content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Continued Fractions and Gaps
Linas Vepstas <linas@linas.org>
Date: 12 Oct... | 4 | [
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Simplifying roots
December 14th 2010, 04:57 PM
Kieth89
Simplifying roots
Alright, I've got a final in College Algebra tomorrow but can't figure out how my teacher got this answer. Here was the original problem (as best I can type it):
1 over the 5th root of 9
I am told to rationalize the denominator. I... | 4 | [
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question about the closed form of a function
up vote 0 down vote favorite
Hi everyone! I have a question about how to find the closed form of a function defined by
$$\phi(\theta)=\inf_{x\geq 2}f(x;\theta)\equiv\inf_{x\geq 2}\frac{(x+2)^2}{\frac{1}{\theta}\left(\frac{x-1}{2}-\frac{1}{x}\right)+\frac{x^2-1}{16}},\ \ \t... | 5 | [
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Taylor's Theorem
November 23rd 2007, 08:07 AM #1
Junior Member
Joined
Nov 2007
Posts
32
Taylor's Theorem
Let r be defined on V (x0) = {x : |x − x0| < a}. If r is n-times differentiable at x0 and r(x0) = r'(x0) = r''(x0) = · · · = r(n)(x0) = 0 (nth derivative),
prove that the limit as x approaches x0 ... | 5 | [
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Uniform Continuity definition
October 16th 2008, 01:32 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Uniform Continuity definition
Let $(M,d)$ and $(N,p)$ be metric spaces, and let $f:A \subset M \rightarrow N$. Prove that f is an uniformly continuous mapping on A iff for every pair of sequen... | 5 | [
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Three Weights
Date: 12/07/97 at 17:08:59
From: Jeff MacDougall
Subject: Advanced Algebra Honors
I can't figure this out, it is a problem for my Algebra 2 class that I
and my friends can't figure out:
A boy selling fruits has only three weights, but with them he can
weigh any whole number of pounds from 1 pound to 1... | 4 | [
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First order ODE integration
October 1st 2013, 12:15 AM #1
Junior Member
Joined
May 2013
From
thailand
Posts
43
First order ODE integration
Hey its me again and I got stuck with my integration for first order ode
this is the question, and what I have done so far
$\frac{dy}{dt}=y(2-y)(y-1)$
... | 4 | [
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Interval of Convergence
April 11th 2009, 11:20 AM #1
Member
Joined
Jan 2009
Posts
100
Interval of Convergence
I'm trying to find the interval of convergence:
$f(x) = \sum^ \infty_ {n=0} \frac{(-1)^{n+1}(x-1)^{n+1}}{n+1} = \mid x-1 \mid$
I still don't know how to find its interval of convergence... | 5 | [
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Which of the following subsets are subspaces?
Hey guys, I'm having trouble with subsets and subspaces (proper way of showing whether it's a subspace or not) I usually go over the 3 statements that have to be true for it to be a subspace, which
is : 1. There exists a 0 vector 2. U and V such that U + V are in the subspa... | 5 | [
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[SOLVED] stuck on a limit and out of ideas
March 5th 2009, 12:25 PM #1
[SOLVED] stuck on a limit and out of ideas
I can't get this limit into any form that does not involve an undefined quantity -- specifically ln(0) or 0^(0).
$\lim_{x\rightarrow0}(e^{x} - 1 - x)^{x}$
This does not work, obviously:
... | 5 | [
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Optimization
April 22nd 2008, 03:37 AM
someone21
Optimization
An isosceles triangle is circumscribed in a circle of a radius 2m.Determine the minimum poosible area the isosecles triangle can have??
Any other good notes or questions for Optimization problems would be welcomed as well
April 22nd 2008, 06:41 ... | 5 | [
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Parametric problems and the Parabola
August 23rd 2009, 01:23 AM #1
Newbie
Joined
Aug 2009
Posts
1
Parametric problems and the Parabola
I've got a one mark question on an assignment, so 'logic' dictates that it should be simple, right? But I just don't get it.
I've got the variable point P(2at, at^2)... | 4 | [
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sum of interior angles of a 7-point star.
April 4th 2011, 02:50 AM
kingman
sum of interior angles of a 7-point star.
Dear sir ,
I would appreciate if anyone can show me the solution to the below question.
thanks
Kingman
What is the value of the angles A+B+C+D+E+F+G in the beolw figure ?
April 4t... | 4 | [
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mathschallenge.net
Prime Power Sum
Problem
For any given prime, p, prove that 2^p + 3^p can never be a perfect square.
Solution
With the exception of p=2, for which 2^2 + 3^2 = 13 and is not square anyway, the sum, 2^p + 3^p, will always be odd.
All odd squares are congruent with 1 mod 4: (2k+1)^2 = 4k^2 + 4k + 1.... | 4 | [
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Question on Kähler/ample cone, cone of curves....
up vote 6 down vote favorite
3
Assume $X$ is smooth "simply connected" complex projective variety and $Y\subset X$ a smooth hyperplane section. ( $Y= X\cap H$, $H\subset \mathbb{P}^n$).
