content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Euler's Phi Function and the Chinese Remainder Theorem
$\phi(n)$ is defined to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
Proving that for prime $p$, $\phi(p)=p-1$ is trivial, as every positive integer less than a prime is relatively prime to that prime.
Further e... | 5 | [
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graphing problem
If the graph of y=ax^2+bx+c passes through the points(-1,12),(0,5) and (2,-3) find the value of a+b+c
Here's how we go about it. We know that the y-intercept occurs when x is 0. And that in a polynomial of this form, the constant is the y-intercept. We see that one point is (0,5), that means when x
is... | 4 | [
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[SOLVED] Finding Arc length
September 24th 2008, 04:16 PM
kl.twilleger
[SOLVED] Finding Arc length
find arc length of y=1-x^2 -1<x<1
i used the arc length formula, found the derivative of the function and squared it and plugged it all in and now i'm stuck at this point....
integrating between 1 and -1 ... | 4 | [
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Patent US5691770 - Device and method for coding video pictures
FIELD OF THE INVENTION
The invention relates to a device for coding video pictures, comprising: a picture transformer for transforming blocks of pixels into coefficients; coding means for encoding said coefficients, the
bit rate R and distortion D of the e... | 4 | [
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How do I integrate this?
September 28th 2009, 06:51 AM #1
How do I integrate this?
I am stuck!
$\int x^{3}\cos{\tan^{-1}{x}}$
I tried
$\mbox{Let } u=\tan^{-1}{x}, du=\frac{1}{x^{2} +1}$
Then with some substituting,
$\int x^{3}\cos{\tan^{-1}{x}} = \int\sin^{3}{u}$
but I don't know how... | 5 | [
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Conic section problem (ellipse)
mfb
How do you get those expression in the square root?
Sorry about that, I was using the fact that any point in the cartesian coordinate system whose sum of the distances from the two points that make up the foci of that particular ellipse equal 2 times
the major axis would end up b... | 4 | [
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Electric Circuits by James W. Nilsson and Susan Riedel
• Author: James W. Nilsson and Susan Riedel
• Title: Electric Circuits
• Amazon Link: http://www.amazon.com/Electric-Circu...dp/0136114997/
• Prerequisities: Calculus/Engineering Mathematics (introductory complex analysis and linear analysis), Introductory ... | 5 | [
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Find the equations of the tangent plane and the normal line to the given surface
March 4th 2010, 10:35 AM
Rhode963
Find the equations of the tangent plane and the normal line to the given surface
Find the equations of the tangent plane and the normal line to the given surface at the given point...
$z=e^xcos... | 4 | [
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Importance of separability vs. second-countability
up vote 7 down vote favorite
For me second-countability always felt like to be the more important and fundamental concept from general topology than separability. I wonder whether there are any points which can be made for the
importance of separability.
Let me subsu... | 4 | [
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Continuity of quotient
November 13th 2009, 06:09 AM #1
Junior Member
Joined
Jul 2009
Posts
25
Continuity of quotient
I'm looking for some help with proving that if f and g are continuous then so is f/g. I need to use the ε and Δ definition of continuity
( │ x - a│< Δ implies │f(x) – f(a)│< ε) to prov... | 5 | [
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Area under two curves by integration
November 6th 2007, 03:25 AM #1
Junior Member
Joined
Aug 2007
Posts
26
Area under two curves by integration
I want to find the area between two curves (see graph attached). But I want to find the area in function of "r", can anybody help?. The first curve is a line (x+... | 5 | [
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[SOLVED] beta function
February 14th 2010, 02:07 PM #1
Junior Member
Joined
Feb 2010
Posts
43
[SOLVED] beta function
Hi,
I'm starting with
$X_1, X_2, ... iid ~ U(0,1)$
and I'm trying to find the density of
$S_N = X_{k:n} - X_{k-2:n}.$
I look at the joint pdf, then do a Jacobian trans... | 5 | [
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Does the sum converge?
July 15th 2009, 08:50 PM
portstar
Does the sum converge?
There are two different questions but I am hoping that if I get help with the first one, I will be able to do the second one on my own.
Find the sum of the series if it converges or show that it diverges
∑ n=0 to infinity o... | 4 | [
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u_{xy}+u_{yz}+u_{zx}-u=0
Using separation of variables $u_{xy}+u_{yz}+u_{zx}-u=0$ $u(x,y,z)=\varphi(x)\psi(y)\omega(z)$ $\varphi'(x)\psi'(y)\omega(z)+\varphi(x)\psi'(y)\om ega'(z)+\varphi'(x)\psi(y)\omega'(z)-\varphi(x)\psi
(y)\omega(z)=0$ $\varphi'(x)[\psi'(y)\omega(z)+\psi(y)\omega'(z)]+\varphi(x)[\psi'(y)\omega'(z)-... | 5 | [
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Patente US20020155615 - Method of determining concentration of glucose in blood
[0001] This application claims priority from a U.S. provisional patent application Serial No. 60/266,774, filed Feb. 5, 2001, which is incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] The present invention relates to n... | 4 | [
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... | 15,714 | 15714 | |
uniform circular motion
September 28th 2008, 11:59 AM #1
Newbie
Joined
Sep 2008
Posts
18
uniform circular motion
A mass m = 8.5 kg is suspended from a string of length L = 1.37 m. It revolves in a horizontal circle. The tangential speed of the mass is 2.75 m/s. What is the angle q between the string and ... | 4 | [
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Modular arithmetic
February 28th 2010, 09:03 AM #1
Modular arithmetic
$\textrm{I\; am\; trying\; to\; learn\; modular\; arithmetic,\; and\; this\; right \; here\; stumped\; me.}$
$<br /> 10\cdot(-13)+27\cdot 6\equiv-122\mathrm{mod}2$
$<br /> <br /> \textrm{I\; thought\; It\; would\; go\; like\; this:}$
... | 4 | [
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3d poisson's equation problem
January 17th 2009, 08:34 AM #1
Newbie
Joined
Jan 2009
Posts
1
3d poisson's equation problem
Problem:
Consider a 3d rectangular region with dimensions 0<=x<=w,0<=y<=h,0<=z<=L.
