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Manipulating Sums October 21st 2010, 11:59 AM #1 Hi there, I am trying to solve the following problem. I have gotten a fair way into it, but the last steps elude me. Here is the problem: Show that $\displaystyle\sum_{r=0}^n ^nC_r 2^r = 3^n$ So, we already know that $\displaystyle\sum_{r=0}^n ^nC_r =...
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Double Integrals - Order of Integration November 24th 2009, 10:05 AM #1 Double Integrals - Order of Integration Find the area of A by evaluating the double integral $\int\int_A \, dxdy$ where the region A is bounded by the curve $y=x^2-x$ and the line $y=2$ Is this correct: $\int\int_A \, dxdy...
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Fourier Coefficients March 30th 2009, 06:21 PM #1 Newbie Joined Feb 2009 Posts 15 Fourier Coefficients Find the Fourier coefficients of the piecewise continuousfunction f(t) = {0 if t <= (less than or equal to) 0 or 1 if t > 0.} I get why Ck is equal to 0. But why is Bk = 2/(k(pi)) when k is ...
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Curiosity about surface are October 4th 2011, 01:03 AM #1 Curiosity about surface are The volume of a sphere is V = 4/3(pi)r^3 If you differentiate with respect to r you get dV/dr = 4(pi)r^2 This is the surface area of the sphere. How come this works so well for the sphere? It doesn't wor...
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Three group Kirman’s agent based model for financial markets | Physics of Risk Three group Kirman’s agent based model for financial markets As we have seen previously application of the original Kirman’s model enables reproduction of single power law spectral density [1]. While actual financial markets and sophisti...
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The Schrödinger equation on a finite graph January 2, 2011 by Qiaochu Yuan One of the most important discoveries in the history of science is the structure of the periodic table. This structure is a consequence of how electrons cluster around atomic nuclei and is essentially quantum-mechanical in nature. Most of it (...
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Math Forum: Teacher2Teacher - Q&A #104 Factoring trinomials T2T || FAQ |...
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Math Forum Discussions Math Forum Ask Dr. Math Discussions Internet Newsletter MathTools Teacher2Teacher Teacher Exchange Workshops Search All of the Math Forum: Views expressed in these public forums are not endorsed by Drexel University or The Math Forum. Topic: Radius algorithm Replies: 1 Last Post: Dec 8, 1996...
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Gordan's Theorem with $Ax=b$ up vote 2 down vote favorite 1 Is there a version of Gordan's Theorem in which $Ax=0$ has been replaced by $Ax=b$? That is, I want a condition (possibly including conditions on $A$) for when $Ax=b$ has a solution $x \neq 0$, for $A \in \mathbb{R}^{m \times n}$ and $b \in \mathbb{R}_+^m \se...
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Prove that R is an equivalence relation. Determine the distinct equivalence classes. November 17th 2013, 03:22 PM MadSoulz Prove that R is an equivalence relation. Determine the distinct equivalence classes. Course: Foundations of Higher Math A relation $R$ is defined on $\mathbb{Z}$ by x R y if $3x-7y$ is ...
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What is the domain of the "average operator"? up vote 4 down vote favorite 1 I can try to define an averaging operator for functions, namely let $$A: D \subset L^\infty([0,\infty]) \to \mathbb{R}$$ by $$Af = \lim_{N\to\infty} \frac{1}{N}\int_0^N f(x)dx$$ whenever the limit converges. My question is: is there any intui...
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Partial derivative November 9th 2009, 05:54 PM #1 Newbie Joined Oct 2008 Posts 4 Partial derivative Find $\frac{dw}{ds}(-2,2)$ and $\frac{dw}{dt}(-2,2)$ if $w= xy -yz -5xz,$ where $x = st, y = e^{st}, z= t^2$ I'm confused since only two coordinates are given but the problem has 3 variables $x,y, z$ ...
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Distance From a Point to a Plane Date: 03/31/98 at 16:57:06 From: Keir Larock Subject: Distance between a point (x0,y0,z0) and the plane ax+by+cz+d Hi, In my calculus class the other day, we went over the proof that the distance from the point (x0,y0,z0) to the plane ax + by + cz = d is |ax0 + by0 + cz0|/((a^...
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Does the function u match the differential equation February 4th 2013, 06:17 AM #1 Junior Member Joined Oct 2010 Posts 29 Does the function u match the differential equation Problem statement: If $u=\frac{1}{r}$ where $r=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}$, for $re0$ prove that $\bigtriangleup u \equiv \frac...
