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Outer measure and measurable sets. October 2nd 2009, 08:31 PM #1 Super Member Joined Mar 2006 Posts 705 Thanks 2 Outer measure and measurable sets. If $\mu$ is an outer measure on X and $\{ A_n \} ^ \infty _{n=1}$ is a sequence of disjointed $\mu$ measurable sets, prove that $\mu ( E \cap ( \bigcup ^...
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[SOLVED] Series May 11th 2010, 02:24 PM #1 MHF Contributor Joined Mar 2010 From Florida Posts 3,093 Thanks 5 [SOLVED] Series Let $x_n$ be the sequence with $x_1=2$ and $x_n=\sqrt{5(x_{n-1})+6}$ for every integer $n\geq 2$. How can this be written in summation notation? $x_1=2$ $x_2=\sqrt...
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A general semi-parametric approach to the analysis of genetic association studies in population-based designs Abstract Background For genetic association studies in designs of unrelated individuals, current statistical methodology typically models the phenotype of interest as a function of the genotype and assumes a ...
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Ideals in Factors up vote 9 down vote favorite 2 One can easily prove that factors have no nontrivial ultraweakly closed 2-sided ideals as these are equivalent to nontrivial central projections. One can also show type $I_n$, type $II_1$, and type $III$ factors are algebraically simple (any 2-sided ideal must contain a...
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True/False : 2 Questions June 4th 2010, 12:58 PM #1 True/False : 2 Questions 1- The following function is one-to-one f(x)= -x if x belongs to [-1,0] f(x)=3x+2 if x belongs to [0,1] 2- The following parametric curve represents a line segment from (0,3) to (2,0) : $x(t)=2sin^2(t)$ and $y(t)=3cos^...
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Eigenvector December 8th 2010, 12:23 PM Revy Eigenvector standardization I have matrix $A=\begin{pmatrix}0&1&0\\2&-2&-1\\-3&0&0\end{pmatrix}$ and I get that $det(A-LE)=-L^3+2L^2+2L+3$ so $L^3-2L^2-2L-3=0$ //after this our lecturer takes random numbers and checks if they can be eigenvalues. Fo...
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[plt-scheme] Graphs From: Guillaume Marceau (gmarceau at cs.brown.edu) Date: Tue Feb 8 13:27:33 EST 2005 On Tue, 2005-02-08 at 16:26 +0000, Paulo Jorge de Oliveira Cantante de Matos wrote: > For list-related administrative tasks: > http://list.cs.brown.edu/mailman/listinfo/plt-scheme > > Hi all, > > Is there an...
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Inquiry Into Inquiry Peirce’s 1870 “Logic Of Relatives” • Comment 12.1 To get a better sense of why the above formulas mean what they do, and to prepare the ground for understanding more complex relational expressions, it will help to assemble the following materials and definitions: $X$ is a set singled out in a par...
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Unirational implies rationally connected up vote 2 down vote favorite It is evidently a well-known fact that a unirational variety $X$ over an algebraic closed field (i.e. there is a dominant rational map from $\mathbb P^n$ to $X$) is rationally connected (by which I mean that any two points can be joined by a chain o...
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LaGrange's Theorem Date: 03/12/2001 at 17:45:53 From: Joan Subject: Number theory Please explain LaGrange's Theorem on the number of roots of a polynomial. Thank you. Date: 03/13/2001 at 10:35:36 From: Doctor Rob Subject: Re: Number theory Thanks for writing to Ask Dr. Math, Joan. This theorem states that a pol...
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A Quartic Diophantine Equation: 10657 + 11579x^2 + x^4 = y^2 Date: 12/29/2008 at 15:16:31 From: colin Subject: The Diophantine equation 10657 + 11579x^2 + x^4 = y^2 How can you find at least one solution to this Diophantine equation? 10657 + 11579x^2 + x^4 = y^2 Why is it solvable? or is it not? What is the gen...
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Complex Analysis Confusion! December 4th 2007, 05:53 AM #1 Newbie Joined Nov 2007 Posts 23 Hi, I'm doing revision for an exam in complex analysis at the mo. I've been going through examples and I've found a couple that I've never seen before and have no idea how to do-any help would be much appre...