Potential is 0 on all surfaces except for the surface on the z=0 plane, where
v(x,y)=(w/... | 4 | [
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trigonometric inequality
October 2nd 2009, 03:22 AM #1
Senior Member
Joined
Jan 2009
Posts
381
trigonometric inequality
Find the value of x , valid between -pi and pi , for the following inequality . (I am not allowed to do these using the graphical method)
(1) tan x < cos x
(2) 2 cos 2x > 3co... | 5 | [
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Patent US3866829 - Method and apparatus for measuring concentricity
United States Patent Egawa et a1.
[451 Feb. 18, 1975 METHOD AND APPARATUS FOR MEASURING CONCENTRICITY [75] Inventors: Mitsuru Egawa; Masahiro Akahane;
Tomohiro Sanada, all of Tokyo, Japan [73] Assignee: Tokyo Seimitsu Co., Ltd., Tokyo,
Japan [22] Fi... | 4 | [
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Equation help.
August 11th 2009, 06:46 AM #1
Newbie
Joined
Aug 2009
Posts
7
Equation help.
The problem is:
"The points A and B have coordinates $(a,a^2)$ and $(2b,4b^2)$ respectively. Determine the gradient of AB in it's simplest form."
The equation for gradient that we use is $m=y^2-y^1 / x^2-... | 4 | [
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Markov Chain Model to Explain the Dynamics of Human Depression
Journal of Nonlinear Dynamics
Volume 2014 (2014), Article ID 107164, 9 pages
http://dx.doi.org/10.1155/2014/107164
Research Article
Markov Chain Model to Explain the Dynamics of Human Depression
Department of Mathematics, University of Florida, 358 Littl... | 5 | [
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Patent US7593487 - Non-redundant differential MSK demodulator with double error correction capability
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a differential minimum shift keying (DMSK) demodulator. More specifically, the invention relates to a DMSK demodulator having non... | 4 | [
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probability--proving that exactly one of two events will happen
January 19th 2009, 04:27 PM
pittsburghsteelers
probability--proving that exactly one of two events will happen
evening
how do I show that the probability that exactly one of the events A or B occurs equals P(A) + P(B) - 2*P(AB)?
i know tha... | 4 | [
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... | 15,723 | 15723 | |
Easy Probability
September 10th 2010, 10:25 AM #1
Easy Probability
If Pr(A) = 4 Pr(B), $Pr(A\cup B) =0.8$ and $Pr(A\cap B) = 0.2$, find:
a) Pr(B)
b) Pr(A)
The bit that confuses me most was probably "Pr(A) = 4 Pr(B)" in the question above. Is this a typo? I've tried figuring this out for few times but... | 4 | [
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Limit problem: adding fractions with variables in the denom.
$\lim_{x \to 1}\frac{1}{x-1}+\frac{1}{x^2-3x+2}$ $\lim_{x \to 1}\frac{1}{x-1}+\frac{1}{(x-1)(x-2)}$ This is where I get lost. Do I multiply $(x-1)$ to both sides?
Is... $\frac{1}{x-1} + \frac{1}{(x-1)\cdot (x-2)} = \frac{x-2+1}{(x-1)\cdot (x-2)} = \frac{1}{x... | 4 | [
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Interesting Identity
Hi,
sum[0 to x](sin(x))=180 * sin(x/2)*sin(x/2) + sin(x)/2
I'm guessing you meant :
sum[k=0 to x](sin(k))=f(180)*sin(x/2)*sin(x/2) + sin(x)/2
If you're interested in a proof, here you go.
Let [itex]x \in \mathbb R, n \in \mathbb N[/itex].
I'll be using radians instead of degrees, so I'll show... | 5 | [
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0.06005... | 15,726 | 15726 | |
Go4Expert - View Single Post - solves systems of linear equations
This question is to develop a program that solves systems of linear equations. Assume the number of equations is always the same as the number of unknowns. The general form of such a system is as
follows:
a11x1 + a12x2 + … + a1nxn = b1,
a21x1 + a22x2 +... | 4 | [
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0.0830078125,
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-0.0172... | 15,727 | 15727 | |
Maclaurin Series(approximation)
December 10th 2009, 03:03 AM #1
Member
Joined
Nov 2009
Posts
151
Maclaurin Series(approximation)
The Maclaurin series for sin x is
$\frac {\sin x}x = \sum\limits_{k = 0}^\infty {\frac{{( - 1)^k x^{2k} }}<br /> {{(2k + 1)!}}} = 1 - \frac {x^2}{3!} + \frac {x^4}{5!} - \... | 5 | [
-0.059326171875,
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-0.000972747802734375,
0.0625... | 15,728 | 15728 | |
Need proving some trig identities!!!!!