Let's $NE(X)$ be the cone of effective 1-cycles modulo numerical-equivalence. Let'... | 5 | [
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Counterexamples in Algebra?
up vote 64 down vote favorite
66
This is certainly related to "What are your favorite instructional counterexamples?", but I thought I would ask a more focused question. We've all seen Counterexamples in Analysis and Counterexamples
in Topology, so I think it's time for: Counterexamples in ... | 5 | [
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truncation in an exact 2-category
In a suitably exact 2-category, we can construct truncations as quotients of suitable congruences.
(-1)-truncation
This case is easy and just like for 1-categories.
Proof
Define the support $supp(A) = A_{\le -1}$ of an object $A$ to be the image of the unique morphism $A\to 1$. Tha... | 5 | [
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16 Paper 30100961 IJCSIS Camera Ready pp113-118
(IJCSIS) International Journal of Computer Science and Information Security,
... | 4 | [
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Complex analysis, infinite series expansion of a function
July 19th 2010, 12:24 PM #1
Complex analysis, infinite series expansion of a function
I'm studying from my class notes and I don't understand a step. The function $\log (x+1)$ is analytic over $\mathbb{C}-\mathbb{R}^{\leq 1}$.
Furthermore $\log (x+1)=\... | 4 | [
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Constrained Steepest descent method - help in constraining it...
March 22nd 2011, 06:52 AM #1
Constrained Steepest descent method - help in constraining it...
I am looking to find the minimum of the function:
f = x1 - x2 + 3x1^2 + 2x1x2 + x2^2 + 1
However I would also like to add a constraint to this so t... | 5 | [
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How to Add Time Dependence and Get a Physical Equation for Three-Dimensional Free Particle Problems
At some point, your quantum physics instructor may want you to add time dependence and get a physical equation for a three-dimensional free particle problem. You can add time dependence to the
solution for
if you remem... | 4 | [
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A delicate measure-theoretic question about Jordan curves and arcs in the plane.
up vote 2 down vote favorite
1
Let E be the Euclidean plane and let M(X) be two-dimensional Lebesgue measure defined for each Borel subset X of E. Suppose that s is an arc in E and that e is a positive real number. Does there
always exist... | 5 | [
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Math Help
December 10th 2009, 06:12 PM #1
Member
Joined
Oct 2008
Posts
93
Determinant
Let A be a 3x3 matrix which satifies the equation:
A^3 -3A^2 - 10A = 0
a) Find all the real numbers which could possibly be eigenvalues of A
alright... so what i did was simplify the equation and got (A)... | 5 | [
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Trapezoidal rule proof
August 26th 2009, 02:01 AM #1
Newbie
Joined
May 2008
Posts
20
Trapezoidal rule proof
Consider the function y=x^2 for x[0,1]. Show using the trapezoidal rule with n intervals that the integral 0 -> 1 of x^2 dx is equivalent to n(n+1)(2n+1)/6n^3 - 1/2n.
I am having a lot of trou... | 5 | [
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Word Problems: Compound Interest AlgebraLAB: Word Problems
In order to solve
compound
interest problems, you should be able to:
There are several types of interest problems. This lesson deals with solving problems where interest is compounded. There are two other types of interest word problems that are dealt ... | 4 | [
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Regarding implicit differentiation
October 25th 2008, 01:41 AM #1
Junior Member
Joined
May 2008
Posts
61
Regarding implicit differentiation
How do I show that the curve x^3+y^3 = 3xy is symmetrical about the line y=x??
The curve is not one-to-one so I cant show that it is a self inverse. All I can th... | 5 | [
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Is the group von Neumann algebra construction functorial?
up vote 13 down vote favorite
4
Let $G$ be a group and $CG$ the complex group algebra over the field $C$ of complex number. The group von Neumann algebra $NG$ is the completion of $CG$ wrt weak operator norm in $B(l^2(G))$, the set
of all bounded linear operato... | 5 | [
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Vector Intersection
April 8th 2010, 11:02 AM #1
Newbie
Joined
Mar 2010
Posts
7
Vector Intersection
Hi, I have a mechanics question here I can't quite get.
A destroyer sights a ship at a point with position vector 600(3i + j)m relative to it and moving with velocity 5j m/s. The destroyer alters cours... | 5 | [
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0.0722656... | 40,327 | 40327 | |
Euler's Power Riffs
Ed Sandifer is an exegete of Euler's methods. In his latest "How Euler Did It", he shows the method through which he arrived at closed polynomials for the sums of n-th powers of the first x integers:
In general, Euler has us multiply the terms of Σx^n by (n + 1)/(n + 2) x, (n + 1)/(n + 1) x, (n... | 5 | [
-0.060546875,
0.0311279296875,
0.0576171875,
0.0274658203125,
0.006195068359375,
-0.0260009765625,
0.061279296875,
0.043701171875,
-0.03125,
-0.041259765625,
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0.0281982421875,
-0.054931640625,
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0.0224609375,
0.017822265625,
0.046386718... | 40,328 | 40328 | |
Relatively prime quadratic integers
October 27th 2008, 03:56 PM #1
Member
Joined
Jul 2008
Posts
78
Relatively prime quadratic integers
I've been stuck on this problem for a while now.
