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Minimizing a function containing an integral up vote 4 down vote favorite I am trying to optimize a function of the following form: $L = \int_{t=0}^{T}(AR-x)dt$, where A is a system parameter i.e. I am trying to find the optimum x(t) that minimizes L over all admissible x(t)s. R is related to x using a relation: $\...
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families of curves on surfaces which are products of curves up vote 3 down vote favorite Let $C$ be a projective curve (over an algebraically closed field) of genus $\geq 1$. Let $S = C \times C$. By normalisation we have a ramified cover $C \to \mathbb{P}^1$ and so a map $p: S \to \ mathbb{P}^1 \times \mathbb{P}^1$. ...
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Painting Cube Faces Green Date: 08/19/2003 at 18:43:32 From: Mike Subject: Combinations Mrs. Jones had some white paint and some green paint, and a bunch of wooden cubes. Her class decided to paint the cubes by making each face either solid white or green. Juan painted his cube with all six faces white. Julie painted...
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Finding the missing side of a triangle? September 1st 2009, 11:25 AM ineedhelp87 Finding the missing side of a triangle? Okay, if you have a right triangle, the hypotenuse of which (side opposite the right angle) is 16 feet long, and the other angle is 68 degrees, how do you calculate the length of the opposite ...
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What's the difference between ZFC+Grothendieck, ZFC+inaccessible cardinals and Tarski-Grothendieck set theory? up vote 12 down vote favorite 2 Say that "U" is the axiom that "For each set x, there exists a Grothendieck universe U such that x $\in$ U", where Grothendieck universes are defined in the usual way (or, if t...
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Area of a Parabola Date: 09/05/97 at 00:52:32 From: GLOBETROTTERS Subject: Parabola How do you find the area of a parabola? (I just finished Algebra 2.) c /\ <- The parabola looks something like this. b{ }d \/ a Point a is at (0,2) Point d is at (3,11) and the distance between point b and point d is 6....
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Find the Bearing Date: 01/17/2003 at 19:47:43 From: Richard Subject: A formula to find the bearing of one point from another. Is there a formula to find the bearing of one point from another on a 2D map (or graph) just using normal co-ordinate systems? (I want to avoid talking about the great circle (it's 2D) and lon...
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What fails when using call/cc as realizer of the Peirce formula up vote 4 down vote favorite Define the axiom constants $p_{A,B}^{((A\rightarrow B)\rightarrow A)\rightarrow A}$ as realizers of the Peirce formula, and $f_A^{\bot\rightarrow A}$ as realizers of the Ex Falso Quodlibet. Then $p_ {A\vee\lnot A,\bot}^{(\lnot...
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when mapping cone is contractible up vote 3 down vote favorite It is quite obvious that if a map is a homotopy equivalence, then its mapping cone is contractible, but is the converse true: mapping cone contractible => the map is a homotopy equivalence? I am thinking about both the topological category and the category...
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Limit infina of ratio test and root test April 21st 2013, 06:16 PM phys251 Limit infina of ratio test and root test For a strictly positive sequence, prove that $\liminf (a_j^{\frac{1}{j}}) \geq \liminf (\frac{a_{j+1}}{a_j})$. I get that it's trying to say that the root test converges faster than the ratio ...
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Generality of the solution 4.2 Generality of the solution We have a solution, but is that a general solution? The answer, yes, is provided by the following result [26 ]: Theorem 2 The most general solution of the harmonic-coordinates Einstein field equations in the vacuum region outside an isolated source, admitting ...
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bl Zentralblatt MATH Publications of (and about) Paul Erdös Zbl.No: 041.36807 Autor: Erdös, Pál Title: Some asymptotic formulas in number theory. (...
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CS502 FINAl Term 2010 Solved  FINALTERM EXAMINATION Spring 2010 CS502- Fundame ntals of Algorithms (Session - 4) Time...
