content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Recursions which define polynomials
up vote 16 down vote favorite
11
There are many examples (Somos sequences, special polynomials related to rational solutions of the Painleve equations) when a recurrence relation, which a priori produces a sequence of rational
functions, in reality results in a polynomial sequence. ... | 5 | [
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0.007049560546875,
0.00823974609375,
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0.056640625,
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-0.017578125,
0.0196533203125,
-0.03... | 35,600 | 35600 | |
Homework Help
Posted by mary on Friday, April 22, 2011 at 7:55pm.
-12x+10/5 = - x/20
I can't decide if I should cross multiply by -20 or just 20. The - is in the middle of the x and 20 (like a fraction)
I came up with 2 possible answers:
x=40/49 and x = 40/47
• algebra - Damon, Friday, April 22, 2011 at 8:04pm
... | 4 | [
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0.03125,
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0.08349609375,... | 35,601 | 35601 | |
Find the angular speed
August 29th 2008, 02:10 AM
jcrodua
Find the angular speed
A car is traveling at 40 mph and has tires that are 94 meters in diameter. Find the angular speed of the wheel in revolution per minute.
August 29th 2008, 07:38 AM
Soroban
Hello, jcrodua!
I'm sure there's typo . . . plea... | 4 | [
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0.080078125,
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0.08984375,
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0.12060546875,
... | 35,602 | 35602 | |
Word Problem Integration
Let $x$ be a function of $t$ such that $\frac{dx}{dt}=2\sin^2 t\cos^2 x$. Suppose that $x\left(\frac{\pi}{4}\right)=\arctan \left(\frac{1}{2}+\frac{\pi}{4}\right)$. Then $x(0)=$ Thanks
$<br /> \begin{gathered}<br /> \frac{{dx}}<br /> {{dt}} = 2\sin ^2 t\cos ^2 x \hfill \\<br /> \hfill \\<br />... | 5 | [
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Level of significance without mean given
November 5th 2008, 08:11 PM
Alex103
Level of significance without mean given
Hi, i can't remember how to do this problem and i have been having trouble finding an answer.
The question is "An SRS of size 15 is taken from a normal distribution with standard deviation o... | 5 | [
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problem with derivative
August 2nd 2010, 08:41 PM #1
problem with derivative
ok so for the function f(x) = (x^(3/5))(x^(2)-13) (the many parentheses are to make it clear) i am supposed to find f'(x) and the intervals in which f(x) is decreasing and increasing
i found f'(x) = (13/5)(x^(-2/5))(x^(2)-3)
i th... | 4 | [
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0.056640625,
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0.002395... | 35,605 | 35605 | |
Fibonnacci sequence
Can anyone explain if the Fibonnacci sequence can be placed into a parabolic or hyperbolic function?
If you're asking if there's a function $\phi:\mathbb{R}^+ \rightarrow \mathbb{R}$ such that the graph of $\phi$ is a parabola or hyperbola, and that $\phi$ satistfies, for all positive integers $n, ... | 4 | [
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-0.09863281... | 35,606 | 35606 | |
Algebraic Expressions and Equations: Solving Equations of the Form x+a=b and x-a=b
7k−4=6k+17k−4=6k+1 size 12{7k - 4=6k+1} {}. In this equation, the variable appears on both sides. We need to isolate it on one side. Although we can choose either side, it will be more convenient to
choose the side with the larger coeffi... | 4 | [
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What is the expected number of maximal bicliques in a random bipartite graph?
up vote 4 down vote favorite
1
Maximal Biclique: A complete bipartite subgraph, that isn't a subgraph of another complete bipartite subgraph.
Given a bipartite graph $G=(V_{1}\cup V_{2}, E)$ where $|V_{1}|=|V_{2}|$ with probability $p$ of t... | 4 | [
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Finite field hypergeometric functions.
up vote 1 down vote favorite
Are there explicit relations between hypergeometric functions over finite fields of different size? In particular, if we consider the function 2F1(A,B,C|x) over Fp (i.e., with characters A,B and C
defined over Fp), and the same hypergeometric function... | 5 | [
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0.018... | 35,609 | 35609 | |
Substitution Method
May 7th 2007, 06:46 AM
alwaysalillost
Substitution Method
Solve and check each of the following problems using the substitution method.
1. 3x + y = 5
-2x + 3y = 4
2. y = 5x
2x + y = 28
3. x + 3y = 23
3x - 2y = 3
x = 1/5y
3x + 2y = 26
I need help in fig... | 4 | [
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Calculus, motion problem
March 22nd 2007, 07:00 PM #1
Junior Member
Joined
Oct 2006
Posts
36
Calculus, motion problem
I have a test tomorrow, and I would really appreciate any help on the following problems. Thanks a lot!!!!
1. A particle moves on a straight line so that its velocity at time t is gi... | 5 | [
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... | 35,611 | 35611 | |
Rate of evaporation from a dish fo water
November 6th 2012, 03:41 PM #1
Newbie
Joined
Nov 2012
From
America
Posts
3
Rate of evaporation from a dish fo water
A dish has a shape described by the equation:
h=(x^2+y^2)^3/2
At time = 0 it is filled to a height of 20cm with a fluid that evaporates ... | 5 | [
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roups
GROUPS
Excerpted from Beachy/Blair, Abstract Algebra, 2nd Ed., © 1996
Chapter 3
Forward | Back | Table of Contents | About this document
... | 4 | [
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-... | 35,613 | 35613 | |
Finding Half-Lives of a word problem
March 1st 2010, 06:16 PM
krzyrice
Finding Half-Lives of a substance
Find the half-lives of the substances:
1) Einsteinium-253, which delays at a rate of 3.406% per day.
