of Gravity.
In his work Newton stated his three laws of motion, laying down the foundation for classical mechanics. He also came to the conclusion of some really important stuff. He would provide another proof for heliocentrism, showing that according to his theory, the sun must be the center of the Solar System. However, Newton would also realize the Sun cannot be center of the Solar System. What I mean by this is that Newton believed no body could be at rest, and so a “center” of anything. Newton rather thought it as “the common center of gravity of the Earth, the Sun and all the planets is to be the esteemed the center of the World” (which is very close to the Sun).
Now finally, let’s get technical!
Newton’s first Law of Motion – Inertia
In states that “an object in motion will remain in motion, and an object at rest will remain at rest, unless acted upon by a force“. This basically means that you need a force to take an object out of its initial state (at rest for example). How hard it is to move the object depends on the object’s inertia. You can measure inertia via the objects mass. The more mass an object has, the harder it is to move!
This is better explained in the second law of motion.
Newton’s second Law of Motion
It states that “net force is equal to mass time acceleration” or as an equation:
Where F is the net force applied, m is the mass of the body, and a is the body’s acceleration. Thus, a net force applied to a body produces acceleration. In the same way, when a object is accelerating it means a force is being applied to it.
Probably the most common and intuitive case of a net force producing acceleration is the gravitational force. Imagine you through a 2 kilogram coconut (because, who doesn’t like coconuts?) straight up in the air. After a second or two, the coconut will start falling due to the gravitational force with an acceleration of about 9.81 m/s^2 (if there is no wind and of course we neglect air resistance).
So, if gravity is the only force acting on the coconut, we can calculate the force of gravity by using F=ma. So the formula will became
Where Fg is now the gravitational force and g the rate of acceleration, 9.81 m/s^2. Now we can calculate the force of gravity:
Fg=mg = 2kg (9.81 m/s^2) = 19.62 kg(m)/s^2 = 19.62 N
And this is how you determine the force of gravity, or the weight of something. Now, those units are a bit too much, so we just call it Newtons (N, as you saw above) in honor of Sir Isaac Newton.
Now, usually gravity isn’t the only force on action, so we must take into account other forces. This’s where we get to a force that tends to show up a lot, which is explained by Newton’s third Law.
Newton’s third Law of Motion
“For every action, there is an equal but opposite reaction“. You should know this one from about ten thousand memes right? But there is more to this law than just that.
We call this reaction force the normal force (N), because it’s perpendicular to whatever surface your object is resting on.
This reaction force is different from other forces (like gravity) however. It’s kind of special. The thing is, the magnitude of the reaction force changes.
Imagine a box on the ground. The box has a weight of 10 N, so it pushes on the ground with a force of 10 N. Now, why doesn’t the box fall through the ground? Because of the reaction force, which pushes back on the box with a equal force (10 N).
If the weight of this box was 20 N, the ground would push back with the same magnitude. This will happen on and on, until the ground can’t counteract anymore and it breaks.
I hope you have liked this article. If you did (or if you didn’t) please comment on your thoughts about it!
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| 7,877 | 41 |
http://www.mathisfunforum.com/viewtopic.php?pid=281552
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math
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You are not logged in.
problem was to prove that ∑(n=0 to n=∞) t^2n ∫(-1 to 1)P^2(n)(x)dx=∫(-1 to 1) (dx ÷(1-2xt+t²)) = (1÷t)(log(1+t) ÷log(1-t))
Re: rodrigues formula
First of all what is P^2(n)(x)? The Legendre polynomials? Did I interpret your problem correctly in my latex?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
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| 512 | 7 |
https://jain108academy.com/the-9-planets-the-navagraha/
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math
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The 9 PLANETS: The NAVAGRAHA:
Magic Squares Of The 9 Planets. Code 9-9-9 Revealed
Here is yet another amazing but quite unusual numerical Revelation Code-Breaking Series based upon the ancient attributes of the Hindu 9 Planets and how they relate to specific Numbers.
Often in my research I make the general claim that Everything In Mathematics has its roots or basis in the Number 3, the Trinity.
This Code 9-9-9 revealed here clearly shows that this whole investigation was based on 3: The Magic Square of 3×3 that was written in 9 various ways, depicts the dance of the 9 planets.
We start with 3, then 3×3 which is 9 numbers contained within the Square, then with the 9 variations we see that there are 9×9 = 81 or 3x3x3x3 or 3^4 numbers contained with the astronomical matrix. And finally, the revelation, that the total sum of all 81 numbers is 9x9x9 or 9 Cubed or 3^6.
We have, in effect, climbed the dimensional ladder, from 9 to 9×9 to 9x9x9.
My question would be, did the ancient Vedic rishis, the Learned Ones who composed this galaxy of numbers, knew it was 9 cubed? Was it by design or chance. Either way, there is more to be revealed.
Cubic also suggests the underpinning Crystalline Matrix of the Creation.
nb: The sum of each row, column and diagonal, called the Magic Square Constant, for each Magic Square or Planet starts with 15 and keeps increasing by increments of 3. But we are interested in the TOTAL SUM OF ALL 81 DIGITS:
which is seen to start from 45 and increases by increments of 9 giving:
= 45 + 54 + 63 + 72 + 81 + 90 + 99 + 108 + 117 = 729 = 9x9x9 = 9 Cubed or 3 to the Power of 6, that is: 3^6.Essentially, this Journey of the 9 Planets, the NavaGraha, from ancient scriptures is a tribute to the Multi-Dimensionality of 9.9 Is the secret code, that reveals the secret geometry and symmetry of the astronomical and numerological world.
Learn Sacred Geometry Online Course
Explore the Fundamentals of Sacred Geometry and the Story Of Creation. If you are interested to Study Sacred Geometry Online, this is the perfect place to start!
HAVE YOU EVER WONDERED HOW WE EVOLVED FROM THE SEED OF LIFE TO THE FLOWER OF LIFE?
Let me take you on a Journey from the Moment of Conception, evolving to the Seed Of Life, to the Flower Of Life. This is the Story of Your Creation, from Biology to Technology, from the Micro to the Macro, from the original Zygote to the formation of Stars.
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CC-MAIN-2023-50
| 2,411 | 16 |
http://mathhelpforum.com/algebra/150602-percentages-word-problem.html
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math
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In a department store 70% of men's clothing sales are catalogue sales and the rest are in store sales. 605% of womens clothing sales are catalogue sales. The men's clothing department accounts for 20% of total sales and the women's is double this. The remaining portion is generated collectively by the other departments of which catalogue and in store sales are equally split.
what percentage of women's clothing sales are in store?
Is it 100%-60%=40% or is this a conditional probability question?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189771.94/warc/CC-MAIN-20170322212949-00455-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 499 | 3 |
https://clickanswer.us/question/what-is-the-sum-of-the-infinite-geometric-series-3-3-2-3-4-3-8-3-16/
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math
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Locating the key to answer at this time is easy. clickanswer.us provides accurate service for answering questions. we provide a concise answer key and complete with the discussion. we provide a variety of answer keys that span from elementary, junior high and upper level schools. The subjects we offer include biology, math, physics, economics, history and many more. below are the questions and answers that we have compiled from numerous sources available online.
What is the sum of the infinite geometric series? -3-3/2-3/4-3/8-3/16
Step-by-step explanation: Given geometric series is-
Here, the first term of the series,
and the common ratio,
Since it is an infinite series, so sum is given by
Thus, the sum of the series is -6.
Use the answer key above to help you study at home or at school. thank you for visiting, hopefully it will be useful for all of us.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494986.94/warc/CC-MAIN-20230127132641-20230127162641-00596.warc.gz
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CC-MAIN-2023-06
| 865 | 8 |
https://acikerisim.iku.edu.tr/handle/11413/1998
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math
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Non-polynomial Spline Method for the Solution of Non-linear Burgers' Equation
MetadataShow full item record
A non-polynomial cubic spline method is proposed in this paper to solve one-dimensional non-linear Burgers' equation [Burger, A Mathematical Model Illustrating the Theory of Turbulence (1948); Rashidinia and Mohammadi, Int. J. Comp. Math. 85, 843-850 (2008)]. An example is solved to assess the accuracy of the method. The numerical results obtained by this way are compared with the exact solution to show the efficiency of the method.
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CC-MAIN-2022-40
| 544 | 3 |
https://www.develup.in/courses/banking
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math
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Days of the week
Exclusively for Kannada students to get high-paying bank jobs!
Be a part of a professional community with people just like you
Solve test series created by IBPS experts.
Extensive Practise to gain exam confidence
• Numerical Ability
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• Reasoning ability and computer Aptitude
• Quantitative Aptitude
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• Pratice Papers
• Doubt Clearing and Q&A Sessions
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CC-MAIN-2023-40
| 510 | 15 |
https://studysoup.com/tsg/22934/probability-and-statistical-inference-9-edition-chapter-4-5-problem-7e
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math
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For a pair of gallinules, let X equal the weight in grams of the male and Y the weight in grams of the female.Assume that X and Y have a bivariate normal distribution with and ρ = −0.25. Find
Step 1 of 3
Chapter 2: Measurement 2.1 Significant Figures A. Accuracy and Precision 1) Accuracy: how close a measured value is to _____ the actual value__. 2) Precision: how close measured values are to _each other (average)_ B. Measured numbers • There will be some _uncertainty_ in where to round off a measured...
Textbook: Probability and Statistical Inference
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
The answer to “For a pair of gallinules, let X equal the weight in grams of the male and Y the weight in grams of the female.Assume that X and Y have a bivariate normal distribution with and ? = ?0.25. Find” is broken down into a number of easy to follow steps, and 39 words. This full solution covers the following key subjects: weight, grams, gallinules, distribution, equal. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Since the solution to 7E from 4.5 chapter was answered, more than 274 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 7E from chapter: 4.5 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271.
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| 1,546 | 6 |
http://teacher-21st.blogspot.com/2009/04/ti-89-graphing-calculators-they-can-do.html
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math
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Wednesday, April 1, 2009
The TI 89 Graphing Calculators: They can do anything!
I have taught Math for many years and have generally used the TI 84, TI-83 Graphing Calculators--pretty cool calculators that can do neat things like add imaginary numbers and output the results in reduced form etc.. But the TI-89 is like getting used to a whole new machine. When you first encounter it, you might not even know how to use it as the main screen's menu and interface is completely different. However, if you work your way through learning it, the 89 can really do some powerful things including algebra! This of course raises the issue of whether or not it is appropriate to use such powerful machines to take a test; many tests, in fact, do not allow the 89's to be used. So before you go out to buy a graphing calculator like the 89, you should first make sure that it a) can be used on any standardized tests that you take and b) isn't too fancy for your own tastes.
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| 964 | 3 |
https://www.computer.org/csdl/trans/tp/1996/04/i0377-abs.html
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math
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Issue No. 04 - April (1996 vol. 18)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.491619
<p><b>Abstract</b>—A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, two-way (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [<it>O</it>(<it>lm</it>), where <it>l</it> and <it>m</it> are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twenty-five thousand experiments conducted on 100 node random graphs of varying types (graphs with only zero-one links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have been reported by any other graph matching algorithm before in the research literature. Twenty-five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated.</p>
Graduated assignment, continuation method, graph matching, weighted graphs, attributed relational graphs, softassign, model matching, relaxation labeling.
A. Rangarajan and S. Gold, "A Graduated Assignment Algorithm for Graph Matching," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 18, no. , pp. 377-388, 1996.
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https://cafedoing.com/distance-and-displacement-worksheet/
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math
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Distance And Displacement Worksheet
Title distance and displacement worksheet author last modified by workstation created date pm other titles distance and displacement worksheet contains basic conceptual questions about distance, displacement, speed, and velocity.whats included in this and editable student worksheet and word digital version for use in google drive prepared This worksheet contains basic conceptual questions about distance, displacement, speed, and velocity.
whats included in this and editable student worksheet and word digital version for use in google drive prepared with google answer Distance miles miles miles displacement because the two legs of the journey point in opposite directions, we subtract.
List of Distance And Displacement Worksheet
The result points in the same direction as the larger leg. displacement miles miles mile north. runs exactly laps around a meter track. express your answer in meters.Oct, distance and displacement worksheet answer key. displacement vs distance guided notes page in text.
the displacement is how far out of place the object is the length of the line segment from a to b. the displacement and distance traveled do not have to be the same. measurement of the actual path traveled displacement.Displaying top worksheets found for distance displacement.
1. 148 Profile
To give a displacement we should give both the size and the direction. to find the size of the displacement, count the number of spaces from the initial to the final position. the following shows a displacement of m meters i is how far you are from the starting point, as if you moved in a straight line.
the displacement and distance traveled do not have to be the same. the runner travels m in the original direction north plus m in the opposite direction south, so the total distance she ran is m.Position, distance and displacement worksheet.physical science to position distance, and displacement lesson.
2. Projectile Motion Worksheets Word Problem Problems
3. Kinematics Ideas Physics Classroom Questions
4. Lab Show Kids Velocity Acceleration Object Incline Physical Science High School
5. Lesson Reviews Distance Displacement Series Interactive Stimulating Act Scientific Method Activities Web Activity Teaching Lessons Plans
Displacement addresses the issue of is the overall change in position. for example gabby starts at point a and walks to the left and arrives at point b.Distance is the total length of the path travelled by an object in motion.direction is the line an object moves along from a particular starting point, expressed in compass degrees north, east, south and west or up, down, left, right and even forwards or backwards.
6. Math Ideas Teaching
7. Motion Review Worksheet Distance Time Graphs Worksheets Physical Science Lessons
8. Motion Study Biology Concept Map
Walks to the pizza place for lunch. he walk km east, then km south and then half a lap around the sun, the earth has traveled a distance of half a circumference. s c r s. but its one diameter away from where it started, so its displacement is r.
9. Physical Science Ideas Middle School
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Oct, distance and displacement worksheet from distance vs displacement worksheet, image source homeschooldressage.com. gallery of distance vs displacement provides this information. distance is the length of the path between two points. displacement is the direction from the starting point and the length of a straight line from the starting point to the ending point.
11. Position Time Graph Graphing Physics Mathematics
Since these rely on our choices for the final velocity, multiple valid answers are possible. some of the worksheets displayed are slope from a graphing quadratic name answer key baseball bar graph name reading and interpreting graphs work motion graphs bar graph work line graphs.
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Love the moment at the end. a sense of surprise in math class is a rare and pretty wonderful thing.As the name suggests, graph it is a math worksheet that requires kids to draw a simple chart. giving kids just the basics to start off with, this graphs worksheet requires them to count the number of various objects and mark it correctly on the chart.
15. Sarn2000 Profile
16. Speed Calculations Ideas Middle School Science Grade Physical
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20. Work Energy Power Worksheet Beautiful Vocabulary Study Guide Teaching Physics
21. Worksheet Created Force Motion Unit Key Concepts Include Average Elementary School Science Activities
Your confidence in your estimate. in scientific measurements we say plus or minus but it means the same as give or take. we write that our measurement of the length, represented by l is m - if you are using a scale such as a ruler to measure the length of an object, then.
22. Worksheet Graphing Distance Displacement Running Wolf Time Graphs Interactive Science Notebook
23. Worksheet Graphing Distance Displacement Running Wolf Worksheets
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PdfTwo displacement vectors that have the same direction. b two displacement vectors with opposite directions are subtracted from each other. chapter measuring displacements combining displacements comparing distance and displacement objective after completing this activity, students will be able to distinguish between distance and.
26. Graphing Motion Worksheet Physics Interpreting Graphs Persuasive Writing Prompts
Velocity time graphs worksheet. split the graph up into distinct sections these can be seen in the image as a b c and d. videos worksheets a day and much more. velocity time graph answer key displaying top worksheets found for this concept.And so what i have constructed here is known as a position time graph, and from this, without an animation, you can immediately get an understanding of how the things position has changed over time.
27. 4 Speed Distance Time Problems Worksheet Math Worksheets Practice
The aka conium.org and scholars web hosting services have been retired as of,. if the site looking for does not appear in the list below, you may also be able to find the materials by.
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29. 7 Distance Time Graphs Ideas Graphing Worksheets
30. Average Velocity Defined Change Position Divided Time Travel Learn Graphing Linear Equations Distance Graphs
Position vs time graph part. shows you how to interpret a position vs. time graph for an object with constant velocity. the slope of the line is used to find the velocity.Graph graph time seconds vs. time time minutes vs explains how to read a position vs.
31. Belong Concept Builder Modeled Classic Game Graphing Linear Equations Interactive Science Notebook
Time graph. he then explains how to use the graph to determine the following quantities displacement, distance, av.The key to using graphs is knowing that the slope of a graph reveals information about the objects velocity. by detecting the slope, one can infer about an objects velocity.
32. Calculating Graphing Speed Distance Time Science Teaching Junkie Teachers Pay Graphs Worksheets Physics Lessons
Determining speed velocity name speed is a measure of how fast an object is moving or traveling. velocity is a measure of. answer in seconds, minutes and hours. the water in the buffalo river flows at an average speed of. if you and a. a wave has a wavelength of meters is moving at a speed of ms.
what is its frequency. a wave has a frequency of and a wavelength of m. at what speed is this wave traveling. a wave has a wavelength of. meters and a frequency of. what is the waves speed. radio waves travel at a speed of,, ms.Carefully sequenced worksheet and calculate average answers about distance divided by the latest feature is free to, total distance the attached.
33. Calculating Speed Time Distance Graphing Motion Graphs
The distance time graphs below represent the Id language school subject science grade,, and age main content speed graphs distance vs time other contents add to my workbooks download file embed in my website or blog add to google answer when there is a positive slope on the graph, the acceleration of.
the ball increases. when there is a negative slope on the graph, the acceleration of the ball. decreases. when there is a slope of zero on the graph, the ball is moving at a constant speed and it is. not speeding up or slowing down.youwillbegivenagraphofspeedvs.
34. Calculating Speed Word Problem Worksheets Writing Linear Equations
35. Circuit Training Particle Motion Calculus
36. Difference Distance Displacement Physics Lessons Teaching Ideas Notes
Net. distance and displacement worksheet from distance and displacement worksheet, sourceguillermotull.comDisplacement and distance displaying top worksheets found for this concept. some of the worksheets for this concept are and acceleration work, work distance displacement, motion distance and displacement, work position displacement and, work distance and displacement, work, describing motion verbally with distance and displacement Created date and displacement worksheet author last modified by, created date pm company company other titles distance and displacement posts of distance and displacement worksheet answer key circuits resistors and capacitors worksheet answers prior to speaking about circuits resistors and capacitors worksheet answers, you need to are aware that schooling is definitely each of our step to an improved the next day, and finding out just halt the moment the.
Some of the worksheets displayed are work distance displacement and acceleration work distance vs displacement describing motion verbally with distance and displacement work work distance and displacement work work distance and displacement. objects to the right of the zero have positive positions.
37. Displacement Velocity Acceleration Worksheet Worksheets Speed
38. Distance Displacement Physics Study Materials Directions
You can make each square on graph paper to. use up for north, down for south, left for west, and right for east. joey drives his car kilometres north. he stops for lunch and then drives kilometres south.Understand how to calculate distance and displacement for objects that move in one dimension and two dimensions.
vocabulary. displacement an objects overall change in position the unit is the meter m. distance a measure of how far an object has traveled the unit is the meter m.Title scanned document created date , distance displacement worksheets use this quiz and worksheet to assess your knowledge of distance and displacement and.
39. Distance Displacement Worksheet Answers Worksheets Reading Strategies Free Printable
Peter smith is the of the company. he has made a huge contribution in the field of education. he has been working on educating the students for the last ten years.Thanks for that we have some pictures of education science worksheet answers that you could download totally free, hall chemistry guided reading and study workbook answer key chapter chemistry assessment introduction to chemistry branches chapter While we talk about education math worksheet answers, below we can see various related photos to inform you more.
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40. Graphing Motion Position Time Graphs Science Creations Teachers Pay Solving Quadratic Equations Worksheets
41. Distance Displacement Worksheet Elegant Worksheets Teaching Methods Template
If the above statement is true, then describe an example of such motion. if the above statement is false, then explain why it is false. suppose you run three different paths from a to b. distance, position, and displacement aphychpp.indd pm tutorial calculating displacement for motion in a straight and displacement practice calculate the distance and displacement in each of the following situations.
include a direction example north or east with your answer. walks km north, and then turns south and walks km. distance km displacement km south. runs miles south, then turns around and runs miles north.Section. distance and displacement pages this section defines distance and displacement.
42. Distance Displacement Worksheet Inspirational Worksheets Favorite Shows
It presents methods of describing motion and introduces vector addition and subtraction. reading strategy page predicting write a definition for frame of reference in your own words in the left column of the table.Distance, displacement, speed and. velocity worksheet.
speed distance divided by time s. velocity displacement divided by time v. the symbol for velocity is the symbol for time is the symbol for displacement is the unit for velocity is. On the front of this worksheet, see a data table. this data table shows the time and the distance of the wolf.
43. Distance Displacement Worksheet Luxury Worksheets Template Answers
The speed calculated, however, is not calculated as average speed. the speed. describe how the wolfs distance and displacement would be exactly Distance vs. displacement worksheet., intro unit test , learning target i can calculate average speed. notes motion part drive to school activity average speed worksheet.
, learning targets. i can use a motion Our printable distance formula worksheets are a resource to equip grade and high school students with the essential practice tools to find the distance between two points.
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Interpreting graphics answer key chapter., , is media groups answer to, and fox. liquid water. chemistry chapter interpreting graphics answer key free download.Prentice hall chemistry chapter interpreting graphics answer key.rar download, interpreting graphics chemistry answers mar.
48. Distance Time Graph Worksheet Elegant Physics Graphs Worksheets
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Both and formats are available. you can choose the types of word problems in the worksheet, the number of problems, metric or customary units, the way time is expressed, fractional hours, or decimal hours, and the amount of workspace.Jan, label each part in the space provided.
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50. Domino Dash Activity Science Select Physics Speed Velocity Physical Middle School Education
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Some of the worksheets for this concept are motion distance and displacement, work distance and displacement, displacement vs distance learning objectives, distance and displacement work, scanned document, distance time speed practice problems, describing motion verbally with distance and displacement, topic kinematics.
Name site distance and displacement worksheet a section animation when the blue dot moves on the red line, what is that demonstrating what does the black line represent what does additional thing does displacement need that is not needed for distance section animation in this animation, what is the distance covered by the displacement is the distance between points.
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https://mynissanleaf.com/viewtopic.php?f=51&t=22460&p=502856
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math
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Good turnout and conversation at EV Breakfast yesterday, Aug 5. In addition to all the discussion about Model 3, there was quite a bit of interest in the Eclipse Mon Aug 21. Jason is going to OR, Sparky, Mark Z, and myself are going to ID. May we all have good clear weather, clouds not allowed.