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Is there an "elementary" proof of the infinitude of completely split primes? up vote 29 down vote favorite 18 Let K be a Galois extension of the rationals with degree n. The Chebotarev Density Theorem guarantees that the rational primes that split completely in K have density 1/n and thus there are infinitely many suc...
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Two discs with no parallel tangent planes up vote 9 down vote favorite 1 Is it possible to construct smooth embedded of 2-discs $\Sigma_1$ and $\Sigma_2$ in $\mathbb R^3$ with the same boundary curve such that there is no pair of points $p_1\in \Sigma_1$ and $p_2\in \ Sigma_2$ with parallel tangent planes? Co...
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Problem Solving August 15th 2008, 12:35 AM #1 Junior Member Joined Feb 2008 From Victoria Posts 39 Problem Solving Please help. Not sure if this is a trick question. What is the sum of the digits of all 2-digit numbers between 10 and 99. Please explain Have you learned how to set up sums using t...
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differentiating functions of several variables September 14th 2008, 10:52 AM #1 Junior Member Joined Sep 2008 Posts 44 differentiating functions of several variables Hello everyone: Could someone please tell me if this is correct? Find the equation of the tangent plane at the given point: ...
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of Degree Name Doctor of Philosophy Department University of Wollongong. School of Mathematics and Applied Statistics Recommended Citation Chen, Wen-Ting, An extensive exploration of three key quantitative approaches for pricing various financial derivatives, Doctor of Philosophy thesis, University of Wollongong...
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Counting problem December 20th 2013, 07:22 AM #1 Counting problem Hi! It's me again with another counting problem. I am trying to find the order of the following set (where $n \in \mathbb{Z}$ is fixed): $G_1 = \{ \sigma \in S_n | \sigma (1) = 1 \}$, the stabilizer of 1 in $S_n$. Now, I have calculated 4...
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Does $(x^2 - 1)(y^2 - 1) = c z^4$ have a rational point, with z non-zero, for any given rational c? MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required. I need this result for something else. It seems fairly hard, but I may ...
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Another double integral If we attempt to do the x integral first, we get an elliptic integral, so we reverse the order of integration: $\int_0^{\pi/2}\int_0^1\frac{dy\,dx}{\sqrt{1-\sqrt y\cdot\sin^2x}}$ Now, integrating with respect to y, we make the change of variables $u=\sqrt{y}\to{dy}=2u\,du$ $\int_0^{\pi/2}\int_0^...
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Find the derivative of the function. Simplify where possible. March 23rd 2013, 08:10 PM #1 Junior Member Joined Oct 2010 Posts 63 Find the derivative of the function. Simplify where possible. Hi guys, i attached the question with the last answear that i got (which i think is right) . I have attempted thi...
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Differentiation & Stationary Points September 8th 2012, 07:03 AM #1 Newbie Joined Sep 2012 From Scotland Posts 4 Differentiation & Stationary Points Having some trouble with the following two questions, I have an answer but it doesn't make sense... A function f is defined by the formula f (x) = ...
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indecomposable vector bundles having proper sub-bundles. up vote 1 down vote favorite 1 Over rational curve we know that any vector bundle is decomposable to direct sum of line bundles. In higher dimensions there are examples of indecomposable bundles. some indecomposable vector bundles have might have proper sub-b...
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Math Forum Discussions - Re: Interpretation of coefficients in multiple regressions which<br> model linear dependence on an IV Date: Nov 26, 2012 3:20 AM Author: Ray Koopman Subject: Re: Interpretation of coefficients in multiple regressions which<br> model linear dependence on an IV On Nov 21, 8:13 pm, djh <halitsk.....
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[SOLVED] Calculate a volume + theoretical question July 11th 2009, 03:51 PM arbolis [SOLVED] Calculate a volume + theoretical question 1)Identify the region of integration and calculate the following integral using spherical coordinates : $\int_{-3}^{3} \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int _0^{\sqrt{9-x^2-y^...
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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: The Condemnation by the Paris Livre of the French ...