2) A radioactive substance that decays at a continuous rate of 11% at minute.
I don't know w... | 5 | [
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... | 35,614 | 35614 | |
Person and week problem.
April 1st 2009, 06:22 AM #1
Junior Member
Joined
Mar 2009
Posts
52
Person and week problem.
Q - In a room there are 7 persons.The chances that the two of them born on the same day of week.
a) 1080/7^5 b) 2160/7^5 c) 540/7^4 d) None of these
Any hint would be greatly app... | 4 | [
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-0.1049804687... | 35,615 | 35615 | |
Help finding the largest and smallest value
September 19th 2009, 12:24 PM #1
Newbie
Joined
Nov 2007
Posts
23
[not solved]Help finding the largest and smallest value
I need to find the largest and smallest value for f(x,y) in a particular domain.
$f(x,y)=x^2+x(y^2-1)$ and $x^2+y^2\leq17$
I found... | 5 | [
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ge
Algebraic Word Problems
A lesson in Algebraic Expressions in Word Problems:
Sharpen your pencils!
Algebra word problems are very useful to solve real-life problems. You CAN do them. Remember the famous words of Albert Einstein
"Do not worry about your difficulties in mathematics, I assure you that mine are greater.... | 4 | [
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0.0296630859375,
-... | 35,617 | 35617 | |
Does homology have a coproduct?
up vote 24 down vote favorite
24
Standard algebraic topology defines the cup product which defines a ring structure on the cohomology of a topological space. This ring structure arises because cohomology is a contravariant functor
and the pullback of the diagonal map induces the product... | 4 | [
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[SOLVED] Differential Equations
April 28th 2008, 12:08 PM #1
Newbie
Joined
Apr 2008
Posts
3
Hi there, I have a question on differential equations I dont understand, here it is:
find the general solution:
t (dx/dt) = x + (sin(x/t))^2
I think you have to use substitution for this one but dont... | 5 | [
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0.010314941406... | 35,619 | 35619 | |
Progressions
December 23rd 2009, 07:22 AM
mastermin346
Progressions
The sum of the first 3 terms of a geometric progression is 13 times its first term.Find the possible values of the common ratio of the geometric progression.
December 23rd 2009, 07:27 AM
mathaddict
Quote:
HI
$S_3=13a$ , where a... | 4 | [
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-0.0093383789062... | 35,620 | 35620 | |
Posts from April 2012 on Random Math
In this note I will give a Galois-theoretic proof that for a prime ${p}$ and positive integer ${n}$,
$\displaystyle n \mid \frac{\varphi(p^n-1)}{\varphi(p-1)}.$
I’d love to see a more elementary proof if you can... | 5 | [
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0... | 35,621 | 35621 | |
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Math Forum » Discussions » Policy and News » geometry.ann... | 5 | [
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What is the probability that the range of a set of N randomly chosen real numbers in [0, 1] is less than the reciprocal of N?
up vote 6 down vote favorite
1
(Random number with uniform distribution over [0, 1])
For clarification, in the case where N = 2, we can use geometric probability. On the coordinate plane consi... | 5 | [
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-0... | 35,623 | 35623 | |
2nd Order PDE hyperbolic
November 17th 2009, 07:13 AM #1
Junior Member
Joined
Oct 2008
Posts
54
2nd Order PDE hyperbolic
Hi, I have to find the general solution to this second order pde.
$x^2Z_{xx} - y^2Z_{yy} = 0$ Where x and y not equal to 0.
I have found characteristics to be n=xy and v=y/x ... | 5 | [
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0.03564453125,
-0.0373535... | 35,624 | 35624 | |
Trigo question. Help needed. Need to pass up on tomorrow.
July 15th 2008, 06:53 AM #1
Newbie
Joined
Jul 2008
Posts
2
Trigo question. Help needed. Need to pass up on tomorrow.
Given that $\cos x = -\frac{2}{3}$ and $\sin y = -\frac{1}{\sqrt 6}$, that $0^\circ\le x \le360^\circ$ and that $x$ and $y$ are in... | 4 | [
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-0.0284423828125,
-0.0... | 35,625 | 35625 | |
another DE problem (well more of a parts prob)
June 7th 2007, 10:45 AM #1
Junior Member
Joined
Jun 2007
Posts
27
another DE problem (well more of a parts prob)
Me agian, catch up on my DE HW...(150ish DE's in 4days
Question: x^2(dy/dx) + x(x+2)y = e^x
I have found roe (p) and now im trying to i... | 5 | [
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0.0010... | 35,626 | 35626 | |
Strong Nullstellensatz
up vote 9 down vote favorite
3
Let $I\subseteq{\mathbb C}[X_1,\dotsc,X_n]$ be an ideal, and
let $V\subseteq{\mathbb C}^n$ be the corresponding algebraic set
($V$ consists of those $x$ at which all $f\in I$ vanish).