Suppose $32 = \alpha\beta$ for $\alpha,\beta$ relatively prime quadratic integers in $\mathbb{Q}[i]$. Show that $\al... | 5 | [
0.044189453125,
0.01165771484375,
-0.02294921875,
0.0023040771484375,
-0.052734375,
-0.0220947265625,
0.1552734375,
-0.03271484375,
-0.01104736328125,
-0.0771484375,
0.025146484375,
0.02880859375,
0.06591796875,
0.03173828125,
-0.03076171875,
0.059326171875,
0.021484375,
0.02148437... | 40,329 | 40329 | |
Determinants (do you notice any thing wrong??)
April 2nd 2008, 05:17 AM #1
Newbie
Joined
Mar 2008
Posts
21
Hi guys,
hoping somebody can check through my calculations for the determinant of $A$ a 4 x 4 matrix.
$A = \begin{vmatrix}<br /> \-1 && 3 && 0 && 5 \\<br /> -2 && 0 && 4 && 0\\<br /> 1 && 2... | 4 | [
-0.01123046875,
-0.06005859375,
-0.034423828125,
-0.09814453125,
0.0020599365234375,
-0.05078125,
-0.00213623046875,
-0.087890625,
-0.0225830078125,
-0.004425048828125,
0.1259765625,
-0.0751953125,
0.01708984375,
-0.0157470703125,
-0.0615234375,
0.0242919921875,
-0.01104736328125,
... | 40,330 | 40330 | |
Phase Angle
Phase Angle Help (page 2)
By
Stan Gibilisco
— McGraw-Hill Professional
Updated on Sep 6, 2011
Vector Representations Of Phase
If a sine wave X is leading a sine wave Y by x degrees, then the two waves can be drawn as vectors, with vector X oriented x degrees counterclockwise from vector Y . If wave X... | 4 | [
-0.11181640625,
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0.0712890625,
-0.00311279296875,
-0.10546875,
-0.02... | 40,331 | 40331 | |
Tricky trigonometric word problem
April 28th 2009, 01:23 PM
juliajank
Tricky trigonometric word problem
I've tried three different approaches to it, and it's taken me well over an hour and I CAN'T figure it out.
The pictures pretty much just for the diagram but in case you can't read the text.
19. The ... | 4 | [
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0.0185546875,
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-0.0152587890625,
0.00701904296... | 40,332 | 40332 | |
Multiplicative Identity Proof
February 9th 2011, 02:24 PM #1
Member
Joined
Nov 2010
Posts
86
Multiplicative Identity Proof
Hey all, I can't seem to figure out the following proof:
Let x be an element of the Integers. If x*x = x then x=0 or x=1.
Any help would be appreciated!
Well it follow... | 4 | [
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0.0267333984375,
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0.091796875,
0.0016937255859375,
0.00101470947265625,
0.024169921875,
-0.032226562... | 40,333 | 40333 | |
Atoms to Grams
February 2nd 2010, 02:45 PM #1
Junior Member
Joined
Sep 2009
Posts
27
Atoms to Grams
Hi, sry again -_- but i have yet another question.. what am i doing wrong!?
im trying to convert Atoms to Grams. EXample
1.0×1023
so im doing
(1.0×1023
96655)=3.3g (putting it to 2 ... | 4 | [
-0.00653076171875,
-0.034912109375,
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0.09375,
0.08203125,
-0.061279296875,
0.02001953125,
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0.0213623046875,
0.059814453125,
0.03076171875,
-0.028076171875,
0.0437011718... | 40,334 | 40334 | |
Need help to find left/right limit of a/0
September 20th 2010, 04:34 PM #1
Need help to find left/right limit of a/0
So I have a pretty good understanding of limits with the exception of one thing. When solving algebraically, as you know the first thing to do is plug in using direct substitution. Well, when you
... | 4 | [
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0.01416015625,
0.040283203125,
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0.1201171875,
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0.037353515625,
0.0013427734375,
-0.... | 40,335 | 40335 | |
Vladnama
Assume we have data (x[i], y[i]), i = 1, …, n.
The data don’t have to be equally spaced.
We can pass a Lagrange polynomial P(x) of degree n−1 through these data points.
function y = lagrange_interp(x,data)
for i = 1:length(x)
y(i) = P(x(i),data);
end
endfunction
The polynomial P(x) is a l... | 5 | [
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-0.018310546875,
0.0625,
-0.10693359375,
... | 40,336 | 40336 | |
partial vs total derivative
August 26th 2008, 02:42 PM #1
Newbie
Joined
Aug 2008
Posts
1
partial vs total derivative
Hi, I have unfortunately forgotten my calculus.... I have a problem regarding partial vs. total derivatives. I have a function f(x,y) = ax - by (this is not the actual function, but for th... | 4 | [
0.030517578125,
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... | 40,337 | 40337 | |
Taylor's theorem and the symmetric group
up vote 27 down vote favorite
23
Anytime I see an $n!$ in some formula, my instinct is to look for the symmetric group on $n$ letters coming in somewhere. I have never done this seriously with the $n!$ in Taylor's theorem.
Question: Is there some way to see the $n!$ in Taylor'... | 4 | [
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0.04638... | 40,338 | 40338 | |
How to factor this rational function and characteristics? (x^3+x^2-6x)/(x^2+2x-8)
May 9th 2010, 12:55 PM #1
Newbie
Joined
May 2010
Posts
2
How to factor this rational function and characteristics? (x^3+x^2-6x)/(x^2+2x-8)
How to factor this rational function and characteristics?