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An informal version of the Furstenberg correspondence principle One of the basic objects of study in combinatorics are finite strings ${(a_n)_{n=0}^N}$ or infinite strings ${(a_n)_{n=0}^\infty}$ of symbols ${a_n}$ from some given alphabet ${{\mathcal A}}$, which could be either finite or infinite (but which we shall us...
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Norman window and greatest possible area of a rectangle February 8th 2009, 12:43 PM #1 Junior Member Joined Feb 2009 Posts 41 Hi everybody I'm a precalculus student, and I'd like some help to understand these two problems? 1 A rectangle is inscribed with its base on the x-axis and its upper corners o...
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The Importance of the First and Third Quartiles There are several ways to measure the center of a set of data. The mean, median, mode and midrange all have their advantages and limitations in expressing the middle of the data. Of all of these ways to find the average, the median is the most resistant to outliers. It ma...
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How do I iso late x in the following eqation: November 26th 2010, 09:31 PM #1 Newbie Joined Nov 2010 Posts 4 How do I iso late x in the following eqation: Lr = Hx -Lx -r²x -rx² In other words how do I define x in terms of the other units: x = Thanks. $\displaystyle L\,r = H\,x - L\,x - r^2...
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Solving Quadratic Equations by Factoring - Concept Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out Solving Quadratic Equations by Factoring - Concept 47,174 views Solving rational equations is substantially easier with like denominators. When solving rationa...
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How Much Material to Purchase? Date: 11/01/97 at 16:58:05 From: kim peterson Subject: Ramp Sanchez warehouse wants to install a 3-foot wide ramp from the level floor to the top of the 4-foot high platform. A regulation states that for every 2 feet that such a ramp rises vertically, the bottom of the ramp must be pla...
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Question - tangents and their equation September 30th 2007, 12:25 AM #1 Junior Member Joined May 2007 Posts 35 Question - tangents and their equation Hello everyone I am studying tangents and come across this kind of problem where I am going to find the equation for one or more tangent with a specif...
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solve this Differential equation by indicial equation Hint: $z=\ln(x)$ Use the chain rule $\frac{dy}{dx}=\frac{dy}{dz}\frac{dz}{dx}=\frac{1}{ x}\frac{dy}{dz}$ Now we need the 2nd derivative using the product and chain rule $\frac{d^2y}{dx^2}=-\frac{1}{x ^2}\frac{dy}{dz}+\frac{1}{x}\left( \frac{d^2y}{dz^2} \cdot \frac{1...
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[Numpy-discussion] Here's what I've done to numpy.fft Jochen Schröder cycomanic@gmail.... Mon Jul 12 21:08:56 CDT 2010 On 13/07/10 08:47, David Goldsmith wrote: > In light of my various questions and the responses thereto, here's what > I've done (but not yet committed) to numpy.fft. > > There are many ways to define...
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Tensor product of acyclic complexes of free abelian groups up vote 1 down vote favorite 1 I am trying to find a relatively elementary proof of the following result: If $(K,d^K)$ and $(L,d^L)$ are acyclic chain complexes of free abelian groups, then their tensor product $(K \otimes L,d^{K \otimes L})$ is acyclic. I am ...
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Almost Complex Structure approach to Deformation of Compact Complex Manifolds up vote 14 down vote favorite 5 I don't know much about the deformation of compact complex manifolds, I've only read chapter 6 of Huybrechts' book Complex Geometry: An Introduction. There are two parts to this chapter. The second goes throug...
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Exponential Taylor Series April 19th 2010, 12:52 PM #1 Member Joined Aug 2008 Posts 88 Exponential Taylor Series Obtain the Taylor series $e^z=e \sum_{n=0}^{\infty}\frac{(z-1)^n}{n!} (\left |z-1 \right |< \infty)$ for the function $f(z)=e^z$ by using $f^{(n)}(1) (n=0,1,2,...)$. So it would seem to m...
