Proof Definition and 999 Threads

Hi all, Can you guys provide a proof of the conservation of etendue (simple/memorable is preferred, if possible!) and a few realistic, practical examples just so I can get the hang of the ideas and the calculations? Much appreciated.

Hello. I have a question about a step in the factorization theorem demonstration. 1. Homework Statement Here is the theorem (begins end of page 1), it is not my course but I have almost the same demonstration : http://math.arizona.edu/~jwatkins/sufficiency.pdf Screenshot of it: Homework...

I am struggling with this question, it would be easy enough if the triangle was equilateral but that is not necessarily the case. Let (ha, hb, hc) be heights in the triangle ABC, and let Z be a point inside the triangle. Further to this, consider the points P, Q, R on the sides AB, BC and AC...

Hi,I have been stuck on this problem The midpoints of the sides AB and AC of the triangle ABC are P and Q respectively. BQ produced and the straight line through A drawn parallel to PQ meet at R. Draw a figure with this information marked on it and prove that, area of ABCR = 8 x area of APQ. I...

Can anyone solve the following question Please try to make you answer detail as possible :)

Homework Statement 2. Homework Equations Vieta's formula, quadratic discriminant 3. The Attempt at a Solution

While deriving ideal gas equation - we take gas molecules to be contained in a cubical container (convinent shape) , but how do we derive it for a gas inside some arbitarily shaped container ? i think this has 2 answers 1) Using maths - but it will be mostly impossible 2) or it will be a...

a and b are integers Prove that: 2ab <= a2 + b2 I have tested various values for a and b and determined that the statement seems to be generally true. I'm having a hard time though constructing a formal proof. It will not do to suppose the statement is wrong and then provide a counterexample...

Homework Statement Let A be a dense set**. Prove that if f is continuous and f(x) = 0 for all x in A, then f(x) = 0 for all x. **A dense set is defined, in the book, as a set which contains a point in every open interval, such as the set of all irrational or all rational numbers.Homework...

Is there a mathematical proof for the existence of black hole.

This is not a homework question. School year has ended for me and I'm doing some revision on my own. I want to proof the following because in an exercise I had to find the equation of the line that passed through a given point and 2 given lines. If a line r intersects with 2 given crossing...

Homework Statement In Griffiths Introduction to Quantum Mechanics textbook, he shows that for any wave function that is time-dependent (which implies that the state of any particle evolves with time), the wave function will stay normalized for all future time. There is a step in the proof that...

Homework Statement : the question wants me to prove that the limit of f(x,y) as x approaches 1.3 and y approaches -1 is (3.3, 4.4, 0.3). f(x,y) is defined as (2y2+x, -2x+7, x+y). [/B] The attempt at a solution: This is the solution my lecturer has given. it's not very neat, sorry...

Hello, I have a question about Heine Borel Theorem. First, I am not sure why we have to show "gamma=Beta" gamma is the supremum of F(which is equivalent to H_squiggly_bar in the text ), and it has to be greater than beta. Otherwise, S contains H_squiggly_barSecond, for the case 1, why...

I have a hard time understanding the variation of mass with velocity, more precisely the proof. In almost every material I've found, the author analyses 2 bodies colliding. The idea of looking at the collision is not hard to grasp and by considering one of the velocities equal zero, you get a...

I was reading this book yesterday and looking at this proof/justification. I was thinking it is possibly incorrect, but wanted to get some other opinions. Here is the example they gave in the book with the work attached.

Hi, this may seem like an odd questions to most of you but I'd still like to ask what could be some visual proofs of being at high altitude, say 10,000 feet above sea level. While any said proof is not extremely rigorous or untamperable and probably little more than a showy capture to add to...

Homework Statement Consider the table: 1 = 0 + 1 2 + 3 + 4 = 1 + 8 5 + 6 + 7 + 8 + 9 = 8 + 27 10 + 11 + 12 + 13 + 14 + 15 + 16 = 27 + 64 Guess the general law suggested by these examples, express it in suitable mathematical notation, and prove it. Homework Equations [/B] It's clear that if...

Homework Statement let be ABC a generic triangle, build on each side of the triangle an equilater triangle, proof that the triangle having as vertices the centers of the equilaters triangles is equilater Homework Equations sum of internal angles in a triangle is 180, rules about congruency in...

Homework Statement I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently...