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inequality in intervals $\frac{1}{x} < 4$. First, it should be abundantly obvious that $x eq 0$. To solve this inequality for $x$, you will need to consider two cases, the first being when $x$ is positive, and the second when $x$ is negative, since multiplying/dividing by a negative reverses the inequality sign. Case 1...
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Every quadrilateral has a side such that the other two vertices lie on the same side October 9th 2010, 12:40 PM oldguynewstudent Every quadrilateral has a side such that the other two vertices lie on the same side Please let me know if the following proof is solid or if it contains errors. Thanks. Show that...
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Ideals and homomorphisms May 18th 2009, 09:40 PM curiousmuch Ideals and homomorphisms Let I and J be ideals of a ring R and let I be contained in J. Show that J/I is an ideal of R/I and also show that (R/I)/(J/I) is isomorphic to R/J. For the second part I am just trying to use a ring homomorphism but ...
5
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A little bit of help needed please! September 2nd 2009, 06:28 AM #1 Newbie Joined Jul 2009 Posts 22 A little bit of help needed please! I need a little bit of help with two questions that are confusing me quite a lot. [1] find the slope and y-intercept of the following: 5x-2y=3 [2] Writ...
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A specific projection and compactness on the Bargmann-Fock space up vote 2 down vote favorite Let $F_2$ be the Bargmann Fock space defined as the space of entire functions $f$ on $\mathbb{C}$ such that \begin{align*} \int_{\mathbb{C}} |f(z)|^2 e^{- |z|^2} dA(z) \end{align*} ($dA$ is just ordinary area measure, and I'm...
5
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Double integral over a triangular domain; getting different answers for x or y simple September 23rd 2011, 07:28 PM #1 Newbie Joined Sep 2011 Posts 1 Double integral over a triangular domain; getting different answers for x or y simple Hello all. Been a lurker of the forums for a little while, thought it...
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Axiomatizing Gross-Zagier formulae up vote 20 down vote favorite 7 Let $\pi$ be a global automorphic representation of some reductive group over a number field, and let $L(\pi,s)$ denote its L-function. Assume $L(\pi,s)$ extends meromorphically to the complex plane and satisfies a functional equation of the form $$ L(...
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My difficulties in the text _How to Prove It: A Structured Approach, 2 ed_ January 30th 2013, 08:27 AM RemiAure My difficulties in the text _How to Prove It: A Structured Approach, 2 ed_ This is a thread for any major difficulties I come across in How to Prove It: A Structured Approach, 2nd edition by Daniel J. ...
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Grade 11 Functions Posted by Jim on Wednesday, November 2, 2011 at 1:07pm. A baseball player hits a foul ball into the stands. He wants to know where the ball would've landed if the stands had not been there. The points they give you are: The y-intercept (0,1), (2,2.5) and (134,18). I'm pretty sure you are looking for...
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Probability Question! April 18th 2007, 06:42 AM #1 mattsh Guest Probability Question! Hi everyone, I need help on a probability question please. Thanks in advance. Here it is: 1/3 of the people in a club are men. The number of men in the club is n. a) Write down an expression, in terms of n, fo...
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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: WHY EINSTEIN PROPOSED HIS SECOND POSTULATE Replies...
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Affine automorphisms of algebraic function field towers up vote 0 down vote favorite Are there any well-known towers of function fields over finite fields whose automorphism groups contain a transitive subgroup consisting solely of affine maps? For a (non)example of what I'm looking for: let $\mathbb{F}$ be the finit...
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Derivative calculations February 4th 2009, 07:20 AM #1 Newbie Joined Jan 2009 Posts 9 Derivative calculations Hi could someone please help me differentiate? $<br /> r(t) = ln(2t\sqrt(t+1))<br />$ I was thinking of using the product rule. Hello, It would come after the chain rule. ...
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Transforming a Diophantine equation to an elliptic curve up vote 12 down vote favorite 6 I heard that the following problem lead to determine the rational points of an elliptic curve: For which integers $n$ there are integers $x,y,z$ such that $x/y+y/z+z/x=n$. Could anyone show me why this question leads to the theor...