(x^3+x^2-6x)/(x^2+2x-8... | 4 | [
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0.0791015625,
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0.05322265625,
0.01220703125,
0.0167236328125,
0.0238037109375,
0.0218505859375,
-0... | 40,339 | 40339 | |
Ensemble forecasting of spring runoff volumes and hydrograph
International conference on innovation advances and implementation of flood forecasting technology
LONG-TERM ENSEMBLE FORECASTING SPRING RUNOFF
VOLUME AND HYDROGRAPH PEAK
L. S. Kuchment (1) and A. N. Gelfan (1)
(1)... | 4 | [
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-0.007598876953125,
-0.1279296875,
-0.030... | 40,340 | 40340 | |
Trigonometric identity proof
July 13th 2012, 01:57 PM #1
Newbie
Joined
Jul 2012
From
USA
Posts
8
Trigonometric identity proof
Hi all, I am stuck on this problem. Help would be appreciated.
Here's the identity I need to prove (will only take a sec to read):
View image: Untitled
Here's m... | 4 | [
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0.0286865234375,
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0.00616455078125,
0.060302734375,
0.01611328125,
-0... | 40,341 | 40341 | |
Difficult integration
May 15th 2011, 10:42 AM
jackie
Difficult integration
I was helping my friend with her integration problems, and both she and I got stuck on this problem. Anyone can gives me a hand. I'd really appreciate it. We were trying to integrate $\frac{\sqrt
(x^2+1)}{x^2}$. We tried to do the fol... | 5 | [
-0.0169677734375,
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0.09912109375,
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0.011474609375,
0.047119140625,... | 40,342 | 40342 | |
A topological puzzle
March 7th 2013, 05:34 AM #1
MHF Contributor
Joined
Apr 2005
Posts
15,386
Thanks
1323
A topological puzzle
Find two sets, P and Q, such that:
1) Both P and Q are contained within the square in $R^2$ with vertices (1, 1), (1, -1), (-1, -1) and (-1, 1). (In other words all (x, ... | 4 | [
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0.08740234375,
-0.037353515625,
-0.046875,
0.002044677734375,
-0.1689453125... | 40,343 | 40343 | |
Functions.
November 19th 2008, 09:44 AM #1
Functions.
Let $g: \Re \rightarrow \Re$ be defined by $g(x)=\frac{x}{1+x^2}$. Find a necessary and sufficient condition on $x_1$ and $x_2$ for $g(x_1)=g(x_2)$. What is the largest interval I you can find on
which g is injective? Find $g(I)$ (ie. find the set {g(x): x... | 5 | [
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-0.0703125,
-0.060791015625,
0.052978515625,
0.07958984375,
... | 40,344 | 40344 | |
What is the characteristic property of surjective submersions?
up vote 9 down vote favorite
1
In Lee's 'Introduction to smooth manifolds' he states that given smooth manifolds X,Y and a surjective submersion f:X→Y, then f is a smoothly final map, that is for any further smooth manifold Z, and
any map g:Y→Z, we have g ... | 4 | [
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0.0206298828125,
0.01757812... | 40,345 | 40345 | |
optimization problem(minimum total area, given the volume)
November 28th 2006, 06:38 AM #1
Newbie
Joined
Nov 2006
From
Canada
Posts
15
A closed Cylinder container needs to have a volume of 128pie dm3. Find the dimensions if the total area must be a minimum.
The surface area is,
$2\pi r^2+2\pi... | 5 | [
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0.044677734375,
-0.0224609375,
-0.033203125,
0.00848388671875,
-0.00... | 40,346 | 40346 | |
U substitution
June 8th 2010, 10:32 AM
mike21
U substitution
Still confused with u substitution. Can someone show me how they would solve this by U substitution?
the integral from .5 to 1 of ln(2x+3) over 2x+3 dx.
u= ln(2x+3)
du=2/2x+3 dx
Where do i go from here? I was just puting the u on top... | 5 | [
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-0.007049560546875,
-0.0206298828125,
-0.091796875,
0.02258... | 40,347 | 40347 | |
Prove similar triangles in parallelogram
November 25th 2012, 10:50 AM #1
Prove similar triangles in parallelogram
Given a parallelogram ABCD and 2 segments FH and EG intersecting the diagonal AC at point P and terminating on 2 opposite parallelogram sides respectively, plus segments HG and EF.
Pprove that tr... | 4 | [
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0.0013275146484375,
0.06640625,
-0.046875,
-0.0194091796875,
-0.002... | 40,348 | 40348 | |
Constant curvature manifolds
up vote 5 down vote favorite
4
In two different books I found these two related statements.
• The book by Jost defines a ``locally symmetric space" as one for which the curvature tensor is constant and which is geodesically complete.
• Andreas' book attributes to Cartan a theorem that... | 4 | [
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0.017333984375,
-0.028... | 40,349 | 40349 | |
Determinant of Transpose (DetA=DetAT)
February 17th 2014, 09:39 AM #1
Banned
Joined
Aug 2010
Posts
961
Thanks
98
Determinant of Transpose (DetA=DetAT)
Convention: No sum over repeated indices unless otherwise stated.
Definition: DetA=e(ijk)a1ia2ja3k, sum, e(ijk) is Levi-Civita symbol.