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Simplify then find derivative June 9th 2009, 01:52 AM #1 Simplify then find derivative Hi All, Can you help me with this please. For this function below simplify f(x + h) – f(x) / h then take lim to find the derivative. h → 0 f(x) = x²+ 3x + 2 = To me, this is a calculus question, ...
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Etale cohomology analogue for the semistable reduction theorem up vote 4 down vote favorite Let $K$ be a field, $X/K$ a smooth projective variety, $l\neq char(K)$ a prime number and $q\ge 0$. Then we define $\overline{X}:=X_{K_{sep}}$ and denote by $\rho_{X, l}^{(q)}$ the representation of $Gal_K$ on $H^q(\overline{X}...
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Math Logic - Determining Truth Date: 04/13/99 at 19:29:50 From: Ricky De Hamer Subject: Math Logic A number divisible by 2 is divisible by 4. I'm suppose to figure out the hypothesis, the conclusion, and a converse statement, say whether the converse statement is true or false, and if it is false give a counterexamp...
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Induction Trig Proof Prove by induction: For every integer n > 1 [cos(x) + i * sin(x)]^n = cos(nx) + i * sin(nx) Base Step: n = 1 \displaystyle \begin{align*} LHS &= \left(\cos{x} + i\sin{x}\right)^1 \\ &= \cos{x} + i\sin{x} \end{align*} \displaystyle \begin{align*} RHS &= \cos{\left(1 \cdot x \right)} + i\sin {\left(...
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Green's Theorem March 1st 2013, 06:37 AM #1 Senior Member Joined Apr 2009 Posts 306 Green's Theorem For the above expression, I was told that it can be proven using Green's Theorem on the line integral on the RHS, however I can't seem the prove the equality. Note that $G$, $H$, $f$ are functi...
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Game theory: problem of the shooters July 29th 2011, 09:19 PM #1 Member Joined May 2009 Posts 146 Game theory: problem of the shooters n shooters numbered 1~n play a game. Their probability of hitting a target are 0<p1<p2<p3<...<pn<1. Before the game, the referee arranges the n players in some order...
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dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: Libniz Group Title Shuffle a deck of card ...
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[SOLVED] Complex Stiffness Solution October 9th 2009, 10:49 AM jfortiv [SOLVED] Complex Stiffness Solution Hi, I'm trying to solve a differential equation of a 1 degree of freedom mechanical system with a complex stiffness: m*d^2u/dt^2 + k*u = A*e^(i*w*t), where k is complex (k = a + i*b), i = sqrt(-1)...
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Euler's Number Date: 01/28/98 at 16:29:49 From: Jeffery Holcomb Subject: Euler's number During a recent math assignment I came in contact with Euler's number. I also heard it referred to as the natural base. When I asked why it was called this my teacher said that he did not know. Since then I have looked in several...
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Cauchy's Integral theorem March 18th 2010, 05:47 AM Tekken Cauchy's Integral theorem Quick question im trying to calculate the integral around the closed curve C of z(bar) dz where z(bar) is the complex conjugate of z where C is the unit circle. Using the subsitution z = e^it i calculated the...
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Find integers What do they mean by 'for all x' in (a)? a) $x^2-8x=(x-p)^2+q\Leftrightarrow x^2-8x=x^2-2px+p^2+q,\forall x\in\mathbf{R}$. That means all coefficients of both members are equal. Then $\left\{\begin{array}{c}-2p=-8\\p^2+q=0\end{array}\right. \Rightarrow p=4,q=-16$. b) The equation can be written $x^2-8x+1...
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Kodaira-Spencer map in a concrete instance up vote 8 down vote favorite 3 Let $\pi:X_{\epsilon} \rightarrow \Delta$ be a family of (say smooth) projective plane curves parametrized by $\Delta:=\operatorname{Spec}(k[\epsilon])$, and let $X=X_0$ be the closed fiber. Suppose that $X_\epsilon$ is given by a polynomial $f(...