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Is it a field? set of real numbers in the form... January 4th 2010, 11:48 PM #1 Is it a field? set of real numbers in the form... Hi, problem: Let $Q(\sqrt{2})$ be the set of all real numbers of the form $\alpha+\beta\sqrt{2}$, where $\alpha\;and\;\beta$ are rational. (a) Is $Q(\sqrt{2})$ a fiel...
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Distribution of primes in smooth moduli From Polymath1Wiki (Difference between revisions) Teorth Teorth ( ( Talk ...
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Planes and parametric equation October 10th 2012, 06:09 AM #1 Junior Member Joined Sep 2012 From sweden Posts 61 Planes and parametric equation Hello everybody We have four planes: x + y + z = 0 2x - y + z= 1 x + y - 2z = 2 x - 2y + 2z = 1 And we know that they have a li...
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Trace = Sum of eigen values - proof? October 18th 2008, 06:04 PM #1 Newbie Joined Oct 2008 Posts 2 Trace = Sum of eigen values - proof? Hi, I recently learnt that trace (sum of diagonal elements) of a matrix is equal to the sum of its eigen values. I was wondering why this holds true. Could anyone e...
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Derivative of Log Function October 31st 2009, 06:57 PM dark-ryder341 Derivative of Log Function Hey guys, I'm really having some difficulty understanding how to find the derivative of log functions - I keep trying these homework questions and getting most of them wrong and I'm really starting to get ann...
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Area, Volume of a Cone Associated Topics || Dr. Math Home || Search Dr. Math Area, Volume of a Cone Date: 6/4/96 ...
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The Backpropagation Algorithm Next: Issues in ANN Learning Up: Artificial Neural Nets Previous: Multilayer Nets, Sigmoid Units 1. Propagates inputs forward in the usual way, i.e. □ All outputs are computed using sigmoid thresholding of the inner product of the corresponding weight and input vectors. ...
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A question about the construction of Francia flip up vote 3 down vote favorite 3 Here is the construction. Start with $U$ a normal variety of dimension 3 with a unique singular point locally isomorphic to the quotient of $(x, y, z) \to (-x, -y, -z)$. Also assume we have a small contraction which contracts a smooth ra...
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M Lab 4 -- MANOVA on SPSS A Multivariate Analysis of Variance (MANOVA) is often used as a multivariate analog of the ANOVA, but when there are multiple dependent variables. (Note that an ANOVA can handle multiple independent variab...
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Another "mixed partials" question September 27th 2011, 02:47 PM s3a Another "mixed partials" question The question and my work are both attached as PDF files. Basically, in my work I only found the partial derivatives to be different and therefore did not proceed because of this but apparently this is wrong...
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Quick probability question November 5th 2009, 11:59 AM #1 Newbie Joined Nov 2009 Posts 1 Quick probability question Hello everyone, I'm finishing up some of my stat HW right now and I have hit a wall. There are two questions that are on the tip of my tongue and I can't answer them! It's maddening! ...
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Matrix problem, please help! January 14th 2010, 05:19 AM #1 Newbie Joined Aug 2009 Posts 21 I have the following problem: I have 2 3x3 matrices, on called M and the other N^-1 (this one has a few unknown numbers, k). I am asked to find the following: (MN)^-1. Now we have NOT learned how to do th...
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Proof of a Theorem in the paper "Construction of bundles on P^n" by Horrocks up vote 3 down vote favorite 1 I am trying to understand Horrocks's construction of vector bundles. However I have been stuck on the proof the first theorem in the paper. In the paper, a trivial bundle is a direct sum of Hopf bundles $\mathc...
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Characteristic functions May 2nd 2010, 04:27 PM #1 Member Joined Jan 2010 Posts 104 Characteristic functions Given that E(e^(itx)) (the characteristic function of a Cauchy rv)=e^(-abs(t)), use this fact to find the pdf for X bar for all n. I have no idea how to do this, and it was on the test. I got...
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Implicit Differentiation Problem February 23rd 2006, 02:04 PM #1 Newbie Joined Dec 2005 Posts 14 Implicit Differentiation Problem Consider the curve given by X^2+4y^2=7+3xy a) show that dy/dx=3y-2x/8y-3x b) show that there is a point P with x-cooridnate 3 at which the line tangent to the curve at...