July 13th 2007, 10:44 PM #1
Newbie
Joined
Jul 2007
Posts
4
Need proving some trig identities!!!!!
I'd greatly appreciate is somebody proved the following true.
1. 1-sinx/1+sinx = (secx-tanx)^2
2. sinx+1/cosx+cotx = tanx
3. sin^2x-tan^2x/1-sec^2x = sin... | 4 | [
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0.051025390625... | 15,729 | 15729 | |
geo circle problem
October 24th 2007, 01:53 PM #1
Junior Member
Joined
Oct 2007
Posts
52
geo circle problem
please help!!!
In the diagram attached, the points A, B, D and E lie on a circle.
AE = BE = BC.
The lines BE and AD intersect at F.
Angle DCB = x°.
Find the size of angle AEB ... | 4 | [
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-0.0373535156... | 15,730 | 15730 | |
Problems on characteristics
May 18th 2010, 09:24 PM
Waikato
Problems on characteristics
Obtain a solution of
u_t + u_x = t^a, where a = alpha, and a > 0.
given that u = u_0(x) on t = t0
May 19th 2010, 06:28 AM
Jester
Quote:
Characteristic equation
$\frac{dt}{1} = \frac{dx}{1} = \frac{... | 5 | [
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-0.0830078125... | 15,731 | 15731 | |
Induction Proof.........
Prove by induction that the number of 2-subsets of an n-set A equals n(n-1)/2.
First please note that a 2-subset is a subset of a set on n elements containing exactly 2 elements, so the number of 2-subsets of an n-set is just $\binom{n}{2}=\frac{n(n-1)}{2}$. Now let's prove it
by induction: Ba... | 4 | [
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-0.0708007... | 15,732 | 15732 | |
Trignometric identities - Express as a single sine or cosine function
September 9th 2009, 02:59 PM #1
Member
Joined
Sep 2009
Posts
83
Trignometric identities - Express as a single sine or cosine function
Okay, I am having trouble understanding how to use trigonometric equations. The question states:
... | 4 | [
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0... | 15,733 | 15733 | |
Find out fallacy
July 1st 2009, 07:17 PM #1
Find out fallacy
FInd out fallcy in the proof. This "proof" will attempt to show that all people in Canada are the same age, by showing by induction that the following statement (which we'll call "S(n)" for
short) is true for all natural numbers n:
Statement S(... | 4 | [
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0.04... | 15,734 | 15734 | |
Solving 2nd order differential equation with non-constant coefficients
JJacquelin
(y')² = y²sin(x)+C
You can find the solutions in the particular case C=0 in terms of exponential of Incomplete elliptic integral of the second kind.
I'm afraid that sin(x) ruins the integration, and as such you're missing a term ##-\i... | 4 | [
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0.040039... | 15,735 | 15735 | |
Adaptive secure data transmission method for OSI level 1
Page 61
Soft Detection of Noisy PSK-Signals
Phase detection is degraded due to phase jitter generated in the delta modulation process. Phase
jitter of the ADM-channel is calculated with a 26-point DFT algorithm as a phase receiver. The
software algorithm is pr... | 4 | [
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Patent US4454590 - Programmable signal processing device
RIGHTS OF THE GOVERNMENT
The invention described herein may be manufactured and used by or for the Government of the United States for all governmental purposes without the payment of any royalty.
BACKGROUND OF THE INVENTION
This invention relates to a program... | 5 | [
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0... | 15,737 | 15737 | |
Rate of change in demand
All you do to find the rate of change is take the first derivative with respect to p, we know that: $D(p) = 2\sqrt{55 - 6p} = 2(55 - 6p)^{\frac{1}{2}}$ So, the derivative would be: $\frac{dD}{dp} =
D'(p) = 2*\frac{1}{2}*\frac{1}{\sqrt{55 - 6p}}*-6$ $D'(p) = \frac{-6}{\sqrt{55 - 6p}}$ All you do... | 5 | [
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0.005126953125,
-0.068359375,
0.0... | 15,738 | 15738 | |
Ordered pair. need help in understanding.
May 5th 2009, 09:52 PM #1
Newbie
Joined
Apr 2009
From
chennai,india
Posts
9
Ordered pair. need help in understanding.
Need help in understanding this theorem..
Theorem 2.1.1. Let <a, b> and <c, d> be ordered pairs. Then <a, b> = <c, d> if and only if a =... | 4 | [
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Need some help with this question with energy
February 13th 2013, 05:57 AM
gordonmckee
Need some help with this question with energy
A horizontal force of 80 N acts on a mass of 6 kg resting on a horizontal surface. The mass is initially at rest and covers a distance of 5 m in 0.92 s under the action of the forc... | 4 | [
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-0.00... | 15,740 | 15740 | |
Logarithmic decrement of a lightly damped oscillator
1. The problem statement, all variables and given/known data
The logarithmic decrement δ of a lightly damped oscillator is defined to be the natural logarithm of the ratio of successive maximum displacements (in the same direction) of a free damped oscillator.