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Length of the crossed belt. September 16th 2011, 10:37 AM Niosama Length of the crossed belt. Hi I am new to the university and yet now I face one problem I cannot solve! Pls help me x.x! Attachment 22288 Thanks :) September 16th 2011, 11:07 AM HallsofIvy Re: Length of the crossed belt! Pls Help! ...
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Determining and Checking Saddle Point for Autonomous System Associated Topics || Dr. Math Home || Search Dr. Math Determining and Checking Saddle Point for Autonomous System ...
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Solving Linear Trig Equations? November 12th 2007, 04:29 PM #1 Junior Member Joined Sep 2007 Posts 55 Solving Linear Trig Equations? Hello again! I need some help on solving linear trig equations! 1. 1 - tan (2x + pi/2) = 0 0 ≤ Θ ≤ 2 pi I was told that there are 4 answers possible for thi...
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Trig Word Problem Help! October 13th 2013, 05:16 PM #1 Newbie Joined Oct 2013 From Cincinnati, OH Posts 2 Trig Word Problem Help! I need help with this word problem: If you stand in shallow water and look at an object below the surface of the water, the object will look farther away from you than...
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Galactic Orbits Here are some examples of how to compute realistic Galactic orbits within NEMO. Again, as shown in the previous example, we first need to select a Galactic potential. To first order the motion in XY and Z are decoupled. We do have a very nice feature in NEMO, called potentials (and the newer 'accelera...
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Lévy's C-curve From Math Images Lévy's C-curve Field: Fractals ...
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Jacobian transformation November 17th 2008, 06:20 AM #1 Newbie Joined Nov 2008 Posts 5 Jacobian transformation Here is a second one I'm not too sure what to do next : Let $X_1$ and $X_2$ be independent, with respective probability density functions of the forms $f_{X_1}(x_1) = x_1 e^{\frac{-x_1^2}{2...
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Can brute force algorithms scale? up vote 7 down vote favorite 4 I have a math problem that I solve by trial and error (I think this is called brute force), and the program works fine when there are a few options, but as I add more variables/data it takes longer and longer to run. My problem is although, the prototyp...
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Foundation Statistics Mod October 27th 2012, 04:39 AM Jon123 Foundation Statistics Mod Hello everyone! I am having trouble getting in contact with my lecturer so I am hoping for assistance here with a few questions and would like support in answering them. The set data given are arrival times e.g. 11.59...
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Ratios of line segments in a triangle March 28th 2009, 01:02 PM #1 Newbie Joined Apr 2008 Posts 11 Ratios of line segments in a triangle I found this problem in one of those foreign Mathematical Olympiad books. The solution is provided, but even then I still can't grasp the steps that lead to it. We...
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Isomorphism beetwenn vector space and sub space November 30th 2008, 09:04 AM Herbststurm Isomorphism beetwenn vector space and sub space Hi, I have to find a vector space V with a real sub space U and a bijective linear map. Here my Ideas and my questions: If the linear map is bijective, than dim ...
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The Golden Ratio The Golden Ratio From Math Images (Difference between revisions) ← Previous diff Next diff → Line 18: Line 18: The golde...
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Dynamics question involving impulse momentum April 20th 2008, 04:40 PM pakman Dynamics question involving impulse momentum The question is: A 5oz baseball is 3ft above the ground when it is struck by a bat. The horizontal distance to the point where the ball strikes the ground is 180ft. Photographic studies...
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differentiation and intergration of sinx/x and d/dt P(t)=P`(t) September 6th 2009, 09:22 PM #1 Newbie Joined Sep 2009 Posts 2 differentiation and intergration of sinx/x and d/dt P(t)=P`(t) (1) problem differentiation [intergration of sint/t], limit from 0 to x^2 let say f(t)=t, F(t)=t^2/2, if f...
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Break even point ( units of the product needs to be sold to achieve a profit ) February 13th 2014, 09:13 PM #1 Member Joined Oct 2009 Posts 202 Break even point ( units of the product needs to be sold to achieve a profit ) A company is selling a product at a price of RM40 per unit. Variable cost per unit...