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linear operator associated with semilinear elliptic pde up vote 2 down vote favorite 1 I am reading a paper where at some point they analyse the following linear operator: $$L_\lambda(\phi)= - \Delta \phi - C_\lambda(x) \phi$$ where $ C_\lambda(x)>0$ (smooth) in $ \Omega$ a bounded domain in $ \mathbb{R}^N$ containi...
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$C^k$ topology of metrics up vote 3 down vote favorite 1 Is the space of Riemannian metrics, over a compact manifold, complete when endowed with the $C^k$-topology of metrics?. Is there a good reference for this? dg.differential-geometry riemannian-geometry Completeness usually refers to a metric space. For exa...
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Variant of Fermat's last theorem up vote 3 down vote favorite By Fermat's last theorem, the equation $u^3+v^3=w^3$ has no solutions in positive integers $u,v,w$. Now consider the following variant : call $\rho(x)$ the distance between $x$ and the nearest integer, for any real number $x$ (thus $\rho(3)=0,\rho(3.2)=0.2,...
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two numbers February 25th 2011, 03:34 PM #1 Newbie Joined Feb 2011 Posts 5 two numbers Hi there wondering if this can be solved using Algebra? the product of two numbers is 72 and their sum is 27. I am interested in the steps to arrive at the numbers 24 and 3. cheers I think you can ...
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Invertibility Proof November 25th 2009, 06:04 PM joe909 Invertibility Proof The question is: Let A be a skew–symmetric n×n–matrix with entries in $R$, i.e. $A^T=-A$ Prove that In+A is an invertible matrix. I have tried solving this both algebraically and non-algebraically. Algebraically I ...
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Regularity for transport equation? up vote 4 down vote favorite 4 In the book of Evans the transport equation, $$\frac{d}{dt} u + b\cdot \nabla u = 0, \quad u(t=0)=u_0,$$ is solved by the method of charateristics for $b$ and $u_0$ smooth enogh (in terms of $\ mathcal{C}^k$ for some $k$). I am not an expert for hyperb...
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Long time behavior of the heat equation on R up vote 3 down vote favorite 4 Let $\mu\in\mathcal{S}'(R)$ be a Schwartz distribution. The solution of a heat equation with $\mu$ as the initial data is $$ u(t,x)= \int_R \frac{e^{-\frac{(x-y)^2}{2t}}}{\sqrt{2\pi t}} \mu(d y) $$ You can assume that $\mu$ is non-negative, ...
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Prove continuous -> graph is closed February 10th 2009, 11:57 AM #1 Member Joined Feb 2009 Posts 103 Prove continuous -> graph is closed Prove that if $f: X \rightarrow Y$ is a continuous map of a space X to a Hausdorff space Y then its graph $G_{f} = ({ (x,f(x)) \in X \times Y : x \in X})$ is...
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Matrix Groups July 25th 2010, 02:42 AM #1 Member Joined Dec 2009 Posts 224 Matrix Groups Any help with the following problem is greatly appreciated: For the part (a) of this problem, I must show that $M_{a,p}$ belongs to the general linear group of 2x2 matrices over p (a prime) iff $a \bmod\ p eq ...
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IS/LM Curves - Macroeconomics help appreciated! The question is at this link, you may need to zoom in (make sure your browser is full screen or it may be too small!): Yfrog Image : yfrog.com/mqeconomicsquestionp Please help! Thx in advance (Happy) There's no chance of reading that my friend, try again or even better j...
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Math Forum Discussions - Re: function arity > 2 Date: Jan 16, 2013 11:07 PM Author: Graham Cooper Subject: Re: function arity > 2 On Jan 16, 7:55 pm, Butch Malahide <fred.gal...@gmail.com> wrote: > > Damned if I know. I've *heard* of lambda calculus, and that's about it. It's a method to Run functions on the fly, tha...