That i... | 4 | [
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0.04125976... | 15,741 | 15741 | |
derivative of a function
Please, what woudl be the derivative of a function? I foudn sth like: $(f(x)=x^a$ $(f(x)'=x^a(a)'$ is that ok???
Hello! I ment, if a = function! some tol dme it is different!!!
Yep, that is different. $(x^{a(x)})'$ $= (e^{a(x) \ln x})'$ $= e^{a(x) \ln x} \cdot (a'(x) \ln x + a(x) \cdot \frac ... | 5 | [
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0.0308837890625,
... | 15,742 | 15742 | |
average value of a funtion
November 15th 2007, 09:25 AM #1
Member
Joined
Aug 2007
Posts
148
average value of a funtion
Hi everyone,
Could you please tell me if this is correct?
Find the average value of the function on the given interval
g(x)=x^2sq.(1+x^3) [0,2]
1/2int. [1/3sq. u]du=
... | 5 | [
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0.038330078125,
0.00787353515... | 15,743 | 15743 | |
4x-5=11x+16
If it's not what You are looking for type in the equation solver your own equation and let us solve it.
Simplifying 4x + -5 = 11x + 16 Reorder the terms: -5 + 4x = 11x + 16 Reorder the terms: -5 + 4x = 16 + 11x Solving -5 + 4x = 16 + 11x Solving for variable 'x'. Move all terms containing x to the
left, a... | 4 | [
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Statistics: E(X) = Integral(0 to infinity) of (1-F(x))dx
[tex]
\begin{align*}
E[X] &= E\bigg[\int_0^X 1\,dx\bigg]\\
&= E\bigg[\int_0^\infty 1_{\{X>x\}}\,dx\bigg]\\
&= \int_0^\infty E[1_{\{X>x\}}]\,dx\\
&= \int_0^\infty P(X > x)\,dx\\
&= \int_0^\infty (1 - F(x))\,dx
\end{align*}
[/tex]
By the way, this formula is true ... | 4 | [
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0.003692626953125,
-0.0434570... | 15,745 | 15745 | |
Metric inducing Discrete Topology
April 7th 2009, 11:35 AM #1
Junior Member
Joined
Feb 2008
Posts
63
Metric inducing Discrete Topology
Show that the discrete topology on X is induced by the metric
$d(x,y)=$ 0 if x=y, 1 if x $eq$y
Is the trivial topology metrizable?
Last edited by Andreamet... | 4 | [
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0.1103515625,
-0.0649414... | 15,746 | 15746 | |
Cholesky Decomposition
14.5 Cholesky Decomposition
A symmetric, positive definite square matrix A has a Cholesky decomposition into a product of a lower triangular matrix L and its transpose L^T,
This is sometimes referred to as taking the square-root of a matrix. The Cholesky decomposition can only be carried out w... | 4 | [
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0.1181640625,
-0.037353515625,
0.023681640... | 15,747 | 15747 | |
Problem with this question
August 29th 2009, 01:55 AM #1
Member
Joined
May 2009
Posts
99
Problem with this question
I have a problem with this particular question:
Expand $(\frac{1 + x}{1 - 3x})^{\frac{1}{3}}$ in ascending powers of x up to and including the term in $x^3$ ad determine the set values... | 5 | [
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-0.0130615234375,
-... | 15,748 | 15748 | |
Factorization
March 17th 2006, 06:11 AM
dgolverk
Factorization
Here are some questions that I can't solve...
factorization:
1.a^2x+2+2a^2+x
2.-(3+a)(5-b)+3c(b-5)
3.-a-b+3ab+3a^2
4.x^2-y^2+x-y
5.x^2-y^2+3x+3y
6.2c^2-8d^2+c-2d
That's all, hope you can help me :)
Thanks
March 1... | 4 | [
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Two Trigonometry Problems
March 1st 2007, 02:11 AM
Amy
Two Trigonometry Problems
I have two problems
1) Express cot 138° 15' 10'' as the same function of a positive acute angle and then find its value.
2) Using exact values find the numerical value of tan 225°+tan(-45°)
tan(-45°) is in 4th quadr... | 4 | [
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... | 15,750 | 15750 | |
Can't understand procession
FrankJ777
I'm curious about how precession works. From what I thought I understood about angular momentum and torque vectors, the direction that they point are by arbitrary convention using the right hand
rule. They are just a convenient expression of the normal or the plane that the torq... | 4 | [
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... | 15,751 | 15751 | |
Intersection
The intersection of the most basic geometric primitives was presented in the Algorithm 5 about Intersections of Lines and Planes. We will now extend those algorithms to include 3D triangles which are
common elements of 3D surface and polyhedron models. We only consider transversal intersections where the t... | 4 | [
0.0126953125,
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-0.0245361328125,
0.076171875,
-0.0262451171875,
0.005096435546875,
-0.05712890625,... | 15,752 | 15752 | |
Integrate dy/dx
Here's a proof of the general case that I got from Courant's Introduction to Calculus and Analysis. This is one of my favourite proofs:
"If a function y = f(x) satisfies an equation of the form [tex] y' = \alpha y [/tex] where [tex] \alpha [/tex] is a constant, then y has the form [tex] y = f(x) = ce^{... | 5 | [
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0.1118164062... | 15,753 | 15753 | |
real analytic function
April 18th 2010, 02:07 AM
Kat-M
real analytic function
let $f:(-1,1) \rightarrow R$ be $C^\infty$. Prove that $f$ is real analytic in some neighborhood of 0 if and only if there is a nonempty interval $(- \sigma, \sigma)$ and a constant $M$ such that
$|(d/dx)^k f(x)| \leq M^k * k!$ for... | 5 | [
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0.04736328125,
-0.07861... | 15,754 | 15754 | |
Probability for the most frequent number in lottery?