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Writing Algebraic Equations(Help Me) February 19th 2008, 06:58 AM huemunyeow Writing Algebraic Equations(Help Me) An apple grower finds that an apple tree produces on an average 400 apples per years, if no more than 16 trees are planted in a limit area. For each additional tree planted per unit area, the gro...
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Diffusion Curves From Inkscape Wiki Diffusion Curves are a way of specifying very free form gradients. It works by letting colors diffuse from curves, seeding the colors along both sides of the curves using gradients (along the curves). Additionally a varying amount of blur can be applied along the curves. This makes...
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Differential equations - seperation of variables October 15th 2009, 08:46 PM wyasser Differential equations - seperation of variables Solve the given differential equation by Separation of variables. (1+x^4)dy + x(1+4y^2)dx = 0, y(1)=0 (3x^2 + 9xy + 5y^2)dx – (6x^2 +4xy)dy = 0, y(2) = -6 (3y^2-x^2 /...
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Combinatorial Probability October 11th 2010, 11:18 AM NOX Andrew Combinatorial Probability There are two exercises in my probability and statistics textbook with which I am experiencing difficulty. Exercise 1-28 A high school lottery uses two sets of numbered balls. One set consists of ten white balls numbe...
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determinant of T linear operator March 26th 2011, 07:51 PM #1 Newbie Joined Mar 2010 Posts 4 determinant of T linear operator Let T be a linear operator on a finite-dimensional vector space V, and let β be an ordered basis for V, we define det(T) = det ( [T]β ) i) 1) Prove that det(T – tIv) = det ( ...
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[SOLVED] Time period of simple pendulum(with a catch!)? June 1st 2009, 10:09 PM #1 [SOLVED] Time period of simple pendulum(with a catch!)? Find the time period of a simple pendulum if the mass of the bob is $m$ and mass of the rod is $M$. Answer: Anyone? Last edited by fardeen_gen; June 1st 2009 a...
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Telescoping Series April 13th 2010, 06:11 AM #1 Member Joined Nov 2009 Posts 76 Telescoping Series Can somebody help with this? Evaluate as a telescoping series: The summation from k=1 to infinity of (k-1)/2^(k+1). The answer is 1/2 but I need to see the workings so I can figure out how it was ...
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Possible arrangements November 29th 2006, 02:03 PM #1 Member Joined Nov 2006 From San Francisco Posts 145 Possible arrangements Four congruent triangular gardening plots form a square. Each plot will contain one kind of flower, and the flowers in plots that share an edge will be different. How many d...
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dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: countonme123 Group Title One man starts ou...
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Trigonometric Limit Question January 14th 2009, 10:20 PM #1 Trigonometric Limit Question Please refresh my memory on how I would take the limit as x -> infinity of $[3x + sin(x)] / [4x - cos(2x)]$ Thanks. This isn't a rigorous way to do it, but it makes sense I think. I feel like a proper proof wou...
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Statistics - Median & Mean June 2nd 2008, 03:56 AM Risrocks Statistics - Median & Mean The table gives marks out of 50 by 40 candidates: Class Frequency 1-10 7 11-20 8 21-30 15 31-40 7 41-50 3 (i) In which class deos the median mark lie? (ii) calculate the mean mark. ...
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problem on Trace of the sum of two matrices October 17th 2012, 07:37 AM MAX09 problem on Trace of the sum of two matrices The following question is in the exercise of my text book. A is 4x4 matrix with 1,-1,2 and -2 as its four eigen values. If B = A^4 - 5A^2 + 5I, which of the following is true? a) det...
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Chessboard problem March 29th 2011, 06:32 PM claws61 Chessboard problem Problem: Imagine a King on an 8x8 chessboard. It's located in a1, bottom left corner. And it wants to get to a8, top left corner. It can only move one step at a time, diagonally, vertically and horizontally.(Surprised) H...
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Finding Products of a Range of Numbers Date: 03/28/2002 at 17:55:21 From: M Subject: Formula for finding products of a range of numbers What method or formula is there to solve for the product of a range of numbers? For example, how can I figure out the product of the numbers from 1 to 100? I know the method for fin...