A comm... | 4 | [
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-0.061767578125,
0.044189453125,
-0.040283203125,
0.0... | 40,350 | 40350 | |
Graph theory proof
September 3rd 2013, 11:21 AM #1
Member
Joined
Oct 2009
From
United States
Posts
169
Graph theory proof
Use ordinary induction on k or on the number of edges (one by one) to prove that a connected graph with 2k odd vertices composes into k trails if k > 0. Does this remain true with... | 4 | [
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0.064453125,
-0.0498046875,
0.004394... | 40,351 | 40351 | |
Bounds on the eigenvalues of a random binary matrix
up vote 0 down vote favorite
Consider $A$, a random binary matrix of zeros and ones in $\mathbb{R}^{{M\times N}}$, and $M>N$. We assume that $P(a_{i,j}=0)=P(a_{i,j}=1)=0.5$ (although I appreciate any advice on the case of
non-even probabilities). Are there any result... | 5 | [
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0.0213623046875,
0.041748046875,
0.076171875,
-0.0751953125,
... | 40,352 | 40352 | |
Partial order relation
April 16th 2006, 05:45 AM
OReilly
Partial order relation
I need to show that relation R is partial order relation.
$R = \{ (a,a),(b,b),(c,c),(a,b),(a,c),(b,c)\}$
I see that it is reflexive and transitive, but I don't see that is antisymmetric.
In the book stands that it is an... | 4 | [
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0.0107421875,
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0.0439453125,
0.025390625,
-0.029052734375... | 40,353 | 40353 | |
Hyperbolic Function Facts
Hyperbolic Function Facts Help (page 2)
By
Stan Gibilisco
— McGraw-Hill Professional
Updated on Aug 30, 2011
Hyperbolic Tangent Of Double Value
The hyperbolic tangent of twice a given variable can be found according to the following formula for all real numbers x :
tanh 2 x = (2 tanh x... | 5 | [
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0.01556396484375,
0.02783203125,
-0.0439453125,
0.0103759765625,
-0.125,
... | 40,354 | 40354 | |
A Ladder Puzzle
Date: 10/20/2000 at 14:40:10
From: Ralf Dueck
Subject: Geometry
A cube is placed flat against a wall. A ladder of length 10m is
leaning against the wall, just touching an edge of the cube. At what
height does the end of the ladder touch the wall?
I tried with Pythagoras, but I didn't find the answer... | 4 | [
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0.032470703125,
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0.0186767578125,
0.003936767578125,
-0.0703125,
0.1337890625,
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-0.052734375,
0.05615234375,
-0.039794921875,
0.0830078125,
-0.025634765625,
0.05566... | 40,355 | 40355 | |
Poisson summation formula
November 10th 2008, 06:49 PM
namelessguy
Poisson summation formula
I just have no idea how to apply Poisson summation formula. Can someone give some help?
a) Let $\tau$ be fixed with $Im(\tau)>0$. Apply the Poisson summation formula to $f(z)=(\tau +z)^{-k}$ where $k \geq 2$ to obtai... | 5 | [
-0.0322265625,
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0.08251953125,
-0... | 40,356 | 40356 | |
Projectile
For motion in 2 dimensions we can calculate components of velocity and acceleration by differentiating x and y as functions of time. We can then use Pythagorean Theory to get the total value
PROJECTILE MOTION
SoftBall Projectile Some Observations
So far we have been dealing with horizontal... | 4 | [
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0.0134277... | 40,357 | 40357 | |
Is a reduced, torsion-free module of finite rank over an Henselian ring free?
up vote 1 down vote favorite
Let $R$ be an Henselian discrete valuation ring with field of fractions $K$. Let $M$ be a torsion-free $R$-module of finite rank (i.e. $dim_K(M\otimes_RK)<+\infty$). Let $D$ be the maximal divisible
$R$-submodule... | 5 | [
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0.026... | 40,358 | 40358 | |
Multiple choice question.
October 15th 2011, 08:11 AM
rbmeee
Multiple choice question.
A multiple choice question has 4 options. Choosing the correct option gives a student 3 marks.Choosing the wrong answer incurs negative marks so if a student chooses an option randomly,his
expected score is zero.Suppose th... | 4 | [
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... | 40,359 | 40359 | |
Math Forum Discussions
Re: Using Solve/FSolve for Multiple Trig Equations
Posted: May 2, 2013 3:22 AM
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <klrqr9$k14$1@newscl01ah.mathworks.com>...
> Alan_Weiss <aweiss@mathworks.com> wrote in message
> > [ snip]
> >
> > So there is no solution to the equation... | 5 | [
-0.1279296875,
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0.0439453125,
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-0.03564453125,
-0.... | 40,360 | 40360 | |
Monday Math: LogarithmsMonday Math: Logarithms
We begin with a joke. What’s a logarithm? It’s a birth control method for lumberjacks. Hahahahaha! Believe it or not, one of my high school math teachers taught me that.