Sounds like you're interested in showing whether or not some observed frequencies are statistically significant.
To formulate the problem more precisely, the lotto consists of
k
samples without replacement from a population of size
n
, repeated
r
times. Let th... | 4 | [
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0.09814453125,
-0.0... | 15,755 | 15755 | |
Smooth function
April 6th 2008, 01:47 PM
namelessguy
Smooth function
Someone can help me attack this problem?
Let e: R into R by
e(x) = e^ (-1/x) if x > 0 and e(x) = 0 if x < or equal 0.
1) Show that e is smooth, that is, e has derivatives of all orders at all points x . Hint use L'Hospital and indu... | 5 | [
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-0.01025390625,
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-0.08935546875,
0.0033416748046875,
-0.11669921... | 15,756 | 15756 | |
Method of undetermined coefficients - Nonhomogeneous Linear Systems
March 23rd 2009, 05:48 PM #1
Method of undetermined coefficients - Nonhomogeneous Linear Systems
Hello,
I am simply trying to understand the way this system was solved in the text:
$<br /> x^{\prime} = \left(\begin{array}{cc}2&-1\\3&-2\... | 4 | [
-0.07470703125,
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0.00775146484375,
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0.0322265625,
-0.109375,
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0.01806640625,
-0.048828125,
-0.... | 15,757 | 15757 | |
Word problem:-
October 22nd 2008, 08:09 AM #1
Word problem:-
There are 2 discs each of radius 'a' placed one above the other.
The bottom disc is fixed and the above disc moves in a straight line with a velocity inversely proportional to the area exposed of the bottom disc. The constant of proportionality is ... | 4 | [
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0.04248046875,
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0.06591796875,
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-0.031... | 15,758 | 15758 | |
Examples
Go to the first, previous, next, last section, table of contents.
In /bin/sh, the following will assign the value of "pi" to the shell variable pi.
pi=$(echo "scale=10; 4*a(1)" | bc -l)
The following is the definition of the exponential function used in the math library. This function is written in POSIX ... | 4 | [
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-0.0966796875,
-0.062255859375,
0... | 15,759 | 15759 | |
2 Limit Questions
January 19th 2009, 04:43 PM #1
Newbie
Joined
Sep 2008
Posts
20
2 Limit Questions
1) lim 1/x+4 - 1/4
------------
x
x->0
This one i have no idea how to start it.....i'm totally lost...
2) lim ------
/ t + 9 - 3
------------- that is suppose to be a square ro... | 5 | [
-0.057373046875,
-0.0164794921875,
0.060791015625,
-0.01422119140625,
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0.06298828125,
0.0390625,
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0.01422119140625,
0.0810546875,
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-0.02734375,
0.03564453125,
-0.037109375,
-... | 15,760 | 15760 | |
STAT 200: Elementary Statistics
Here is the key. Email or visit my office if you have questions.
regression_hw_key.pdf
Office hours for finals week:
Monday: 10-Noon
Tuesday: 10-Noon
Wednesday: 10-Noon
Friday: 10-Noon
Or by appointment
The final (150 points) will take place Wednesday, April 5th at 2:00. The locat... | 5 | [
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0.04833984375,
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-0.1494140625,
... | 15,761 | 15761 | |
Please help with these Quadratic Equations
June 2nd 2008, 11:25 PM #1
Newbie
Joined
Jun 2008
Posts
20
Please help with these Quadratic Equations
Any chance i can have a step by step demo of these. thanks.
-x + 8X - 15 = 0
6x^2 - 17x + 5 = 0
-3b^2 - 26b = -9
Thanks
It should be ... | 4 | [
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0.0272216796875,
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0.0177001953125,
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0.09619140625,
0.025146484375,
-0.04809570312... | 15,762 | 15762 | |
Music Review
Sound and Music Review
Navigate to Answers for:
Questions #1-#9
Questions #10-#52
Questions #53-#64
Questions #65-#75
65. A guitar string has a fundamental frequency of 262 Hz. Determine the frequency of the ...
a. ... second harmonic.
b. ... third harmonic.
c. ... fifth harmonic.
d. ... eighth h... | 4 | [
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0.050048828125,
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0.0380859375,
0.... | 15,763 | 15763 | |
On the Incompressible Limit for the Compressible Flows of Liquid Crystals under Strong Stratification on Bounded Domains
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 253260, 10 pages
http://dx.doi.org/10.1155/2013/253260
Research Article
On the Incompressible Limit for the Compressible Flows of Liquid... | 4 | [
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0.0205078125,
-0.... | 15,764 | 15764 | |
Number of solutions
November 13th 2008, 06:43 AM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Number of solutions
Prove that $f(x) = 4x^4+2x^2-6x+2=0$ has exactly two solutions.