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Math Forum Discussions - Plot:Connect few points and form a line Date: Nov 12, 2013 4:30 PM Author: HsiaoTing Ko Subject: Plot:Connect few points and form a line %Elastic Modulus--YM=YA=Y(MPa) Y=62000; %Transformation Temp(degree C) MF=10; MS=17; AS=31; AF=44; %Transformation Constatns--CM=CA=C(MPa/degree) C=7; %Ma...
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Differential Eqns May 4th 2009, 06:44 PM ny_chow Differential Eqns At time t, t $\ge$ 0, the volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t = 0, the radius of the sphere is 1 and at t = 15, the radius is 2. (Volume of sphere is V = 4/3pir^3) a) Find the rad...
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Line intersecting implicit function January 18th 2010, 09:28 AM hciR Line intersecting implicit function Hi, I have to find the co-ordinates where the line y=-x+1 intersects f(x,y) = x^2 + y^2 -xy - y -1 I can do this with explicit functions by making them equal, but it doesn't work with this. The actu...
5
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Second Order Implicit Partial Derivatives May 31st 2009, 10:55 PM wceagles10 Second Order Implicit Partial Derivatives This problem is doing my head in... If $z$ is defined implicitly as a function of $x$ and $y$ by the equation $xze^y + yz^3 = 1$, find the values of $dz/dx, dz/dy$ and $d^2z/dxdy$...
4
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Logarithm problem (sorry if this in the wrong section!) March 30th 2008, 06:36 AM #1 Newbie Joined Mar 2008 Posts 1 Logarithm problem (sorry if this in the wrong section!) I couldn't seem to find a board on logarithms so apologised if this is in the incorrect section. Apologies for formatting too. I...
4
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word problem I claim 103138 divides that number for all positive integer values of n. This is done by observing that $a-b$ divides $a^n - b^n$ and then rearranging the given number into sums of such differences. For example, $278 = 2141-1863$ and $-278 = 1492 - 1770$ Thus $278|2141^n -1863^n + 1492^n - 1770^n$ Similarl...
5
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Homework Help Posted by steve on Tuesday, May 24, 2011 at 10:43pm. which term in the expansion of (1/(3x^2)-x)^15 is the constant term? A. 10th B. 11th C. 12th D. 13th • math - MathMate, Wednesday, May 25, 2011 at 12:17am The constant term is the term where the power of x in the product (1/(3x²))^r*x^(15-r...
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proof in modern algebra October 28th 2012, 02:31 PM amyw proof in modern algebra Prove that (G, *) is an abelian group if an only if f:G--->G defined by f(x)=x^-1 is a homomorphism. I understand that I need to prove two things. 1) If (G, *) is abelian, then the function is a homomorphism. 2) If the ...
5
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Perimeter of Pascal's Triangle Date: 06/04/2001 at 20:43:23 From: Bobby Mcdonald Subject: Formula for Pascal's triangle Is there a general formula for finding the perimeter of Pascal's triangle using the number of rows? Formula for Perimeter of Pascal's Triangle Number of rows Perimeter sum ---------------------...
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Zonohedra and the Sylvester-Gallai theorem When I was in Melbourne recently, I spent some time browsing through a copy of “Twelve Geometric Essays” by Harold Coxeter in the (small) library at AMSI. One of these essays was entitled “The classification of zonohedra by means of projective diagrams”, and it contained a ver...
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Construction of GL_2(F) counting issues November 12th 2013, 09:40 AM #1 Construction of GL_2(F) counting issues Counting principles (however easy they may be) are not something I'm all that good with. I am trying to find all 2 x 2 matrices with elements in $\mathbb{F}_p = \mathbb{Z}/n \mathbb{Z}$ where p is...
5
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Equivalent metrics on Fréchet spaces and Lipschitz maps up vote 4 down vote favorite Lipschitz maps are defined over metric space as maps $f:(X,d_X) \to (Y,d_Y)$ such that $$ d\left( f(x),f(x^\prime) \right)_Y \le k d(x,x^\prime)_X \ \forall x,x^\prime \in X, $$ where $k$ is a positive constant. We usually say that $f...