Is it true that then there exists an integer $N$ such that:
if a function $f\... | 5 | [
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-0.0615234375,
-0.01361083984375,
0.01458740234375,
0.04931640625,
-0.006256103515625,
0.0... | 35,627 | 35627 | |
Derivative of x^tan(x)
September 12th 2012, 05:31 PM #1
Junior Member
Joined
Apr 2012
From
Maryland
Posts
27
Thanks
3
Derivative of x^tan(x)
I thought I knew how to do this but I keep coming up with the wrong answer. Here is what I've done:
$y=x^\tan(x)$
$ln y= tan(x) ln x$
$\frac{... | 5 | [
-0.01300048828125,
-0.045654296875,
0.0771484375,
0.062255859375,
0.032470703125,
-0.0035400390625,
0.0859375,
-0.045654296875,
0.0150146484375,
0.0155029296875,
0.11181640625,
0.0042724609375,
-0.0126953125,
0.083984375,
0.0341796875,
0.06787109375,
-0.048583984375,
-0.01635742187... | 35,628 | 35628 | |
Math Help
I am trying to simplify the end of this half angle problem How do I get from $\sqrt{(9-\sqrt{17})/(18)}$ to: $(1/3)\sqrt{(9-\sqrt{17})/(2)}$
Working backwards: Since the two is on the denominator it is essentially multiplying the (9-(17)^(1/2)) by 1/2. So to get 1/3 into the denominator you would square it,... | 4 | [
0.020263671875,
0.0595703125,
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0.0311279296875,
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0.035888671875,
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0.0810546875,
0.024169921875,
0.039794921875,
-0.06640625,
0.1220703125,... | 35,629 | 35629 | |
Math Help
I got AY = -3a + 1/2 b for the first one. The other two I can't work out.
Last edited by GAdams; July 6th 2007 at 11:49 AM.
i) $\overrightarrow{AY}=\overrightarrow{AO}+\overright arrow{OY}=-\overrightarrow{OA}+\frac{1}{2}\overrightarrow{OB} =-3\mathbf{a}+\frac{3}{2}\mathbf{b}$. ii) $\overrightarrow{OX}=\fr... | 4 | [
-0.064453125,
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0.033935546875,
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0.1015625,
-0.12060546875,
-0.0639648437... | 35,630 | 35630 | |
Application of integration - Work
July 22nd 2012, 08:52 AM #1
Newbie
Joined
Jul 2012
From
United States
Posts
11
Application of integration - Work
I was wondering if I could elicit some help with this problem. I feel as if I understand it but cannot get the right answer.
It is number 21.... | 5 | [
0.016845703125,
-0.048828125,
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-0.12060546875,
0.0... | 35,631 | 35631 | |
Cartesian equation
April 6th 2010, 07:58 PM #1
Newbie
Joined
Oct 2009
Posts
22
Cartesian equation
Hey I am studying Linear and Abstract Algebra and came across this:
Find the Cartesian equation of the line that passes through the point $P(2, 0, -5)$ and is perpendicular to both the vectors $u = (0,... | 5 | [
-0.045654296875,
0.032470703125,
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0.052978515625,
0.009033203125,
0.006561279296875,
0.0185546875,
0.06591796875,
-0.0849609375,
0.06591796875,
-0.033935546875,
-0.... | 35,632 | 35632 | |
Equation of a tangent to a curve calculus help!
January 31st 2009, 01:28 PM #1
Newbie
Joined
Jan 2009
Posts
3
Equation of a tangent to a curve calculus help!
So for the following question, I have gone through the steps to solve it. I am just not confident in my answer so if anyone could help that would b... | 4 | [
-0.07666015625,
-0.0810546875,
-0.03466796875,
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0.02099609375,
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0.0673828125,
-0.00157928466796875,
0.07177734375,
0.046875,
-0.06591796875,
0.0177001953125,
-0.0030517578125,
0.00145721435546875,
0.09228515625,
-0.09912109375,
-0.019165... | 35,633 | 35633 | |
Logs :(
December 10th 2012, 07:54 AM
Twinkie
Logs :(
Ok, I'm having some issues with these questions. So could you show me step by step on how to come to an answer.
1. write as a single logarithm in simplest form
(Log 16x^8)/4 - (Log 27x)/3
2. isolate x using laws of logarithims
3 Logx(4)=2
De... | 4 | [
0.0123291015625,
0.034912109375,
0.06201171875,
-0.04833984375,
-0.0034332275390625,
-0.03515625,
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0.04296875,
0.0034332275390625,
0.07568359375,
-0.0098876953125,
-0.08837890625,
0.0003185272216796875,
0.04443359375,
0.0703125,
0.109375,
-0.0859375,
0.06494140625... | 35,634 | 35634 | |
Math Help
December 6th 2008, 09:08 PM #1
Junior Member
Joined
Sep 2008
Posts
27
Proof
1. In triangle ABC ,angle c=90 degree and ABPQ is a square on AB.If PN is perpendicular to AC from P, prove that PN=AC + CB.
Thank You.