Proof so far.
Now $f'(x)=4x^3+4x-6$, set it equals to zero, we have $2x^3+2x-3=0$, so this equation have 3 ... | 4 | [
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0.0225830078125,
-0.09423828125,
-... | 15,765 | 15765 | |
n people standing in a line
September 16th 2007, 11:10 AM #1
Junior Member
Joined
Nov 2006
Posts
43
Thanks
1
n people standing in a line
Here is the question:
If Sam and Peter are among n men who are arranged at random in a line, what is the probability that exactly k men stand between them?
... | 4 | [
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0.0155029296875,
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-0.05078125,
... | 15,766 | 15766 | |
Volume and centre of mass
May 13th 2008, 12:08 PM #1
Newbie
Joined
May 2008
Posts
5
Using the result Пa2, determine the volume of a cone of height h and radius a. Find the position of its centre of mass.
Orient the cone with the vertex at the origin and the axis along the y-axis.
$M=\int_{0}^{h}... | 5 | [
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-0.053955078125,
-... | 15,767 | 15767 | |
Hi, im terrible at maths and need a dumbed down explanation of something simple
October 1st 2013, 11:31 AM #1
Newbie
Joined
Oct 2013
From
Uk
Posts
5
Hi, im terrible at maths and need a dumbed down explanation of something simple
Hi guys, im working through some chemistry problems and i have zero math... | 4 | [
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0.... | 15,768 | 15768 | |
First Passage Time Moments of Jump-Diffusions with Markovian Switching
International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 501360, 11 pages
http://dx.doi.org/10.1155/2011/501360
Research Article
First Passage Time Moments of Jump-Diffusions with Markovian Switching
Department of Mathematical ... | 4 | [
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0.0067138671875,
-0.080... | 15,769 | 15769 | |
Integrals
March 27th 2008, 12:04 AM #1
Newbie
Joined
Mar 2008
Posts
2
Integrals
and
Are the only ones left in my assignment, please help me if you can, i haven't got much time. Thank you
I love this proceedure
We will use integration by parts twice and then solve for the integral
use ... | 5 | [
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0.... | 15,770 | 15770 | |
*Official* The School Help Thread
Okay, so to simplify the one that you just gave me, you're first going to distribute the 6x to both terms in the parentheses. So you end up with two answers which you'll stick back together to form
the final answer.
6x * 3x = 18x^2
6x * -x = -6x^2
Stick them back together:
18x^2 - ... | 4 | [
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Approximating an infinite series
October 8th 2012, 06:41 PM #1
Member
Joined
Oct 2011
Posts
86
Thanks
1
Approximating an infinite series
Approximate a sum for the infinite series:
$\sum_{n=1}^{\infty}\frac{1}{n^4}$
with a maximum error of $0.02$
Answer:
$\sum_{n=1}^{\infty}\frac{1}{n... | 5 | [
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0.017578125,
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0.00628662109375,
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0.060546875,
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-0.0257568359375,
0.024536... | 15,772 | 15772 | |
Matrix Question
The point of intersection of the lines $2x+3y=a$ and $x-2y=5$ is $(2,1)$. Use a matrix method to find $a$. Thanks
You need to apply row reduction methods to this matrix: $\left[\begin{array}{cc|c}2&3&a\\1&-2&5\end{array}\right]\xrightarrow{R_1\leftrightarrow R_2}{}\left[\begin{array}{cc|c}1&-2&5\\2&3&a... | 5 | [
-0.05078125,
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0.0311279296875,
-0.130859375,
-0.0... | 15,773 | 15773 | |
Understanding float datatype in C
Pretty sure, one must have used the datatype ‘float’ numerous number of times since the day one has started programming. However, there are many times, when we mishandle floats and doubles, or get
unexpected results while using float variables or find ourselves being perplexed while u... | 5 | [
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0.023193359375,
-0.0103759765625,
-0.10400390625,
-0.08984375,
0.0693359375,... | 15,774 | 15774 | |
homogeneous solution??
November 19th 2009, 08:02 AM #1
Newbie
Joined
Nov 2009
Posts
6
homogeneous solution??
Hi guys I am really stuck on this differential equation can anyone help?
dy/dt = (t^2 + y^2) / (3ty)
condition - y=1 and t=2
Thank you in advance
This is an example of A DE wit... | 4 | [
-0.12353515625,
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0.03369140625,
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0.012451171875,
0.046875,
0.00970458984375,
-0.061279296875,
-0.044677734375,
-0.02416... | 15,775 | 15775 | |
Hyperbolic Functions
November 17th 2008, 12:49 AM #1
Member
Joined
Oct 2008
Posts
88
Hyperbolic Functions
Show that $cosh(x-y) = cosh(x)cosh(y) - sinh(x)sinh(y)$
Everytime I try this with exponential it ends up being really messy and no doubt I'm cancelling something wrong or something similar. Is t... | 5 | [
0.04052734375,
0.0234375,
0.030517578125,
-0.0142822265625,
-0.0128173828125,
-0.035400390625,
0.0242919921875,
-0.07080078125,
-0.00347900390625,
0.016357421875,
0.09765625,
-0.05859375,
-0.033935546875,
0.059326171875,
0.03466796875,
-0.0240478515625,
-0.0081787109375,
-0.0747070... | 15,776 | 15776 | |
Bézier Curves for your Games: A Tutorial
We all know what a curve is. Here are some examples.