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Question regarding a Lemma on axiom of choice January 2nd 2012, 03:59 AM #1 Newbie Joined Jan 2012 Posts 7 Hello all, I am currently reading a book on set theory "Joy of Sets" by Keith Delvin. In page 58 he proves a lemma which is stepping stone for proving that axiom of choice(AC) and 'Every set ca...
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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: kirk.freedman Group Title Simplify (sqrt x...
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The Marlins and their Hitting Streak: What are the Odds?               Before anyone gets too worked up over this 14-game streak by the Marlins of 10 or more hits, let's remember that the last team to do it -- the 1937 St. Louis Browns -- finished with the worst record in the majors that season: 46-108. You're correct ...
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Integration December 11th 2010, 09:40 AM #1 Junior Member Joined Oct 2010 Posts 28 Hi, I am still bad in integration, I do not know which way to choose, integration by part or substination. integration x^2cos(x) So I shoul do like this integration x^2cos(x)=x^2 (-sinx)-integration2x (-sinx...
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||x-y||+||y-z||=||x-z|| iff y= ax + (1-a)z September 22nd 2009, 02:39 AM #1 Newbie Joined Sep 2009 Posts 7 Dear mathematician, I need to show that: ||x-y||+||y-z||=||x-z|| if and only if y= ax + (1-a)z with 0<=a<=1 In other words, if x,y and z are on the same line, that relation b...
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hard time with graph problems June 11th 2007, 05:53 PM #1 Newbie Joined Jun 2007 Posts 24 hard time with graph problems Identify the exponential function of the form f (x) = a(2 x ) + b whose graph is shown in the figure. a. f (x) = 3(2 x ) b. f (x) = 2(2 x ) − 4 d. ...
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counting inverses of finite group June 21st 2011, 09:22 AM #1 Member Joined Oct 2010 From Mumbai, India Posts 203 counting inverses of finite group Hi I am using Charles Pinter's book on abstract algebra . I have to prove that for any finite group G, if we define the set $S=\{x\in G : x...
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Minimum Investment and Number of Assets Portfolio Cardinality Constraints October 19, 2011 By systematicinvestor The Minimum Investment and Number of Assets Portfolio Cardinality Constraints are practical constraints that are not easily incorporated in the standard mean-variance optimization framework. To help us im...
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Newton's Cooling January 15th 2006, 06:11 AM jacs Newton's Cooling Hi, I have tried this many times and just can't seem to figure it out. A body, initially at room temperature 20C, is heated so that its temperature would rise by 5C/min if no cooling took place. Cooling does occur in accordance with Newton's...
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SU(2) spin 1/2 functions April 27th 2006, 06:28 AM #1 SU(2) spin 1/2 functions It's been a while since I posted a Physics question for y'all to ponder so here's another one. One of the deficiencies in learning Physics is that no one seems to want to explicitly write down SU(2) invariant functions for spin 1/...
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A tricky equation of the first order March 7th 2011, 10:29 AM #1 Newbie Joined Mar 2011 From Karlskrona, Sweden Posts 7 A tricky equation of the first order My teacher gave me a "bonus" assignment the other day, and I've been racking my brain trying to solve it. Here it is: $xy'(ln(\frac{x}{y}) ...
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Real Analysis - Sequences 3 d.) Assuming this sequence is in the metric space $(M,d)$, if $\{b_n\}$ converges, then it is bounded. ( $\exists x_0\in M, R\in\mathbb{R}$ such that $d(x_0,b_n)<R~\forall n$) So $d(a_n,x_0)-R<d (a_n,b_n)~\forall n$. (Triangle Inequality) But since $\{a_n\}$ is unbounded, so is $d(a_n,x_0)$,...
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Integral equation From Encyclopedia of Mathematics 2010 Mathematics Subject Classification: Primary: 45-XX [MSN][ZBL] An equation containing the unknown function under the integral sign. Integral equations can be divided into two main classes: linear and non-linear integral equations (cf. also Linear integral equati...
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Temperature and Pressure Gradient in Ideal Gas Introduction Consider a narrow horizontal tube. The curved surface made with perfect insulator. The flat faces made with perfect heat conductor. One end of the tube is maintained at 100 oC and the other end is maintained at 0 oC. Once the steady state is attained, heat...
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Sir Isaac Newton – Book 1: Of The Motion of Bodies: Section 1: Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow SECTION I Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow LEMMA I Q...