Actually, logarithms are a computational tool for turning products into sums. They are defined as fo... | 4 | [
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0.08935546875... | 40,361 | 40361 | |
extremal problem (calculus of variations?)
up vote 2 down vote favorite
I have a (given) real-valued function defined over an area, $b(x)$, with $x\in \Omega \subset \mathbb{R}^2$. I would like to find a smooth real-valued function $a(x)$ that maximises $J = \int_{x \in
\Omega} a^3(x) + a(x)b(x)~dx$ with the constrain... | 5 | [
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0.125,
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0.045166015625,
... | 40,362 | 40362 | |
Centralizing four red vectors in six green sectors
up vote 4 down vote favorite
1
Four red vectors are given, one per quadrant, $[0,90^\circ)$, $[90^\circ,180^\circ)$, etc. A rigid star of six green vectors separated by $60^\circ$ can be positioned at $(\theta, \theta+60^\circ, \
theta+120^\circ, \theta+180^\circ, \th... | 5 | [
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0.04736328125,
-0.0101928710... | 40,363 | 40363 | |
e powers (cancel down)
Hello, How do you cancel this equation down further? Thanks $((exp(x)exp(-x))/4) + ((exp(x)exp(-x))/4) + ((exp(-2x))/4) + ((exp(2x))/4)$
$\dfrac{e^x e^{-x}}{4} + \dfrac{e^x e^{-x}}{4} + \dfrac{e^{-2x}}{4} + \dfrac{e^{2x}}{4}$ Is this what you mean? Remember that: $a^b a^c = a^{b+c}$
Hello, Matt... | 4 | [
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Joint Probability mass problem
December 6th 2010, 02:56 PM
jackroberts4
Joint Probability mass problem
Hello All,
This is my first time visitnig math helop forum and I was wondering if anyone could help me with a HW problem. I have posted it below. Thanks a lot:
1. The problem statement, all variables... | 4 | [
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0.0712890625,
0.000579833984375,
-0.04956054687... | 40,365 | 40365 | |
Leslie matrix
November 21st 2012, 03:17 PM
tinabaker
Leslie matrix
A certain colony of bats has a life span of less than 3 years. Suppose that the females are divided into three age groups: those under age 1, those of age 1, and those of
age 2. Suppose further that the proportion of newborn females that surv... | 4 | [
0.00653076171875,
0.0732421875,
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0.0023193359375,
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0.059814453125,
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0.1572265625,
0.1259765625,
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0.032470703125,
0.046630859375,
0.0150146484375,
0.0712890625,
-0.038818359375,
-0.034423828... | 40,366 | 40366 | |
Pyramid Math Problem.
October 29th 2008, 04:57 PM
Crysolice
Pyramid Math Problem.
Kay so we had this problem today that we're sposed to do tonight. Goes something like this:
There's a pyramid 150m tall, with a square base. Each side of the base is 230m. Find the area of the horizontal cross section 50m abov... | 4 | [
0.00897216796875,
0.10888671875,
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Reference for decomposition in invariants and derived subgroup in a semidirect product of abelian groups
up vote 3 down vote favorite
1
Let $A$ and $B$ be finite abelian groups with coprime order, and let $G=A\rtimes{}B$ be a semidirect product, via any action. Let $C\subseteq{}A$ be the subgroup of the elements of $A... | 4 | [
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0.06640625,
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0.06... | 40,368 | 40368 | |
Sketching level curves
December 9th 2011, 04:37 AM
SyNtHeSiS
Sketching level curves
Sketch the level curves for the function $z = ln(x^2 + y^2)$.
Attempt:
$k = ln(x^2 + y^2)$
$z = ln(k^2 + y^2)$
$z = ln(x^2 + k^2)$
Now I am not sure how I would draw each of these graphs due to the $ln(x^... | 4 | [
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0.048828125,
-0.1513671875,
0.000486... | 40,369 | 40369 | |
I'm confused between probability density function andcumulative distribution function
September 7th 2012, 11:54 AM
supermario88
I'm confused between probability density function andcumulative distribution function
If you could, please open up the following link
http://www.math.dartmouth.edu/~prob/prob/prob.... | 5 | [
0.00168609619140625,
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-0... | 40,370 | 40370 | |
Black_
Analysis of Algorithms
CS 477/677
Instructor: Monica Nicolescu
Lecture 12
Red-Black Trees
• “Balanced” binary trees guarantee an O(lgn)
running time on the basic dynamic-set
operations
• Red-black tree
– Binary tree with an additional... | 5 | [
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0.03759765625,
-0.0... | 40,371 | 40371 | |
Trouble Finding Tangent Lines
October 17th 2011, 09:00 AM #1
Junior Member
Joined
Sep 2011
Posts
27
Trouble Finding Tangent Lines
The graph of $y = 6(3x^2)^x$ has two horizontal tangent lines. Find the equations for both of them.
Alright, so my approach will be to find the derivative of the function... | 5 | [
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0.0245361328125,
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0.036865234375,
0.10302734375,
-0.177734375,
-0.009... | 40,372 | 40372 | |
Derivs heeelp
December 14th 2008, 08:58 AM #1
Newbie
Joined
May 2008
Posts
1
Derivs heeelp
f(x)=[(x+2)/(x+1)](2x-7)
I keep getting [-2x^2+7x-3] / (x+1)
but that is not one of the answer choices.