Hello,
There are assumptions on the orientation of the figure, becaus... | 4 | [
-0.08349609375,
0.080078125,
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0.0272216796875,... | 35,635 | 35635 | |
Indefinite Integral
The best we can do is to let $u = \sqrt{x} \implies 2u~du = dx$, so $\int \frac{sin(\sqrt{x})}{x}~dx = \int \frac{sin(u)}{u^2} \cdot 2u~du = 2 \int \frac{sin(u)}{u}~du$ This integral (at least)
sometimes goes by the name of "Si." (So as a function of x it is $Si(x)$.) There is no closed-form solutio... | 4 | [
0.026123046875,
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0.01422119140625,
0.049072265625,
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0.03369140625,
0.08447265625,
... | 35,636 | 35636 | |
Math Help
November 30th 2008, 08:56 PM #1
Newbie
Joined
Sep 2008
Posts
17
A triangle is increasing in size. The base is increasing at a rate of 5 ft/s while the height is increasing at a rate of 2 ft/s. At what rate is the area increasing at the instant the base of the
triangle is 10 ft and the heigh... | 4 | [
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0.05419921875,
-0... | 35,637 | 35637 | |
Definate Integral Help
August 26th 2009, 01:35 PM #1
Newbie
Joined
Aug 2009
Posts
1
Definate Integral Help
I feel like the solution to this is painfully obviously, but I just can't seem to get it right... Any help would be greatly appreciated.
$f(x)=\int_{3}^{x^3}{t^2}{dt}$
It wants to know $f'... | 5 | [
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0.080078125,
-0.02978515625,... | 35,638 | 35638 | |
Arithmetic product of symmetric functions: why is it integral?
up vote 8 down vote favorite
4
For every commutative ring $A$, let $\mathbf{Symm}_A$ be the ring of symmetric functions over $A$. Let $\mathbf{Symm}$ without a subscript denote $\mathbf{Symm}_{\mathbb{Z}}$.
We can define a bilinear map $\boxdot : \mathbf{... | 4 | [
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-0.0240478515625,
0.10791015625,
-... | 35,639 | 35639 | |
Introduction to Graph Drawing
WOLFRAM LANGUAGE TUTORIAL
Introduction to Graph Drawing
Graph Theory Notations Selecting the Appropriate Graph Drawing Function
Input Formats References
Graph Drawing Algorithms
The Wolfram Language provides functions for the aesthetic drawing of graphs. Algorithms implemen... | 4 | [
-0.01708984375,
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0.041015625,
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0.022216796875,
0.06298828125,
0.001495361328125,
0.06884765625,
-0.0191650390625,
0.035... | 35,640 | 35640 | |
Ellipse
Talk0
871pages on
this wiki
In mathematics, an ellipse (Greek ἔλλειψις (elleipsis), a 'falling short') is the finite or bounded case of a conic section, the geometric shape that results from cutting a circular conical or
cylindrical surface with an oblique plane (the other two cases being the parabola an... | 4 | [
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-0.006072998046875,
0.0301513671875,
-0.04296875,
-0.049072265625,
... | 35,641 | 35641 | |
Graph theory
How do I show that the k-cube has 2^k vertices and k2^k-1 edges? Any advice? Thanks in advance.
I'm taking my first Graph Theory course now as a undergrad. I may not be the best person to answer this question. However, it's been sitting in the Urgent Homework Help forum for over 24 hours. Even
if I can't ... | 4 | [
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... | 35,642 | 35642 | |
rational number
$a = \frac{\sqrt{7}}{\sqrt[3]{15}} = \sqrt[6]{\frac{7^3}{15^2}}$ Assume $a=\frac{p}{q}$, where $(p,q)=1$. Then $a^6 = \frac{p^6}{q^6}$. So $7^3\cdot q^6 = 15^2\cdot p^6$. This means $7^3\mid p^6 \
implies 7\mid p$ since $7$ is prime. So $15^2\cdot p^6 =15^2\cdot (7k)^6 = 7^6\cdot 15^2\cdot k^6 = 7^3\cdo... | 5 | [
0.0216064453125,
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0.044677734375,
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0.068359375,
-0.01043701171875,
-0.035888671875,
-0.06884765625,
0.03442382... | 35,643 | 35643 | |
I lied, one more (first-order DE). :)
June 27th 2007, 12:23 AM #1
I lied, one more (first-order DE). :)
$x\frac{dy}{dx}+y=\sin(x)$, $x>0$, initial condition: $y(\frac{\pi}{2})=1$
What I have so far...
$\frac{dy}{dx}+\frac{1}{x}y=\frac{\sin(x)}{x}<br /> \Rightarrow \int \frac{1}{x}dx=\ln|x| \Rightarrow e... | 5 | [
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0.0029296875,
0.00738525390625,
0.020751953125,
-0.012... | 35,644 | 35644 | |
Calc problem
April 28th 2014, 03:46 PM #1
Calc problem
I dug this one up from the internet and thought I'd post it for the next challenge problem. Trouble is I have been unable to find a solution. So I decided to post it here and give what little
progress I've made and see if anyone can do any better.