At the previous breakfast, talking about the eclipse, some opinion was expressed that the Earth's axial rotation was the dominant factor in the speed that the Moon's shadow moves across the country. I was skeptical, so I put on my physicist's hat. My calculations are rough, taking some approximations to keep math simple and avoid 3D vectors which are hard to visualize:
R, lunar orbital radius = .238 10^6 miles
2 Pi R, orbital circumference, = 1.50 10^6 miles
We choose a reference frame centered on the Earth-Moon system, so we can ignore their common motion about the sun, which is almost 100 10^6 miles/hr relative to the Sun. One Lunar month, new Full Moon to next Full Moon, is called the Synodic Period.
T = (Lunar Synodic Period = 29.5 days) * (30 * 24 = 720 hrs/mo) = 708 hrs
Lunar contribution to shadow speed = 2 Pi R/T = 2,120 mi/hr.
Earth rotational speed at Equator = 24.5 10^3 miles/24 hrs = 1,037 mph.
If we look down on the system at Eclipse from above the North pole, we see the Sun, Moon and Earth all in a line, with both the Moon's orbital motion and the Earth's rotation counterclockwise. Note, at this time, the Earth's spin and Moon's motion are in the same approximate direction, so the Earth's spin reduces the speed at which the Moon's shadow moves across the surface. We apply some correction factors to both speeds:
Because the Earth is farther from the Sun than the Moon at a New Moon, the speed of the Lunar shadow is amplified by the ratio of their distances (in 10^6 miles):
(98 + .25)/98 but we can ignore this.
The local latitude determines how far one is away from the Earth's axis, and hence how much speed you have from the spin. It does not affect the Lunar speed. Latitude(Rexburg, ID) = 44 deg,
Cos(44 deg) = .72
Finally, there is the local time of day. If the sun is not directly overhead, the shadow will be elongated by its projection on the surface, an enlargement of 1/Cos(angle from zenith). The speed of the shadow along the surface will be affected by east-west tilt, but not north-south tilt.
In Idaho, Eclipse Totality is at 11:30 am MDT, 10:30 MST, 1.5 hrs before Noon.
Cos( 360 * (1.5/24) = 22 deg ) = .92
This factor reduces the spin speed while amplifying the lunar speed.
Putting these all together, we have:
Net speed of shadow measured along Earth's surface =
Moon's contribution - Earth spin contribution
= (2,120/Cos(22)) - (1,037 * Cos(44) * Cos(22)) =
2304 - 687 = 1620 mph
Again, this is only approximate, since the angles interact somewhat, but it gives the idea.
LEAF Ocean Blue SL, "100 % Electric" decals, Delivered June 3, 2011
Sold June 2014 27K miles, 18% capacity loss, 1 bar, 5.0 mi/kWh.
Solar 4.6 KW DC with both string and micro-inverters.
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| 3,011 | 26 |
https://www.911metallurgist.com/power-scale-up-agitating-slurries-laminar/
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math
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An interesting problem with which the senior author has been concerned with is the scale-up of power requirements for slurry agitators operating in the laminar region with pseudo-plastic materials. Pulps of shaly ores, after various chemical reactions in aqueous leaching systems, are often difficult to settle and filter if agitation is violent. In these cases agitation must be at a minimum, yet prevent tling such as in copper uranium ores. This mild agitation is on the laminar region.
The starting point of this investigation is the known relationships for agitating Newtonian fluids. The Reynolds number is a measure of similitude in agitation and is derived from the ratio of the internal reaction per unit volume of fluid (V²D) and a viscous force present per unit of volume (µV/D²).
For flow through pipes, this is:
RE = P V²/D/µ V/D² = D V P/µ
where: RE = Reynolds numbers
D = diam. of pipe
V = velocity
p = specific gravity
µ = viscosity
all in consistent units.
For agitation, velocity is the speed at the tip of the impeller. If N is agitator revolutions per second, then: π D N = V. Since π is a constant, the Reynolds number of agitation becomes:
RE = N D² p/µ
NP = P g/p N³D5
Where P = net power input, ft-lbs/sec
g = gravity constant, ft/sec²
f = specific gravity of fluid with respect to water
N = revolutions/sec.
D = diameter of impeller in feet.
Ore, slurries are non-Newtonian, and, for the most part, pseudo-plastic. This means that the apparent viscosity constantly varies as the rate of shearing (agitation) varies. The calculation of the Reynolds number is more difficult, because of the variable apparent viscosity.
We could not test the coal slurry in the same manner as the iron ore slurry because we could not clearly discern a settling line. We found a 50% by weight slurry of anthracite coal ground to 17% minus 150-mesh apparently settled quickly because viscosity readings increased rapidly for the.10 minutes tested. On the other hand, when testing a 5.0% slurry ;made up of coal ground to 55% minus 150-mesh, we obtained consistent readings for ten minutes. This indicates at worst, a slow settling rate.
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| 2,154 | 20 |
https://www.taylorfrancis.com/books/9781315221656/chapters/10.1201/9781315221656-5
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math
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Estimation for Nonlinear Systems
The optimal estimation problem for nonlinear systems is in general very complicated, and only in a few special cases do algorithms exist that are easy to implement or understand. This chapter focuses on the time and measurement updates for the entire hyper-state. It explores how to find update equations for the estimate and error covariance that are in general not computationally realizable. The chapter presents general equations for time and measurement updates of the hyperstate considering the discrete systems, and then continuous systems. Combining the time and measurement updates yields the desired recursion for the hyperstate. The chapter discusses the exact time and measurement updates for the mean and covariance of the nonlinear continuous system with discrete measurements. Higher-order approximations to the optimal nonlinear updates can also be derived by retaining higher-order terms in the Taylor series expansions.
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| 970 | 2 |
https://momath.org/home/varsity-math/varsity-math-week-83/
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math
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I made a big cooler full of lemonade, and then filled a two-quart pitcher from it. When my wife tasted it, she told me it was too strong. So I gave that first pitcher to the neighbors we don’t get along with so well, and topped the cooler off to its original volume with plain water and mixed it thoroughly. I filled up the pitcher again, and my wife tasted it, but she said it was still too strong. So I drank that pitcher myself, since I thought it was fine, and again topped off the cooler with plain water and mixed it thoroughly. Now my wife thought it was perfect. I wondered how I would adjust the recipe next time, until I suddenly realized that the lemonade was now diluted to exactly half its original strength as given to the neighbors.
What was the volume of the cooler, to the nearest ounce?
What is the smallest number of line segments you must use to draw 20 squares? (Note that some of the squares may share portions of their perimeters.)
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Solutions to week 82
Curious Clock. First, let’s figure out what hour it is. The weathervane is yellow, so it must be one, four, seven, or ten hours after midnight or noon, since the color goes on a three-hour cycle. And it is pointing due south, so it must be two, six, or ten hours after midnight or noon, since the direction goes on a four-hour cycle. There’s only one possibility in common, so we conclude that it is ten hours after midnight or noon — presumably 10 AM since Coach Taylor is in her office.
OK, so what about the number of minutes past the hour? From the positions of the three polygons, the number of minutes must be one more than a multiple of three, one less than a multiple of four, and one more than a multiple of five. The only way to be both one more than a multiple of three and one more than a multiple of five is to be one more than a multiple of fifteen. So the possibilities are 1, 16, 31, or 46 minutes past the hour. But since the number of minutes must also be one less than a multiple of four, the option that works is 31, so we conclude that it is 10:31 am.
Quadratic Triple. If we absorb the four into the second squared term, we get that (2x-1)² + (2x+6)² = (2x+7)². Inspecting this equation, we see that it expresses that there are three numbers so that the sum of the squares of the first two equals the square of the third. That means that the three quantities 2x-1, 2x+6, and 2x+7 are the sides of a right triangle, by the Pythagorean Theorem. In addition the longer leg is seven units longer than the shorter leg, and the hypotenuse is eight units longer than the shorter leg. But that’s exactly what happens in the Pythagorean triple of integers 5-12-13. Thus, the three sides must be 5, 12, and 13. Therefore, we conclude that 2x-1 = 5, or in other words, x = 3.
It was a colleague named Antonella Perucca at the University of Regensburg who inspired me to build the clock. And I learned how to solve three-term quadratics from Edward R. Forringer at Georgia Gwinnett College.
Links to all of the puzzles and solutions are on the Complete Varsity Math page.
Come back next week for answers and more puzzles.
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| 3,146 | 11 |
http://wpressutexas.net/coursewiki/index.php?title=Segment_1._Let%27s_Talk_about_Probability&oldid=3450
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math
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Segment 1. Let's Talk about Probability
Watch this segment
The direct YouTube link is http://youtu.be/H5WjVgL6Nh4
Bill's comments on this segment
Well, I do sound nervous! This was one of my first webcasts. The production values get a little better with later segments. However, the material here is important, so be sure you understand it before going on.
Here is a link to the paper by R.T. Cox, discussed on slide 2. It's surprisingly readable for something so fundamental.
1. Prove that .
2. What is the probability that the sum of two dice is odd with neither being a 4?
To Think About
1. First-order logic is a type of propositional calculus with propositions and quantifier symbols and . This allows statements like "Socrates is a philosopher", "Socrates is a man", "There exists a philosopher who is not a man", etc. Can you use first-order logic as a calculus of inference? Is it the same as using the probability axioms? If not, then which of Cox's suppositions is violated?
2. You are an oracle that, when asked, says "yes" with probability and "no" with probability . How do you do this using only a fair, two-sided coin? As we did in class. Represent P as a binary number. Whenever
3. For the trout/minnow problem, what if you want to know the probability that the Nth fish caught is a trout, for N=1,2,3,... What is an efficient way to set up this calculation? (Hint: If you ever learned the word "Markov", this might be a good time to remember it!)
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CC-MAIN-2020-29
| 1,463 | 12 |
https://www.learncram.com/physics/perpendicular-axis-theorem/
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math
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Perpendicular Axis Theorem Statement:
The moment of inertia of any two dimensional body about an axis perpendicular to its plane (Iz) is equal to the sum of moments of inertia of the body about two mutually perpendicular axes lying in its own plane and intersecting each other at a point, where the perpendicular axis passes through it.
We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.
Perpendicular Axis Theorem in Physics | Definition, Formula – Rotational Motion
Perpendicular axis Theorem Diagram:
Mathematically, IZ =IX + IY
IX and IY are the moments of inertia of plane lamina about the perpendicular axes X and Y, respectively which lie in the plane of lamina and intersect each other.
Theorem of parallel axes is applicable for any type of rigid body whether it is a two dimensional or three dimensional, while the theorem of perpendicular is applicable for laminar type or two dimensional bodies only.
In this portion, we will learn about the rotational motion of the objects. A body moves completely in rotational motion when each particle of the body moves in a circle about a single line. When a force is applied on a body about an axis it causes a rotational motion. The force applied here is called the torque. The axis of the rotation usually goes through the body. Also, learn the two theorems such as parallel axes and perpendicular theorem explained with respect to rotational motion of objects.
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CC-MAIN-2024-18
| 1,491 | 9 |
https://www.arxiv-vanity.com/papers/hep-ph/9708329/
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math
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Towards an Effective Particle-String Resolution
of the Cosmological Constant Problem
Raman Sundrum Department of Physics
Boston, MA 02215, USA
The Cosmological Constant Problem is re-examined from an effective field theory perspective. While the connection between gravity and particle physics has not been experimentally probed in the quantum regime, it is severely constrained by the successes of Standard Model quantum field theory at short distances, and classical General Relativity at large distances. At first sight, it appears that combining particle physics and gravity inevitably leads to an effective field theory below the weak scale which suffers from large radiative corrections to the cosmological constant. Consequently, this parameter must be very finely tuned to lie within the experimental bounds. An analog of just this type of predicament, and its resolution, are described in some detail using only familiar quantum field theory. The loop-hole abstracted from the analogy is the possibility of graviton “compositeness” at a scale less than eV, which cuts off the large contributions to the cosmological constant from standard model physics. Experimentally, this would show up as a dramatic breakdown of Newton’s Law in upcoming sub-centimeter tests of gravity. Currently, strings are the only known example of such compositeness. It is proposed that the gravitational sector comprises strings of very low tension, which couple to a stringy “halo” surrounding each point-like standard model particle.
A naturalness problem is like the sight of a needle standing upright on a table; it is consistent to assume a delicate balance, but one strongly suspects an invisible stabilizing force. The balance one must explain has the form of an extremely fine cancellation between large virtual contributions to an observable from physics at very different length scales. The grandest and most baffling of all the naturalness problems in fundamental physics is the Cosmological Constant Problem (CCP). It emerges upon putting together the two separately successful parts of our physical understanding: classical General Relativity and the quantum field theoretic Standard Model (SM). Ref. provides a good review. The problem is so tightly constrained that one can hope that its final resolution will reveal an essentially unique and qualitatively new stabilizing mechanism.
Here is an outline of the problem. The classical theory of general relativity that has been tested at long distances can be thought of as the result of integrating out short distance quantum fluctuations from both the SM and gravitational sectors. Einstein’s equations describing the leading long-distance behavior of the metric field, , are,
Here and are the curvature tensor and scalar respectively, is the classical energy-momentum tensor for the matter and radiation in the universe, Newton’s constant has been written in terms of the Planck mass, , and is the cosmological constant.111This definition of the cosmological constant differs by a factor of from the astrophysical convention, in order to give the units of energy-density. is very sensitive to the short distance physics which has been integrated out. The SM contributes its “vacuum energy”, very roughly given by,
where is the scale of electroweak symmetry breaking. The other contributions are from less well-understood sources, namely short-distance quantum gravity and particle physics beyond the standard model.222My language assumes that the standard model (possibly with the exclusion of the physical Higgs degree of freedom) is just an effective theory valid below roughly , and is superseded by some other theory at higher energies. However, as long as these exotic contributions do not unexpectedly finely cancel the SM contribution, we must have the following rough lower bound on the cosmological constant,
On the other hand, in solutions to eq. (1), contributes to the cosmological expansion rate. This permits a conservative bound to be put on by using the measured expansion rate of the universe and estimates of . With high confidence, the experimental bound is given by
Now, eqs. (3) and (4) are in wild disagreement. To lower the bound in eq. (3) sufficiently to accord with eq. (4) requires an unbelievably fine cancellation between the contributions to from quantum fluctuations below and above the weak scale. This is the CCP.
The attitude taken in this paper is that some part of the preceding story is simply wrong, and the true story must eliminate the need for fine-tuning in order to obtain an acceptably small value for . It is frequently believed that the true account cannot be understood by conventional means. According to this view, the resolution of the CCP may not be expressible in terms of the local quanta and interactions of a relativistic quantum theory. This is not the viewpoint of the present paper; the fundamental principles of relativity, quantum mechanics and locality are central to the understanding of the CCP, and the proposed resolution does not transcend them.
However, the CCP as described above is extremely robust, based only on the co-existence of gravity and mass scales of order (and supersymmetry-breaking of at least the same magnitude). The CCP then follows by elementary power-counting. Section 2 of this paper describes the CCP in greater detail using effective field theory methodology. Effective field theory provides a clear and economical separation of the facts and principles which we have already tested experimentally, from the physics which is still beyond our reach, both in the gravitational and particle physics sectors. It is a useful language for examining assumptions which we may need to discard, as well as for evaluating new proposals for solving the CCP.
In order to solve the CCP we must change the power-counting which determines how sensitive to SM mass scales the long-distance theory of eq. (1) is. In quantum field theory, whenever the physics of a large mass scale is integrated out, the sensitivity of the low-energy effective theory is determined by power-counting for the weakly-coupled degrees of freedom at that mass scale, not just the degrees of freedom at the lowest energies. To use this observation in the case of the CCP, we must ensure that at particle physics energies, the gravitational degrees of freedom are profoundly different from those in eq. (1). We can loosely speak of the graviton as a “composite” of these new degrees of freedom. How can this crucial new physics be right underfoot without our having noticed, and how exactly can compositeness help with the CCP? Section 3 provides a detailed analogy of the CCP where these questions, and others, can be understood in the context of a simple toy universe. This serves as a useful warm-up because the resolution of the toy naturalness problem is based on completely familiar physics.
Finally, in section 4, a possible new mechanism for stabilizing an acceptably small cosmological constant is put forward. Below the weak scale, it consists of a gravitational sector made of extremely low-tension strings, with string-scale less than eV, interacting with the stringy “halos” carried by SM particles. The low string tension cuts off the virtual contributions to so that it naturally satisfies eq. (4). At very large distances only the massless string mode, namely the graviton, is relevant, and the dynamics reduces to general relativity. In accelerator experiments, the macroscopic string halo carried by particles is unobserved because the stringy gravitational physics is too weakly coupled to compete with point-like SM interactions. The detailed structure of such an effective particle-string theory has not yet been worked out, but I discuss its necessary properties as well as possible directions towards its construction. If this scenario is correct there will be a striking experimental signature: Newton’s Law will completely break down when gravity is tested at sub-centimeter distances!
This proposal may appear heretical from the view of traditional field theory and string theory. However, recent developments in string theory offer some encouragement. There is evidence that strings can co-exist with objects of different dimensionality, D-branes, including -branes which are point-like states. For a review see ref. . There have already been several calculations of the scattering of D-branes with strings and with each other, which reveal a stringy halo about the D-branes . These results may be useful for constructing effective particle-string theories. Refs. are some initial forays in this direction.
However, I wish to point out an important difference between the goal of the present work and the goal of most of the string literature. The recent string theory upheaval is part of a very ambitious program aimed at a non-perturbative understanding of fundamental interactions at at the highest energies. On the other hand, the CCP is a puzzle whose answer lies at present-day energies, but is presumably hidden from view because of the weakness of the gravitational force. The purpose here is to develop an effective theory which has an ultraviolet cutoff given by the weak scale, and whose parameters can naturally be fit to experiment. The effective theory is permitted to break down above the weak scale, and be replaced by a more fundamental description there.
Sections 2, 3 and 4 may be read in any order depending on the background and interests of the reader. Section 5 provides the conclusions.
I make use of rough estimates in several places. It is customary when power-counting to keep track of factors of that arise from the dimensionality of space-time. In this paper, I will consider all such factors to be order one since the Cosmological Constant Problem involves such large numbers that, by comparsion, factors are unremarkable. When estimating Feynman diagrams, dimensional regularization is implicit for simplicity. This will not remove any important physics (for example it does not eliminate the CCP) because the important mass scales will be explict and will not need to be represented by a dimensionful cutoff.
2 The Problem in Context
2.1 The standard effective theory of particles and gravity
The most straightforward way to put together the SM and general relativity is to write the lagrangian
where appears in , minimally coupled to maintain general covariance.333To be more precise, for fermions we must work in terms of the vierbein, but this detail is inessential in this paper. In order to compute quantum mechanical fluctuations of the metric around a Minkowski space vacuum we note that,
where is the Minkowski metric, and is the canonically normalized spin- graviton field. For most regions of spacetime, this weak field expansion about a Minkowski metric is justified. The broad perspective of general relativity adopted in this paper, as a phenomenological theory of gravity, is detailed in refs. . It is based on the generally observed principles of relativity and quantum mechanical unitarity.
As is well-known, the inclusion of gravity renders the lagrangian non-renormalizeable by elementary power-counting. This means that the resultant theory cannot be a fundamental description of nature at all energies (at least perturbatively). However, the lagrangian is a sensible basis for a quantum theory effective at energies far below the Planck scale, . Recall how this works in a general non-renormalizeable theory. Technically a non-renormalizeable theory requires an infinite number of counterterms, which at first sight appears disasterous. The situation greatly improves if we restrict ourselves to physical processes at energies, , far below the (smallest) mass scale suppressing the non-renormalizeable interactions, . This allows us to work to any fixed order in the small parameter , say . To this order only the finite number of interactions and counterterms of dimension less than or equal to are relevant. While this statement is rather obvious at tree-level, non-trivially it survives loops and renormalization. For we thereby obtain a well-defined and predictive effective field theory. The effective theory must give way to a more fundamental description at some scale below , or perhaps be sensible but strongly-coupled above . The best known example of a non-renormalizeable effective field theory is the chiral lagrangian description of pions, treated as Nambu-Goldstone bosons of chiral symmetry breaking. For a review see ref. . The typical scale appearing in the non-renormalizeable interactions is the hadronic scale, GeV. The effective field theory is therefore sensible and weakly-coupled for GeV. For GeV, the effective theory fails completely and must be replaced by the more fundamental QCD description.
In the case at hand, the scale suppressing the non-renormalizeable interactions is . Therefore the theory given by eq. (5) makes sense at energies . In fact let us take the ultraviolet cutoff of our effective theory to be the weak scale, as denoted by the appearing on the left-hand side of eq. (5). This allows us to remain agnostic about the nature of physics beyond the weak scale. The ellipsis in eq. (5) can contain higher-dimension gauge and coordinate invariant interactions, whose effects are small at energies far below the weak scale.444More precisely, they are irrelevant in that their dominant effects can be absorbed into finite renormalizations of the lower dimension interactions.
As far as accelerator experiments are concerned, eq. (5), provides a very economical summary of what has been actually observed. They overwhelmingly confirm a relativistic quantum field theory given by the SM for energies below the weak scale, with gravitational forces being negligible. Thus the “laboratory tested” part of eqs. (5, 6) is given by the formal limit,
At macroscopic distances, with large amounts of matter and radiation, the SM forces are effectively neutralized and gravity dominates. Because of the large distances, masses and numbers of quanta, the classical approximation is justified. Conceptually, one arrives at a classical effective theory for this regime by integrating out all quantum fluctuations from eq. (5). The result must have the form of classical general relativity, eq. (1). This is because eq. (1) is the most general form consistent with the general covariance of our starting point, eq. (5), up to terms involving higher-dimension metric invariants which are irrelevant at macroscopic distances.
It is important to note that only the classical macroscopic effective theory, rather than the full effective quantum field theory of eq. (5), has been tested gravitationally. This is in contrast to the SM sector, where the full quantum field theoretic implications of eq. (5) have been tested. Therefore we must bear in mind that while eq. (5) is in accord with all gravitational tests since it reduces to eq. (1), the “bare” parameter allowing us to fit the experimental bound of eq. (4), eq. (5) may not be unique in this respect.
It is somewhat of a nuisance that eq. (1) combines two steps in its derivation, the integrating out of microscopic physics and the classical limit for large numbers of quanta. It is useful to separate the two issues by considering a long distance effective theory in a simplified setting, involving just a few SM particles, but treated fully quantum field theoretically. I will develop such an effective theory in the next subsection. It will provide a useful point of contact when we discuss the analogy in Section 3.