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vectors with entries from a finite ring up vote 2 down vote favorite I've been working recently with vectors over finite fields, but I was hoping to work in a more general setting and consider vectors over finite commutative rings. The question I had is as follows: if I fill $n$ vectors with random entries over a give...
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Computing the Galois group of a polynomial up vote 25 down vote favorite 23 Does there exist an algorithm which computes the Galois group of a polynomial $p(x) \in \mathbb{Z}[x]$? Feel free to interpret this question in any reasonable manner. For example, if the degree of $p (x)$ is $n$, then the algorithm could give ...
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If (x-2) and (x-1) are factors of polynomial `x^3+px^2+qx+1` what is the sum of p and q. - Homework Help - eNotes.com If (x-2) and (x-1) are factors of polynomial `x^3+px^2+qx+1`  what is the sum of p and q. Please note the error: The factors are `(x-2) (x-1)` `therefore x=2 or x=1` As we have : `x^3 + px^2 + qx+1`...
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sequence converge, finding its limit. October 7th 2010, 02:52 PM jax sequence converge, finding its limit. Hello, I was wondering if this sequence converges, and if it does what is the limit? (a_n), where a_n=(1)+(1/2)+(1/2^2)+(1/2^3)+...+(1/2^n). p.s- I know that the sequence a_n=(1/2,1/4,1/6...) ...
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Logs of Motion, how do i do this???? November 20th 2008, 05:05 PM freepancakes Logs of Motion, how do i do this???? the question is.... position equation: x(t)= t ln t - 3t + c Velocity equation: v(t)= ln t -2 a.) if particle is located at the orgin at t=1, find c and an equation for x(t) b.) f...
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Probability. Not for the faint of heart February 3rd 2009, 05:40 PM zhupolongjoe Probability. Not for the faint of heart Let S be a given set. If, for some k>0, S1,S2,....Sk are mutually exclusive nonempty subsets of S such that union (i=1 to k) Si=S, , then we call the set {S1,S2,…,Sk} a partition of S. Let...
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Why does CH imply that there is a unique ultrapower of $\mathbb{N}$? up vote 13 down vote favorite 2 I've read these words: "How many ultra products $∏_Uℕ$ exist up to isomorphism, where $U$ is a non-principal ultrafilter over $ℕ$? If continuum hypothesis(CH) holds, then obviously just one ..." i don't know why "obvi...
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Roots of the Equation November 17th 2008, 10:18 PM #1 MHF Contributor Joined Jul 2008 From NYC Posts 1,489 Roots of the Equation The roots of the equation ax^2 + 4x = –2 are real, rational, and equal when a has a value of (1) 1 (3) 3 (2) 2 (4) 4 If a=1, then $x^2+4x+2=0$ h...
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Convergence Craziness May 19th 2009, 01:15 PM #1 Senior Member Joined Apr 2009 From Atlanta, GA Posts 408 Convergence Craziness Take some infinite subset of natural numbers $A \subset \mathbb{N}$ . Define $\sigma_A= \sum_{n\in A} \frac{1}{n}$ . For some sets A, $\sigma$ diverges, like the primes $P=\...
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Solving trinomial February 8th 2008, 11:09 AM #1 Newbie Joined Feb 2008 Posts 2 Solving trinomial Help! Solve algebraically: 10x^3+x^2-69x+54 = 0 How do i solve this? How do i find one root so i can find the other 2? Thanks so much for any help, mike Hello, Mike! Solve a...
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Challenges David Bressoud, Macalester College Visualizing the Future of Mathematics Education, USC, April 13, 2007 This PowerPoint will be available at www.macalester.edu/~bressoud/talks 80% precalculus and precollege 53% introductory and precollege 53% introductory and precolleg...