Le... | 5 | [
-0.03662109375,
-0.034423828125,
0.05322265625,
0.10498046875,
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0.041748046875,
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0.03564453125,
-0.03662109375,
0.00225830078125,
0.04931640625,
-0.0001544952392578125,
0.037109375,
-0.033203125,
... | 35,645 | 35645 | |
linear equation help
November 30th 2009, 01:54 PM #1
Newbie
Joined
Jul 2008
Posts
13
linear equation help
can anyone help me with this question
solve completely the following system
x+2y+mz=0
2x+3y-2z=m
mx+y+m^2z=3
Im a bit stumped on what to do with the m? any help would be apprec... | 5 | [
-0.006103515625,
-0.03857421875,
-0.09228515625,
0.05126953125,
-0.00164031982421875,
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0.07421875,
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-0.035888671875,
0.01080322265625,
0.138671875,
0.0196533203125,
0.0170... | 35,646 | 35646 | |
For those that never learned well the epsilon-delta proofs
May 3rd 2014, 02:42 PM #31
Re: For those that never learned well the epsilon-delta proofs
I know that direct and indirect geometric proofs using the statement vs reason chart are not taught in most high schools across the USA. They cover the basics of pro... | 5 | [
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0.044921875,
-0.002349853515625,
-0.01336669921875,
-0.00994873046875,
0.034... | 35,647 | 35647 | |
A circle packing conjecture
up vote 13 down vote favorite
7
Consider $n$ circles with variable radii $r_1,\ldots, r_n$ that pack inside a fixed circle of unit radius. In other words, all $n$ variable-radius circles are contained in the unit radius circle and
their interiors have empty intersections. The tangency graph... | 4 | [
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0.00014495849609375,
-0.04150390... | 35,648 | 35648 | |
using mathematical induction to prove..
March 11th 2009, 07:19 PM #1
Super Member
Joined
Oct 2007
From
Santiago
Posts
517
using mathematical induction to prove..
hi guys having trouble proving this result.
$<br /> \sum_{k=0}^n(-\frac{1}{2})^k =\frac{2}{3} + \frac{1}{3}\frac{(-1)^n}{2^n},$
f... | 5 | [
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0.11865234375,
... | 35,649 | 35649 | |
factoring rational expression
November 15th 2011, 11:13 PM
fran1942
factoring rational expression
Hello, I want to factor the following:
1-(1/y^2)
I thought that this would be the correct answer:
1/y * (y-(1/y))
however my textbook says that this is correct:
(1-1/y) (1+1/y)
Can someone... | 4 | [
0.0223388671875,
0.007598876953125,
0.0211181640625,
0.046142578125,
0.01104736328125,
-0.0341796875,
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-0.0306396484375,
-0.005157470703125,
-0.0223388671875,
-0.000949859619140625,
0.0036773681640625,
0.040771484375,
0.1572265625,
0.013427734375,
0.08203125,
0.03515625,... | 35,650 | 35650 | |
Derivation of Geometric Formulas
Date: 5/29/96 at 18:35:16
From: Anonymous
Subject: Derivation of Geometric Formulas
Could you please answer these questions? Your help would be very much
appreciated.
How were the formulas for surface area, total surface area, and volume
of a sphere derived? How were the formulas fo... | 5 | [
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0.09228515625,
0.046875,
0.0478515625,
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0.02978515625,
0.008544921875,
0.048828125,
-0.0216064453125,
0.004302978515625,
-0.07373046875,
0.0458984375,
-... | 35,651 | 35651 | |
Probability of Shirts...
April 19th 2010, 12:33 PM #1
Junior Member
Joined
Apr 2010
From
Riverside, CA
Posts
58
Probability of Shirts...
The soccer team's shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extr... | 5 | [
0.1005859375,
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0.042724609375,
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0.03955078125,
0.043212890625,
0.0263671875,
0.0012969970703125,
0.00286865234375,
-0.06884765... | 35,652 | 35652 | |
Showing a family is actually an algebra
January 12th 2012, 09:39 AM
matt.qmar
Showing a family is actually an algebra
Hello!
I am struggling with just the very last stage of the solution and any suggestions would be much appriciated!! Thanks!
I am trying to show that given a set $X$ and a collection of... | 5 | [
0.031494140625,
0.04345703125,
0.037841796875,
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-0.054931640625,
-0.017578125,
-0.00762939453125,
0.0299072265625,
-... | 35,653 | 35653 | |
Climate change math made simple
What’s being billed as the U.S. Senate’s last chance to pass a bill that deals with climate change, the American Power Act, aims for a now-familiar target: a reduction in greenhouse gas emissions of
83% by 2050. The idea is that if the developed world can manage to reach that goal, the g... | 4 | [
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0.07080078125,
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0.042236328125,
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-0.0021514892578125,
... | 35,654 | 35654 | |
Simplifying
If $270^\circ < x < 360^\circ$, simplify $\sqrt{2+\sqrt{2+2cosx}}$ I couldn't do anything else after getting rid of the square roots..
Use the half angle identity for cosine: $\cos{\frac{\theta}{2}} = \sqrt{\frac{1 + \cos{\theta}}{2}}$. $\sqrt{2 + 2\cos{x}} = \sqrt{2(1 + \cos{x})}$ $= \sqrt{\frac{4(1 + \co... | 4 | [
0.0673828125,
0.0223388671875,
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0.0673828125,
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0.0185546875,
0.0194091796875,
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0.056884765... | 35,655 | 35655 | |
Sufficient and necessary conditions on equality of Cauchy-Schwarz inequality of determinants
up vote 1 down vote favorite
Cauchy-Schwarz inequality of determinants:
for $A_{n\times k}$, $B_{n\times k}$, and $B'B$ non-singular, we have
$|A'B|^2\leq |A'A||B'B|$
I was wondering what's the sufficient and necessary cond... | 5 | [
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0.125,
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-0.0258... | 35,656 | 35656 | |
Calc hmwk- extend the fucntion and remove discontinuity
September 28th 2008, 01:02 PM
h4hv4hd4si4n
Calc hmwk- extend the fucntion and remove discontinuity
I don't understand how to remove the discontinuity on this problem:
(x-4)/( (sq. root of x) - 2), x=4
please help!