2.2 A macroscopic quantum effective lagrangian with gravity
Consider a few stable massive spin- particles, , with relative momenta only of order , interacting with soft gravitons with energies of order . The length scale, will act as our short-distance cutoff. We can take mm, which is less than the shortest range over which gravity has been tested. One can imagine to be a ground state hydrogen atom say, whose compositeness cannot be resolved by the long wavelength gravitons. Alternatively we can take to be just a proxy for more fundamental particles like an electron, neglecting the complications of spin and charge. For simplicity I will also neglect the other soft massless particles, photons and neutrinos. We therefore have an isolated sector which should be described by an effective lagrangian containing only the and fields. This type of theory is entirely analogous to the heavy particle effective theories used in studying the strong interactions, where soft pions interact with a massive hadron, or gluons interact with a heavy quark. This is reviewed in ref. . I will simply take over the methodology to the case at hand.
The first observation is that since , the -velocity of , , is approximately conserved in collisions with soft gravitons, to within . Thus the momenta have the form,
For the simple case considered here, is common to all the particles involved, since their relative momenta were assumed to be of order . We perform a field redefinition of the scalar field to remove the large fixed component of the momentum, ,
The field thereby has residual momentum , just like the gravitons. Because is a Minkowski space vector, not a generally covariant vector, it is important to note that the generally covariant derivative for is , rather than just for .
The general form of the -scale effective lagrangian in this sector is,
The effective lagrangian is manifestly generally coordinate invariant, a symmetry of the starting point, eq. (5). The ellipsis contains higher dimension operators constructed from and , including local self-interactions, whose effects are small at large distances (but can be systematically included). If , we can expand the quantum theory about a Minkowski vacuum, . In the frame of the particles, given by , eq. (10) then becomes,
describing non-relativistic particles coupled to gravity, predominantly through their gravitational “charge”, . After gauge-fixing the gravitational fields (see for example ref. ), we can integrate out -graviton exchange which dominates the interactions, to obtain a non-local Newtonian potential interaction between particles. If , the field theory must be expanded about an “expanding universe” metric rather than Minkowski space.
Since eq. (10) describes a quantum field theory, we may ask if can naturally be as small as eq. (4) under quantum corrections within this effective theory. The answer is yes! Conceptually, all the fields in eq. (10) have their momenta cut off at , because of the field redefinition, eq. (9). Thus although by power-counting we estimate that should get radiative corrections of order four powers of the cutoff, this is just , which for mm, is well within the experimental bound, eq. (4). In fact if we adopt dimensional regularization, the -loop corrections to vanish.
The effective field theory described above reproduces some familiar phenomena of classical general relativity, such as the Newtonian force between non-relativistic masses, and gravitational radiation. On the other hand the effective theory is fully quantum mechanical and unitary in its domain of validity, and predicts inherently quantum corrections to the classical approximation. (An example of such corrections is described in ref. .) Yet, it has a naturally small cosmological constant. For these reasons it is a useful conceptual link between microscopic physics and classical general relativity.
2.3 The Cosmological Constant Problem
The -scale effective theory given by eq. (10) and the classical effective theory of eq. (1) both share the same cosmological constant, . I will focus on eq. (10) since it is a straightforward quantum effective field theory, though analogous statements follow for classical general relativity, eq. (1). If we do not look beyond the effective theory of eq. (10), can naturally satisfy the experimental bound, eq. (4), as pointed out above. However, our present point of view is that is determined by matching the effective theory of eq. (10) with the more fundamental theory of eq. (5), or conceptually, by integrating out the physics below . If one fixes a particular regularization and renormalization scheme, say dimensional regularization with minimal subtraction, one can actually perform the matching computations. Here we only require the results of simple power-counting, which shows that is negligibly renormalized in matching at , while by contrast, is quartically sensitive to the mass scales of the SM, so that,
We have no way of understanding why the physics above the weak scale, which determines , should so precisely cancel against the SM contributions, in order for eq. (4) to hold.
Thus I conclude, although eq. (5) reduces to the SM at short distances, (eq. (7)), reproducing all accelerator experiments, and though it reduces to eqs. (1) and (10) at macroscopic distances, thereby accomodating all gravitational measurements, it is not the correct effective theory below the weak scale because it involves a fantastic and inexplicable fine-tuning of . We must therefore see what room we have for changing the weak scale theory without destroying its highly non-trivial theoretical consistency and agreement with experiment.
What seems highly significant to me is this. The cosmological constant is usefully thought of as a non-derivative graviton self-coupling (which de-stabilizes Minkowski spacetime). Quantum corrections to come from loops of massive SM states, coupled to external graviton lines at essentially zero momentum. Therefore necessarily, these massive SM states are far off-shell. On the other hand, experimentally we have only tested the gravitational couplings of SM states which are very nearly on-shell.555By contrast note that accelerator experiments have very successfully probed highly virtual, purely SM effects, in the form of running couplings and precision electroweak tests. For example, the particles of the previous subsection are very nearly on-shell in the domain of validity of the -scale effective theory. It follows that all the large quantum corrections to from the weak-scale theory of eq. (5) come from a tremendous theoretical extrapolation to the regime where gravitons couple to SM particles which are far off-shell. We can hold out some hope that the CCP can be avoided by a different weak scale effective theory, which however still reduces to eqs. (1) and (10) in the domain of on-shell SM matter coupled to soft gravitons.
2.4 Constraints on alternative weak-scale theories
In thinking about alternative effective theories, it is crucial to observe two powerful fundamental principles, at least as far as physics below the weak scale is concerned. First, to quite large distances, spacetime appears as a Minkowski continuum. It also appears to be true down to distances of order , since the highly successful SM loop computations depend sensitively on this assumption. Secondly, nature is quantum mechanical, at least up to weak scale energies. Furthermore, it is difficult to perturb the quantum principle withut leading to physical absurdities. Therefore it would appear that we cannot seriously doubt the principles of (local) special relativity and quantum mechanics in the gravitational sector below the weak scale. These two principles impose very severe constraints on model-building. Taken with the experimental success of general relativity at large distances they necessarily imply the existence of a massless spin-two particle, the graviton, which must underlie any effective theory of gravity. Furthermore, this effective theory must obey the gauge symmetry of general coordinate invariance . This is similar to the case of light spin-one particles, where a gauge symmetry is needed to decouple unphysical degrees of freedom, but in the case of spin-two the gauge symmetry is unique!666There have been suggestions that general coordinate invariance can be replaced by restricted invariance under coordinate transformations with unit Jacobian. However, both classically and quantum mechanically this is precisely equivalent to a generally invariant theory with an arbitrary (but not naturally small) cosmological constant. See ref. for a brief review, plus references.
Now, if we restrict ourselves to the minimal particle content, namely the SM particles and the graviton, the form of the effective theory is given by eq. (5), this being the most general invariant form that reduces to the SM when , and containing the kinetic term for the graviton field. But eq. (5) is just the effective theory we are trying to avoid. Thus we conclude that new particles associated with gravity must be present. They must be very light indeed in order to remain in the effective theory down to the very low energies necessary to protect the cosmological constant, as has recently been emphasized in ref. .
Unfortunately, all proposals to couple extra particles to eq. (5) have failed to cure the naturalness problem. Generic addition of extra light particles does not evade the simple power-counting which says that the cosmological constant is quartically sensitive to the highest mass scales in the theory. Supersymmetrizing eq. (5) does in fact stabilize a suitably small . However this requires supersymmetry to be unbroken in the SM sector to very high precision, in order to suitably reduce the contribution in eq. (12). Experimentally however, we know that supersymmetry is badly broken in this sector. Other than supersymmetry the only other special symmetry that can control the cosmological constant is conformal symmetry. This is also badly broken in nature, but there have been several attempts to make a dynamical field that relaxes to zero as a consequence of the conformal anomaly, similarly to the way an axion can relax the strong interactions to a CP-conserving vacuum in the presence of a angle, as a consequence of the axial anomaly. For the CCP all such attempts have failed for the general reason described in ref. . To summarize, while we can always weakly couple eq. (5) to new light particles, there is no reason for these to significantly reduce the SM loop contributions to .
The seemingly impossible predicament posed by the CCP has given rise to proposals which play by different rules from those we have adopted. They cannot be evaluated within any local effective theory and are difficult to test experimentally. It is possible that one of these proposals is nevertheless true. Perhaps the best-known is Coleman’s wormhole proposal . Here, wormhole physics, just below the Planck scale, gives rise to peculiar non-local effects (from the viewpoint of our macroscopic spacetime), whereby the fundamental “constants” of nature become dynamical variables, but without any local spacetime variations. The relevant path integral is infinitely peaked at values of these constants such that the bottom-line cosmological constant vanishes, .
The present paper describes a deliberately restricted search for a resolution of the CCP which can be described by a natural effective theory, expressed in terms of local degrees of freedom. This is the time-honored approach taken towards other naturalness problems such as the the Strong CP problem or the Higgs naturalness problem. However, the arguments of this section seem to suggest that we are at an impasse. There may be a way out though, as suggested by the following parable.
3 An Analogy
In this section I describe a naturalness problem, analogous to the CCP, which occurs within a toy model universe. This toy problem has the advantage of involving only the familiar quantum field theory of particles with spins less than or equal to one. Nevertheless, the resolution sheds light on how the CCP might be resolved. The model consists of two sectors, a toy “Standard Model” (TSM) accounting for short-distance “laboratory” physics, and a toy “gravity” (TG) only noticeable at very large distances.
The TSM is simply the quantum electrodynamics of eight identical flavors of charged fermions, , . I will cut off the electromagnetic interactions at larger than laboratory distances by giving the photon a very small mass.777Of course, in the real world the electromagnetic force is negligible on large distance scales because of the neutrality of massive gravitating objects, like planets and stars. The toy photon mass makes for a simpler story. Recall that for an abelian gauge field, a mass term is both renormalizable and naturally small (only receiving logarithmic quantum corrections). The renormalizeable and natural TSM theory is then given by
with . We will consider the TSM to have been tested at lab momenta, very roughly of order (where the photon mass is negligible), and to a precision given by . For example, our momentum resolution is of order , and we are insensitive to -loop QED effects for such that . Nevertheless I will consider to be small enough that eq. (13) has been non-trivially tested as a quantum field theory.
On the other hand, TG corresponds to the observation of a very weak classical scalar Yukawa force, , between non-relativistic particles888Unlike the real world, in the toy universe the photon does not “gravitate”. over very large distances and times,
Notice this implies that the exponential suppression is always turned on in the Yukawa force, but clearly it is still the dominant force at very large distances. The TG force is too weak to be observed at short distances in the lab, against the background of electromagnetism, but is seen outside the photon range. To be concrete let us take,
The mass scale is extremely small,
At the purely classical level this is acceptable, as is a very small or zero cosmological constant in classical general relativity.
The minimal relativistic quantum field theory incorporating both the TSM and TG necessarily associates a scalar field, , with the Yukawa force,
where the scalar coupling is included for renormalizability, though it is too small to observe and plays no further role. Eq. (17) is the analog of eq. (5). Like eq. (5), it suffers from a naturalness problem. Here, the problem is why the scalar mass, , is so small, despite much larger quantum corrections coming from TSM loops. Standard power-counting and eqs. (15, 16) give,
Physicists of the toy universe may note that a small scalar mass is stabilized by supersymmetry. But the fact that no superpartners have been observed for energies well above means that supersymmetry is badly broken, and eq. (18) still holds. This is closely analogous to the situation with the cosmological constant and supersymmetry in the real world.
Other than supersymmetry there is no mechanism by which a weakly coupled fundamental scalar can naturally avoid corrections like eq. (18). One might think that the spin- particle could be fundamental and light if it is a Nambu-Goldstone boson of a spontaneously broken symmetry, but this possibility can be ruled out as well. Even though fundamental Nambu-Goldstone bosons are naturally massless, their “decay constants” are naturally of order the highest scale in the theory, in the present case, . The fact that the spin- particle has non-derivative couplings to the ’s means that the spontaneously broken symmetry must also be explicitly broken. The same explicit breaking which gives rise to a Yukawa coupling, , naturally gives rise to a pseudo-Nambu-Goldstone boson mass-squared of order , which is incompatible with eq. (16).
The only remaining means of obtaining a naturally light spin- particle is to make it a composite, like a hadron, with a very low compositeness scale. Even this approach offers no comfort at first sight. The basic reason is that the self-energy estimate due to TSM loops, yielding eq. (18), is performed at essentially zero external momentum, and so is completely insensitive to whether is composite or fundamental. Thus in any model where has a low enough compositeness scale to naturally satisfy eq. (16), it will be impossible to arrange for a Yukawa coupling as large as in eq. (15). I will illustrate this with a specific example. Suppose we try to make a scalar glueball of a Yang-Mills sector, with a confinement scale , which sets the glueball mass. To obtain a Yukawa coupling to the ’s we can use a higher dimension interaction,
where is a dimensionless coupling, and tr is the Yang-Mills operator that interpolates the glueball, ,
Recall that a non-renormalizable interaction such as eq. (19) is acceptable within effective field theory. Taking the effective theory cutoff to be of order , the energy scale probed in the lab, the theory remains weakly coupled at the cutoff provided . (In fact we must have in order for the -gluon interactions to have not been directly seen in the lab.) Therefore we arrive at the unsatisfactory result,
in contradiction to eq. (15).
I hope to have convinced the reader that, like the CCP, this toy naturalness problem seems to leave no room for manoeuvre. However, this is a false impression.
Fortunately, compositeness does allow the resolution of the naturalness problem. In order to invalidate the reasoning behind the large quantum corrections to from the TSM, we must not only take to be a composite light hadron, but we must also consider the massive particles it interacts with in TG to be heavy hadrons containing the TSM particles as heavy quarks! The specific resolution I have in mind is given by,
where I have introduced an gauge theory, under which the and quarks are triplets, and the eight TSM fields form an adjoint representation. Only the ’s are electrically charged however.
The is a particular combination of the three QCD pions, , made out of and quarks, while the heavy fermion it interacts with hadronically in TG, , is a composite of the adjoint quark and glue. The light quark masses are needed to produce non-derivative Yukawa couplings of to , and to generate a small . The Yukawa coupling we need, , breaks isospin symmetry under which the pions form a triplet, whereas is a singlet. The requisite isospin breaking is arranged by taking . Another technicality is that QCD is normally a parity-conserving theory, so a single pseudo-scalar pion cannot couple to the scalar as required. I have therefore added an order one CP-violating -term.999In fact, even for , the Yukawa coupling is not generated at first order in because of a vacuum re-alignment induced by . However, the Yukawa coupling is generated at higher order in . The resulting Yukawa coupling is then of order a small power of , while
By taking , we can consistently choose so that and , as desired!
There are three issues we would like to understand better: (i) Why is the composite QCD structure not already observed in the long distance TG sector? (ii) Why is the composite structure not visible in the lab? (iii) How does the composite structure cure the mass of extreme sensitivity to the TSM mass scale, ? Some of the discussion will be similar to that of ref. , where a model with very small was also considered.
(i) The interactions of very low-energy pions with slow heavy hadrons can be described using a Heavy Hadron Effective Lagrangian (reviewed in ref. ),
Recall that is some linear combination of the fields depending on and . The ellipsis contains terms whose effects on are negligible at the very low momentum transfers, , corresponding to eq. (14). These include the higher dimension couplings (suppressed by powers of ) of to itself and to the , and all couplings involving fields other than . Eq. (24) is just the analog of eq. (11). Integrating out -exchange, which dominates the interactions at long distance, yields the simple Yukawa potential. The next lightest state above the that can be exchanged between ’s is a two-pion state. But in the regime of eq. (14), even the two-pion exchanges are exponentially suppressed relative to single- exchange.
As far as eq. (24) is concerned the scalar mass is naturally small because of the very low cutoff on the effective theory. Compositeness effects are invisible because the compositeness scale is too high compared with the (virtual) momenta corresponding to eq. (14). We see that the first-conjectured form of the TG field theory is wrong. does not interact with the quarks, but rather with the hadronic “brown muck” of the heavy hadron.
One might worry that there can be excited composites, which have different Yukawa couplings , but over the time scales of eq. (14) such states would decay to the lowest stable state. A minor technical dynamical assumption that must be made (but which fortunately has no analog in the real CCP) is that any exotic composites of and two or more light quarks are heavy enough to decay to via pion emission, so that their possibly different Yukawa couplings are not seen.
(ii) Typical lab momenta are of order , where the running QCD coupling is weak. In the limit where it vanishes, the TSM sector completely decouples from the QCD sector. We can work out the actual value of the coupling renormalized at the laboratory momentum resolution, , using the one-loop QCD -function and the fact that we have already chosen . The result is,
Therefore QCD-induced momentum transfers larger than have amplitudes suppressed by , so they are too small to be seen against TSM interactions. On the other hand, amplitudes where the QCD-induced momentum transfers are less than remain unsuppressed, corresponding to soft radiation of light hadrons and excitation of the resonances. But such momentum transfers are smaller than our momentum resolution. The QCD sector is therefore invisible in the lab! Note, it is only the particles which feel the electromagnetic force and determine the outcome of lab experiments.
In the absence of the electromagnetic interaction the ’s would also form heavy quarkonium bound states, but with electromagnetism the QCD interactions will only negligibly perturb the electromagnetically bound states.
(iii) We now see that the unnaturally large quantum corrections in eq. (18) arose because of loops, where the appears far off-shell, with a Yukawa coupling to . But this simple coupling is only valid in eq. (24), where the is nearly on-shell. The extrapolation off-shell is completely invalid since the compositeness scale is very low. The true quantum corrections to the mass from the TSM sector require knowledge of the full QCD dynamics. We will now correctly compute the sensitivity to . To make the question precise let us fix some ultraviolet cutoff, , relative to which we can measure masses. This could be the scale of some new physics beyond the toy standard model. We also fix and ask how changes as a function of . We already have the mass formula for pseudo-Nambu-Goldstone bosons, eq. (23). We can integrate out the effects of the very heavy (adjoint) quark because of the asymptotic freedom of QCD. The dominant behavior follows from the one-loop renormalization group. The infrared renormalized quark mass parameters that appear in eq. (23) are the result of running down from . To one-loop order however, this mass renormalization is independent of the heavy quark mass, . Only is changed at one loop because the heavy quark slows down the running of between and . A standard perturbative matching computation then leads to,
We see that is not unnaturally sensitive to . Doubling only leads to a doubling of , as compared to the extreme and unnatural sensitivity implied by the naive result, eq. (18). The quadratic sensitivity of scalar radiative corrections to the ultraviolet scale has been eliminated by having no scalar degree of freedom present at , only quarks and gluons. These constituents of the scalar are only logarithmically sensitive to .
To summarize, we were able to resolve the toy naturalness problem by giving the TG sector a very low compositeness scale and making the “gravitating” TSM particles into constituents of composite states. The toy composite “graviton” interacts with the compositeness “halo” that surrounds the TSM particles. At very low momenta this is indistinguishable from a direct coupling to the nearly on-shell TSM particles. If this is extrapolated to when the TSM particles are far off-shell, one runs into the naturalness problem. In reality though, the off-shell contributions are cut off by compositeness. The naive extrapolation misses this composite softness of the interactions in the TG dynamics. On the other hand the compositeness interactions are invisible in the lab, compared with the much stronger hard interactions of the TSM. The obvious regime to discover the compositeness dynamics is at intermediate distances, where TSM interactions are still neutralized but compositeness effects are unsuppressed in the TG dynamics.
4 The Effective Particle-String Scenario
The moral of the previous section is that the power-counting that points to the inevitability of the CCP only holds if the graviton is fundamental, not if it is “composite”. To exploit this observation we must ensure that there simply is no graviton at the energies at which we integrate out SM particles, en route to obtaining the long-distance theory of gravity. At these SM energies there should only be the degrees of freedom which will bind into the graviton at much lower energies. A second requirement is that the SM particles must couple to composite gravity, and yet their couplings to other SM particles must be point-like at least down to distances. Unlike the case of the scalar in the toy model though, the compositeness of the graviton cannot be accomplished within the ordinary Minkowski space quantum field theory of point particles. This is due to the following very general theorem : a theory in Minkowski space which admits a well-behaved, conserved energy-momentum tensor cannot have a graviton in its spectrum.
Fortunately, string theory evades this theorem and gives a sensible meaning to graviton compositeness. Though formulated in Minkowski space, its energy-momentum tensor is not “well-behaved” and there is a massless graviton in the spectrum, as discussed in ref. . In terms of the well-known similarity between string theory and QCD (which of course was important historically for the discovery of string theory ), the graviton can be thought of as a massless “glueball” of string theory. Now in QCD there are sum rules that can be derived in terms of the fundamental description which look miraculous or finely-tuned in terms of the hadronic description. They are not enforced by any symmetry but by the special nature of the dynamics. The same is true in string theory with respect to the cosmological constant.
For simplicity let us consider the case of the perturbative bosonic string in 26 dimensions . There are effectively two parameters, the string mass-scale, , which plays the role of the graviton compositeness scale, and the string coupling, . For , the string spectrum corresponds to an infinite number of “composite” particle-modes of varying spins and masses, including a graviton. The Planck scale is very large, . If we ignore the string principle, we can compute the -loop contributions to the cosmological constant from each of the particles. Each contribution is quartically sensitive to the particle mass, and there are an infinite number of such contributions. Clearly we must introduce an ultraviolet cutoff, which cuts off both the infinity of contributions and the infinity in each contribution. This still leaves many large contributions to the cosmological constant. If we want the renormalized cosmological constant to come out very small, we must also add a counterterm chosen very precisely to finely cancel the large -loop contributions. Of course, in string theory the sum of one-loop diagrams plus counterterm is not calculated in this piecemeal fashion, but rather at one stroke. The result is an ultraviolet finite cosmological constant, . Note, this is just the power-counting dependence on an ultraviolet cutoff, , in 26-dimensional general relativity. This illustrates our expectation that the compositeness scale should cut off the divergences of general relativity. Since the -dimensional Planck scale is given by
can be made arbitrarily small compared to by taking small enough . In Planck units this corresponds to a very low tension string theory.
However, in the usual string formulation of particle physics, the SM particles are also identified as string vibrational modes, and we must have so that the stringy excitations of the SM particles are too massive to appear in present-day experiments. Strings with such a large string-scale cannot solve the CCP. In fact we can integrate out the excited string states and return to eq. (5) and its unpleasant consequences. Instead, we wish to pursue the possibility that there are strings in the gravitational sector with extremely low string-scale, , but the SM particles are not themselves made of these strings. Instead SM particles are point-like, at least up to the weak scale. Just as the heavy quarks of the last section were surrounded by a light hadronic halo to form a heavy meson, the SM particles may be surrounded by a stringy halo with which the graviton string mode interacts.