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Limit : ln-expo the limit is 1 because $\underset{x\to 0}{\mathop{\lim }}\,\frac{e^{x}-1}{x}=\underset{x\to 0}{\mathop{\lim }}\,\frac{\ln (1+x)}{x}=1.$ same can be done using L'Hospital rule (if on putting limit you get a indeterminate form like 0/0 or infinity/infinity, then keep on differentiating both numerator and...
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Basic facts about Exterior of sets April 17th 2011, 12:47 AM #1 Basic facts about Exterior of sets I'm minutely studying "Counterexamples in Topology" by Steen and Seebach (great book! Recommended) and have reached a statement on Page 7 which I can't prove. "The exterior ext(A) of a set A is the co...
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Lagrange multipliers February 22nd 2009, 01:35 PM #1 Member Joined Oct 2007 Posts 159 Lagrange multipliers I am suppose to calculate the max and min of f(x,y,z) = x^2 - 2y + 2z^2 with the constraint function of x^2 + y^2 + z^2 = 1 I am to use Lagrange multipliers for this. When I do I get F sub y eq...
5
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[SOLVED] Parametric Representation of a Curve May 20th 2009, 02:46 PM #1 Newbie Joined Jan 2009 Posts 21 [SOLVED] Parametric Representation of a Curve Hey, Find the equation in $x$ and $y$ for the curve given parametrically by $x = sec(t)$ and $y = tan(t)$, where $\frac{-\pi}{2} < t < \frac{\pi}...
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parabolic arch Need help with a problem having to do with parabolas. A tunnel has a height of 20m and a width of 36m at the base. If the vertex is at the top of the arch, at which point in above the base is it 18m wide? Thanks! The standard equation of a vertical parabola that opens downward is (y-k) = -a(x-h)^2 where...
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Weakest Hypothesis Needed for Axiom of Replacement up vote 2 down vote favorite A typical formal statement of the Axiom of Replacement is (leaving out some technical details about extra "parameter variables" that $\phi$ sometimes takes.) $[\forall x,y,z\ (\phi(x,y) \wedge \phi(x,z) \implies y=z)] \implies [\forall X ...
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System of ordinary differential equations up vote 1 down vote favorite 1 I am trying to solve the system of differential equations dx/dt = (y-x)/(x+y), dy/dt = -y/(x+y), where x and y are functions of t, and x(0)=0, y(0)=c (positive constant). I would like to find x and y explicitly in terms of t. This problem is rel...
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Blank Page 1 PART 2b. PLANAR KINETICS OF LUMPED MASS SYSTEMS Motion and Deformation of Mechanical Systems with 2 Degrees of Freedom (2DOF) Textbook Chapter 3.5 (Lectures 14-18) Acronyms: M: mass, K: stiffness, C: damping, ODE: ordinary differential equation, EOM: equation of motion, SEP: static equilibrium position...
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Cohomology and fundamental classes MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required. Let X be a real orientable compact differentiable manifold. Is the (co)homology of X generated by the fundamental classes of oriented subvar...
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Interior coordinates in the Mandelbrot set There is an algorithm to find points on the boundary of the Mandelbrot set, given a particular hyperbolic component and the desired internal angle. It involves Newton's method in two complex variables to solve \[ F^p(z,c) = z \\ \frac{\partial}{\partial z} F^p(z,c) = b \] wh...
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Partial Differential Equations July 9th 2007, 06:57 AM #1 Newbie Joined Jul 2007 Posts 4 Partial Differential Equations Hi I am stuck on a PDE boundary question, I think I have shown the equation seperates and understand what the boundarys mean but I am not sure how to show the general solution and then ...
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Calculas question February 7th 2010, 11:36 PM Awsom Guy Calculas question I hope this is the right area to post this question. Find the equation of the tangent to the curve y=2/x+1 at the point where x=3. I had a go can somebody please check it thanks, y=2/x+1 y=2/4 =1/2 (3,1/2) 2(x+1...