Also, (x-2)/sqrt(x^2-1)
Find an equation for the tan line to the graph f at the point P(pi/... | 5 | [
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0.051025390625,
-0.00017547607421875,
-0.052978515625,
-0.0751953125,
-0.0322... | 40,373 | 40373 | |
exotic configuration spaces
Introduction
For a topological space $X$, its (colored) configuration space is the collection of $n$-tuples of distinct points in $X$, or, equivalently, \[\color{lightgray}{ \conf(X,n)=X^n-\bigcup_{i\neq j}\
Delta_{ij}, }\] the $n$-th Cartesian power of $X$ with the union of the diagonals $... | 4 | [
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-0.05712890625,
0.044921875,
0.06884765625,
0.00433349609375,
-0.021728... | 40,374 | 40374 | |
A graph with few edges everywhere
up vote 21 down vote favorite
6
Given a graph $G(V,E)$ whose edges are colored in two colors: red and blue. Suppose the following two conditions hold:
• for any $S\subseteq V$, there are at most $O(|S|)$ red edges in $G[S]$
• for any $S\subseteq V$, if $G[S]$ contains no red edge... | 5 | [
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0.00341796875,
0.0419921875,
0.05810546875,
0.08740234375,
-0.049... | 40,375 | 40375 | |
A Tangent to a Graph
January 4th 2010, 05:48 PM #8
January 4th 2010, 05:47 PM #7
Super Member
January 4th 2010, 05:44 PM #6
January 4th 2010, 05:37 PM #5
January 4th 2010, 04:39 PM #4
January 4th 2010, 04:27 PM #3
Senior Member
January 4th 2010, 04:24 PM #2
January 4th 2010, 04:06 PM #1
$16 x e^{4x^2} = 3$ can... | 5 | [
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0.07470703125,
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-0.0673828125,
-... | 40,376 | 40376 | |
solution of the equation $a^2+pb^2-2c^2-2kcd+(p+k^2)d^2=0$
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
i am wondering if there is a complete solution for the equation $a^2+pb^2-2c^2-2kcd+(p+k^2)d^2=0$ in which $a,b,... | 5 | [
-0.05126953125,
0.00579833984375,
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0.040771484375,
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0.034423828125,
0.0019073486328125,
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-0.0830078125,
0.01336669921875,
-0.004913330078125,
0.042724609375,
-... | 40,377 | 40377 | |
Finding the Angle of Solar Collectors on a Sloped Roof
Date: 08/30/2008 at 03:13:19
From: Neill
Subject: Angle of solar collectors on a sloped roof
After three days of thinking about it, making paper models and drawing
sketches, I am absolutely stumped.
On the roof of my house I have solar collectors and would like ... | 5 | [
-0.061767578125,
0.0927734375,
0.00244140625,
-0.0179443359375,
-0.0233154296875,
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0.035888671875,
0.006744384765625,
0.0216064453125,
-0.0159912109375,
-0.06298828125,
0.00182342529296875,
-0.0069580078125,
-0.0225830078125,
0.002105712890625,
-0.107... | 40,378 | 40378 | |
complete the square
September 29th 2005, 06:02 PM
u317d
help with precal problems plz
Can someone please help me figure out what I did wrong with these problems?
1. complete the square to write the equation of the parabola f(x) = -8x^2 - 24x + 15 in (h,k) form.
I can up with:
-8(x-3/2)^2 -3
( 3... | 4 | [
-0.0576171875,
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-0.029296875,
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0.005035400390625,
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-0.0213623046875,
0.0322265625,
0.0146484375,
0.00726318359375,
0.0439453125,
-0.0086669921875,
... | 40,379 | 40379 | |
Solve a System of Linear Equations
The Mathematics Behind It
The above solves a system of 3 equations and 3 unknowns, for example :
x + 2y + 3z = 9
2x - y + z = 8
3x - z = 3
This would be entered into the matrix above as :
1 2 3 : 9
2 -1 1 : 8
3 0 -1 : 3
And the resul... | 4 | [
-0.09130859375,
0.0537109375,
-0.10498046875,
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0.1064453125,
-0.04638671875,
-0.072265625,
-0.021484375,
-0.09619140625,
0.067... | 40,380 | 40380 | |
monoidal
Haskell does not have full-fledged dependent types. For example, there is no way to create naturals as a subset of integers. One way to sidestep this restriction is creating an abstract datatype.
Define
newtype Natural = N Integer
and add a collection of methods (addition, printing etc.). Clients can interac... | 4 | [
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0.1318359375,
0.01336... | 40,381 | 40381 | |
Let Y = F(x) = X-3/x+4 I Have Already Answered ... | Chegg.com
Domain and a sketch of the graph of f needed.
Let y = f(x) = x-3/x+4
I have already answered most of the questions and they are listed with the questions. I think they should be correct, but if they could be checked for accuracy, please.
I also do still... | 4 | [
-0.0242919921875,
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-0.01025390625,
-0.11328125,
-0.0076... | 40,382 | 40382 | |
Linear Algebra: Determinant question
December 25th 2008, 01:26 AM #1
Linear Algebra: Determinant question
Hello,
Problem:
If A,B,C,D are matrices such that C and D commute and D is invertible, then
$\text{det}\begin{pmatrix} A & B \\ C & D \end{pmatrix} = \text{det}(AD - BC)$
There is a hint t... | 5 | [
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Perimeter of an Inscribed Regular Polygon
Date: 12/10/98 at 09:17:06
From: Aaron Willems
Subject: Polygons and the perimeter of a polygon
I am trying to figure out how to find the perimeter of a polygon, and
one that is inscribed in a circle.