A Bézier curve is a type of curve that is easy to use, and can describe many shapes. Bézier curves are famously used for representing characters in fonts, and shapes in vehicle design. Bézier curves
are also used in vector a... | 4 | [
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0.0615234375,
-0.0035858154296875,
0.004608154296875,
-0.03369140625,
... | 15,777 | 15777 | |
How fast Coil Springs are? Greatest mystery today?
Chestermiller
OK. I did a quick analysis of the problem, and came up with a first order approximation you can use to ballpark the release velocity. This is based on the method alluded to by AlephZero, and it is
similar in form to the equation given by the Institute.... | 5 | [
-0.02880859375,
0.059814453125,
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0.0029754638671875,
-0.03125,
-0.01324462890625,
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-0.0289306640625,
-0.058349609375,
0.0017852783203125,
0.005523681640625,
0.0238037109375,
0.06982421875,
0.0322265625,
-0.064453125,
0.041015625,
0.072265625,
0.020996093... | 15,778 | 15778 | |
Potential Difference and Potential Near a Charged Sheet
1. The problem statement, all variables and given/known data
Let [tex]{\rm A} = \left(x_1,y_1 \right)[/tex] and [tex]{\rm B} = \left( x_2,y_2 \right)[/tex] be two points near and on the same side of a charged sheet with surface charge density [tex]+ \sigma[/
tex] ... | 4 | [
-0.07861328125,
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0.09033203125,
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0.0225830078125,
0.0234375,
0.0107421875,
0.049072265625,
-0.0174560546875,
0.04736328125,
0.052490234375,
0.0673828125,
0.026123046875,
-0.01025390625,
-0.0952148... | 15,779 | 15779 | |
Euclidean Isometries - Help Please!
Need examples of Euclidean isometries f and g such that $f\circ{g}$ ≠ $g\circ{f}$.
let A be the matrix [cos90 -sin90|sin90 cos90] a rotation of 90. let X=(x,y) vector. let f(X)=AX so the action of f on X rotates it by 90. and let g be a rotation with respect to the point (1,0) not
t... | 5 | [
-0.0634765625,
-0.043701171875,
-0.037841796875,
-0.06640625,
-0.04541015625,
0.05419921875,
0.078125,
-0.08154296875,
-0.006195068359375,
-0.0257568359375,
0.154296875,
0.005584716796875,
-0.0537109375,
0.0194091796875,
-0.0157470703125,
-0.031005859375,
-0.051513671875,
-0.002349... | 15,780 | 15780 | |
Cubic surface
We define the cubic $V$ in $\mathbb{R}^3$ by the equations: $y-x^2=0, z-x^3=0$. Prove that $\mathcal{I}(V)=<y-x^2,z-x^3>$ thanks!
let $J=<y-x^2,z-x^3>.$ clearly $J \subseteq \mathcal{I}(V).$ now suppose $f(x,y,z) \in \mathcal{I}(V).$ then $f(x,x^2,x^3)=0.$ since $f \in \mathbb{R}[x,y,z],$ we have: $f(x,y... | 5 | [
0.03076171875,
0.06640625,
-0.01507568359375,
-0.01220703125,
-0.0341796875,
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One chain-link pulls another
Register to reply
by drawar
Tags: chainlink, pulls
P: 132 1. The problem statement, all variables and given/known data
A student tries to raise a chain consisting of three ... | 4 | [
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0.1279296875,
-0.0888... | 15,782 | 15782 | |
Existence of series of random variables
January 8th 2011, 11:48 AM
slavert
Existence of series of random variables
Is it possible that following series of random variables exists?
$P({\omega \in \Omega : lim_{n -> \infty} X_{n}=0})=0.5$
Thx for any help
January 8th 2011, 12:34 PM
Moo
Hello,
... | 5 | [
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0.0390625,
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0.01806640625,
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-0.... | 15,783 | 15783 | |
Remainder Theorem
September 28th 2008, 07:21 PM
Himerzi
Remainder Theorem
Hey guys, check this question out - its a toughie for sure :
The expression f(x) = ax^3+bx^2-10x+24 is exactly divisible by x^2-2x-8. Find a and b. Solve f(x) = 0. Find the remainder when f(x) is divided by x-2.
September 28th 2008, ... | 4 | [
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Patente US5566100 - Estimation of signal frequency using fast walsh transform
This is a division of application Ser. No. 08/209,962, filed Mar. 14, 1994 for ESTIMATION OF SIGNAL FREQUENCY USING FAST WALSH TRANSFORM, now abandoned.
FIELD OF THE INVENTION
The present invention relates to a method and circuit for estima... | 5 | [
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Bode's Law (Or better attributed as Titius' Rule)
It seems that Bode published Titius' discovery without crediting Titius, so I will call it Titius' Rule.