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[SOLVED] Surface integrals and flux September 24th 2008, 10:15 AM #1 [SOLVED] Surface integrals and flux 1) $S: x^2 + 4y^2 = 4$, $0 \leq z \leq 1$. Calculate the flux of the vector field $\overline{A}(x,y,z) = \left(\frac{-6x}{x^2+y^2},\frac{-6y}{x^2+y^2}, z+1\right)$ out through the z-axis. 2) $S: z...
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antiderivative of 7^cost sint dt ∫(from 0 to pi/2) 7^cost sint dt i know that it is a^u du but sin needs to be negative so I tried this: -∫(from 0 to pi/2) 7^cost (-sint) dt then made u=cost and du= -sint so: ∫ 7^u du= 7^u/ ln7= 7^cost /ln7 and when i plug in pi/2 i get 1/ln7 but the ans...
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Building a scale by diagonalization and transfinite induction up vote 2 down vote favorite I'm asking a question following the reading of Set Theory from Jech (page 126). For the record, a $\kappa$-sequence of functions $\langle f_\alpha : \alpha < \kappa\rangle$ is called a $\kappa$-scale if $f_\beta < f_\alpha$ whe...
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equation of plane tangent March 11th 2011, 04:51 AM maximus101 equation of plane tangent Let S be the surface parameterised by $r(u,v):=(e^ucosv,u,e^usinv), <br /> u\in\Re, v\in[0,2\pi]$ (i) Find the equation of the plane tangent to S at r(u,v). (ii) At what points is the tangent plane to S parallel ...
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Smallest integer not divisible by integers in a finite set up vote 7 down vote favorite Hello all, if $a_1,a_2, \ldots a_t$ are $t$ integers $\geq 2$, the set $G(a_1,a_2, \ldots a_t)=\lbrace N \geq 1 |$ In any sequence of $N$ consecutive integers there is at least one not divisible by any of $a_1,a_2, \ldots a_t\rbrac...
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Sum of reciprocals of squares of integers congruent to 1 mod 3 ? up vote 2 down vote favorite What is the value of $$\sum_{i=0}^\infty \frac{1}{(3i+1)^2} ?$$ Methods for other $a\pmod p$ would be helpful, i.e., the value of $$\sum_{i=0}^\infty \frac{1}{(pi+a)^2} .$$ Thanks in advance Herman :+) nt.number-theory ...
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Rational Expressions March 2nd 2009, 04:15 PM #1 Newbie Joined Aug 2008 From San Ramon, CA Posts 17 Rational Expressions $\frac {y^2}{y^2-9} + \frac {9-6y}{y^2-9}$ $\frac {3x}{x^2-4} + \frac {5x}{x^2+x-2} - \frac {3}{x^2-4x+4}$ Complex Fraction: $\frac {x+2}{x-2}- \frac {x-2}{x+2} over \fra...
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Poincare's Universe: simple Calculus question April 29th 2010, 04:36 PM #1 Newbie Joined Apr 2010 Posts 4 Poincare's Universe: simple Calculus question I have been reading "Prelude to Mathematics" by W.W. Sawyer. In it he describes Poincare's hypothetical universe. This universe is contained in the ...
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Special values of L-functions as periods up vote 21 down vote favorite 9 If $M$ is a pure motive over $\mathbb{Q}$, one cas define its $L$-function $L(M,s)$ which conjecturaly is a meromorphic function over $\mathbb{C}$ with finitely many poles. For example, when $M=\ mathbb{Q}$ is the trivial motive, $L(\mathbb{Q},s)...
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Solving Trigonometry November 20th 2011, 08:20 PM BlackOut14 Solving Trigonometry 1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum ...
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Work Out Percentages - PowerPoint SATs Mathematics Preparation Number, Algebra and Shape and Space Questions Levels 3 - 6 in Yellow Levels 7 - 8 in Red Reading Scales • Remember to check what one mark on the scale is – • If there are 5...
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deductive geometry (2) October 30th 2009, 02:52 AM #1 Senior Member Joined Jan 2009 Posts 381 deductive geometry (2) Vertices B and C of the triangle ABC lie on the circumference of a circle . AB and AC cut the circumference of the circle at X and Y respectively . Show that angle CBX +angle CYZ =180 ...
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a dilogarithm identity: known or new? up vote 4 down vote favorite 2 I was playing around with dilogarithms and numerically found the following dilogarithm identity: $$\text{Li}_2\left(\frac{2 m}{m^2+m-\sqrt{((m-3) m+1) \left(m^2+m+1\right)}-1}\right)$$ $$-\text{Li}_2\left(\frac{m^2+m-\sqrt{((m-3) m+1) \left(m^2+m+1\...