As yet there are no fully realisitic candidates known within string theory, which are point-like on the string scale and can be identified with the SM particles. However the recently discovered solitonic D-branes do possess some promising qualitative features. For example, 0-branes are point-like objects with masses much larger than , which can probe a continuum spacetime down to distances much shorter than . At long distance their interactions conform to general relativistic expectations in terms of graviton exchange. At distances smaller than the composite graviton is an entirely inappropriate degree of freedom, and the force between 0-branes becomes intrinisically stringy .
I therefore propose that in nature the SM particles are dynamically more akin to 0-branes than they are to perturbative string modes such as the graviton. Since string theories are only consistently formulated with supersymmetry, it remains a problem to explain how supersymmetry ends up badly broken in the SM sector. Nevertheless, supposing this is possible, we would like to explicitly understand how the cosmological constant can be cut off by the scale of graviton compositeness, , rather than being sensitive to the much larger SM masses. Below I offer a picture of how this might work. I can make no pretence of rigor.
4.1 How the particle-string might solve the CCP
Let us consider a simple, abstracted version of our problem. To eliminate the complication of supersymmetry-breaking and compactification, let us simply work within bosonic string theory in 26 euclidean dimensions (turning a blind eye to the existence of a tachyon). This will be our gravitational string sector. Let the 0-brane of this theory represent a “SM particle”, with mass . For , the 0-branes are much more massive than the string scale. Strings are permitted to end on the 0-brane worldline, the attached string constituting a string “halo”. Closed strings, including the graviton, are emitted and absorbed by this halo, inducing gravitational interactions for the 0-branes. We want to estimate the contributions of virtual 0-brane loops to the cosmological constant, .101010Strictly speaking, the notion of a 0-brane perturbative loop expansion is ill-defined, since these 0-branes are so massive that their gravitational couplings are large. I will however use this language since it is the most familiar one, and because it is likely to apply to a more realistic construction. The naive power-counting guess, ignoring the string principle, would be . I will argue that the cosmological constant is instead set by the graviton compositeness scale, , so that .
The simplifying consideration is that the euclidean action for a particle of mass, , will suppress 0-brane world-line loops which are much bigger than . Thus on the string scale they are essentially point-like events in spacetime, to which string worldsheet boundaries can attach.111111This is very much like ordinary quantum field theory, where integrating out a massive field introduces local interactions for the light fields. In the string literature, such events are known as “D-instantons”. The sized strings should be insensitive to the tiny -scale structure.
The contribution to the cosmological constant due to D-instantons has been computed and the result is finite and of order . This result can be understood as follows. The cosmological constant correction is given by the sum of (first-quantized) connected string diagrams with no vertex operators, where the string worldsheet boundaries attach to the D-instanton. The dominant contribution from a single worldsheet is of order , corresponding to a disk topology, more complicated topologies being suppressed by powers of . The sign of this contribution requires a detailed calculation and is negative. The dominant contribution from worldsheets is given by identical disks, whose boundaries attach to the D-instanton. Their contribution is just the th power of the single-disk result, divided by a symmetry factor of !. Summing over gives the factor .
Thus we expect that the contribution to the cosmological constant from 0-brane loops is suppressed by (without being careful about the prefactor) and is therefore negligible for ! Therefore the cosmological constant is dominated by the string-loop correction discussed earlier,
4.2 Phenomenological aspects of this scenario
A fully realistic effective particle-string theory has not yet been constructed. I will just list some important features that it ought to have.
The theory must contain SM particles and critical strings. The particles must live in four spacetime dimensions and be point-like at least down to distances. The string length scale and compactification radii can however be much larger. Examples of four-dimensional particle-like behavior co-existing with strings, and large compactification radii “seen” only by the strings, have been found and discussed in refs. .
The theory must be unitary below the weak scale. It is permitted to break down above the weak scale, since we are not trying to guess the very high energy physics.
The spin-2 graviton must be the only massless non-SM state with couplings to matter (unless they are even weaker than gravity). Then unitarity ensures that at long distances the dynamics reduces to general relativity . For distances of order or smaller, the massive string physics will become important and general relativity must break down. The fact that gravity has already been tested at distances of a few centimeters without deviation from Newton’s Law, gives the bound,
The compositeness of gravity must make the cosmological constant insensitive to the large SM masses, its size being set instead by the compositeness scale, ,
This is also the power-counting result that follows from thinking of as an ultraviolet cutoff for the effective theory of general relativity.
To satisfy the bound of eq. (4), we must have,
If the string compactification radii are of order , the string coupling is given by,
This may seem absurdly small, but recall that in string theory, , and the stabilization of the dilaton vev is still not understood. It may be related to the other absurdly small number in nature, . In any case, small is not technically unnatural.
The new stringy physics must be negligible in SM experiments. While the strings have typical length mm, their couplings are so incredibly weak that they should not interefere with the SM interactions. At lab momenta, the strings should form an insubstantial cloud about the SM particles. In particular, they should not upset the theoretical agreement with SM experiments which are sensitive to very small mass splittings, such as kaon mixing or atomic structure. This may be of concern given eq. (29).
String theories are presently formulated with supersymmetry as an essential ingredient for full consistency, yet supersymmetry must appear broken by at least in the particle sector. This suggests a minimal supersymmetry breaking in the string sector of order . This scale may set the minimal permissible string-scale. If so, eV.
Finally, let us consider how this scenario might be experimentally tested. We expect that the nature of the gravitational force should dramatically change for distances smaller than the compositeness length scale, , in a manner which cannot be described by the exchange of a finite variety of massive particles (such as the light scalars discussed in refs. or , for example). For example, the interaction between a pair of 0-branes is described at long distance in terms of the exchange of massless closed string modes such as the graviton, while at short distance it is described by open strings connecting the 0-branes . In this regime the gravitational force can become weaker with shorter distances!
Eqs. (29) and (31) narrowly constrain the compositeness length scale at which the radical departures from general relativity (Newton’s Law) must occur,
It is therefore our very good fortune that this is just the range over which gravity will be sensitively tested in the experiment proposed in ref. . If composite gravity resolves the CCP as proposed here, it will show itself in this experiment and be quite distinct from any other “fifth force” phenomenon which can be described within field theory!
The Cosmological Constant Problem was argued to be intractable as a naturalness problem in effective field theory unless the graviton was “composite” with a scale of compositeness below eV. The standard model particles must also participate in this compositeness and yet retain their point-like behavior in accelerator experiments up to very high energies. The only sensible version of graviton compositeness that is known, is string theory. It was proposed that the standard model particles inherit their gravitational interactions by virtue of their their stringy “halos”, coupled to a gravitational string sector. The string-scale plays the role of the compositeness scale. It was argued that this stringiness can acceptably cut off contributions to the cosmological constant from ultraviolet mass scales. The mechanism is reminiscent of the relative insensitivity of light hadron masses to heavy quark masses in QCD. This was the basis for the detailed analogy discussed in the paper.
If this particle-string scenario is realized in nature, it will lead to a dramatic breakdown of Newton’s Law on the millimeter scale, which will be experimentally probed. On the theoretical side, much work still remains in order to construct a fully realistic effective particle-string theory and demonstrate its requisite properties. The particle-string scenario considered here would obviously also have deep implications for physics at the highest energy scales.
Finally, it is worth keeping in mind that there may be other, presently undiscovered, manifestations of graviton compositeness that can also reduce the sensitivity of the cosmological constant to ultraviolet mass scales. Fortunately, independently of the form of graviton compositeness which resolves the CCP, power-counting suggests that eq. (33) constrains the compositeness length scale. Therefore, the composite behavior should still show up in upcoming experimental tests of gravity at short distances.
This research was supported by the U.S. Department of Energy under grant #DE-FG02-94ER40818. I wish to thank Tom Banks, Sekhar Chivukula, Andrew Cohen, Nick Evans, Shamit Kachru, Martin Schmaltz and especially my father, R. M. Sundrum, and my wife, Jamuna Sundrum, for useful conversations on the subject of this paper.
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- N. Ishibashi, Particle-Particle-String Vertex, hep-th/9609173; S. Hirano and Y. Kazama, Scattering of Closed String States from a Quantized D-Particle, hep-th/9612064; Y. Kazama, Scattering of Quantized Dirichlet Particles, hep-th/9705111.
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- J. Donoghue, Phys. Rev. D50 (1994) 3874; Introduction to the Effective Field Theory description of Gravity, gr-qc/9512024.
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- M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory, Cambridge University Press (1987) chapter 1.
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- John Stewart Bell
John Stewart Bell (
June 28 1928– October 1 1990) was a physicist, and the originator of Bell's Theorem, one of the most important theorems in quantum physics.
Life and work
He was born in
Belfast, Northern Ireland, and graduated in experimental physics at the Queen's University of Belfast, in 1948. He went on to complete a PhD at the University of Birmingham, specialising in nuclear physicsand quantum field theory. His career began with the British Atomic Energy Agency, in Malvern, Britain's, then Harwell Laboratory. After several years he moved to the European Center for Nuclear Research ( CERN, "Conseil Européen pour la Recherche Nucléaire"). Here he worked almost exclusively on theoretical particle physicsand on accelerator design, but found time to pursue a major avocation, investigating the fundamentals of quantum theory.
In 1964, after a year's leave from CERN that he spent at
Stanford University, the University of Wisconsin-Madisonand Brandeis University, he wrote a paper entitled "On the Einstein-Podolsky-Rosen Paradox" [John Bell, "Speakable and Unspeakable in Quantum Mechanics", p. 14] . In this work, he showed that the carrying forward EPR's analysis [Einstein, "et al.", "Can Quantum Mechanical Description of Physical Reality Be Considered Complete?"] permits one to derive the famous Bell's inequality. This inequality, derived from some basic philosophical assumptions, conflicts with the predictions of quantum mechanics.
There is some disagreement regarding what Bell's inequality—in conjunction with the EPR paradox—can be said to imply. Bell held that not only local hidden variables, but any and all local theoretical explanations must conflict with quantum theory: "It is known that with Bohm's example of EPR correlations, involving particles with spin, there is an irreducible
nonlocality." [Bell, p. 196 ] According to an alternate interpretation, not all local theories in general, but only local hidden variables have shown incompatibility with quantum theory.
Despite the fact that hidden variable schemes are often associated with the issue of indeterminism, or uncertainty, Bell was instead concerned with the fact that orthodox quantum mechanics is a subjective theory, and the concept of measurement figures prominently in its formulation. It was not that Bell found measurement unacceptable in itself. He objected to its appearance at quantum mechanics' most fundamental theoretical level, which he insisted must be concerned only with sharply-defined mathematical quantities and unambiguous physical concepts.
In Bell's words: "The concept of 'measurement' becomes so fuzzy on reflection that it is quite surprising to have it appearing in physical theory at the most fundamental level... does not any analysis of measurement require concepts more fundamental than measurement? And should not the fundamental theory be about these more fundamental concepts?" [Bell, p. 117 ]
Bell was impressed that within Bohm’s
nonlocal hidden variable theory, reference to this concept was not needed, and it was this which sparked his interest in the field of research.
But if he were to thoroughly explore the viability of Bohm's theory, Bell needed to answer the challenge of the so-called impossibility proofs against hidden variables. Bell addressed these in a paper entitled "On the Problem of Hidden Variables in Quantum Mechanics". [ Bell, p.1 ] Here he showed that von Neumann’s argument [John von Neumann, "Mathematical Foundations of Quantum Mechanics"] does not prove impossibility, as it claims. The argument fails in this regard due to its reliance on a physically unreasonable assumption. In this same work, Bell showed that a stronger effort at such a proof (based upon
Gleason's theorem) also fails to eliminate the hidden variables program. (The flaw in von Neumann's proof was previously discovered by Grete Hermannin 1935, but did not become common knowledge until rediscovered by Bell.)
If these attempts to disprove hidden variables failed, can Bell's resolution of the EPR paradox be considered a success? According to Bell's interpretation, quantum mechanics itself has been demonstrated to be irreducibly nonlocal. Therefore, one cannot fault a hidden variables scheme if, as in the pilot wave theory of de Broglie and Bohm, it includes "
superluminal signalling", i.e., nonlocality.
In 1972 the first of many experiments that have shown (under the extrapolation to ideal detector efficiencies) a violation of Bell's Inequality was conducted. Bell himself concludes from these experiments that "It now seems that the non-locality is deeply rooted in quantum mechanics itself and will persist in any completion." [Bell, p. 132] This, according to Bell, also implied that quantum mechanics cannot be embedded into a locally causal hidden variables theory.
Bell remained interested in objective 'observer-free' quantum mechanics. He stressed that at the most fundamental level, physical theories ought not to be concerned with observables, but with 'be-ables': "The beables of the theory are those elements which might correspond to elements of reality, to things which exist. Their existence does not depend on 'observation'." [Bell, p. 174] He remained impressed with Bohm's hidden variables as an example of such a scheme and he attacked the more subjective alternatives such as the Copenhagen and Everett "many-worlds" interpretations. [Bell, p. 92, 133, 181]
Bell seemed to be quite comfortable with the notion that future experiments would continue to agree with quantum mechanics and violate his inequalities. Referring to the
Bell test experiments, he remarked:
::"It is difficult for me to believe that quantum mechanics, working very well for currently practical set-ups, will nevertheless fail badly with improvements in counter efficiency ..." [Bell, p. 109]
Some people continue to believe that agreement with Bell's inequalities might yet be saved. They argue that in the future much more precise experiments could reveal that one of the known loopholes, for example the so-called "fair sampling loophole", had been biasing the interpretations. This latter loophole, first publicized by Philip Pearle in 1970 [Philip Pearle, "Hidden-Variable Example Based upon Data Rejection"] , is such that "increases" in counter efficiency "decrease" the measured quantum correlation, eventually destroying the empirical match with quantum mechanics. Most mainstream physicists are highly skeptical about all these "loopholes", admitting their existence but continuing to believe that Bell's inequalities must fail.
Bell died unexpectedly of a
cerebral hemorrhagein Belfast in 1990. His contribution to the issues raised by EPR was significant. Some regard him as having demonstrated the failure of local realism (local hidden variables). Bell's own interpretation is that locality itself met its demise.
Bell's theorem, published in the mid-1960s
Bell's spaceship paradox
EPR paradox, a thought experiment by Einstein, Podolsky, and Rosen published in 1935 as an attack on quantum theory
CHSH Bell test, an application of Bell's theorem
Quantum mechanical Bell test prediction
Local hidden variable theory
*Aczel, Amir D, "Entanglement: The Greatest Mystery in Physics" (2001), New York: Four Walls Eight Windows
*Bell, John S, "Speakable and Unspeakable in Quantum Mechanics" (1987), Cambridge University Press, ISBN 0-521-36869-3, 2004 edition with introduction by
Alain Aspectand two additional papers: ISBN 0-521-52338-9
*Einstein, Podolsky, Rosen, "Can Quantum Mechanical Description of Physical Reality Be Considered Complete?", "Phys. Rev." 47, 777 (1935).
*von Neumann, John, "Mathematical Foundations of Quantum Mechanics" (1932), Princeton University Press 1996 edition: ISBN 0-691-02893-1
*Pearle, Philip, "Hidden-Variable Example Based upon Data Rejection", Physical Review D, 2, 1418-25 (1970)
* [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Bell_John.html MacTutor profile (University of St. Andrews)]
* [http://physicsweb.org/articles/world/11/12/8 John Bell and the most profound discovery of science (December 1998)]
* [http://www.rds.ie/home/index.aspx?id=1755 The Most Profound Discovery of Science (September 2006)]
Wikimedia Foundation. 2010.
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https://bigladdersoftware.com/epx/docs/8-7/engineering-reference/moisture-predictor-corrector.html
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The transient air mass balance equation for the change in the zone humidity ratio = sum of internal scheduled latent loads + infiltration + system + multizone airflows + convection to the zone surfaces may be expressed as follows:
CW = humidity capacity multiplier (See the InputOutput Reference for additional information on the object ZoneCapacitanceMultiplier:ResearchSpecial)
In the same manner as described above for zone air temperature (ref. Basis for the Zone and Air System Integration), the solution algorithms provided in the ZoneAirHeatBalanceAlgorithm object are also applied to zone air moisture calculations.
In order to calculate the derivative term with respect to time, the first order backward finite difference method, defined as the EulerMethod in the ZoneAirHeatBalanceAlgorithm object, may be used:
The zone air humidity ratio update at the current time step using the EulerMethod may be expressed as follows:
To preserve the stability of the calculation of the zone humidity ratio, the third order differential approximation, derived by a Taylor Series and used in the calculation of the next time step’s zone air temperature, is also applied to the zone air humidity ratio calculations. This algorithm is the default choice and is defined as 3rdOrderBackwardDifference in the ZoneAirHeatBalanceAlgorithm object.
The third order derivative derived from a Taylor Series expansion is defined as:
The coefficients of the approximated derivative are very close to the coefficients of the analogous Adams-Bashforth algorithm. Then the approximated derivative is substituted into the mass balance and the terms with the humidity ratio at past time steps are all put on the right hand side of the equation. This third order derivative zone humidity ratio update increases the number of previous time steps that are used in calculating the new zone humidity ratio, and decreases the dependence on the most recent. The higher order derivative approximations have the potential to allow the use of larger time steps by smoothing transitions through sudden changes in zone operating conditions.
This gives us the basic air mass balance equation that will be solved two different ways, one way for the predict step and one way for the correct step.
Since the third choice of solution algorithms uses an integration approach, defined as AnalyticalSolution in the ZoneAirHeatBalanceAlgorithm object, it does not require any approximations and has no truncation errors. The solutions in both prediction and correction are provided below in detail.
For the moisture prediction case the equation is solved for the anticipated system response as shown below.
Since the program provides three solution algorithms, the moisture prediction from each solution algorithm is given below.
For this solution algorithm, the air mass balance for the predicted air system load or response is:
For this solution algorithm, the air mass balance for the predicted system load or response is given below:
Then, using the following substitutions, the air mass balance equation becomes:
For this solution algorithm, the air mass balance for the predicted air system load or response is given below:
PredictedSystemLoad[kgWater/sec]=[Nsurfaces∑i=1Aihmiρairz+Nzones∑i=1˙miWzi+˙minf]∗⎡⎢ ⎢ ⎢⎣Wtsetpoint−Wt−δtz∗exp⎛⎜ ⎜ ⎜⎝−Nsurfaces∑i=1Aihmiρairz+Nzones∑i=1˙miWzi+˙minfρairVzCWδt⎞⎟ ⎟ ⎟⎠⎤⎥ ⎥ ⎥⎦∗⎡⎢ ⎢ ⎢⎣1−exp⎛⎜ ⎜ ⎜⎝−Nsurfaces∑i=1Aihmiρairz+Nzones∑i=1˙mi+˙minfρairVzCWδt⎞⎟ ⎟ ⎟⎠⎤⎥ ⎥ ⎥⎦−1−(Nsl∑i=1kgmassschedloadNsurfaces∑i=1AihmiρairzWsurfsi+Nzones∑i=1˙miWzi+˙minfW∞)
At the prediction point in the simulation, the system air mass flows are not known; therefore, the system response is approximated. The predicted air system moisture load is then used in the system simulation to achieve the best results possible. The system simulation components that have moisture control will try to meet this predicted moisture load. For example, humidifiers will look for positive moisture loads and add moisture at the specified rate to achieve the relative humidity setpoint. Likewise, dehumidification processes will try to remove moisture at the specified negative predicted moisture load to meet the relative humidity setpoint.
After the system simulation is completed the actual response from the air system is used in the moisture correction of step, which is shown next.
For the correct step the expanded air mass balance equation is solved for the final zone humidity ratio at the current time step. When the air system is operating, the mass flow for the system outlet includes the infiltration mass flow rate, therefore the infiltration mass flow rate is not included as a separate term in the air mass balance equation. But when the air system is off, the infiltration mass flow in is then exhausted out of the zone directly.
In the same manner as described above for predicting the moisture load to be met by the air system, the zone air moisture correction calculation will be described individually for the three solution algorithms.
Using the same A, B, and C parameters from the prediction step modified with actual zone mass flows with the air system ON and OFF result in:
If (ZoneSupplyAirMassFlowRate > 0.0) Then
Else If (ZoneSupplyAirMassFlowRate < = 0.0) Then
Inserting in the parameters A, B and C above in the air mass balance equation, it simplifies to:
Wtz=⎡⎢ ⎢⎣B+C∗(3Wt−δtz−32Wt−2δtz+13Wt−3δtz)(116)∗C+A⎤⎥ ⎥⎦
Wtz=⎡⎢ ⎢ ⎢⎣Wt−δtz−Nsl∑i=1kgmassschedload+Nsurfaces∑i=1AihmiρairzWsurfsi+Nzones∑i=1˙miWzi+˙minfW∞+˙msysWsupNsurfaces∑i=1Aihmiρairz+Nzones∑i=1˙mi+˙minf+˙msys⎤⎥ ⎥ ⎥⎦∗exp⎛⎜ ⎜ ⎜⎝−Nsurfaces∑i=1Aihmiρairz+Nzones∑i=1˙mi+˙minf+˙msysρairVzCWδt⎞⎟ ⎟ ⎟⎠+Nsl∑i=1kgmassschedload+Nsurfaces∑i=1AihmiρairzWsurfsi+Nzones∑i=1˙miWzi+˙minfW∞+˙msysWsupNsurfaces∑i=1Aihmiρairz+Nzones∑i=1˙mi+˙minf+˙msys
The above solutions are implemented in the Correct Zone Air Humidity Ratio step in EnergyPlus. This moisture update equation is used for the Conduction Transfer Function (CTF) heat balance algorithm, in addition to the effective moisture penetration depth (EMPD) with conduction transfer function heat balance algorithm. The equations are identical except that the convection to the zone surfaces is non-zero for the moisture penetration depth case. This moisture update allows both methods to be updated in the same way, with the only difference being the additional moisture capacitance of the zone surfaces for the Effective Moisture Penetration Depth (EMPD) solution approach.
When the HAMT (Combined Heat And Moisture Finite Element) defined in the HeatBalanceAlgorithm object is applied, the moisture update equations are also the same as the equations used in the effective moisture penetration depth (EMPD) with conduction transfer function solution algorithm.
Which moisture buffering model is best?[LINK]
The ’correct’ moisture buffering model depends on the questions being answered by the building energy simulation. Previous research (Woods et al., 2013a) has shown that using the effective capacitance model to account for moisture buffering of materials will provide a good estimate of energy use when humidity is not being actively controlled. See the InputOutput Reference for additional information on the object ZoneCapacitanceMultiplier:ResearchSpecial. This model has some limitations (Woods et al., 2013b):
- it will not accurately predict indoor humidity (or thermal comfort),
it will not accurately predict energy use when humidity is being actively controlled, and
it will not provide insight into the moisture content and potential moisture problems associated with a specific wall construction.