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Mechanical Aptitude Tests - Are you faced with a mechanical aptitude test as part of an interview? Do you want to ...
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First Order Ordinary differential Equation December 1st 2009, 06:19 PM Fallen186 First Order Ordinary differential Equation I have the first order Initial Value Problem ODE of $y' = 1 + 4y^2$ , $y = \frac{1}{2}*tan(2x+C)$ , $y(0) = 0$ I calculate that $y' = sec^2(2x+c)$ $<br /> sec^2(2x+ C) = 1 + ...
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Show n^3 + 11n Divisible by 6 Date: 12/11/2002 at 00:41:56 From: Jasmine Subject: Algebra If n is a natural number, show that for all values of n, (n^3+11n) is divisible by 6. Date: 12/11/2002 at 10:33:52 From: Doctor Ian Subject: Re: Algebra Hi Jasmine, I would probably try to use induction. That is, I know that...
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Problem - Onto mapping with power set. November 11th 2009, 07:29 AM #1 Super Member Joined Apr 2009 Posts 677 Problem - Onto mapping with power set. Let S be a set. S* is the power set of S. Prove there can't be any onto mapping from S->S* My approach: 1. Let f be a onto mapping from S->S* 2...
5
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0! A silly poem I wrote while in college: Man has wondered Since time immemorial Why 1 is the value Of 0!. Hello 0! is a convention without demonstration. Same $2^0 = 1$ $<br />$ We can show this is the case using calculus (if this is a bit advanced for you, please bear with me (Nod) ) The Gamma Function is defined b...
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Determinants and linear transformations A linear transformation $\vc{T}: \R^n \to \R^m$ (confused?) is a mapping from $n$-dimensional space to $m$-dimensional space. Such a linear transformation can be associated with an $m \times n$ matrix. If we restrict ourselves to mappings within the same space, such as $\vc{T}: ...
5
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Fat Tails COMPUTING SCIENCE Fat Tails Sometimes the average is anything but average By No Means How different are the statistics of the factoidal process! When I first began playing with the n? function, I was curious about its average value, and so I did a quick computation with a small sample—100 repetitions of 1...
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Rigorous Limits September 30th 2010, 02:41 PM #1 Rigorous Limits We've begun limits, but the more rigorous approach I have not fully understood yet, so I'm hoping someone could help me please Question $lim_{n\rightarrow{\infty}} \frac{n^2+1}{n^2+2}$ Answer Determine some real number $L$ such tha...
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When the rate of unemployment will fall to 5%? Likely never Update: A working paper is available with more technical details. The intuition behind Okun’s law is very simple. Everybody can feel that the rate unemployment is likely to rise when real economic growth is very low or negative. An economy needs fewer employee...
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Is the given expression, monotonically increasing or decreasing with increasing x? up vote -2 down vote favorite Is the given expression, monotonically increasing or decreasing with increasing x? $\frac{1}{x \log(x)} \sum_{i=1}^{\infty} \frac{\mu(i)}{i} x^{1/i}$ EDIT: This is the derivative of the prime counting fu...
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Math Help show that 37^n+2 + 16^n+1 + 23^n is divisible by 7 whenever n is natural thank you I assume you're having trouble with step 3. Then note: $37^{k+3} + 16^{k+2} + 23^{k+1} = 37 \cdot 37^{k+2} + 16 \cdot 16^{k+1} + 23 \cdot 23^{k}$ $= 37 \left( 37^{k+2} + 16^{k+1} + 23^{k} \right) - 21 \cdot 16^{k+1} - 14 \cdo...
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Planar Graphs and Skew Binary Spaces up vote 2 down vote favorite Let $G$ be a planar triangulation on $3m$ edges and $m+2$ vertices. Let $A$ be the binary matrix obtained from the incidence matrix of $G$ by deleting a row (equivalently we require the rows of $A$ to form a basis of the cocycle space of $G$ over $GF(2)...