September 28th 2008, 01:14 PM
M... | 4 | [
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-0.047119140... | 35,657 | 35657 | |
General Solution of DE
April 11th 2010, 04:33 PM
cdlegendary
General Solution of DE
Find the general solution of http://homework.math.ucsb.edu/webwor...ea6562ac51.png, where y is a function of t.
Could someone help me out with this? I'm not sure how to go about solving for the general solution. All I've got... | 5 | [
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0.125,
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0.00... | 35,658 | 35658 | |
Math Help
September 9th 2008, 09:51 AM #1
Junior Member
Joined
Sep 2008
Posts
62
proportions
show that there is a magnitude p such that the area of a circle of radius r is to the area of a square of side r as p is to 1. a:b=d:d
Proof is based on:
The proof depends on three earlier results in th... | 4 | [
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-0... | 35,659 | 35659 | |
HS_Algebra_1A_1B
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
... | 4 | [
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0.04833984375,
-0.0302734375... | 35,660 | 35660 | |
Find a generalized hypergeometric-based function yielding certain ratios of fifth-degree polynomials
up vote 0 down vote favorite
Find a (presumably, generalized hypergeometric-based function $f(n,a,k)$), yielding for $n=1, a=\frac{1}{2}$,the rational function (ratio of fifth-degree polynomials) $$f(1,\frac{1}{2},k)=\... | 5 | [
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-0... | 35,661 | 35661 | |
How to define the equivalence of Maurer-Cartan elements in an $L_{\infty}$-algebra?
up vote 3 down vote favorite
5
First let $L^{\bullet}$ be a pro-nilpotent differential graded Lie algebra (dgla). We have the set of Maurer-Cartan elements in $L^{\bullet}$ ($MC(L^{\bullet})$) which are $\alpha \in L^1$ such that
it sa... | 4 | [
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... | 35,662 | 35662 | |
Linear programming world problem; system of inequalities
April 23rd 2012, 09:16 AM
kyliealana
Linear programming world problem; system of inequalities
A hospital dietician wishes. To prepare a corn-squash vegetable dish that will provide at least 3 grams of protein and cost no more that .36 per serving. And ounc... | 4 | [
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-0.02062988... | 35,663 | 35663 | |
Two Related Rate Problems
October 15th 2007, 07:13 PM #1
Junior Member
Joined
Sep 2007
Posts
48
Two Related Rate Problems
I'm not sure why I'm having trouble with these... can someone give me a start or some help through them?
A man walks a straight path at a speed of 4 ft/sec. A search light is loc... | 5 | [
0.01446533203125,
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-0.020141601562... | 35,664 | 35664 | |
Actions orbit equivalent to profinite ones
up vote 6 down vote favorite
1
Let $G$ be a countable discrete residually finite group.
Is there a way to characterise the actions of $G$ that are orbit-equivalent to profinite ones?
Ozawa and Popa introduced the concept of weakly compact actions. Weakly compact actions are... | 5 | [
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0.0478515625,... | 35,665 | 35665 | |
Math Help
June 21st 2005, 01:49 PM #1
Junior Member
Joined
Jun 2005
Posts
58
Plz Help
Write an equation in slope-intercept form of the line passing through each pair of points: (6, -2) and (3, -4)
-4 - (-2)
--------- = -2/3
3 - 6
next
y - (-2) = -2/3(x - 6)
y - (-2) -2/3x -9
... | 4 | [
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Chessboard Proof
October 16th 2012, 10:12 AM
gfbrd
Chessboard Proof
Hey there I also need some help on this proof as well.
Imagine an infinite chessboard that contains a positive integer in each square. If the value in each square is equal to the average of its four neighbors to the north, east, south and w... | 5 | [
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... | 35,667 | 35667 | |
"Let f and g be twice differentiable functions ..." - Derivitive problem
March 11th 2009, 03:36 PM #1
Junior Member
Joined
Mar 2009
Posts
32
"Let f and g be twice differentiable functions ..." - Derivitive problem
There's a problem that our professor wanted us to look at and I'd really like to understand... | 4 | [
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Nonlinear matrix equation 2
up vote 0 down vote favorite
Solve the following nonlinear equations for $v$ and $w$
$Avv^TAw+Bvv^TBw=\lambda_1v+\lambda_2w$
$Aww^TAv+Bww^TBv=\lambda_1w+\lambda_2v$
$v^Tw=w^Tv=0$
$v^Tv=w^Tw=1$
where $\lambda_1, \lambda_2, \lambda_3$ are real. $A$, $B$ are n-by-n symmetric matrices. Fur... | 4 | [
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-0.035... | 35,669 | 35669 | |
Combinatorial equation
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Can any one help me in proving the following equality:
$$n^n= \sum_{i=1}^n {n \choose i}\cdot i^{i-1}\cdot (n-i)^{n-i}$... | 5 | [
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0.07... | 35,670 | 35670 | |
Homogeneous system of polynomial equations
up vote 4 down vote favorite
3
Hi all,
Previously I asked a question that currently has no satisfactory answer Least sum squares given constraints on subcomponents
It comes from an engineering problem. I was thinking to formulate it differently and hope that someone becomes... | 4 | [
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0.11962890625,
-0.0196533203125... | 35,671 | 35671 | |
What is the maximum diameter of $N$ steps of a random walk?
up vote 12 down vote favorite
2
Since probability is quite far away from my daily buisiness, please forgive me if my use of terminology is wrong or the question is too trivial. However, I was not able to find the right keyword to
find an answer by googling...... | 5 | [
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... | 35,672 | 35672 | |
Maximal order of Hooley's Delta function?
up vote 4 down vote favorite
There is a large literature on Hooley's $$ \Delta(n)=\max_u\sum_{d|n,\ e^u\le d< e^{u+1}}1 $$ giving its normal and average order. What is known of its maximal order?