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GMAT question March 26th 2011, 10:43 AM #1 Newbie Joined Mar 2011 Posts 3 GMAT question I put this one under the high school level because it really shouldn't be that hard, but it has me stumped. Any advice? Question: what is the value of m in the following expression? (1/5)^m * (1/4)^18 = 1/(2...
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Differential equation check? May 19th 2009, 06:25 AM dankelly07 Differential equation check? COuld someone check this out for me and see if If done this right.. I'm worried incase I went wrong somewhere... $<br /> \begin{gathered}<br /> 4\frac{{d^2 y}}<br /> {{dx^2 }} + 8\frac{{dy}}<br /> {{dx}} + 3y = ...
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Computing Competing Probabilities How do we deal with games having more points? For this we use recursion. Suppose again that both teams shoot only three point shots under "loser-takes-out." Let probAwin(Aposs, x, y) mean "the probability that A wins when A has possession, A has x points to win, and B has y points to w...
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11. Math module - Fraction and Percentege MEP Practice Book SA11 11 Fractions and Percentages 11.1 Fractions, Decimals and Percentages 1. Express each of the following percentages as a fraction in its lowest terms. (a) ...
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Set theory/ Cardinal Help February 14th 2010, 12:32 PM #1 Newbie Joined Feb 2010 Posts 4 Set theory/ Cardinal Help If f : A-B is the given function, the graph f is the subset of AcrossB consisting of all (a,f(a)). 1. Prove that a-(a,f(a)) is a one-to-one map of A onto the graph of f. 2. Let D a...
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23: Calculus Chapter 23: Calculus This chapter covers J operators for differentiation and integration. It covers • The conjunction d. which differentiates and integrates analytically, that is, it transforms expressions denoting functions into expressions denoting functions. • The conjunction D. which differenti...
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Please help with these function problems! November 8th 2006, 06:52 PM #1 Newbie Joined Oct 2006 Posts 24 Please help with these function problems! Hey guys any help I could get on these few questions would be amazing. Thanks! 1) Find the average rate of change of the function f(x)=e^x - e^(-x) as x ...
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Expressing a Fraction as a Decimal Associated Topics || Dr. Math Home || Search Dr. Math Expressing a Fraction as a Decimal ...
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[SOLVED] Method of differences problems February 11th 2009, 02:29 AM #1 MHF Contributor Joined Sep 2008 From West Malaysia Posts 1,261 [SOLVED] Method of differences problems If $f(r)=\frac{1}{r^2}$ , simpify f(r)-f(r+1) . Hence , find the sum of the first n terms of the series $<br /> \frac{3}{...
5
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go Bogobogosort Introduction Bogobogosort is a sorting algorithm based on the popular bogosort algorithm. Algorithm Description To understand bogobogosort, it is necessary to first have an understanding of the finer points of bogosort. Bogosort can be described as follows: 1. Check if your list of number is sort...
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Introducing 'propagate' Introducing ‘propagate’ With this post, I want to introduce the new ‘propagate’ package on CRAN. It has one single purpose: propagation of uncertainties (“error propagation”). There is already one package on CRAN available for this task, named ‘metRology’ (http://cran.r-project.org/web/packages...
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Centre of gravity of a right angled triangle?! is this right? June 3rd 2009, 03:55 AM #1 Newbie Joined May 2009 Posts 17 Centre of gravity of a right angled triangle?! is this right? If I have a triangle with the coodinates A(0,0) B (30,0) and C (30,40) Is the centre of gravity 1/3 of the base and 1...
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Basic identity proving April 5th 2009, 01:10 PM #1 Newbie Joined Apr 2009 Posts 1 Basic identity proving Hi, I just started with trig and trig proofs are like really hard for me, I just can't seem to understand them. This is the first question in my workbook.. $\frac{\cot \theta -1}{\tan \theta...
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Joseph-Louis Lagrange Back to the front page ...
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Vector Arithmetic for Physics Help By Stan Gibilisco — McGraw-Hill Professional Updated on Apr 25, 2014 Introduction A vector has two independently variable properties: magnitude and direction. Vectors are used commonly in physics to represent phenomena such as force, velocity, and acceleration. In contrast, real...