The effective moisture penetration depth (EMPD) model will address the first two concerns above: it can accurately predict indoor humidity, and can accurately predict energy use associated with controlling humidity. The EMPD model requires more user input than the effective capacitance model, specifically some of the moisture properties of the materials in the building. For more information, see the Effective Moisture Penetration Depth Model section in this document.
Like the EMPD model, the combined heat, air, and moisture transfer (HAMT) model addresses the first two issues discussed above for the effective capacitance model. It also addresses the third, by providing temperature and moisture profiles through composite building walls, and helping to identify surfaces with high surface humidity. The HAMT model requires a few more user inputs on moisture properties of materials than the EMPD model, and this model also increases the required simulation time by an order of magnitude. For more information on this model, see the Combined Heat and Moisture Transfer (HAMT) Model section in this document.
Note that the EMPD and HAMT models above ensure accurate calculations of the effect of moisture buffering, but it will only be accurate relative to reality when given appropriate inputs for the material properties.
Woods, J., J. Winkler, D. Christensen, Moisture modeling: Effective moisture penetration depth versus effective capacitance, in Thermal Performance of the Exterior Envelopes of Whole Buildings XII International Conference. 2013a: Clearwater, FL.
Woods, J., Winkler, J, and Christensen, D. Evaluation of the Effective Moisture Penetration Depth Model for Estimating Moisture Buffering in Buildings, NREL/TP-5500-57441, 2013b.
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http://www.learntechlib.org/p/168048/
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math
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Tribonacci-Like Sequences and Generalized Pascal's Pyramids
IJMEST Volume 45, Number 8, ISSN 0020-739X
A well-known result of Feinberg and Shannon states that the tribonacci sequence can be detected by the so-called "Pascal's pyramid." Here we will show that any tribonacci-like sequence can be obtained by the diagonals of the "Feinberg's triangle" associated to a suitable "generalized Pascal's pyramid." The results also extend similar properties of Fibonacci-like sequences.
Anatriello, G. & Vincenzi, G. (2014). Tribonacci-Like Sequences and Generalized Pascal's Pyramids. International Journal of Mathematical Education in Science and Technology, 45(8), 1220-1232.
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| 670 | 4 |
https://projecteuclid.org/euclid.cbms/1462061034
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math
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NSF-CBMS Regional Conference Series in Probability and Statistics
Chapter 4: Models invariant under compact groups
Our goal here is to understand the structure of probability measures which are invariant under a compact group. In the first section, a basic representation theorem is proved and is interpreted in terms of random variables. Section 2 contains some basic examples while applications to some robustness problems are given in Section 3.
First available in Project Euclid: 1 May 2016
Permanent link to this document
Easton, Morris L. Chapter 4: Models invariant under compact groups. Group invariance in applications in statistics, 55--67, Institute of Mathematical Statistics and American Statistical Association, Haywood CA and Alexandria VA, 1989. https://projecteuclid.org/euclid.cbms/1462061034
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| 810 | 6 |
http://math.mapua.edu.ph/contest/mmw2019
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math
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Mapua University holds 13th Math Wizard Competition
Mapúa University held its 13th Math Wizard Competition last January 21 to 23, 2019 in its Intramuros campus.
The competition was headed by Mapúa’s Department of Mathematics with a total of 92 student participants from various schools and departments of the University.
Earl John Salamat, a first year Civil Engineering student, earned the top spot in this year’s Math Wizard Competition. Jian Matthew Tumali, a first year Mechanical Engineering student, landed the second spot followed by June Lorenz Capin, in third place, a first year Electronics Engineering student. Also completing the top five winners are Kyle Reifel Del Villar, in fourth place, a first year Electronics Engineering student and Simon Felix Briones, in fifth place, a fourth year Electronics Engineering student.
Started in 2007, the search for Mapúa Math wizards is an annual competition opened to all students which aims to promote excellence in Mathematics through a series of quizzes. It is also an avenue for the University to choose its official representatives for numerous Mathematics contests in the country.
The competition covers topics in Algebra, Trigonometry, Solid Mensuration, Analytic Geometry, Differential Calculus, Integral Calculus, and Probability and Statistics.
In photo: Top 5 winners of Mapúa’s 13th Math Wizard Competition with Engr. Richard T. Earnhart (third from left) of the University’s Department of Mathematics
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https://igotanoffer.com/blogs/mckinsey-case-interview-blog/case-interview-maths
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math
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At IGotAnOffer, we have helped more than 30,000 candidates prepare for their consulting interviews. Students who go through our full training programme are a happy bunch: more than 80% of them get an offer at McKinsey, BCG or Bain.
Developing fast and accurate maths skills is a big part of being successful at case interviews. In the following guide we've listed a number of free tools, formulas and tips you can use to become much faster at maths and radically improve your chances of getting an offer.
Part 1: Case maths apps and tools
Mental maths is a muscle. But if you are like us, you probably haven't exercised that muscle much since you left high school. As a consequence, your case interview preparation should include some maths training.
If you don't remember how to calculate basic additions, substractions, divisions and multiplications without a calculator that's what you should focus on first. Our McKinsey and BCG & Bain case interview programmes both include a refresher on the topic.
In addition, Khan Academy has also put together helpful resources. Here are the ones we recommend taking a look at if you need an in-depth arithmetic refresher:
Once you're feeling comfortable with the basics you'll need to regularly exercise your mental maths muscle in order to become as fast and accurate as possible. Our McKinsey and BCG & Bain case interview programmes include a calculation workbook PDF with maths drills. We recommend doing a few everyday so you get more and more comfortable over time.
In addition, you can also use the following resources. We haven't tested all of them but some of the candidates we work with have used them in the past and found them helpful.
- Preplounge's maths tool. This web tool is very helpful to practice additions, subtractions, multiplications, divisions and percentages. You can both sharpen your precise and estimation maths with it.
- Victor Cheng's maths tool. This tool is similar to the Preplounge one but the user experience is less smooth in our opinion.
- Magoosh's mental maths app (iOS + Android). If you want to practice your mental maths on the go this free mobile app is great. It lets you work on different types of calculations using mental maths flashcards. You can also track your progress as you study.
- Mental math cards challenge app (iOS). This mobile app let's you work on your mental maths in a similar way to the previous one. Don't let the old school graphics deter you from using it. The app itself is actually very good.
- Mental math games (Android). If you're an Android user this one is a good substitute to the mental math cards challenge one on iOS.
Part 2: Case maths formulas
The links we have listed above should go a long way in helping you bring your maths skills to a good level. In addition, you will also need to learn the formulas for the main business and finance concepts you will come across in your interviews.
We've put together a list of the important maths formulas for you with concepts that you should really master for your interviews and concepts which are optional in our experience.
2.1. Must-know maths formulas
Revenue = Volume x Price
Cost = Fixed costs + Variable costs
Profit = Revenue - Cost
Profit margin (aka Profitability) = Profit / Revenue
Return on investment (ROI) = Annual profit / Initial investment
Breakeven (aka Payback period) = Initial investment / Annual profit
If you have any questions about the formulas above you can ask them at the bottom of this page and our team will answer them. Alternatively, you can also read our in-depth articles about finance concepts for case interviews and for the McKinsey PST or watch this video where we explain these concepts in great detail.
2.2. Optional maths formulas
Having an in-depth knowledge of the business terms below and their corresponding formula is NOT required to get offers at McKinsey, BCG, Bain and other firms in our experience. But having a rough idea of what they are can be handy.
EBITDA = Earnings Before Interest Tax Depreciation and Amortisation
EBIDTA is essentially profits with interest, taxes, depreciation and amortization added back to it. It's useful to compare companies across industries as it takes out the accounting effects of debt and taxes which vary widely between say Facebook (little to no debt) and ExxonMobil (tons of debt to finance infrastructure projects). More here.
NPV = Net Present Value
Let's say you invest $1,000 in project A and $1,000 in project B. You expect to receive your initial investment + $500 from A in one week. And you expect to receive your initial investment + $500 from B in 5 years. Intuitively you probably feel that A is more valuable than B as you'll get the same amount of money but quicker. NPV aims to adjust future cashflows so different investments such as A and B can easily be compared. More here.
Return on equity = Profits / Shareholder equity
Return on equity (ROE) is a measure of financial performance similar to ROI. ROI is usually used for standalone projects while ROE is used for companies. More here.
Return on assets = Profits / Total assets
Return on assets (ROA) is an alternative measure to ROE and a good indicator of how profitable a company is compared to its total assets. More here.
Part 3: Fast maths tips and tricks
The standard long divisions and multiplications approaches are great because they're generic and you can use them for any calculation. But they are also extremely slow. In our experience, you can become MUCH faster at maths by using non-standard approaches we've listed below.
All these approaches have ONE thing in common: they aim at rearranging and simplifying calculations to find the EASIEST path to the result. Let's step through each of them one by one.
3.1. Rounding numbers
The first step towards becoming faster is to round numbers whenever you can. 365 days becomes 350. The US population of 326m becomes 300m. Etc. You get the idea.
The tricky thing about rounding numbers is that if you round them too much you risk a) distorting the final result / finding, and b) your interviewer telling you to round the numbers less.
Rounding numbers is more of an art than a science, but in our experience the following two tips tend to work well:
- We usually recommend to not round numbers by more than +/- 10%. This is a rough rule of thumb but gives good results based on conversations with past candidates.
- You also need to alternate between rounding up and rounding down so the effects cancel out. For instance, if you're calculating A x B, we would recommend rounding A UP, and rounding B DOWN so the roundings compensate each other.
Note you won't always be able to round numbers. In addition, even after you round numbers the calculations could still be difficult. So let's go through a few tips that can help in these situations.
3.2. Handling large numbers
Large numbers are difficult to deal with because of all the 0s. To be faster you need to use notations that enable you to get rid of these annoying 0s. We recommend you use labels and the scientific notation if you aren't already doing so.
Labels (k, m, b)
Use labels for thousand (k), million (m) and billion (b). You'll write numbers faster and it will force you to simplify calculations. Let's use 20,000 x 6,000,000 as an example.
- No labels: 20,000 x 60,000,000 = ... ???
- Labels: 20k x 6m = 120k x m = 120b
This approach also works for divisions. Let's try 480,000,000,000 divided by 240,000,000.
- No labels: 480,000,000,000 / 240,000,000 = ... ???
- Labes: 480b / 240m = 480k / 240 = 2k
When you can't use labels, the scientific notation is a good alternative. If you're not sure what this is, you're really missing out. But fortunately Khan Academy has put together a good primer on the topic here.
- Multiplication example: 600 x 500 = 6 x 5 x 102 X 102 = 30 x 104 = 300,000 = 300k
- Division example: (720,000 / 1,200) / 30 = (72 / (12 x 3)) x (104 / (102 x 10)) = (72 / 36) x (10) = 20
When you're comfortable with labels and the scientific notation you can even start mixing them:
- 200k x 600k = 2 x 6 x 104 x m = 2 x 6 x 10 x b = 120b
To be fast at maths, you need to avoid writing down long divisions and multiplications as they take a LOT of time. In our experience, doing multiple easy calculations is faster and leads to less errors than doing one big long calculation.
A great way to achieve this is to factor and expand expressions to create simpler calculations. If you're not sure what the basics of factoring and expanding are, you can use Khan Academy again here and here. Let's start with factoring.
Simple numbers: 5, 15, 25, 50, 75, etc.
In case interviews and tests like the McKinsey PST or BCG Potential Test some numbers come up very frequently and it's useful to know shortcuts to handle them. Here are some of these numbers: 5, 15, 25, 50, 75, etc. These numbers are frequent but not particularly easy to deal with.
For instance, consider 36 x 25. It's not obvious what the result is. And a lot of people would need to write down the multiplication on paper to find the answer. However there's a MUCH faster way based on the fact that 25 = 100 / 4. Here's the fast way to get to the answer:
- 36 x 25 = (36 / 4) x 100 = 9 x 100 = 900
- 68 x 25 = (68 / 4) x 100 = 17 x 100 = 1,700
- 2,600 / 25 = (2,600 / 100) x 4 = 26 x 4 = 104
- 1,625 / 25 = (1,625 / 100) x 4 = 16.25 x 4 = 65
- 2.5 = 10 / 4
- 5 = 10 / 2
- 7.5 = 10 x 3 / 4
- 15 = 10 x 3 / 2
- 25 = 100 / 4
- 50 = 100 / 2
- 75 = 100 x 3 / 4
Once you're comfortable using this approach you can also mix it with the scientific notation on numbers such as 0.75, 0.5, 0.25, etc.
Factoring the numerator / denominator
For divisions, if there are no simple numbers (e.g. 5, 25, 50, etc.), the next best thing you can do is to try to factor the numerator and / or denominator to simplify the calculations. Here are a few examples:
- Factoring the numerator: 300 / 4 = 3 x 100 / 4 = 3 x 25 = 75
- Factoring the denominator: 432 / 12 = (432 / 4) / 3 = 108 / 3 = 36
- Looking for common factors: 90 / 42 = 6 x 15 / 6 x 7 = 15 / 7
Another easy way to avoid writing down long divisions and multiplications is to expand calculations into simple expressions.
Expanding with additions
Expanding with additions is intuitive to most people. The idea is to break down one of the terms into two simpler numbers (e.g. 5; 10; 25; etc.) so the calculations become easier. Here are a couple of examples:
- Multiplication: 68 x 35 = 68 x (10 + 25) = 680 + 68 x 100 / 4 = 680 + 1,700 = 2,380
- Division: 705 / 15 = (600 + 105) / 15 = (15 x 40) / 15 + 105 / 15 = 40 + 7 = 47
Notice that when expanding 35 we've carefully chosen to expand to 25 so that we could use the helpful tip we learned in the factoring section. You should keep that in mind when expanding expressions.
Expanding with subtractions
Expanding with subtractions is less intuitive to most people. But it's actually extremely effective, especially if one of the terms you are dealing with ends with a high digit like 7, 8 or 9. Here are a couple of examples:
- Multiplication: 68 x 35 = (70 - 2) x 35 = 70 x 35 - 70 = 70 x 100 / 4 + 700 - 70 = 1,750 + 630 = 2,380
- Division: 570 / 30 = (600 - 30) / 30 = 20 - 1= 19
3.5. Growth rates
Finally, you will also often have to deal with growth rates in case interviews. These can lead to extremely time-consuming calculations so it's important that you learn how to deal with them efficiently.
Multiply growth rates together
Let's imagine your client's revenue is $100m. You estimate it will grow by 20% next year and 10% the year after that. In that situation, the revenues in two years will be equal to:
- Revenue in two years = $100m x (1 + 20%) x (1 + 10%) = $100m x 1.2 x 1.1 = $100m x (1.2 + 0.12) = $100m x 1.32 = $132m
Growing at 20% for one year followed by 10% for another year therefore corresponds to growing by 32% overall. To find the compound growth you simply need to multiply them together and subtract one: (1.1 x 1.2) - 1= 1.32 - 1 = 0.32 = 32%. This is the quickest way to calculate compound growth rates precisely.
Note that this approach also works perfectly with negative growth rates. Let's imagine for instance that sales grow by 20% next year, and then decrease by 20% the following year. Here's the corresponding compound growth rate:
- Compound growth rate = (1.2 x 0.8) - 1 = 0.96 - 1 = -0.04 = -4%
Note how growing by 20% and then shrinking by 20% is not equal to flat growth (0%). This is an important result to keep in mind.
Estimate compound growth rates
Multiplying growth rates is a really efficient approach when calculating compound growth over a short period of time (e.g. 2 or 3 years). But let's imagine you want to calculate the effect of 7% growth over five years. The precise calculation you would need to do is:
- Precise growth rate: 1.07 x 1.07 x 1.07 x 1.07 x 1.07 - 1 = ... ???
- Estimate growth rate = Growth rate x Number of years
In our example:
- Estimate growth rate: 7% x 5 years = 35%
In reality if you do the precise calculation (1.075 - 1) you will find that the actual growth rate is 40%. The estimation method therefore gives a result that's actually quite close. In case interviews your interviewer will always be happy with you taking that shortcut as doing the precise calculation takes too much time.
If you would like to fast track your case interview preparation and maximise your chances of getting an offer at McKinsey, BCG or Bain, come and train with us. More than 80% of the candidates training with our programmes end up getting an offer at their target firm. We know this because we give half of their money back to people who don't.
McKinsey Case Interview Training Programme
BCG & Bain Case Interview Training Programme
Any questions about case interview maths?
If you have any questions about case interview maths, do not hesitate to ask them below and we will be more than happy to answer them. All questions are good questions, so go ahead!
The IGotAnOffer team
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https://brainmass.com/chemistry/general-chemistry/assorted-general-chemistry-problems-154731
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math
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1) In a combustion analysis, 2.00mg of vitamin C yielded 3.00mg CO2 and 0.816mg H2o. From mass spectrometry, it was found that the molecular weight of vitamin C is 176amu. Determine the mass composition of vitamin C, its empirical formula, and its molecular formula.
3) What is the name of each of the three quantum numbers used to describe orbitals in atoms? What orbital characteristics does each quantum number describe? What are the limitations on the values of these quantum numbers?
Element: He (2377kJ/mol), Ne (2088kJ/mol), Ar (1527kJ/mol),
Kr (1356kJ/mol), Xe (1176 kJ/mol), Rn (1042kJ/mol
Assorted general chemistry problems about combustion, quantum numbers and ionization energies are solved with full working shown.
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| 728 | 5 |
https://www.shaalaa.com/question-bank-solutions/explain-return-on-investment-roi-return-investment-roi_90681
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math
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Explain return on investment (ROI).
Return on Investment (ROI) is a performance measure used to evaluate the efficiency of an investment or compare the efficiency of a number of different investments. ROI tries to directly measure the amount of return on a particular investment, relative to the investment’s cost. To calculate ROI, the benefit (or return) of an investment is divided by the cost of the investment. The result is expressed as a percentage or a ratio.
(i) "Current Value of Investment” refers to the proceeds obtained from the sale of the investment of interest. Because ROI is measured as a percentage, it can be easily compared with returns from other investments, allowing one to measure a variety of types of investments against one another.
(ii) ROI is a popular metric because of its versatility and simplicity. Essentially, ROI can be used as a rudimentary gauge of an investment’s profitability. This could be the ROI on a stock investment, the ROI a company expects on expanding a factory, or the ROI generated in a real estate transaction
(iii) ROI can be used in conjunction with rate of return which takes into account a project’s time frame. One may also use Net present value which accounts for differences in the value of money over time, due to inflation. The application of NPV when calculating rate of return is often called the real rate of return.
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https://edurev.in/studytube/Chapter-1-Simple-Stresses-In-Machine-Parts-Machine/f600e658-319c-4818-9724-52aed838b4ff_t
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math
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SIMPLE STRESSES IN MACHINE PARTS
The ratio of the increases in length to the original length is known as tensile strain.
Tensile stress st = P/A and tensile strain =
P = Tensile or compressive force acting on the body
A = Cross-sectional area of the body
ℓ = original length
dℓ = Change in length
d = diameter of rivet
t = thickness of the plate
d.t = projected area of the rivet
n = number of rivet per pitch length in bearing.
Thermal stress s =Î .E =a .t.E
Thermal stress is independent of length and cross - section dimensions.
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https://im.kendallhunt.com/MS/students/2/8/7/practice.html
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math
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Priya’s cat is pregnant with a litter of 5 kittens. Each kitten has a 30% chance of being chocolate brown. Priya wants to know the probability that at least two of the kittens will be chocolate brown.
To simulate this, Priya put 3 white cubes and 7 green cubes in a bag. For each trial, Priya pulled out and returned a cube 5 times. Priya conducted 12 trials.
Here is a table with the results.
How many successful trials were there? Describe how you determined if a trial was a success.
- Based on this simulation, estimate the probability that exactly two kittens will be chocolate brown.
- Based on this simulation, estimate the probability that at least two kittens will be chocolate brown.
Write and answer another question Priya could answer using this simulation.
How could Priya increase the accuracy of the simulation?
A team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces of paper in a bag, 3 labeled “win” and 1 labeled “lose.” She draws a paper, writes down the result, then replaces the paper and repeats the process two more times. Clare gets the result: win, win, lose. What can Clare do to estimate the probability the team will win at least 2 games?
- List the sample space for selecting a letter a random from the word “PINEAPPLE.”
- A letter is randomly selected from the word “PINEAPPLE.” Which is more likely, selecting “E” or selecting “P?” Explain your reasoning.
On a graph of side length of a square vs. its perimeter, a few points are plotted.
- Add at least two more ordered pairs to the graph.
- Is there a proportional relationship between the perimeter and side length? Explain how you know.
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| 1,723 | 14 |
https://olsurfschool.com.au/individual-surf-lessons-packages-adelaide
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math
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Surf Lessons - Individual Lessons & Packages
Book or Enquire About Surf Lessons
Book Lessons Ahead ...
Want to learn to surf in Adelaide? Then Goolwa Beach is a great spot to learn with the guidance of Ocean Living Surf School instructor Phil Ball.
Take it lesson-by lesson or book head with a surf lesson package deal.
1 X Surf Lesson ( 2 hour )
$40 per person
2 X Surf Lesson ( 2 X 2 hour )
$70 per person
3 X Surf Lesson ( 3 x 2 hour )
$95 per person
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https://www.studypool.com/discuss/1139845/help-me-solve-this-problem-4?free
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math
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There is a formula that estimates how much your puppy will weigh when it reaches adulthood. The method we present applies to medium-sized breeds. First find your puppy's weight w, in pounds, at an age of a weeks, where a is 16 weeks or less. Then the predicted adult weight
W = W(a, w),
in pounds, is given by the formula
W = 52
(a) Use functional notation to express the adult weight of a puppy that weighs 4 pounds at 11 weeks.
(b) Calculate the predicted adult weight for the puppy from part (a). (Round your answer to two decimal places.)
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https://direct.mit.edu/neco/article-abstract/8/2/270/5939/Neural-Network-Models-of-Perceptual-Learning-of?redirectedFrom=fulltext
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math
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We study neural network models of discriminating between stimuli with two similar angles, using the two-alternative forced choice (2AFC) paradigm. Two network architectures are investigated: a two-layer perceptron network and a gating network. In the two-layer network all hidden units contribute to the decision at all angles, while in the other architecture the gating units select, for each stimulus, the appropriate hidden units that will dominate the decision. We find that both architectures can perform the task reasonably well for all angles. Perceptual learning has been modeled by training the networks to perform the task, using unsupervised Hebb learning algorithms with pairs of stimuli at fixed angles θ and δθ. Perceptual transfer is studied by measuring the performance of the network on stimuli with θ′ ≠ θ. The two-layer perceptron shows a partial transfer for angles that are within a distance a from θ, where a is the angular width of the input tuning curves. The change in performance due to learning is positive for angles close to θ, but for |θ − θ′| ≈ a it is negative, i.e., its performance after training is worse than before. In contrast, negative transfer can be avoided in the gating network by limiting the effects of learning to hidden units that are optimized for angles that are close to the trained angle.