Clearly $\Delta(n)\le d(n)$ and so the usual upper bounds apply, but these are n... | 4 | [
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-0.... | 35,673 | 35673 | |
simplify..need help
January 28th 2010, 12:17 PM #1
Senior Member
Joined
Sep 2009
Posts
300
simplify..need help
Hello,
Please look at my picture
I need someone to show me how to get the end bit of my sum finished, the correct answer is in green I cant seem to get it?
Please help
Last edi... | 4 | [
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0... | 35,674 | 35674 | |
De Moivre's Theorem
August 30th 2009, 02:58 AM #1
Junior Member
Joined
Aug 2009
Posts
25
Q: Prove that,
(1 + sin 0 + i cos 0)^n
-------------------- = cos n (pi/2 - 0) + i sin n(pi/2 - 0)
(1 + sin 0 - i cos 0)^n
where, 0 = theta (Cant type it)
Thanks !
I've thought about multipy... | 5 | [
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... | 35,675 | 35675 | |
Kernel of linear representation of Baumslag-Solitar group
up vote 13 down vote favorite
1
Let $BS(m,n)$ be the Baumslag-Solitar group defined by $B(m,n) = < a,b ~|~ b a^m b^{-1} = a^n > $, $mn \neq 0$. There is a linear representation of $BS(m,n)$ by mapping $a$ to the matrix $\left(\
begin{matrix} 1&1 \cr 0&1\end{mat... | 5 | [
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0.158203125,
-0.00323486328125,
... | 35,676 | 35676 | |
Math Help
June 18th 2007, 01:38 PM #1
Junior Member
Joined
Feb 2007
Posts
44
solving the differential equations
1. y'' - 2xy' + 3y = 0
2. (1+2x)y'' - 3xy' + 2y = 0
solving the differential equations by using method of Frobenius
3. 3x^2 y'' + 2xy' + x^2 y = 0
4. 3xy'' + 2y' + 2y =... | 5 | [
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... | 35,677 | 35677 | |
Boundary of the Upper Hemisphere
May 2nd 2007, 07:36 AM
mpetnuch
Boundary of the Upper Hemisphere
Hello.
I am trying to do a problem from Munkres "Analysis on Manifolds", pg. 209 problem 4.
The problem asks to show that E^(n-1) = S^(n-1)(a) n H^n is an n-1 manifold. It that asks you to find the boundar... | 5 | [
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-0.0208740234375,
-0.0800781... | 35,678 | 35678 | |
Countable ordinal mapping w/ order preserving function
October 19th 2009, 07:36 PM #1
Junior Member
Joined
Jul 2008
Posts
38
Countable ordinal mapping w/ order preserving function
Here's the problem as stated:
Show if $\alpha$ is any countable ordinal, then $\exists f:\alpha \rightarrow \Re$ (to the ... | 5 | [
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0.0157470703125,
-0.0201416015625,
-0.... | 35,679 | 35679 | |
Volume of Gr(2,4)
up vote 6 down vote favorite
2
Hello
I was wondering if anybody can direct me to a paper or a book regarding the volume of $Gr(2,4) $ or generic complex Grassmanian manifolds of order $k$. My own heuristic method seems not to work! It
is based on the adaption of the same procedure one has to follow ... | 4 | [
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-0.004669189453125,... | 35,680 | 35680 | |
Are there uncountably many essentially inequivalent versions of Mathematics?
up vote 7 down vote favorite
1
Hi everyone,
Disclaimer 1: logic and set theory are a long way from my field, so apologies in advance if I demonstrate extreme ignorance or stupidity, and please correct me if (when?) I write stupid things. But... | 5 | [
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Trig Word Problem
January 17th 2008, 03:50 PM #1
Newbie
Joined
Jan 2008
Posts
4
Trig Word Problem
Hey, just stopping by, need some help on a review question and any help would be appreciated.
Question:
The following describes the height in, in meters, of a cart on a ferris wheel as a function o... | 4 | [
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0.0834... | 35,682 | 35682 | |
Logistic function story problem
July 25th 2010, 02:45 PM #1
Logistic function story problem
"Suppose that the water in a hot water heater is 70° Celsius above room temperature. When you first turn on the faucet, the water coming out is only 2° above room temperature. Ten seconds later
it has warmed to 15° abo... | 5 | [
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Prove: each square is the sum of 2 consecutive triangular numbers
October 1st 2010, 01:24 AM
courteous
Prove: each square is the sum of 2 consecutive triangular numbers
Is the following an acceptable proof (be harsh (Nod))?
$t_k=1+2+3+\ldots+k=\frac{(k+1)k}{2}$
$t_{k-1}=1+2+3+\ldots+(k-1)=\frac{k(k-1)}{... | 4 | [
-0.035400390625,
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0.01263427734375... | 35,684 | 35684 | |
Optimal knot placement for fitting piecewise-continuous linear functions to a nonlinear function
up vote 4 down vote favorite
2
I encountered this problem in my research and it is turning out to be a surprisingly difficult one(for me, at least).