4
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Problem Solving: Using Systems November 2nd 2008, 12:00 PM #1 Newbie Joined Oct 2008 Posts 7 1. Kerry asked a bank teller to cash a $390 check using $20 bills and $50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive? 2. Tickets for the homecoming dance...
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Sigma Proof by Induction August 31st 2012, 05:20 PM renolovexoxo Sigma Proof by Induction Prove 1/1(2)+2/2(3)+...+1/n(n+1)=n/n+1 I've been using induction to prove this. For the base case I got: 1/1(2)=1/2 Then I go on and get a little more stuck: Assume 1/1(2)+2/2(3)+...+1/n(n+1)=n/n+1 for a...
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Locus of circumcentre? April 30th 2009, 07:32 AM fardeen_gen Locus of circumcentre? A triangle has two of its sides along the axes. Its 3rd side touches the circle $x^2 + y^2 - 2ax - 2ay + a^2 = 0$. Find the equation of locus of the circumcentre of the triangle. April 30th 2009, 11:37 PM earboth Quote: ...
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Radicals #1 imgur: the simple image sharer My attempt: imgur: the simple image sharer I'm not sure if I was right about dividing .3 in the beginning from the radical. You didn't need to divide by 0.3. You also divided 6.3 by 0.3 as well as dividing $\sqrt{48}$ by $\sqrt{0.3}$ so in total you divided by $0.3\sqrt{0.3}$...
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Basic Electrodynamics (V): Electron Beam Deflection Electron beam deflection relates to the behavior of a beam of electrons when fired from an electron "gun" and through a defined field. The diagram accompanying shows the path of a beam through an electric field, E, set up inside a cathode ray tube. Note that althou...
4
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Cohen-Lenstra Heuristics reference up vote 3 down vote favorite 3 I am looking for good references (preferably, books) on Cohen-Lenstra Heuristics (on Real Quadratic fields) which explain in detail the reasons behind its fundamental assumption (higher the cardinality of the automorphism group less likely it is cyclic)...
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Tips on How to Manipulate the Ideal Gas Law Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out Tips on How to Manipulate the Ideal Gas Law 2,484 views So we are working with Gas Laws. And we're going to be come across the Ideal Gas Law. We want to manipulate th...
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Partial derivatives of arccos June 18th 2013, 12:46 PM Vulpes Partial derivatives of arccos Hi All, To be able to construct a Jacobian, I am asked to find the two partial derivatives of the following inverse trigonometric function: $w_{1}(u,v) = \frac{1}{2\pi} \arccos (\frac{u}{\sqrt{u^{2} + v^{2}}})$ ...
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Trig Problem June 29th 2010, 11:18 AM #1 Junior Member Joined Feb 2010 From New Jersey, USA Posts 36 Trig Problem Hi all. I'm trying to show that... 1 - ( tan (x/2) )^2 = sec x + tan x Any help will be appreciated. Thanks. expand the difference of squares given: $1 - ( \...
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Find All Three Angles September 10th 2008, 01:11 PM magentarita Find All Three Angles Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his gardenwill be 55 square yards, find, to the nearest tenth of a degree, the three an...
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[ 0.0252685546875, 0.103515625, -0.0277099609375, -0.03662109375, -0.01611328125, -0.033935546875, -0.05078125, 0.033935546875, -0.053955078125, 0.019287109375, -0.01068115234375, -0.06982421875, -0.0096435546875, 0.055908203125, 0.1416015625, 0.056640625, -0.091796875, 0.03833007812...
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prove this Highest Common Factor property Hello, Let d=gcd(m,n) and d'=gcd(m+kn,n) 1st part d divides m. It also divides n. So it divides every linear combination of the two, and in particular m+kn. Therefore, d divides both m+kn and n. We can conclude that d divides d' (because d' is the highest common factor) 2nd par...
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[ -0.006195068359375, -0.004364013671875, -0.025634765625, -0.033935546875, 0.07958984375, -0.06689453125, 0.11328125, 0.0247802734375, -0.07568359375, 0.060791015625, 0.00567626953125, 0.043212890625, 0.03466796875, -0.01519775390625, -0.025634765625, 0.00194549560546875, -0.003402709...
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