Titius' Rule, in it's modern adaption, says there is a geometric progression in the distance the planets circle the Sun. It's not a perfect rule, and Neptune doesn'... | 4 | [
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0.004150390625,
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-... | 15,786 | 15786 | |
implicit differentiation
$\frac{1}{xy} = x+y$ is the same as $xy(x+y) = 1$ $\frac{d}{dx} \left(xy(x+y)\right) = \frac{d}{dx} \left(1 \right)$ use the product rule $xy \frac{d}{dx} \left(x+y \right) + (x+y)\frac{d}{dx} \left
(xy \right) = 0$ Note: by the chain rule, $\frac{d}{dx} \left(f(y) \right) = f'(y)\frac{dy}{dx}$... | 5 | [
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0.050... | 15,787 | 15787 | |
Classifcation of Markov States, Convergence
September 14th 2009, 07:11 AM #1
Classifcation of Markov States, Convergence
A markov chain X has the state space transition matrix P (see attached image) where q = 1-p and 0 < p < 1
Classify the states of X and give the stationary distributions.
Show that $P^... | 5 | [
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-0.075683... | 15,788 | 15788 | |
Distance traveled by airplane
Hellabyte
Lets look at exactly what the problem is asking:
"how far is it from Taupo after 63 min of flying at constant altitude?"
Notice that it says how far. not how far east or west, just how far. So make a graph, draw a point at the origin, and a point where the plane is at after ... | 4 | [
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Complex Roots/Multiplication
July 22nd 2006, 04:48 PM #1
Junior Member
Joined
Jul 2006
Posts
45
Complex Roots/Multiplication
I'm having trouble multiplying out the conjugates to obtain a quadratic for the following. Both quadratics should multiply to the polynomial $x^4 + 3$ when finished...any help??
... | 5 | [
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Function of x (P and A of a Rectangle)
July 29th 2010, 06:04 AM #1
Newbie
Joined
May 2010
Posts
8
Function of x (P and A of a Rectangle)
Hello,
Here's a problem which I'm unable to solve. I'd be grateful if you helped me through:
A rectangle with altitude x is inscribed in a triangle ABC with b... | 5 | [
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0.00497436523437... | 15,791 | 15791 | |
solve algebraically
Note that $2\log_4x-\log_4\left(x+3\right)=1\implies \log_4\left(x^2\right)-\log_4\left(x+3\right)=1$ Now recall that $\log_ab-\log_ac=\log_a\left(\frac bc\right)$ Thus, $\log_4\left(x^2\right)-\
log_4\left(x+3\right)=1\implies\log_4\left(\frac{ x^2}{x+3}\right)=1$ Now, note that $\log_44=1$ Thus, w... | 4 | [
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0.010009765625,
-0.0908... | 15,792 | 15792 | |
triple integration in spherical
April 8th 2006, 08:23 AM #1
Newbie
Joined
Apr 2006
Posts
5
triple integration in spherical
I am having trouble setting up the following integral problem: "Find the volume of the solid that lies inside the cone z^2 = 3x^2 + 3y^2 and between the spheres x^2 + y^2 + z^2 = 1 a... | 5 | [
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-0.052978515625,
-0.03295898437... | 15,793 | 15793 | |
Difficult differentiation question
It's just a "show" question. So could it have something to do with starting from $\frac{d^2y}{dx^2}$ and reducing it into a form which only has x and t. Not really sure, how you would do that though.
this question is a pretty straight forward use of the chain rule in higher derivativ... | 5 | [
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0.0022277... | 15,794 | 15794 | |
Terminating Decimal Proof
January 15th 2010, 10:38 AM #1
Terminating Decimal Proof
I am having troubles with this deceptively simple problem:
Show that for any integer n that $\frac{1}{n}$ will be a terminating sexagesimal iff n's prime factors only consist of 2,3 and 5.
In other words $\frac{1}{n}$ wil... | 4 | [
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0... | 15,795 | 15795 | |
Word Problem-Related Rates
December 9th 2007, 11:14 AM #1
Junior Member
Joined
Sep 2007
Posts
37
You are standing under a 20 foot lamppost. Your 5 foot friend is 10 feet away from you and sprints away at a speed of 20 feet per second.
(a) how fast is the tip of her shadow moving
(b) at that same i... | 5 | [
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Calculating Skewness using s non iteratice aproach
July 24th 2008, 02:08 AM #1
Newbie
Joined
Aug 2007
Posts
8
Calculating Skewness using s non iteratice aproach
Hi guys,
A while back I was kindly helped with a non iterative algorithm to calculate a weighted average and its variance outlined here htt... | 4 | [
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Radiation from Electric Current
Figure 4. Graphical illustration of determining the relative phase between the two vectors.
In Figure 4, we define r and R. By using some geometry, we see that the gold line has a distance equal to
By observing the geometrical relationships in Figure 4, you see that the vector r trave... | 5 | [
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Integrable function
there are various definitions of the integral, that apply to different classes of funtions.
riemann's definition applies only to bounded ones, i.e. the limit of riemann sums is finite and independent of choice of partitions and choice points, only if the function is bounded.
this is easy to prove ... | 4 | [
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