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How to invert this series? up vote 0 down vote favorite 1 Hi guys, I'm working on a problem where I ended up with the following series: $z(Q) = \exp(-Q) [ 1 + \frac{a_1}{Q} + \frac{a_2}{Q^2} + \ldots]$ valid around $Q \to \infty$ Is there a systematic way of obtaining Q as a series in z, such as: $Q(z) = - \log(z)...
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coefficient help February 10th 2007, 01:26 AM #1 Junior Member Joined Jan 2007 Posts 40 coefficient help Could someone give me a hand at this one? What is the coefficient of x[5th power] in the expansion of (x+3)[8th power]? Possible solutions: 56 336 504 1512 Hello, Gretch...
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Vector calc center and radius of circle problem February 4th 2009, 05:38 PM #1 Member Joined Oct 2007 Posts 159 Vector calc center and radius of circle problem I am studying for a test and one of the review questions is stumping me. I am suppose to find the center and radius of a circle with the fol...
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Probability a polynomial has a root which is a root of unity up vote 17 down vote favorite 7 Consider a degree $n$ polynomial $P(x)$ with coefficients $c_i \in \{-1,0,1\}$ chosen uniformly and independently. What is the probability that $P(x)$ has a root which is a root of unity? Previously asked at http://math....
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complex analysis: integrals how can i do this, applying Rouche Theorem and Cauchy Argument Principle? Use Cauchy's Argument Principle. 1) $\frac{1}{2\pi i}\oint_{\Gamma}\frac{f'(z)}{f(z)}dz = \mathbb{Z} - \mathbb{P}$ where $\mathbb{P}$ is the number of poles and $\mathbb{Z}$ is the number of zeros (both counting multi...
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Sine and Cosine of i (imaginary unit) March 2nd 2008, 07:06 AM Spud Sine and Cosine of i (imaginary unit) The following is my working for the Sine and Cosine of the imaginary unit, $i$. $e^{ix}=cos(x)+i(sin(x))$ Substituting $x=i$ gives $e^{-1}=cos(i)+i(sin(i))$ Squaring both sides $e^{-2}=(...
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Distributions on product spaces up vote 6 down vote favorite 3 I hope this is suitable to MO. Question. Let $X$ and $Y$ be two open sets in $\mathbb R^n$ and $\mathbb R^m$, respectively. In what sense can we consider $\mathcal{D}^{\prime} \left(X\times Y\right)$ as a tensor product of $\ mathcal{D}^{\prime} \left(X\r...
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Supersymmetry: transformations of superspace In a November 2011 article, I discussed the Grassmann anticommuting numbers that satisfy \[ \theta_1 \theta_2 = -\theta_2 \theta_1 \] My goal was to convince you that this new kind of abstract numbers is, in some sense, equally natural if it is employed as the basic number t...
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Advanced Functions (dont run away) need help badly October 3rd 2009, 10:06 AM #1 Junior Member Joined Oct 2009 Posts 32 Advanced Functions (dont run away) need help badly 1. Find the number of digits in the expansion of (2^120)(5^125) without any calculator or computer. 2. Find the coordinates of th...
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Final Exam Help:/ ? May 25th 2010, 04:48 PM #1 Newbie Joined May 2010 From Daytona Beach , Florida . Posts 1 So my Algebra2 Final exam is on thursday and my teacher was/is none the less incompitent . SO needless to say i'm not doing well in his class , just like every other student he teaches . So my ...
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A Hundred Thousand Switches, One Defect: How Few Tests? Date: 04/19/2011 at 22:39:14 From: David Subject: How many robots required to detect the defective lamps Suppose there are 100,000 lamps. One of them is defective. An operator has robots to identify the bad lamp. Each robot can test any number of lamps in one b...
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Proof - Limit of a function August 25th 2010, 09:18 AM #1 Member Joined Oct 2009 From United States Posts 169 Proof - Limit of a function Suppose that f(x) = mx + b with m > 0. Let c be a real number. Prove that lim x-> c (f(x)) = mc + b. What ideas have you had so far? I know that |mx ...