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How many well orderings of $\aleph_0$ are there? up vote 8 down vote favorite 1 What is known about the set of well orderings of $\aleph_0$ in set theory without choice? I do not mean the set of countable well-order types, but the set of all subsets of $\aleph_0$ which (relative to a pairing function) code well orderi...
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Power Series Representation June 3rd 2013, 04:24 PM #1 Power Series Representation I need help finding the power series representation of ln(root(4-x^2)). I have gathered that I pull out the root 4, so I'll have ln(2)+something, but I'm not sure where to go from there. I know that ln(1-x) is -x^k/k, but...
5
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Need help for Proving Quadratic Equations August 27th 2009, 10:51 PM #1 Junior Member Joined Aug 2009 Posts 62 Hello people, How do i prove these? 1) If a, b and c are real, show that the roots of the following equations are real: (i) (b+c)x^2 - (a + b + c)x + a = 0 (ii) (a + b)(x^2 + 5...
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Radical Equations Dimensions Problem September 20th 2009, 03:03 PM #16 $(\sqrt{x+1} + 2)^2 = (\sqrt{3x+1})^2$ $(x+1) + 4\sqrt{x+1} + 4 = 3x+1$ combine like terms on the left side ... $4\sqrt{x+1} + x + 5 = 3x + 1$ $4\sqrt{x+1} = 2x - 4$ divide all terms by 2 ... $2\sqrt{x+1} = x - 2$ ...
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More Triangles April 30th 2007, 05:58 PM #1 Please help me solve this! Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle. Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB To Prove: Line CD bisects Angle ACB...
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Amortization - LOGS!! Help September 12th 2008, 01:02 AM #1 Newbie Joined Sep 2008 Posts 1 Amortization - LOGS!! Help I'm actually working on an amortization problem. I am trying to solve for n. I have all of the other values. In order to do this I end up using logs (i think...) A/P/r = (...
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Functions: Newton's Quotient July 27th 2010, 12:04 PM #1 Newbie Joined Jul 2010 Posts 1 Functions: Newton's Quotient I'm doing some math over the summer for fun. I have a very weak background in math, but have come around and thoroughly enjoy it. Can someone explain what is going on with this problem inv...
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prove that a^2sin(B-C) = prove that: $a^{2}sin\left(B-C\right) = \left(b^{2} - c^{2}\right)sinA$ where $a,b,c$ are sides of triangle and $A,B,C$ are the corresponding angles I'll use the sine and cosine rules. $a^2\sin(B-C)=a^2(\sin B\cos C-\sin C\cos B)=$ $=a^2\left(\frac{b}{2R}\cdot\frac{a^2+b^2-c^2}{2ab}-\frac{c}{2...
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Solve the following...I keep getting strange answers May 26th 2012, 02:22 AM fcabanski Solve the following...I keep getting strange answers $x + \frac{7-2x}{x-2}<= \frac{5x+7}{x-2}$ Solve and express solution as a graph and in interval or set notation. The solutions are x=0 or x=9. (That's given.) ...
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Questions regarding solving an ODE January 22nd 2011, 07:11 AM #1 Newbie Joined Jan 2011 Posts 6 Questions regarding solving an ODE Is it possible to use Euler's method to numerically approximate the solution of this system of ODEs: dx/dt = -y + x(p - x^2 - y^2) dy/dt = x + y(p - x^2 - y^2) ...
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Proof or disproof the following April 2nd 2011, 05:35 AM gordo151091 Proof or disproof the following I have been asigned this problem in class. $C\subseteq A \Rightarrow (A \cup B) \cap C \subseteq A$ Can you aid me in how should i start. I thought of puting it in terms of propositional logic, then pro...
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Formula for Calculating original quantities from a price September 16th 2010, 01:02 AM #1 Newbie Joined Sep 2010 Posts 3 Formula for Calculating original quantities from a price Hi I need a formula to solve the following problem, unfortunately my maths is pretty basic. Item A = 0.23 per unit up to a...
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Working with expressions. March 11th 2011, 09:44 AM #1 Newbie Joined Feb 2011 Posts 24 Working with expressions. Please, if anyone could solve and explain to me the process of solving these two problems I would be extremely grateful. (It's not about the result, I really need to know HOW to do this, so If...
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formal power series convergence up vote 22 down vote favorite 15 I have spent some time using gp-pari. There is, of course, a formal power series solution to $ f(f(x)) = \sin x.$ It is displayed, below, identified by the symbol $g$ because I am not entirely sure whether it is a function of anything. On the other hand,...