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http://parimatch-stavka7.com/free-essays/Eco-365-Final-Examination-University-Of-762615.html
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math
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ECO 365 Final Exam Assignment
1). The DeBeers company is a profit-maximizing monopolist that exercises monopoly power in the distribution of diamonds. If the company earns positive economic profits this year, the price of diamonds will:
• Exceed the marginal cost of diamonds but equal to the average total cost of diamonds.
• Exceed both the marginal cost and the average total cost of diamonds.
• Be equal to the marginal cost of diamonds.
• Be equal to the average total cost of diamonds.
2). Using 100 workers and 10 machines, a firm can produce 10,000 units of output; using 250 workers and 25 machines, the firm produces 21,000 units of output. These facts are best explained by:
• Economies of scope
• Diseconomies of scale
• Diminishing marginal productivity
• Economies of scale
Complete paper here ECO 365 Final Exam
3). Suppose that college tuition is higher this year than last and that more students are enrolled in college this year than last year. Based on this information, we can best conclude that:
• despite the increase in price, quantity demanded rose due to some other factors changing.
• the demand for a college education is positively sloped.
• the law of demand is invalid.
• this situation has nothing to do with the law of demand.
4). A monopoly firm is different from a perfectly competitive firm in that:
• A monopolist’s demand curve is perfectly inelastic whereas a perfectly competitive firm’s demand curve is perfectly elastic.
• A competitive firm has a u-shaped average cost curve whereas a monopolist does not.
• A monopolist can influence market price whereas a perfectly competitive firm cannot.
• There are many substitutes for a monopolist’s product whereas there are no substitutes for a competitive firm’s product.
To download the complete answer check ECO 365 Week 2 Knowledge Check
5). The best example of positive externality is:
• Alcoholic beverages
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823442.17/warc/CC-MAIN-20181210191406-20181210212906-00455.warc.gz
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CC-MAIN-2018-51
| 1,939 | 25 |
https://essaybizlab.com/accounting-treatment-for-change-in-estimated-life/
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math
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The depreciation charge is calculated on the estimated useful economic life of the assets at the time of acquisition. If there is a change in the estimated economic life during a period when the asset is under use by the businesses, then there is a need to amend the depreciation amount charged against the income. This can be explained by giving a small example of a physical asset that is purchased by a business for $500,000, and it is expected to have a useful life of 25 years, and it has no residual value. For the first year and subsequent years, the depreciation charge is calculated using the straight-line method as $500,000/25=$20,000 per annum. This amount is charged against the income from the business every year. However, if after five years of the asset using, the expected life of that asset is revised to only ten years. Then the depreciation expense needs to be revised accordingly to spread out the economic value of the asset over the remaining period of time.
Since for the first five years depreciation has been charged at a rate of $20,000 per year, this implies that by the end of the 5th year, there is an accumulated depreciation of $250,000 recorded in the balance sheet. The netbook value of the asset at the beginning of the 6th year is $250,000, which will be required to spread over the remaining useful life of 5 years. This implies that a depreciation charge of 250,000/5=$50,000 per annum will be made against the income for the next years in order to achieve a salvage value of nil. However, the change in the estimated life of an asset is considered to be a change in estimate that can affect the present status and expected future benefits, and this must be disclosed by the businesses in their annual report.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679102469.83/warc/CC-MAIN-20231210123756-20231210153756-00883.warc.gz
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CC-MAIN-2023-50
| 1,748 | 2 |
https://testbook.com/question-answer/the-line-of-sight-generates-a-vertical-plane-when--5f85c7fd57cf531bcd1c9b00
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math
|
Compass Surveying and Theodolite
Download Solution PDF
The line of sight generates a vertical plane when:
This question was previously asked in
MP Sub Engg Official Civil Paper Held on 9th July 2017 - Shift 2
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Vertical axis is parallel to horizontal axis
Vertical axis is perpendicular to horizontal axis
Horizontal axis is parallel to vertical axis
Horizontal axis is perpendicular to vertical axis
(Detailed Solution Below)
Option 4 : Horizontal axis is perpendicular to vertical axis
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Building Material & Concrete Technology
Download Solution PDF
Line of sight:
It is the
passing through the
intersection of the crosshair on the diaphragm
optical center of the objective lens.
when a line of sight comes in a horizontal plane, it is called a
line of collimation.
line of sight
horizontal axis is perpendicular to the vertical axis.
Fundamental lines of theodolite:
The fundamental lines of a theodolite are the vertical axis, the axis of plate levels, the line of collimation, the horizontal axis, and the bubble line of altitude.
When the theodolite is in proper adjustment, the following conditions should be satisfied.
Horizontal circle perpendicular to the vertical axis.
Vertical circle perpendicular to a horizontal axis
The vertical axis must pass through the center of the graduated horizontal circle.
The horizontal axis must pass through the center of the vertical circle.
Tangent to plate bubble must be perpendicular to the vertical axis.
Line of sight must be perpendicular to the transit axis (trunnion axis)
Transit axis(Horizontal axis or trunnion axis) must be perpendicular to the vertical axis.
For the horizontal position of the telescope and for the altitude bubble at the center, the reading on the vertical circle must be zero.
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More Compass Surveying and Theodolite Questions
Reiteration method is also called as
In theodolites, the axis of rotation of telescope in the vertical plane indicates:
Which of the following statements is/are incorrect about the Prismatic Compass? A. The needle is broad but it does not act as an index. B. The graduated ring is attached with the needle. This does not rotate along with the line of sight. C. The readings are taken directly seeing through the top of the glass.
The angle between true meridian and magnetic meridian is termed as:
The Theodolite is an instrument used for measuring very accurately
Agate cap is fitted with a-
In order to measure the magnetic bearing of a line, the theodolite should be provided with-
In a quadrantal bearing system the angle is N44° - 30' W in whole bearing system it will be:
What is the whole circle bearing of a quadrant bearing N 15° 28' W?
Agonic line is the line joining points having declination-
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More Surveying Questions
Choose the correct statement. a) The sum of the measured interior angles should be equal (2N - 4) right angles. b) If the exterior angles are measured, their sum should be equal to (2N + 4) right angle. Where N is the number of sides of the traverse.
Convert 327°24' whole circle bearing to quadrantal bearing. Select the correct option.
A flagpole appears in two successive photographs taken at an altitude of 2,000 m above datum. The focal length of the camera is 120 mm and the length of the air base is 200 m. The parallax for the top of the pole is 52.52 mm and for the bottom is 48.27 mm. Find the difference in elevation between the top and the bottom of the pole.
______ is the process of rephotographing an aerial photograph so that the effects of tilt are eliminated.
The point on the upper portion of the celestial sphere marked by the plumb line above the observer is called the:
Instrument used for ocean sounding where the depth of water is too much, and to make a continuous and accurate record of the depth of water below the boat or ship at which it is installed, is called as:
The process of determining the differences of elevations of stations from observed vertical angles and known distances is known as:
A surveyor measured the distance between two points on the plan drawn to a scale 1 cm = 40 m and the result was 468 m. Later however, he discovered that he had used a scale of 1 cm = 20 m. Find the true distance between the two points.
The line passing through the intersection of the horizontal and vertical cross hairs and optical centre of the subject glass and its continuation is called:
The magnetic bearing of a line AB is 48°24. Calculate the true bearing if the magnetic declination is E 5°38.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780055632.65/warc/CC-MAIN-20210917090202-20210917120202-00083.warc.gz
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CC-MAIN-2021-39
| 5,163 | 83 |
https://www.computerhope.com/jargon/q/quantum-computer.htm
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math
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A quantum computer is a device that uses quantum mechanical phenomena such as superposition and entanglement to perform operations on data. A conventional digital computer uses electronic circuits on a plate of semiconducting material (e.g., silicon) to represent binary digits (bits), each in a state of either 1 or 0. In contrast, quantum computers use qubits that represent a "superposition" of both 1 and 0, simultaneously.
The field of quantum computing was first proposed in 1969, and formally introduced in 1980 by Yuri Manin and in 1982 by Richard Feynman. As of 2014, quantum computing is still in its infancy, with experiments yielding computations on a small number of qubits. On December 9, 2015, Google presented its findings that using D-Wave quantum computers it was able to solve some problems 100 million times faster than a conventional system.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571987.60/warc/CC-MAIN-20220813202507-20220813232507-00260.warc.gz
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CC-MAIN-2022-33
| 862 | 2 |
http://www.answerlib.org/qv/20151129163553AAlESQA.html
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math
|
Three less than five times a certain number is equal to 67 more than one third of the number. find the number?
Below is the recommendation and reference answer for question "Three less than five times a certain number is equal to 67 more than one third of the number. find the number?" It was collected and sorted by the editor of this site but not sure the answer is entirely accurate.
5x-3 = 67+1/3 x
14/3x = 70
x = 15
- If three numbers from 100 to 999 are chosen at random, one at a time, find the probability that they will be chosen in increasing order?
- Half of 3/4?
- If 5 cats catch 5 rats in 5 minutes, how many cats are needed to catch 72 rats in 2 hours?
- Geometry help?
- What is infinity minus one?
- I have 3 boxes, each box contains 10 balls numbered from 0-9. what is the probability that the sum of 3 balls i get from each box will be 1?
- What is the nearest shape to a circle?
- A tank holds 20 gallons of water. When a tap over it is turned on water flows from it into the tank at the rate of 4 gallns a minute.?
- What is the probability of NOT drawing a red face card in a deck of 52?
- What is the value of x when 2x + 1 = 7?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170651.78/warc/CC-MAIN-20170219104610-00257-ip-10-171-10-108.ec2.internal.warc.gz
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CC-MAIN-2017-09
| 1,151 | 15 |
https://mol-logistics.de/en/academy/volume-weight-calculate/
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math
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Calculate volume weight.
Not only the weight, but also the space a shipment takes up play an important role in determining the shipping costs. You can imagine that there is less space available in an airplane than in a container ship. That is why we take into account the so-called volume weight and the "figure weight" when calculating the price of your shipment. The "number weight" originated as a conversion factor to bridge the distinction between volume and weight.
The difference between springs and lead
You can imagine that 1,000 kilos of feathers have a larger volume than 1,000 kilos of lead. In order to be able to tax this difference equally, certain conversion factors were agreed upon in the handling.
What weight determines the cost?
We calculate the volume weight for each shipment and compare it with the actual weight in kilos. We perform this calculation based on an approved formula. For air freight, 1 cbm (cubic meter) is equivalent to 167 kg. For sea freight (LCL), we take into account that 1 cbm is equivalent to a maximum of 1000 kg, while for road freight 1 cbm is equivalent to 333 kg. The highest weight (volume or actual) is loaded.
For air freight: 1 cbm = 167 kg (volume ratio 1: 6)
For road transport: 1 cbm = 333 kg (volume ratio 1: 3)
For sea freight, the following applies: 1 cbm = 1,000 kg (volume ratio 1: 1)
We calculate the final shipping costs based on the higher of the two "weights": this is the "taxable weight". Therefore, when goods take up "too much" space (e.g., large, bulky products), we usually charge by volume weight.
How to calculate the dimensional weight?
To calculate the volume weight, first determine the volume: length x width x height (in centimeters). Then divide this figure by one of the following factors:
Air freight: 6,000
Road transport: 3,000
Sea transport: 1,000
What about charge meters on the road?
We often use load counters for road transport. 1 load meter is equal to 1 linear meter of loading space in the truck. This is often used as a unit of account for goods that cannot be stacked or on which you cannot stack. As a result, the trucker makes up for the lost space, so to speak. Typically, 1 load meter equals 1,750 kilos. If you use pallets, you can also switch to load counters: 1 Euro pallet (80 × 120 cm) is 0.4 load counters and 1 block pallet (100 × 120 cm) is 0.5 load counters.
What does size / weight mean under sea freight?
For sea freight, you can opt for a full container, but also for a so-called LCL shipment. Then we load several LCL shipments from different owners into one container. In this case you pay for the space used in the container. We calculate with the method size / weight (M / W): per cubic meter ( size ) or per ton ( weight ). Basically the same as the taxable weight, but with a different name.
Is your transport & logistics up-to-date?
Take the free check and get a water bottle.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988966.82/warc/CC-MAIN-20210509092814-20210509122814-00596.warc.gz
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CC-MAIN-2021-21
| 2,896 | 21 |
http://www.hawaii.edu/suremath/tickets.html
|
math
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Reliable problem Solving applied to mixture problems
Observe the simplicity of the two variable mixture problem. It is simpler than the Mary's Apples problem. It involves only one indented step (subproblem) and a result step. Mary's Apples involves two indented steps (subproblems) and a result step.
To solve problems reliably use the following steps recursively.
STEP 1: Identify what the problem/equation asks for.
STEP 2: Respond to the request. Ask "How Would I Find Out?"
STEP 3: Substitute the response(s) to obtain the result.
Copyright 1997. Howard C. McAllister
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CC-MAIN-2015-27
| 571 | 7 |
https://community.filemaker.com/thread/191628
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math
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this is my first post on this community.
Hi would like to know if is possibile and how is possible to customize a pdf export.
Suppose that I have a product list... I would like to export this product list as a customized catalogue.
Everyone as solved it?
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583792784.64/warc/CC-MAIN-20190121131658-20190121153658-00367.warc.gz
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CC-MAIN-2019-04
| 254 | 4 |
http://applet-magic.com/perturbscheme.htm
|
math
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|San José State University|
& Tornado Alley
Suppose there is an equation system
which is not solvable, but there is a related system
that is solvable; say
Typically this means that L(u)=v is a linear system; i.e., L(u1+u2)=L(u1+L(u2). This means that also T(v1+v2)=T(v1)+T(v2).
The scheme of perturbation analysis is to express the unsolvable system as
and work with the deviation function N(u)= (L(u)−M(u)). The above equation is then
Then a scale parameter ε is introduced so the equation under analysis is
A solution of the form
is then sought.
If ε=0 then L(u)=v and hence u0=T(v).
Because of the linearity of L( ) the LHS of the above is
If N(u) is analytic in u then
If the LHS and RHS of the previous equation are equated the coefficients of the correspondin powers of ε must be equal. This means
The solution is then recursive; i.e.,
The solution to the original system is the general solution with ε set equal to 1.
Richard Bellman, Perturbation Techniques in Mathematics, Physics, and Engineering, Holt, Rhinehart and Winston, Inc., New York, 1964.
HOME PAGE OF Thayer Watkins
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662534773.36/warc/CC-MAIN-20220521014358-20220521044358-00437.warc.gz
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CC-MAIN-2022-21
| 1,093 | 19 |
https://techcommunity.microsoft.com/t5/excel/summing-of-vlookup-values/td-p/3129459
|
math
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That's difficult to say without seeing the file or the formula in column H. Can you communicate the formula you entered in cell H8? Probably too many calculations are required to return the result of the formula.
Thank you dear. @Quadruple_Pawn. I have sorted it. That error was because the formula was referring to the entire column. I have one more doubt. In the same way can we count the values instead of summing. Please see the attached image.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662631064.64/warc/CC-MAIN-20220527015812-20220527045812-00619.warc.gz
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CC-MAIN-2022-21
| 448 | 2 |
https://www.mysciencework.com/publication/show/gravitational-microlensing-events-due-stellar-mass-black-holes-3ba99fc5
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math
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We present an analysis of the longest timescale microlensing events discovered by the MACHO Collaboration during a 7 year survey of the Galactic bulge. We find 6 events that exhibit very strong microlensing parallax signals due, in part, to accurate photometric data from the GMAN and MPS collaborations. The microlensing parallax fit parameters are used in a likelihood analysis, which is able to estimate the distance and masses of the lens objects based upon a standard model of the Galactic velocity distribution. This analysis indicates that the most likely masses of 5 of the 6 lenses are > 1 Msun, which suggests that a substantial fraction of the Galactic lenses may be massive stellar remnants. This could explain the observed excess of long timescale microlensing events. The lenses for events MACHO-96-BLG-5 and MACHO-98-BLG-6 are the most massive, with mass estimates of M/Msun = 6 +10/-3 and M/Msun = 6 +7/-3, respectively. The observed upper limits on the absolute brightness of main sequence stars for these lenses are < 1 Lsun, so both lenses are black hole candidates. The black hole interpretation is also favored by a likelihood analysis with a Bayesian prior using a conventional model for the lens mass function. We consider the possibility that the source stars for some of these 6 events may lie in the foreground or background of the Galactic bulge, but we find that this is unlikely. Future HST observations of these events can either confirm the black hole lens hypothesis or detect the lens stars and provide a direct measurement of their masses. Future observations of similar events by SIM or the Keck or VLTI interferometers will allow direct measurements of the lens masses for stellar remnant lenses as well.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583660877.4/warc/CC-MAIN-20190118233719-20190119015719-00418.warc.gz
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CC-MAIN-2019-04
| 1,740 | 1 |
https://ittutoria.net/when-would-there-be-only-four-different-equations-for-a-set-of-math-mountain-numbers/
|
math
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. Advertisement .
. Advertisement .
Hi everyone! If you are confused with the question “When would there be only four different equations for a set of math mountain numbers?” this is also happening to you, don’t worry because the fastest answer and significant knowledge will be right in the information below. Continue reading!
When would there be only four different equations for a set of math mountain numbers?
You can only simplify any equation among these numbers into one of the main equations if it is possible. This means that you have only four true statements and many equivalences.
40 + 40 = 80
80 – 40 = 40
80 = 40 + 40
40 = 80 – 40.
As the two addends are the same, so there would be only four different equations for a set of math mountain numbers.
A system of equations is a set of two sets of x or y values. You can use forms like slope-intercept form (y = mx+ b) or standard form (Ax + By = C) to solve for one variable. The other value will be found by solving for the other. A visual model of the point at intersection can be created by graphing on a coordinate plan.
There are many ways to solve a system equation. One solution to a system of equations can be found. This is either the point at which an ordered pair or graph shows. If the lines are parallel, there can be no solution. If the equations fall on the same line, they can represent the same values and there are infinite solutions.
Above is the answer for the exercise “When would there be only four different equations for a set of math mountain numbers?” and relevant information as well. One day you are confronted with this kind of task. We trust that our method will assist you in completing your assignment quickly. Please offer your thoughts in the comment box if you have any alternative key to this question. Thank you!
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100508.53/warc/CC-MAIN-20231203193127-20231203223127-00416.warc.gz
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CC-MAIN-2023-50
| 1,826 | 13 |
https://asep.lib.cas.cz/arl-cav/sk/detail-cav_un_epca-0360426-Combined-matrices-in-special-classes-of-matrices/
|
math
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Počet záznamů: 1
Combined matrices in special classes of matrices
0360426 - UIVT-O 2012 RIV US eng J - Článek v odborném periodiku
Fiedler, Miroslav - Markham, T. L.
Combined matrices in special classes of matrices.
Linear Algebra and Its Applications. Roč. 435, č. 8 (2011), s. 1945-1955 ISSN 0024-3795
Výzkumný záměr: CEZ:AV0Z10300504
Klíčová slova: combined matrix * Hadamard product * positive definite matrix * M-matrix * totally positive matrix * oscillatory matrix * Cauchy matrix
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.974, rok: 2011
The combined matrix of a nonsingular matrix A is the matrix A o (A(-1))(T), where o means the Hadamard (entrywise) product. It has simple properties, its row- as well as column-sums are always one, and it is not changed if A is multiplied from either side by a nonsingular diagonal matrix. Although it is usually difficult to compute, its further properties deserve attention. In the paper, we concentrate on the sequence of the diagonal entries of combined matrices in various classes of matrices.
Trvalý link: http://hdl.handle.net/11104/0197986
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084889473.61/warc/CC-MAIN-20180120063253-20180120083253-00637.warc.gz
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CC-MAIN-2018-05
| 1,123 | 12 |
https://www.allinterview.com/company/1111/infosys/aptitude-test-questions.html
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math
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Sum of two consecutive nos is 55, larger one is?3 20537
80% pass in english, 70%pass in maths , 10%fail in both , 144 pass in both . How many all appeared to the test?14 80606
If a man stands in front of sun what is the first letter of the direction which is left to him:8 18446
Rearrange MERGANY4 4449
Rearrange BBIRAT4 4210
a group of friends goes for dinner and gets bill of Rs 2400 . Two of them says that they have forgotten their purse so remaining make an extra contribution of Rs 100 to pay up the bill. Tell the no. of person in that group21 65021
9 cards are there. u have to arrange them in a 3*3 matrix. cards are of 4 colors.they are red,yellow,blue,green. conditions for arrangement: one red card must be in first row or second row.2 green cards should be in 3rd column.Yellow cards must be in the 3 corners only. Two blue cards must be in the 2nd row. Atleast one green card in each row.8 11257
4 cards are placed on a table, each card has two colors. U don't know the color of the back side of eachcard.4 persons A B C and D are sitting on the table before the cards. They can see Red, Green Red and blue .Out of the 4 poeple 2 always lie. They see the color on the reverse side and give the following comment A: Yello/green B: Neither Blue/nor Green c: Blue/Yello D: Blue/ Yello find out the color on the other side of the 4 cards.2 5773
There is a 5digit no. 3 pairs of sum is eleven each. Last digit is 3 times the first one. 3 rd digit is 3 less than the second. 4 th digit is 4 more than the second one. Find the digit.9 29058
There are five thieves, each loot a bakery one after the other such that the first one takes 1/2 of the total no. of the breads plus 1/2 of a bread. Similarly 2nd, 3rd,4th and 5th also did the same. After the fifth one no. of breads remained are 3. Initially how many breads were there?12 28903
There are some chicken in a poultry. They are fed with corn One sack of corn will come for 9 days.The farmer decides to sell some chicken and wanted to hold 12 chicken with him. He cuts the feed by 10% and sack of corn comes for 30 days. So initially how many chicken are there?1 8211
Two people X & Y walk on the wall of a godown in opposite direction. They meet at a point on one side and then go ahead. X after walking for some time, walks in opposite direction for 15 mtrs.Then again he turns back and walks in the original direction. What distance did Y walk before they met again, if X walks 11 mtrs by the time Y walks5 7454
There is a 50m long army platoon marching ahead. The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position. In the mean time the whole platoon has moved ahead by 50m. The question is how much distance did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.4 18928
In a sports contest there were m medals awarded on n successive days (n > 1). 1. On the first day 1 medal and 1/7 of the remaining m - 1 medals were awarded. 2. On the second day 2 medals and 1/7 of the now remaining medals was awarded; and so on. 3. On the nth and last day, the remaining n medals were awarded. How many days did the contest last, and how many medals were awarded altogether?1 10498
What causes a hard drive to fail?
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Will you join our company if paid less your current CTC?
Define personnel area. What are its characteristics?
tell me about a time you had to deal with a conflict between a licensed and unlicensed personnel and how handled the situation?