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Linear dielectrics (recursion approach) I’ve been prepping for my fall course, Advanced Electricity and Magnetism for juniors and seniors, taught out of Griffiths great book. One of the topics that I want to deal with better this time around is electrostatics in materials (chapter 4, for those of you following along)....
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Panel thickness, flexing and resonance. - diyAudio Quote: Originally posted by Circlotron (2) [The load-bearing capacity] is directly proportional to the square of the height for beams of the same length and breadth, instead of as the =cube of this dimension as in stiffness=. In case you're interested... As given pr...
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Help with Green's theorem May 13th 2010, 05:37 PM #1 Newbie Joined May 2010 Posts 1 Help with Green's theorem <b>The Problem:</b> a) Use Green's Theorem to calculate ∫F*dr over C, where F(x,y)=(2e^x-3y^2+5x)i+(xy-2x+ysiny)j and C is a piecewise smooth curve defined as C1: y=0, -2 ≤x ≤-1; C2: arc of x...
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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: DrPepperx3 Group Title @Directrix • 7 m...
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find eqaution of a plane March 11th 2008, 06:59 PM ramzouzy find eqaution of a plane find the equation of the plane that goes through (1,2,-1) and making equal angles with the positive directions of the coordinate axes March 11th 2008, 09:38 PM Soroban Hello, ramzouzy! Quote: Find the equation ...
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what is quadratic vatiation February 26th 2007, 02:43 AM #1 Member Joined Nov 2006 Posts 136 what is quadratic vatiation hi all, Ive searched online for ages but even though i can find formulas and definitions i dont quite understand what quadratic variation is. The reason i want to know this is, i'...
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Solution in distinct elements for a system of $n$ equations over finite fields up vote 0 down vote favorite The following problem is motivated by pure curiosity; it is not a part of any research project and I do not have any applications. Problem: Let $\{y_1 , y_2 , \dots, y_n \}$ be arbitrary (distinct) elements of...
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Is this morphism the normalization of P^1 in this curve up vote 2 down vote favorite 1 Let $S$ be an integral Dedekind scheme. Let $f:X\longrightarrow \mathbf{P}^1_{S}$ be a finite flat surjective morphism, where $X$ is an integral normal scheme. Let $\eta$ be the generic point of $S$. Note that $f_\eta:X_\eta\long...
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Long Numbers and Logarithms Date: 10/11/2002 at 20:05:43 From: Richard Subject: Numbers, exponents Hi, I have a problem figuring out how many terms are there when I raise a number to another large number or a large exponent. Is there a formula for these problems? Example: (12)^5 = 248832 There are 6 terms in...
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Quadratic Equation Pronunciation: /kwɒˈdræ tɪk ɪˈkweɪ ʃən/ ? ┌────────────────────────────────────────────────────────┐ ├────────────────────────────────────────────────────────┤ │Figure 1: Graph of the quadratic equation f(x) = x^2+2x.│ └────────────────────────────────────────────────────────┘ Manipulative 1: Quad...
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Finding Cartesian equation of parametric surface. October 6th 2009, 06:37 PM #1 Newbie Joined Oct 2009 Posts 1 Finding Cartesian equation of parametric surface. I'm a little confused with this problem. Find the Cartesian equation of the parametric surface: [2cos(t)cos(s), 3sin(s), sin(t)cos(s)] ...
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real analysis May 7th 2010, 04:21 AM abk6690 real analysis 1a) suppose that f is continuous on [a b] and differentiable on (a b) with f(a) = f(b) = 0. Show that for every k in R, there exists a c in (a b) with f '(c) = kf(c). (Hintconsider the function g (x) = exp^(-kx)f(x) for x in [a b] b) sho that f(...
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Uriel's Machine This page last modified 2003 January 23 Uriel's Machine — a Commentary on some of the Astronomical Assertions Uriel's Machine by Christopher Knight and Robert Lomas Arrow Books, London, 1999 ISBN 0-09-928182-1 This commentary will concentrate on the astronomical assertions used. I am not competent to...
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