Can you give me the formulas for the perimeter of an inscribed polygon?
A... | 4 | [
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inertia, moment ofin physics, quantitative measure of the rotational inertia of a body—ibody—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the
application of a torque (turning force). The axis may be internal or external and may or may not be fixed. The moment of i... | 4 | [
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0... | 40,385 | 40385 | |
If the reciprocal of x+1 is...
Hello, ceasar_19134! If the reciprocal of x + 1 is x - 1, determine x . . . . . . . . . . . . . . .1 The equation is: . ------- .= . x - 1 . . . . . . . . . . . . . x + 1 Assuming x ≠ -1, multiply
both sides by (x + 1): . 1 .= .(x + 1)(x - 1) - - . . . . . . . . . . . . . . . . . . . . . ... | 4 | [
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Lecture _16
Lecture 16 FIN 625: Class Notes
THE BASICS OF CAPITAL BUDGETING
What is the Capital Investment Decision?
Project Evaluation Models
Focus on: Payback Period
... | 5 | [
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Integration of e with Jacobian
February 19th 2010, 04:22 AM #1
Newbie
Joined
Jan 2010
Posts
9
Integration of e with Jacobian
Hi, could someone please explain how I integrate this?
$\int \int e^(-g(3x-4y)^4)dxdy$
where g is a positive constant
I have a Jacobian of -3, from
x = 2u + v; y... | 5 | [
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0.01... | 40,388 | 40388 | |
Trouble with the second root
September 9th 2012, 10:45 PM #1
Member
Joined
Jun 2012
From
Georgia
Posts
179
Thanks
22
Trouble with the second root
Original equation: xy'' + y' + 0. I have found that the roots are both 0, and one of the solutions is:
$y_1=\sum_{m=0}^\infty \frac{(-1)^m a_0}{(m... | 4 | [
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When the second derivative test fails
May 5th 2012, 03:33 PM #1
Newbie
Joined
May 2012
From
california
Posts
7
When the second derivative test fails
Hi,
My teacher has asked us to find the local extrema using the second derivative test. However I find one of my critical values fails the second de... | 4 | [
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Coloring The Edges of an Icosahedron
It's possible to color the edges of an icosahedron in five different
colors such that the colors of the edges meeting at each vertex are
all different. In fact, this can be done in several distinct ways.
The exact number of distinct ways depends on how we define "distinct-
ness". ... | 4 | [
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... | 40,391 | 40391 | |
Homework Help
Posted by Antonio on Wednesday, August 1, 2012 at 8:18am.
find the flux of F=<0,y,z> across the parabolic sheet given by x=2y^2+2z^2+3, with x <= 5
• Calculus - MathMate, Wednesday, August 1, 2012 at 9:29am
Flux = I = ∫∫F.n dS
for S over the surface, g(x,y,z), where
g(x,y,z) is the part o... | 5 | [
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Circle in Triangle
October 27th 2009, 11:08 AM
Aquafina
Circle in Triangle
Hi I have attached the question as a word file. I have worked through it, and need help with the last bit.
I do not understand how to show the relationship between A and B in ii)
he first time I did the question, I tried to use ... | 4 | [
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Solving cubic equations?
September 25th 2012, 02:33 PM #1
Newbie
Joined
Sep 2012
From
canada
Posts
5
Solving cubic equations?
A function that represents the volume of a cardboard box is V(x) = -0.65x^3 + 4x^2 + 3x, where x is the width of the box. Determine the width that will maximize the volume. Wh... | 5 | [
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Using Properties of Parabolas to Graph a Parabola
Posted on January 5, 2010 by Mr. Pi
Recent Comments
quadratic equation c… on Modeling Data With Quadratic…
Lemuel on Quadratic Functions and Their…
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Suemac on Proving Lines Parallel with Tr…
Mr. Pi on Subsets of... | 4 | [
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first order differential equation
January 26th 2007, 06:58 AM
thedoge
first order differential equation
Solve for dy/dx+y/x=1/x
I'd like to see the correct way to solve it. I did it a ridiculous way and ended up with the answer, but I don't want to spend so much time next time.
General formula is y=e^-... | 5 | [
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pythagoras question
October 23rd 2009, 11:56 PM #1
Newbie
Joined
Oct 2009
Posts
4
pythagoras question
My first post and hope it is not a stupid one and related to this thread:
Can there be 4 whole numbers a, b, c, d all greater than zero such that:
a^2 + b^2 = c^2 and b^2 + c^2 = d^2?
If t... | 5 | [
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Solving inequality
December 14th 2009, 12:09 PM #1
Member
Joined
Dec 2008
Posts
152
Solving inequality
See this example:
$\frac{x - 1}{x + 1} \geq \frac{2x}{x - 1}$
We multiply both sides by $(x + 1) (x - 1)$
and get:
$(x - 1)^2 \geq 2x(x +1)$
Criteria 1:
x < -1
$(x - 1)... | 4 | [
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Elemetary question: Group Theory
August 12th 2009, 10:40 AM #1
Super Member
Joined
Apr 2009
Posts
677
Elemetary question: Group Theory
If G is a group, and if If N1, N2, N3..... etc are Normal Sub-Groups of G.
Q1. How do I prove that the largest of the above will contain all the rest?
Thanks,
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