Why is database important?
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How to resolve loops? : bo designer
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What is meant by biotransformation and swertiamarin?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323584554.98/warc/CC-MAIN-20211016074500-20211016104500-00264.warc.gz
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CC-MAIN-2021-43
| 4,084 | 29 |
https://researchwith.njit.edu/en/publications/algorithms-and-applications-to-weighted-rank-one-binary-matrix-fa
|
math
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Many applications use data that are better represented in the binary matrix form, such as click-stream data, market basket data, document-term data, user-permission data in access control, and others. Matrix factorization methods have been widely used tools for the analysis of high-dimensional data, as they automatically extract sparse and meaningful features from data vectors. However, existing matrix factorization methods do not work well for the binary data. One crucial limitation is interpretability, as many matrix factorization methods decompose an input matrix into matrices with fractional or even negative components, which are hard to interpret in many real settings. Some matrix factorization methods, like binary matrix factorization, do limit decomposed matrices to binary values. However, these models are not flexible to accommodate some data analysis tasks, like trading off summary size with quality and discriminating different types of approximation errors. To address those issues, this article presents weighted rank-one binary matrix factorization, which is to approximate a binary matrix by the product of two binary vectors, with parameters controlling different types of approximation errors. By systematically running weighted rank-one binary matrix factorization, one can effectively perform various binary data analysis tasks, like compression, clustering, and pattern discovery. Theoretical properties on weighted rank-one binary matrix factorization are investigated and its connection to problems in other research domains are examined. As weighted rank-one binary matrix factorization in general is NP-hard, efficient and effective algorithms are presented. Extensive studies on applications of weighted rank-one binary matrix factorization are also conducted.
|ACM Transactions on Management Information Systems
|Published - Jul 2020
All Science Journal Classification (ASJC) codes
- Management Information Systems
- General Computer Science
- Discrete data
- pattern discovery
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817699.6/warc/CC-MAIN-20240421005612-20240421035612-00755.warc.gz
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CC-MAIN-2024-18
| 2,015 | 8 |
http://the3dpalette.com/graphic-design/other-art/art/other-art-56
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math
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Hours for phone are
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3D Animation (Maya) Screen shot from Senior Thesis "Head Games"
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s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320368.57/warc/CC-MAIN-20170624235551-20170625015551-00119.warc.gz
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CC-MAIN-2017-26
| 266 | 9 |
https://short-fact.com/what-is-the-most-appropriate-bond-angles-for-a-molecule-with-a-trigonal-pyramid-molecular-geometry/
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math
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Table of Contents
What is the most appropriate bond angles for a molecule with a trigonal pyramid molecular geometry?
Notice that the tetrahedral arrangement of the four electron domains leads us to predict the trigonal-pyramidal molecular geometry. Because the trigonal-pyramidal molecular geometry is based on a tetrahedral electron-domain geometry, the ideal bond angles are 109.5°.
What is a trigonal planar bond?
In chemistry, trigonal planar is a molecular geometry model with one atom at the center and three atoms at the corners of an equilateral triangle, called peripheral atoms, all in one plane. In an ideal trigonal planar species, all three ligands are identical and all bond angles are 120°.
What are the bond angles present in a bent molecule?
In bent molecules, the bond angle is slightly less than 120∘ . This is because lone pairs take up more room than single bonds do. Therefore, the lone pair in a bent molecule takes up more room than the 3rd bond in a trigonal planar molecule does, thereby reducing the angle to slightly less than 120∘ .
Can trigonal planar have double bond?
This molecule has regions of high electron density that consist of two single bonds and one double bond. The basic geometry is trigonal planar with 120° bond angles, but we see that the double bond causes slightly larger angles (121°), and the angle between the single bonds is slightly smaller (118°).
How do you know if a molecule is planar?
If the atoms arrange themselves around the central molecule so that they exist on a single two-dimensional plane, the molecule is planar. The molecule may otherwise form any of several three-dimensional shapes, including tetrahedrons, octahedrons or bipyramids.
How do we calculate bond angle?
Given the distances between 3 atoms, one simple method for calculating bond angles is by use of the trigonometric cosine rule: cosγ = (A2 + B2 − C2) / 2 AB where A, B, C are the lengths of the sides of the triangle ABC, and γ is the angle A-C-B.
Do lone pairs have effect on bond angles?
Lone pair repulsion: Bond angle is affected by the presence of lone pair of electrons at the central atom. A lone pair of electrons at the central atom always tries to repel the shared pair (bonded pair) of electrons. Due to this, the bonds are displaced slightly inside resulting in a decrease of bond angle.
What is the bond angle for PBr3?
As a result they will be pushed apart giving the PBr3 molecule a trigonal pyramidal geometry or shape. The PBr3 bond angle will be about 109 degrees since it has a trigonal pyramidal molecular geometry.
Is NH3 trigonal planar or pyramidal?
The NH3 molecule is trigonal pyramidal, while BF3 is trigonal planar.
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https://www.ivyloungetestprep.com/blog/linear-equation-basics
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math
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Welcome back to the Ivy Lounge Test Prep series on the SAT “math paradox” and the math upgrades you need to beat it! In this series, I’m helping you level up the math skills that are supposed to be “simple” so that you can pick up the (many) points that the SAT offers you for applying these “simple” skills in sophisticated ways. (Check out this refresher course on why you may not know the math you think you know, if you missed the beginning of the series—it explains what it is we’re doing here, and why it will help you snag math points you might otherwise miss!)
So now that you know that we’re here to upgrade your baby Algebra so you can use it in the sophisticated ways the SAT (and, to a lesser extent, the ACT) demands…where do we start? I’ve got you covered. This week, we’re kicking things off with the two baby Algebra upgrades that make the absolute biggest difference. These make everything else I’ll teach afterward possible. So listen up!
Baby Algebra Upgrade #1: Recognize what constitutes a linear equation in the first place.
As you may recall, a line (or linear equation) is simply an equation where both y and x are raised to the first power. In other words, there is no y2 or x3 or sin(x) or 1/x. Just y and x, maybe multiplied by a number, and everything is a different term (i.e. added or subtracted together).
Here’s the most popular form of a line:
y = mx + b
This way of representing the line is called “slope-intercept form,” where “m” is the slope and “b” is the y-intercept.
But these are also legit:
y – y1 = m(x – x1)
This is “point-slope form,” where (x1, y1) is a point on the line and “m” is the slope.
Ax + By = C
This is “standard form,” where “A,” “B,” & “C” are constants, usually integers.
Notice: in all of these examples, x and y are never multiplied or divided together. They might be multiplied or divided by a number and then added or subtracted after that.
For example, these equations are NOT lines:
x/y = 14
2xy + x = 5
But these ARE:
y = 3x – 5
y + 1 = 2(x – 4)
4x – 3y = 9
So now that you get what makes a line in the first place, here’s your trick:
If you need to find out the slope or the y-intercept, just take the equation they gave you and solve for y, putting the equation in the format y = mx + b!
Need to know which line in the answer choices is parallel to (i.e. has the same slope as) the line equation given? Just solve it for y and you’ll see your slope next to the x!
Need to know where the equation will cross the y-axis on the coordinate plane? Just solve it for y and you’ll see your y-intercept as the random number that's being added or subtracted and is NOT multiplied by x.
So there you have your first baby Algebra upgrade!
Knowing what you’re looking at and how to work with it is the foundation of all of the upgrades we’re doing in this series, so pat yourself on the back if you’ve mastered this one, and take a moment to go back and reread if you’re not quite sure yet. If you are…let’s go on to the next one!
Baby Algebra Upgrade #2: Understand the real-world interpretations of a line.
This is my favorite, because it often blows students’ minds.
Say you have a scenario as follows: the wind speed (s) in miles per hour on a mountain relates to the height above sea level (h) in feet with the equation:
s = 3h + 10
What does the 10 signify? What about the 3?
If you’re like most of my students, you’d say, “Kristina, the 10 is the y-intercept and the 3 is the slope!”
To which I’d say, “Okay, but what does that mean?” and get…crickets.
But it’s really helpful to understand what we’re talking about in the real world when we’re talking about linear equations. So I’ve made a couple “mad libs” to help you out in a real-world linear equation scenario:
“Even if my ____ (x) were 0, my ____ (y) would still be ____ (y-intercept).”
In this case:
“Even if my height above sea level were 0, my wind speed would still be 10.”
“For every ____ (unit of x), my ____ (y) increases/decreases by ____ (m).”
In this example:
“For every foot above sea level, my wind speed increases by 3.”
Here’s the best part: the SAT always asks these questions, in pretty much exactly this way. They’ll literally test whether you know what the numbers in a linear equation refer to—so now you have it in your back pocket!
You’re welcome. ;)
So that’s the foundation you need to upgrade your skills with linear equations!
This is literally the tip of the iceberg of upgrading simple Algebra skills, but I felt they were so relevant that even sharing a little bit would help out. If you need the depth and individuality that I can only offer if we’re working one on one, though, you can contact me here.
In my next post, I’ll be showing you what you can do with this upgraded foundation…so stay tuned!
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| 4,908 | 45 |
https://projecteuclid.org/journals/african-diaspora-journal-of-mathematics/volume-14/issue-2/Sasakian-Metrics-with-an-Additional-Contact-Structure/adjm/1375293541.full
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math
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The question of whether a Sasakian metric can admit an additional compatible ($K$)contact structure is addressed. In the complete case if the second structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that the manifold must be 3-Sasakian or an odd dimensional sphere with constant curvature. Some extensions of this result are obtained, mainly in dimensions 3 and 5.
"Sasakian Metrics with an Additional Contact Structure." Afr. Diaspora J. Math. (N.S.) 14 (2) 118 - 133, 2012.
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| 498 | 2 |
http://forums.wolfram.com/mathgroup/archive/2009/May/msg00832.html
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math
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[Date Index] [Thread Index] [Author Index]
Re: Re: 100,000 posts!
Bruce Colletti wrote: > Steve > > Thank you for all you have done for your communities, especially MathGroup. > Without your efforts, history would've unfolded differently: many > collaborations emerged from correspondence on this forum, collaboration that > changed our lives in ways we cannot fathom. All due to you. > > And DeWitt, your professor, friend, and guide. > > We're all looking for the 200K mark and beyond. You'll be around for a very > long time. That reminds me, a talk I give next month is about work that happened through MathGroup. http://aca2009.etsmtl.ca/proposal-details.asp?id=335 The main person behind the method was a fellow from Colombia named Juergen Tischer, who was active in MathGroup around 1998-9. He was, in my opinion, quite adept at using Mathematica to do math. In point of fact, a fair amount of the more interesting computations I have encountered came about through MathGroup interactions. At least three problems I discussed in our 2006 Tech Conference came from MathGroup. http://library.wolfram.com/infocenter/Conferences/6530/ Anyway, I'll add my voice of thanks, and best wishes down what I hope will be a long road. Best, Daniel
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| 1,241 | 3 |
https://mcqslearn.com/math/inverse-of-a-function-multiple-choice-questions.php
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math
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College Degrees Online Courses
College Math MCQs
College Math MCQs - Topic
Practice Inverse of a Function Multiple Choice Questions (MCQ), college math quiz answers PDF with live worksheets for online degrees. Solve functions and limits Multiple Choice Questions and Answers (MCQs), Inverse of a Function quiz questions bank for GRE test. "Inverse of a Function MCQ" PDF book: notation and value of function, odd functions, composition of functions test prep for two year online colleges.
"If ƒ(x) = 2x+1/x-1, then f-1(1) =" Multiple Choice Questions (MCQ) on inverse of a function with choices 1, 0, −1, and −2 for GRE test. Solve inverse of a function quiz questions for merit scholarship test and certificate programs for ACT test prep classes.
If ƒ(x) = 2x+1/x-1, then f-1(1) =
If f is a bijective function, then f-1ƒ(x)) =
If ƒ(x) = ex, then f-1(x) =
If f is a bijective function, then ƒ(f-1(x)) =
If ƒ(x) = 2x+1/x-1, then
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| 937 | 10 |
https://likesoy.com/linear-inequalities-word-problems-worksheet/
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math
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- Title : 19 Inspirational Photos Of Inequality Word Problems Worksheet ... linear inequalities word problems worksheet in Common Worksheets category
- Filename : Common Worksheets-19 Inspirational Photos Of Inequality Word Problems Worksheet ...-linear inequalities word problems worksheet
- Filetype: PNG
- Original Size: 1024 x 581 pixels
- Resolution: HD
- Category : Common Worksheets
- Labeled with: systems of linear inequalities word problems worksheet‚ systems of inequalities word problems worksheet pdf‚ systems of linear inequalities word problems worksheet answers and linear inequalities word problems worksheet with answers‚ systems of linear inequalities word problems worksheet with answers‚ graphing linear inequalities word problems worksheet or common worksheets category
Some questions frequently asked by users : open question: help with algebra homework? anyone? pretty please?
so i'm doing a worksheet on writing systems of inequalities to solve word problems. i've got a quiz on the material tomorrow, and of course i'm completely stuck. one problem is as follows: you can work at most 20 hours next week. you need to earn at least $92 to cover your weekly expenses. your dog-walking job pays $7.50 per hour and your job as a car wash attendant pays $6 per hour. write a system of linear inequalities to model the situation. any help would be greatly appreciated! thanks!this may be long but im paying 10 points and money algebra a homework..slope of a line?
i'm kind of totally lost on this bull i kind of know how to find slope but this doesn't make sense ok at the bottom says write letters in order after you solve the front.. ok i got 16 problems..heres the answer box.. o.0 r.-2 n.3/2 y.2 d. some 0 with a cross over it diagnol. t.-1/3 g.3 h.-1 i.1/4 u.-3/5 a-3 e.6 ok those are the answers we have to pick for these type of problems.. 1.(0,2)(5,2) 2.(-3,1)(2,-2) 3.y=3x+4 4.(6,-3)(1,2) 5.(-1,0)(-4,1) 6.2x+y=-1 7.y=6x-1 8.(-3,8)(-3,4) 9.y=-x-7 10.(0,1)(1,7) 11.(1,-2)(-2,4) 12.x-4y=7 13.3x-y=10 14.(-3,-4)(2,-4) 15.-3x+2y=6 16.18x-3y=-20 ok so for all of those i had to find the slope of a line.. i did most of them but the sentence under doesn't make any sense at all..and i think i did it wrong all.. here is how the sentence goes already has some words in it william (8 underscores to put in letters)first used the symbol for parallel and pierre(8 underscores to put in letters)first used the symbol for perpendicular if someone could help me with this whole thing i would admire it and might pay you via paypal if you have an account a few bucks to help me figure this stuff out.. i cant find the worksheet online title is finding the slope of a line at top right corner says 4-6 and bottom right i think page is 135 and on left bottom says graphing linear equations and inequalities copyright c 2003 john wiley & sons, inc.
- Total Download : 188
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s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221219469.90/warc/CC-MAIN-20180822030004-20180822050004-00357.warc.gz
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CC-MAIN-2018-34
| 2,891 | 11 |
https://www.jiskha.com/display.cgi?id=1382707507
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math
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posted by cal .
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
y(x) = 6x/(x-9)^2
when i workout this problem I get this:
by quotient rule:
dy/dx = ( (x-9)^2 (6) - 6x(2)(x-9))/(x-9)^4
= 0 at a horizontal tangent
6(x-9)^2 - 12x(x-9) = 0
6(x-9)[x-9 - 2] = 0
6(x-9)(x-11) = 0
x=9 or x=11 , but x≠9 , there is a vertical asymptote at x=9
x = 11
but I have these answer choices to choose from:
A. x=9 and x=6
C. x=-9 and x=6
D. x= 6
E. The graph has no horizontal tangents.
is it E then
you lost an x there when factoring out the 6(x-9)
y' = -6(x+9)/(x-9)^3
y'=0 at x = -9
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| 622 | 21 |
https://app-wiringdiagram.herokuapp.com/post/geometry-semester-exam-answers-semester-2
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math
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GEOMETRY SEMESTER EXAM ANSWERS SEMESTER 2
Geometry Semester 2 Final Exam Flashcards | Quizlet
Start studying Geometry Semester 2 Final Exam. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
Semester 2 Exam Review - Geometry
semester 2 exam review The semester exam is going to have Multiple Choice questions covering skills and Free Response questions covering Applications from Units 1-6. If you complete and understand this review packet then you will do very well on the exam.
Geometry Semester 2 Exam Review - District Home page
Home: Rochester High School Home Page: Teacher Web Pages: Mathematics: Mrs. Smith: Geometry: Geometry Semester 2 Exam Review Files & Folders Geometry Semester 2 Exam Formulas[PDF]
Geometry Semester 2 Exam Review - tippcityschools
2. Class: Date: Geometl,g Geometry Semester 2 Exam Review (Chapters 7-12) Short Answer l. The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the hei t of the actual Sears Tower? I 6. 8. A
Geometry Semester 2 Final Exam - Ms. Mancini's Website
Final Exam Review Packet Solutions Formula Sheet List of Topics Covered in Second Semester Geometry Review Videos Circles & Polygons Surface Area & Volume Circles, Arcs, & Angles Scale Factors & Similarity Trigonometry Coordinate Geometry Transformations General Exam Info Second Semester Exam Schedule 2016 Semester Grade Calculator
geometry review semester 2 Flashcards - Quizlet
Learn geometry review semester 2 with free interactive flashcards. Choose from 500 different sets of geometry review semester 2 flashcards on Quizlet.
Geometry Semester 2 Review - Printable Worksheets
Geometry Semester 2 Review. Showing top 8 worksheets in the category - Geometry Semester 2 Review. Some of the worksheets displayed are 2014 2015 geometry review answers, Final exam review packet, Geometry 1 semester review answers, Review basic mathematics math 010, Sandia high school name geometrysecond semester final exam, 2 line segments and measure inches, First semester exam
Geometry Honors STCE - Final Exam: Semester 2
Made with the new Google Sites, an effortless way to create beautiful sites.[PDF]
2015-2016 Geometry A Review Answers
GEOMETRY A Semester Exam Review Answers © MCPS Unit 1, Topic 2 8. A 4,2 9. a. A translation five units to the right and three units down. b.[PDF]
Sandia High School Name: Geometry—Second Semester
Geometry: Second Semester Final Exam Page 1 of 11 Sandia High School Name: _____ Geometry—Second Semester FINAL EXAM Mark the letter to the single, correct (or most accurate) answer to each problem. 1. What is the value of x in the triangle on the right? A. 12 B. 6 C. 2 3 D. 4 E. 8 2.
Related searches for geometry semester exam answers semester 2
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| 3,044 | 23 |
https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/all/213/2/88361/conformal-actions-with-prescribed-periods-on-riemann-surfaces
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math
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Conformal actions with prescribed periods on Riemann surfaces
Volume 213 / 2011
Fundamenta Mathematicae 213 (2011), 169-190 MSC: Primary 30F10; Secondary 30F35, 37E30, 14H37. DOI: 10.4064/fm213-2-3
It is a natural question what is the set of minimal periods of a holomorphic maps on a Riemann surface of negative Euler characteristic. Sierakowski studied ordinary holomorphic periods on classical Riemann surfaces. Here we study orientation reversing automorphisms acting on classical Riemann surfaces, and also automorphisms of non-orientable unbordered Klein surfaces to which, following Singerman, we shall refer to as non-orientable Riemann surfaces. We get a complete set of conditions for the existence of conformal actions with a prescribed order and a prescribed set of periods together with multiplicities. This lets us determine the minimal genus of a surface which admits such an action.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224646076.50/warc/CC-MAIN-20230530163210-20230530193210-00047.warc.gz
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CC-MAIN-2023-23
| 898 | 4 |
http://www.e-booksdirectory.com/details.php?ebook=4583
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math
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Foliations and the Geometry of 3-manifolds
by Danny Calegari
Publisher: Oxford University Press 2007
Number of pages: 371
The purpose of this book is to give an exposition of the "pseudo-Anosov" theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms, and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
Home page url
Download or read it online for free here:
by Bruce Hughes, Andrew Ranicki - Cambridge University Press
The book gathers together the main strands of the theory of ends of manifolds from the last thirty years and presents a unified and coherent treatment of them. It also contains authoritative expositions of mapping tori and telescopes.
by William P Thurston - Mathematical Sciences Research Institute
The text describes the connection between geometry and lowdimensional topology, it is useful to graduate students and mathematicians working in related fields, particularly 3-manifolds and Kleinian groups. Much of the material or technique is new.
by Allen Hatcher
These pages are really just an early draft of the initial chapters of a real book on 3-manifolds. The text does contain a few things that aren't readily available elsewhere, like the Jaco-Shalen/Johannson torus decomposition theorem.
by Nigel Hitchin
Geometry of Surfaces by Nigel Hitchin is a textbook on surfaces. However the author is also going to try and consider surfaces intrinsically, or abstractly, and not necessarily embedded in three-dimensional Euclidean space.
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| 1,548 | 15 |
https://projecteuclid.org/journals/duke-mathematical-journal/volume-108/issue-1/Braid-group-actions-on-derived-categories-of-coherent-sheaves/10.1215/S0012-7094-01-10812-0.short
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math
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This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety $X$. The motivation for this is M. Kontsevich's homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results is that when dim $X\geq 2$, our braid group actions are always faithful.
We describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities. Relations with the McKay correspondence and with exceptional sheaves on Fano manifolds are given. Moreover, the case of an elliptic curve is worked out in some detail.
"Braid group actions on derived categories of coherent sheaves." Duke Math. J. 108 (1) 37 - 108, 15 May 2001. https://doi.org/10.1215/S0012-7094-01-10812-0
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CC-MAIN-2024-10
| 902 | 3 |
https://forum.dynare.org/t/subscript-indices-must-either-be-real-positive-integers/546
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math
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I have just tried to conduct a simulation of a deterministic model and received the above message from Matlab, after it returned the steady state values of the model (which were all correct). The model is linear and all variables are expressed in deviations from the steady state. I have used the command “linear” but this does not seem to be responsible for the problem as the problem persists when I delete it. I have attached the mod file. Many thanks for your help!
nonstochlinear.mod (1.87 KB)
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662520936.24/warc/CC-MAIN-20220517225809-20220518015809-00708.warc.gz
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CC-MAIN-2022-21
| 502 | 2 |
https://www.arxiv-vanity.com/papers/0906.1021/
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math
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Integrable and superintegrable systems with spin in three-dimensional Euclidean space
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin and , is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components of linear momentum. Several such systems are found and for one non-trivial example we show how superintegrability leads to exact solvability: we obtain exact (nonperturbative) bound state energy formulas and exact expressions for the wave functions in terms of products of Laguerre and Jacobi polynomials.