Suppose we have a univariate nonlinear function $f(x)$ where $x \in [L,U... | 5 | [
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Everything Scheme
Compression: Integer Encodings
Quick! How many bits are needed to store a natural number
n
?
Well, let's look at the standard encoding. One bit is needed for 1 (1). Two bits are needed for 2 (10) and 3 (11), furthermore three bits are needed for 4 (100), ..., 7 (111). Hmm. log(1)=0, log(2)=
1, log... | 4 | [
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0.0... | 35,686 | 35686 | |
a Ramsey-type question
up vote 6 down vote favorite
This question is related to this one but feels more Ramsey-type, so perhaps it is easier. Let $S$ be a finite set, $|S|=k$. Suppose we color all subsets of $S$ in $1000$ colors. What is the maximal
(in terms of $k$) guaranteed length $l=l(k)$ of a monochromatic seque... | 5 | [
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Topic: Lesson Plan: Cube to Hexapent Mapping
Replies: 1 L... | 4 | [
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0.0668945... | 35,688 | 35688 | |
Irreducible "family" of relative effective divisors of a smooth morphism
up vote 5 down vote favorite
Let $\pi:X\rightarrow Y$ be a smooth proper (assume projective if needed) morphism of schemes with $Y$ locally noetherian, and let $Z\subset X$ be an irreducible integral closed subscheme containing
no fiber of $\pi$.... | 4 | [
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-0.029541015625... | 35,689 | 35689 | |
Finding Equation of a Parabola from Tangent Slopes
February 22nd 2008, 05:22 PM #1
Finding Equation of a Parabola from Tangent Slopes
Find a parabola of the form given below that has slope $m_1$ at $x_1$, slope $m_2$ at $x_2$, and passes through the point $P$.
$<br /> y = ax^2 + bx + c$
$m_1 = 9, x_1 = ... | 4 | [
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0.125,
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-0.00009727478027343... | 35,690 | 35690 | |
[SOLVED] Proof - Can somebody please check my work
April 25th 2009, 12:57 PM #1
Junior Member
Joined
Apr 2009
Posts
70
[SOLVED] Proof - Can somebody please check my work
Hi,
I am to prove the following:
If a, b, c are real numbers s.t. a & c are NOT 0, then there is a unique number x s.t. x/a +... | 4 | [
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Vertical Integration
October 16th 2010, 09:14 AM
bloodyfinger
Vertical Integration
Here is the problem:
To illustrate the double marginalization problem, let’s assume that a manufacturer, m, and a retailer, r, use linear pricing
Inverse demand: p = 10 - q
Marginal cost of the manufacturer: c = 2
... | 4 | [
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Chain rule
Talk0
872pages on
this wiki
The chain rule is a formula for finding the derivative of a composite function. It uses a variable y depending on a second variable, u, which in turn depend on a third variable, x.
${dy\over dx} = {dy\over du} \cdot {du\over dx}$
The derivative of any function is the deri... | 5 | [
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Trig intergral help
April 19th 2010, 02:32 PM #1
Junior Member
Joined
Dec 2009
Posts
46
Trig intergral help
$integrate: \frac{(sec2x)^2}{(tan2x)^5} dx$
After i convert to tangets and such and do the u substitution i end up with this
$\frac{1}{2} integrate<img src=$ u ^{-4} + 4u^{-3} + 6u^{-1} ... | 5 | [
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show that the equation has only one solution
October 31st 2010, 09:02 AM #1
Junior Member
Joined
May 2010
Posts
57
show that the equation has only one solution
This question really has me stumped.....
a^2 + b^2 = 6( c^2 + d^2 )
Any clues or hints to start this question...
I think we suppos... | 4 | [
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0.00665283203125... | 35,695 | 35695 | |
Need Solution Today..
July 5th 2013, 08:14 PM #1
Newbie
Joined
Jul 2013
From
Karachi, Pakistan
Posts
1
Need Solution Today..
Question#1
__________________________________________________ ___________________________
Evaluate the integral.
Question#2
____________________________... | 5 | [
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Normalizer of a von Neumann algebra
up vote 6 down vote favorite
3
Let $(A,H)$ be a von Neumann algebra in standard form (which means that $H=L^2A$), and recall that the automorphism group $Aut(A)$ acts on both $A$ and $H$. Let $$N:=\{u\in U(H): uAu^*=A\}$$ be the
normalizer of $A$, equipped with the strong topoloy (t... | 5 | [
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What is the structure of $SO(3)$ and its Lie Algebra?
up vote 2 down vote favorite
First I want to give you some background how the question arised, before actually asking it.
Recently, in the context of quantum mechanics, I thought about the group $SO(3)$ and its Lie Algebra $so(3)$. Wherever I looked, I could only... | 4 | [
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integral of region
January 24th 2009, 11:10 AM #1
Newbie
Joined
Dec 2008
Posts
22
Q1 - Find the volume of the solids generated by revolving the regions bounded by the lines and curves about x-axis
y=√cosx where 0 ≤ x ≤ π/2 and y=0 , x=0
Q2 - Evaluate the integral
$\int_0^1$e^-√x/√x dx
... | 4 | [
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