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algebra equations March 13th 2008, 12:41 PM miramontes algebra equations Hi I need help on these problems, these are practice problems for my final because the questions will be similar to these but I need help with these. I am lost. Any help would be greatly appreciated (Speechless)(Thinking)(Cryi...
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Ratio of consecutive divisors and average up vote 3 down vote favorite Let $2\leq d_1 < d_2,...,d_l < n$ be all the proper nontrivial divisors of $n$. I like to understand how much these divisors deviates from each other. Here are two questions in this regard: (1) What is the maximum of the set $\{d_i/d_{i-1}: 1\leq...
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A Haskell monad for infinite search in finite time I show how monads in Haskell can be used to structure infinite search algorithms, and indeed get them for free. This is a follow-up to my blog post Seemingly impossible functional programs. In the two papers Infinite sets that admit fast exhaustive search (LICS07) and...
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Multiplicativity of the Phi Function. January 3rd 2006, 02:40 PM #1 Global Moderator Joined Nov 2005 From New York City Posts 10,616 Thanks 9 Multiplicativity of the Phi Function. It is a classic and fundamental result that the $\phi$function is multiplicative. Meaning, $\phi (nm)=\phi (n)\ph...
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The idea behind Green's theorem When $\dlc$ is an oriented simple closed curve, the integral \begin{align*} \dlint \end{align*} represents the circulation of $\dlvf$ around $\dlc$. If $\dlvf$ were the velocity field of water flow, for example, this integral would indicate how much the water tends to circulate around th...
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derivates February 13th 2006, 12:12 PM lilheadbaby1 derivates Find the derivate of p(x)= (3x)^1/2 using the alternative formula for the derivate f ' (x)= lim f(z)-f(x)/z-x z>x my answer was 1/2(3x)^1/2 but its wrong February 13th 2006, 01:48 PM CaptainBlack Quote: Originally Pos...
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Which Turing machines accept the language of trivial words in a finitely presented group? up vote 10 down vote favorite 3 Let $G$ be a finitely presented group with generators $g_1, g_1^{-1},\ldots, g_n, g_n^{-1}$. Let $L(G)$ be the language of all those words in $g_1, \ldots, g_n$ which represent the trivial element ...
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Help with finance calculator October 19th 2011, 08:52 AM #1 Newbie Joined Sep 2009 Posts 17 Help with finance calculator Poor Dog, Inc. borrowed $135,000 from the bank today. They must repay this money over the next six years by making monthly payments of $2,215.10. What is the interest rate on the loan?...
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Interpreting the Garnir relations in terms of the Yang-Baxter equation up vote 6 down vote favorite 4 One possible construction of the Specht modules goes as follows. Given a partition $\lambda$ of $n$, we can write down Young's seminormal form for the representation of $S_n$ corresponding to $\lambda$. Writing a bas...
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Two exercises about real numbers April 16th 2012, 11:50 AM #1 Junior Member Joined Jun 2009 Posts 58 Two exercises about real numbers Hello!! Could you please help me with these two exercises 1.- Let $a,b,c$ be real positive numbers and $abc = 1$ Prove that: $\displaystyle\frac{a}{(a+1)(b+1...
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Area between curve and x axis August 3rd 2006, 10:09 AM #1 Newbie Joined Jul 2006 Posts 15 Area between curve and x axis If y = √ 4 - x^2 then the area of the region limited by this curve y and the x axis is a) ¶ b) 2¶ Calculate the correct result. bret80 If y = √ 4 - x^2 then the ...
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Maximum and bound for a multivariate function December 18th 2008, 04:45 AM #1 Maximum and bound for a multivariate function Hi there guys, I'm having alot of trouble verifying the following: Verify that the maximum of $\displaystyle x(1-x)y(1-y)w(1-w)(1-(1-xy)w)^{-1}$ occurs for $x=y$, and then tha...
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Annuities Finance > Annuities Annuities An annuity is a series of equal payments over a specified time frame. For example, a cash payment of C made at the end of each year for four years at annual interest rate i is shown in the following time line: This time line is for an ordinary annuity, in which the cash paymen...
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improper integral February 8th 2013, 07:07 AM happymatthematics improper integral Hello. Attachment 26906 I don't know how to solve the above improper integral. I tried to get rid of dy, but turn out to be Attachment 26907 which is even more difficult to me. I don't know how to get rid of x...
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