PACS numbers: 02.30.Ik, 03.65.-w, 11.30.-j, 25.80.Dj
The purpose of this research program is to perform a systematic study of integrability and superintegrability in the interaction of two particles with spin. Specifically in this article we consider a system of two nonrelativistic particles, one with spin (e.g. a nucleon) the other with spin (e.g. a pion), moving in the three-dimensional Euclidean space .
The Pauli-Schrödinger equation in this case will have the form
where the term represents the spin-orbital interaction. We use the notation
for the linear momentum, angular momentum and Pauli matrices, respectively. The curly bracket in (1.1) denotes an anticommutator.
For spinless particles the Hamiltonian
is a scalar operator, whereas in (1.1) is a matrix operator and is a two component spinor.
In the spinless case (1.5) the Hamiltonian is integrable if there exists a pair of commuting integrals of motion , that are well-defined quantum mechanical operators, such that , and are algebraically independent. If further algebraically independent integrals exist, the system is superintegrable. The best known superintegrable systems in are the hydrogen atom and the harmonic oscillator. Each of them is maximally superintegrable with independent integrals, generating an and an algebra, respectively [1, 2].
A systematic search for quantum and classical superintegrable scalar potentials in (1.5) with integrals that are first- and second-order polynomials in the momenta was performed some time ago [3, 4, 5]. First-order integrals correspond to geometrical symmetries of the potential, second-order ones are directly related to the separation of variables in the Schrödinger equation or Hamilton-Jacobi equation in the classical case [3, 6, 7, 8].
First- and second-order integrals of motion are rather easy to find for Hamiltonians of the type (1.5) in Euclidean space. The situation with third- and higher-order integrals is much more difficult [9, 10, 11].
If a vector potential term, corresponding e.g. to a magnetic field is added, the problem becomes much more difficult and the existence of second-order integrals no longer implies the separation of variables [12, 13].
The case (1.1) with a spin-orbital interaction turns out to be quite rich and rather difficult to treat systematically. In a previous article we have considered the same problem in . Here we concentrate on the Hamiltonian (1.1) in but restrict to first-order integrals. Thus we search for integrals of motion of the form
where , , , and , , , () are all scalar functions of .
In Section 2 we show that a spin-orbital interaction of the form
can be induced by a gauge transformation from a purely scalar potential (in particular from ). In Section 3 we derive and discuss the determining equations for the existence of first-order integrals. In Section 4 we restrict to rotationally invariant potentials and and classify the integrals of motion into multiplets. Solutions of the determining equations are obtained in Section 5. Superintegrable potentials are discussed in Section 6. In Section 7 we solve the Pauli-Schrödinger equation for one superintegrable system explicitly and exactly. Finally, the conclusions and outlook are given in Section 8.
2 Spin-orbital interaction induced by a gauge transformation
In this Subsection we show that a spin-orbit term could be gauge induced from a scalar Hamiltonian (1.5) by a gauge transformation. The transformation matrix must be an element of
where () are real functions of (). It is seen that in order to generate a spin-orbit term we need to have
where is an arbitrary real scalar function of (). Equation (2.2) implies first-order partial differential equations for and , three of which are , . Hence, without loss of generality we choose and then write the remaining equations as
which could be solved for the highest-order derivatives of (i.e. , and ). Then, the compatibility conditions of these give
which implies that . Hence, we conclude that is gauge induced and it is the only potential which could be generated from a scalar Hamiltonian by a gauge transformation.
The explicit form of the gauge transformation is found as
where , and are the following constants
With this transformation matrix the transformed Hamiltonian is found to be
2.2 Integrals for and
The potential is gauge induced from a Hamiltonian of the form (1.5) (though each term is multiplied by a identity matrix). Hence the integrals for this case are just the gauge transforms of the integrals of motion of this Hamiltonian (i.e. and ). They can be written as
and satisfy the following commutation relations
The Lie algebra is isomorphic to a direct sum of the algebra with itself
2.3 Integrals for and
Since these potentials are gauge induced from a free Hamiltonian, the integrals are just the gauge transforms of , and , which can be written as
They satisfy the following commutation relations
Hence the -dimensional Lie algebra is isomorphic to a direct sum of the Euclidean Lie algebra with the algebra
3 Determining equations for an integral of motion
In this Subsection we give the full set of determining equations obtained from the commutativity condition , where is the Hamiltonian given in (1.1) and is the most general first-order integral of motion given in (1.6). This commutator has second-, first- and zero-order terms in the momenta. By setting the coefficients of different powers of the momenta equal to zero in each entry of this matrix we obtain the following determining equations. Since, the Planck constant enters into the determiming equations in a nontrivial way we keep it throughout the whole set of determining equations. However, after giving the determining equations we set for simplicity.
i) Determining equations coming from the second-order terms
From the diagonal elements it is immediately found that , and are linear functions and are expressed for any potentials and as
where and () are real constants. After introducing (3.1) into the rest of the coefficients of the second-order terms and separating the imaginary and real parts of the coefficients coming from the off-diagonal elements we are left with an overdetermined system of eighteen partial differential equations for , , () and . These are,
ii) Determining equations coming from the first-order terms
After introducing (3.1) and separating the real and imaginary parts, we have the following twelve partial differential equations
where , and are given in (3.1). There are also nine other second-order partial differential equations for , , and , coming from the coefficients of the first-order terms. However, these are differential consequences of (3.2) so we do not present them here.
iii) Determining equations coming from the zero-order terms
Setting the coefficients of the zero-order terms in each entry of the commutation relation equal to zero and separating the real and imaginary parts, we have the following four partial differential equations
3.2 Discussion of solution in general case
In general the solution of the determining equations (3.2)-(3.5) for the unknowns , , and , , , () turns out to be a difficult problem. However, it is seen that the determining equations (3.3) do not involve , , , () and and hence could be analyzed separately.
In order to determine the unknown functions and , we express the first-order derivatives of ’s from (3.3) and require the compatibility of the mixed partial derivatives. This requirement gives us another equations for ’s and first-order derivatives of them. Now, if we introduce the first-order derivatives of ’s from (3.3) into this system, we get a system of algebraic equations for ’s (). This system of algebraic equations can be written in the following way:
where is a matrix and and are and vectors, respectively. The matrix can be written as:
where () are defined as follows
The vector is and the entries of the vector are given as follows:
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500250.51/warc/CC-MAIN-20230205063441-20230205093441-00425.warc.gz
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CC-MAIN-2023-06
| 8,568 | 50 |
https://www.thestudentroom.co.uk/showthread.php?t=507132
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math
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im really confused about certain ways to get the domain of a function. how do you tell when it is a one tail or two tail domain? and when do you use the inequalities < and > or <_ and >_?
also how do you find the range?
Turn on thread page Beta
domain and range watch
- Thread Starter
- 10-01-2008 21:04
- 10-01-2008 21:58
The range of the function is the y-co-ordinates that the function produces.
I am not sure what you're talking about with a one-tail or two tail domain though.
has a domain of x e R (x is a real number) and a range of
The inverse function, has a domain of since you can only put positive numbers under the square root sigh, and it has a range of since you will only get a positive answer. (You can only find the inverse of a function if each value of x produces only one value of f(x), which means the function is called one to one, and so you can't have +/- before the square root sign. )
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823618.14/warc/CC-MAIN-20181211104429-20181211125929-00082.warc.gz
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CC-MAIN-2018-51
| 911 | 11 |
https://kopavguldvxtd.web.app/27073/54830.html
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math
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Taylor- och Maclaurinutvecklingar - Envariabelanalys - Ludu
C. 1,2. D. 2,1. Easy. Answer.
Red. 9. −. Blue. 1. Sine.
Stability analysis for periodic solutions of fuzzy shunting
y y, and the right side with respect to. x. x x. ∫ 1 d y = ∫ sin ( 5 x) d x.
PDF Existence of almost periodic solution for SICNN with a neutral
Therefore, the desired solution is y = 1. 2 cos(2x) +. √. 3. 2 sin(2x). 4.
4 4 sin( ) 0
Se hela listan på mathsisfun.com
Solving Trigonometric Equations – General Solutions. Since trig functions go on and on in both directions of the \(x\)-axis, we’ll also have to know how to solve trig equations over the set of real numbers; this is called finding the general solutions for these equations. Differential Equations Book: Elementary Differential Equations with Boundary Value Problems (Trench) 6: Applications of Linear Second Order Equations
Differential Equations . When storage elements such as capacitors and inductors are in a circuit that is to be analyzed, the analysis of the circuit will yield differential equations. This section will deal with solving the types of first and second order differential equations which will be encountered in
(iii) The highest order derivative present in the differential equation is y¢¢¢, so its order is three. The given differential equation is not a polynomial equation in its derivatives and so its degree is not defined. EXERCISE 9.1 Determine order and degree (if defined) of differential equations given in E˜ercises 1 to 10.
Trust in media
differential equations. 3rd ed. (sin au du = cos alle + c.
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C cos px + D sin px kepx. Cepx sum of the above sum of the 19 Aug 2018 We say that sinusoidal forcing occurs in the differential equation dtxc+5xc=d2dt 2(xRe+ixIm)+6ddt(xRe+ixIm)+5(xRe+ixIm)=e2it=cos2t+isin2t. 26 Mar 2012 A similar procedure will allow us to define an “inverse” for the trigonometric functions sin, cos, and tan.
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CC-MAIN-2022-49
| 2,350 | 29 |
https://testbook.com/question-answer/statement-i-in-fanno-flow-heat-transfer-is-neg--5ea3d1a6f60d5d53736f952a
|
math
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Statement (I): In Fanno flow, heat transfer is neglected and friction is considered.Statement (II): In Rayleigh flow, heat transfer is considered and friction is neglected.
Free Practice With Testbook Mock Tests
This question was previously asked in
Fanno Flow: Flow in a constant area duct with friction and without heat transfer is known as Fanno Flow
Rayleigh Flow: Flow in a constant area duct with heat transfer and without friction is called Rayleigh Flow.
Conclusion: Statement I) is condition for fanno flow and statement II) is condition for Rayleigh flow but statement II) is not explaining the statement I).
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CC-MAIN-2021-31
| 618 | 6 |
http://vixra.org/abs/1910.0317
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math
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Authors: Wu Ye TangYin
According to the random theory and hypothesis theory, the calculation of any number is pushed to infinity. In this paper, 2n-a = 2 * B (B does not know whether it is prime number, or compound number. So the hypothesis plays an important role in judgment. If B is equal to prime, then there is no need to calculate. If B is a compound number, its factorization prime factor, we can get the prime number, and then we can calculate it. But infinity belongs to the unknown. We don't know what it is to decompose prime factors. Only a, B, C, D.. Then suppose it is a composite number. In this paper, it is only for infinite odd numbers. Is there an inverse column? Odd numbers are not equal to two same prime numbers, plus the sum of odd prime numbers.)
Comments: 13 Pages. Please forgive me for my low level of mathematics writing. The article is right
[v1] 2019-10-17 02:18:31
Unique-IP document downloads: 11 times
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Add your own feedback and questions here:
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s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251678287.60/warc/CC-MAIN-20200125161753-20200125190753-00509.warc.gz
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CC-MAIN-2020-05
| 1,624 | 8 |
https://www.bakersfieldcollege.edu/academics/pathways/stem/mathematics.html
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math
|
The Mathematics program at Bakersfield College is designed to provide students with a strong foundation in mathematics and its applications. This program covers a wide range of mathematical topics such as calculus, differential equations, linear algebra, and statistics.
Students will gain problem-solving skills and critical thinking abilities that are highly valued in the workforce. Additionally, this program offers a pathway to transfer to a four-year university for students who wish to pursue further education in mathematics or related fields. The Mathematics Associate in Science for Transfer Degree from Bakersfield College prepares students for various careers that require mathematical skills or advanced studies in mathematics.
What is Mathematics?
Mathematics is a field of study that deals with the concepts of numbers, quantities, shapes, and patterns. It is a systematic approach to understanding the world around us and involves the use of logical reasoning, problem-solving, and critical thinking. Mathematics is an essential tool for various fields such as science, engineering, finance, and technology. It encompasses various subfields such as algebra, geometry, calculus, statistics, and probability, and has applications in everyday life, from calculating expenses to designing bridges and buildings. Mathematics is a universal language that allows us to communicate and solve problems in a precise and consistent manner.
Is it Mathematics Right for Me?
A Mathematics associate degree is beneficial for individuals who have an aptitude for logical reasoning and problem-solving and who enjoy working with numbers and abstract concepts. This associate in science for transfer degree program is ideal for individuals who are interested in pursuing a career in a math-related field or who want to transfer to a four-year university to continue their studies in mathematics or a related field. A Mathematics associate degree also provides a solid foundation for individuals who plan to pursue further studies in fields such as physics, engineering, computer science, and economics.
There are several key traits and skills that would make someone a good fit for studying Mathematics, including:
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Overall, a strong work ethic, a love for learning, and a passion for problem-solving are essential traits for those who wish to study Mathematics.
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A degree in Mathematics can lead to various careers in fields such as science, technology, engineering, and finance. Some career options for individuals with a Mathematics associate degree include:
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Overall, a Mathematics associate degree can lead to various career opportunities that require analytical skills and mathematical knowledge. It also provides a foundation for further studies in mathematics or related fields. You can research more about what you can do with a math degree at these resources:
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Transfer to a University
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See the entire list of Mathematics (MATH) courses available at BC in the catalog.
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For students who need help with reviewing or relearning foundational mathematics skils, the Mathematics Department has started two new non-credit courses. You may take either of these courses while you are taking a credit math course, or you can sign up for only a non-credit class to get some structured math review, especially to improve algebra skills.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510924.74/warc/CC-MAIN-20231001173415-20231001203415-00335.warc.gz
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CC-MAIN-2023-40
| 4,970 | 35 |
http://www.saharaincorporated.com/lib/algorithm-for-approximating-complex-polynomial-zeros-1998
|
math
|
By Pan V.
Read or Download Algorithm for approximating complex polynomial zeros (1998) PDF
Best algorithms and data structures books
Symposium on Algorithms (ESA '93), held in undesirable Honnef, close to Boon, in Germany, September 30 - October 2, 1993. The symposium is meant to launchan annual sequence of foreign meetings, held in early fall, overlaying the sector of algorithms. in the scope of the symposium lies all study on algorithms, theoretical in addition to utilized, that's performed within the fields of desktop technological know-how and discrete utilized arithmetic.
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Extra resources for Algorithm for approximating complex polynomial zeros (1998)
There is a source s that feeds all the lines. The capacity of each arc (s, S) emanating from the source equals x(S) · c(S). There is a sink t that is fed by all the rectangles. The capacity of every arc (u, t) entering the sink equals 1. Observation 1. There is a one-to-one correspondence between vectors y such that (x, y) is a partial cover and flows f in Nx . The correspondence y ↔ fy satisfies fy (u, t) = S|u∈S y(S, u), for every rectangle u ∈ U, and fy (s, S) = u∈S y(S, u), for every line S ∈ S.
6: for each rank ρ in DR ∩ [c, . . , c + ci1 ] do 7: Let be the line stored at A2 [ρ − c]. 8: Update DI to record the pair ( 1 , ) as the intersection with rank ρ. } 10: Let c := c + ci1 . 11: i1 := i1 + 1. } 13: i2 := i2 + 1. 14: end if 15: end for algorithm CountAndRecord is an iterative algorithm that computes, during the i-th iteration the element with rank i in the final sorted order (Line 3 of Algorithm 2). Thus we only need to be able to find out whether the line that will be the i-th element in sorted order is an element involved in an intersection.
We denote the LP-relaxation by lp-soft. The integrality gap of both lp-hard and lp-soft is at least 2 − o(1) even in the one-dimensional case. Consider an instance that contains k + 1 rectangles and two lines of capacity k that intersect all the rectangles. A fractional optimal solution is x∗ (S) = (k + 1)/(2k) for each line S and y ∗ (S, u) = 1/2 for every line S and rectangle u. This means that the value of the fractional minimum is 1 + k1 , while the integral optimum is 2. The following definitions apply to both lp-hard and lp-soft.
Algorithm for approximating complex polynomial zeros (1998) by Pan V.
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CC-MAIN-2019-09
| 3,342 | 17 |
https://lists.gnu.org/archive/html/help-glpk/2011-05/msg00064.html
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math
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I first studied linear programming in the mid-70's, and the course textbook was by David Gale (originally out in 1960). Using Google Books, I was able to dig it up
- he uses canonical form for the equality constraint version:
Look on Page 75.
Another textbook popular at that time was by Saul Gass (1958) who uses standard form for the equality constraint version:
Look on page 129.
Bob Vanderbei, a ex-colleague (but still a friend) of mine from Bell Labs, now a professor at Princeton, uses standard form to apply to the inequality version in his book
(first edition from 1996):
Look on page 57
A book by Dantzig and Thapa uses standard form to apply to equality constraint version:
See page 48
A more recent book by Karloff (2009) uses standard form to apply to equality and canonical form to apply to the inequality case.
Look at page 5
So, just based on my not-so random sample, I have to go with Andrew's terminology (that the Standard Form applies to the equality version) since it seems like that is used a little more than the others. Breaks
my heart to do so :)
Sent: Thursday, May 12, 2011 1:21 PM
To: Meketon, Marc
Cc: Robbie Morrison; GLPK help
Subject: Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations)
> > Many books call the min c'x, s.t. Ax=b, x>=0 form the "canonical"
> > linear programming program. The min c'x s.t. Ax >= b, x>=0 is
> > often called the "standard" form, because it has more symmetry with
> > the dual (which is max b'y s.t. A'y<=c, y>=0).
I consulted the "Encyclopedia on Optimization" by Floudas and Pardalos (Eds.), Springer, 2009. The article "Linear Programming" by P.Pardalos, pp.1883-1886, Section "Problem Description", says:
"Consider the linear programming problem (in standard form):
s.t. Ax = b
x >= 0
The same term "standard form" is used in the next article "Linear
Programming: Interior Point Methods" by K.M.Anstreicher, and some other articles dedicated to linear programming.
This e-mail and any attachments may be confidential or legally privileged. If you received this message in error or are not the intended recipient, you should destroy the e-mail message and any attachments
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CC-MAIN-2021-43
| 2,370 | 30 |
http://commodity-mcx-tips.blogspot.com/2011/02/commodity-gold-next-week-outlook.html
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math
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COMEX Gold is in an upward consolidation phase. Last week COMEX Gold sustain above
the level of 1340 and able to sustain it. In the coming week 1310$ will act as a major
support in COMEX Gold, if COMEX Gold sustains above 1368$ an ounce then above 1370 $
an ounce it can touch the level of 1390$ an ounce and if COMEX Gold sustains below
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For the next week traders can use buy on lower level strategy if COMEX Gold sustains above
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Major support for COMEX Gold in the coming week is 1310$ and 1260$.
Major resistance for COMEX Gold in the coming week is 1400$ and 1435$
Major support in MCX Gold is 19700 and 19300
Major resistance in MCX Gold is 20550 and 20850
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122933.39/warc/CC-MAIN-20170423031202-00261-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 890 | 12 |
http://www.tectechnicsclassroom.tectechnics.com/s7p6a66/amount-of-energy-produced-when-methane-is-combusted-to-form-water.php
|
math
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Pj Problems - Overview
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The combustion of 1 molecule of methane gas has water as a product:
(a) Calculate the amount of energy produced during this reaction.
(b) A typical X-ray photon has an energy of 8eV. How does the energy produced in(a) compare to the energy of the X-ray photon?
S7P6A66 (grouping/interaction - chemical).
Pj Problem of Interest is of type grouping/interaction (chemical).
(a) The balanced chemical equation is:
CH4(g) + 2O2(g) -------> CO2(g) + 2H2O(l)
ΔH0reaction = ΣnΔH0f(products) - ΣmΔH0f(reactants)
Where ΔH0 = standard enthalpy change at standard pressure (1 atm) and temperature 250C (298 K).
ΔHf = enthalpy of formation
n is coefficients of products and m is coefficients of reactants.
Enthalpy Of Formation From Enthalpy Table:
ΔH0f of CH4 = -74.80 kJ
ΔH0f of O2 = 0 (since this is the most stble state of oxygen)
ΔH0f of CO2 = -393.5 kJ
ΔH0f of H2O = -285.8 kJ
ΔH0reaction = -393.5 -2(285.8) - (-74.8) = -965.1 + 74.8 = -890.4 kJ.
So 890.4 kJ of energy is released when 1 mole of CH4 is combusted
1 mole contains 6.022 x 1023 molecules (Avogadro's number)
So, energy released from combustion of 1 molecule of CH4(g) = (890.4)/(6.022 x 1023) = 1.479 x 10-18 J/molecule.
(b) 1eV = 1.602 x 10-19 J
So, 8eV = 8(1.602 x 10-19) = 1.2 x 10-15 J/photon
So, the energy from a photon of X-ray is 1000 times more than that produced from the combustion of 1 molecule of CH4(g).
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
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CC-MAIN-2023-40
| 2,638 | 49 |
https://www.splashlearn.com/s/math-lesson-plans/decimal-division-math-adventures-await
|
math
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The objective of this lesson is to help students master the skill of dividing decimals by whole numbers and other decimals. They will learn different strategies and techniques to solve division problems involving decimals.
Estimating the quotient in decimal division involves rounding the decimal to the nearest whole number. This helps in getting a rough idea of what the actual quotient might be.
Certainly! In this lesson, students will learn how to divide two decimals by converting one or both numbers into whole numbers using powers of 10. They will then follow similar steps as dividing by a whole number.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679099892.46/warc/CC-MAIN-20231128151412-20231128181412-00164.warc.gz
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CC-MAIN-2023-50
| 612 | 3 |
http://www.chegg.com/homework-help/managerial-accounting-14th-edition-chapter-8-solutions-9780078111006
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math
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Midwest Products is a wholesale distributor of leaf rakes. Thus, peak sales occur in August of each year as shown in the company’s sales budget for the third quarter, given below:
Budgeted sales (all on account)
From past experience, the company has learned that 20% of a month’s sales are collected in the month of sale, another 70% are collected in the month following sale, and the remaining 10% are collected in the second month following sale. Bad debts are negligible and can be ignored. May sales totaled $430,000. and June sales totaled $540,000.
1. Prepare a schedule of expected cash collections from sales, by month and in total, for the third quarter.
2. Assume that the company will prepare a budgeted balance sheet as of September 30. Compute the accounts receivable as of that date.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660706.30/warc/CC-MAIN-20160924173740-00164-ip-10-143-35-109.ec2.internal.warc.gz
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CC-MAIN-2016-40
| 801 | 5 |
https://internetoracle.org/digest.cgi?N=193
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math
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} Yes. I do circumcisions. I also do circumscriptions, subscriptions,
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988741.20/warc/CC-MAIN-20210506053729-20210506083729-00450.warc.gz
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CC-MAIN-2021-21
| 844 | 13 |
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