Hi all, I'm slowly working through "Mathematical Methods in the Physical Sciences" by Mary Boas, which I highly recommend, and I'm stumped on one of the questions. The problem is to prove the double angle formulas sin (2Θ)=2sinΘcosΘ and cos(2Θ)=cos2Θ-sin2Θ by using Euler's formula (raised to...

Homework Statement I am posting this for another student who I noticed did not have the proof in the problem. Here is what she said. Let's try and help her out. I have been working on the problem below and I am stuck. I am stuck primarily because of the part where is says x=0. If x-0, it...

Very curious. Is there a supply and demand imbalance? When there is a recession and businesses are stagnant and new ones aren't starting up, how do accountants still get good work?

Hello, i'm trying to prove this statements, but I'm stuck. Be ##V=R^n## furnished with the standard inner product and the standard basis S. And let W ##\subseteq## V be a subspace of V and let ##W^\bot## be the orthogonal complement. a) Show that there is exactly one linear map ##\Phi:V...

Homework Statement Hey guys. I am having a little trouble answering this question. I am teaching myself calc 3 and am a little confused here (and thus can't ask a teacher). I need to find the limit as (x,y) approaches (0,1) of f(x,y) when f(x,y)=(xy-x)/(x^2+y^2-2y+1). Homework Equations...

I mean, look this stupidity: [Mentor's note - link to crackpot site deleted] This guy denies that light photons exist, and that we are 'magically creating it' like cyclops X-Men This is worst than flat-earthers, I wonder If there is some evidence or is it unfalsifiable, like solipsism? Because I...

Homework Statement The signum function is defined by$$sgn(t)=\left\{\begin{matrix}-1, \ t<0\\0, \ t=0 \\ 1, \ t>0 \end{matrix}\right.$$It has derivative$$\frac{d}{dt} sign(t) = 2 \delta(t)$$Use this result to show that ##j2\pi \nu S(\nu)=2,## and give an argument why ##S(0)=0.## Where...

The following identity is found in a book on Turbulence: Can someone provide a proof of this identity? It isn't listed in the list of vector calculus identities on Wiki. Thanks

Hello, I started to learn divergent series/sums, to practice I calculated some basic ones, you know: 1+2+3+4+5+6...= -1/12, but I really had problems when i tried to demonstrate that 1+4+9+16+...= 0(the sum of squares of natural numbers), I've tried to add, subtract etc, but I couldn't prove it...

I developed two algorithms for calculating the density of close packed congruent identical spheres in two different arrangements: A tetrahedron with four equilateral triangular faces, and A square pyramid with a square base and four equilateral triangular faces, as shown below. Figure...

Homework Statement Consider the bivariate vector random variable ##(X,Y)^T## which has the probability density function $$f_{X,Y}(x,y) = \theta xe^{-x(y+\theta)}, \quad x\geq 0, y\geq 0 \; \; \text{and} \; \; \theta > 0.$$ I have shown that the marginal distribution of ##X## is ##f_X(x|\theta)...

I'm reading "Time Series Analysis and Its Applications with R examples", 3rd edition, by Shumway and Stoffer, and I don't really understand a proof. This is not for homework, just my own edification. It goes like this: Σt=1n cos2(2πtj/n) = ¼ ∑t=1n (e2πitj/n - e2πitj/n)2 = ¼∑t=1ne4πtj/n + 1 + 1...

Homework Statement Prove that ##{1/3} < log_{34} 5 < {1/ 2}## Homework Equations ##log_b a = {1/ log_a b}## ##logmn = logm + logn##The Attempt at a Solution ##log_{34} 5 = {1/ log_5 34}## ##= 1/(log_5 17 + log_5 2)## ##=1/(1 + log_5 3 + log_5 2 + something)##...

the first step of the Plancherel's Theorem proof found in: http://mathworld.wolfram.com/PlancherelsTheorem.html, says: let be a function that is sufficiently smooth and that decays sufficiently quickly near infinity so that its integrals exist. Further, let and be FT pairs so that...

I am currently working my way though Calculus by Tom Apostol. One of the really early proofs ask the reader to prove: a(b-c)=ab-ac. Here is what I did, I let x=b-c which by the definition of subtraction equals x+c=b. Substituting that value into the right hand side I got...

Hi. I'm trying to proof the image formation property of a concave spherical mirror. I know you can do this easily with a particular choice of rays (namely one that hits the vertex and one that passes through the center of the sphere) but I would like to show that a generic ray yields the same...

Homework Statement Prove the following statement: Let f be a polynomial, which can be written in the form fix) = a(n)X^(n) + a(n-1)X^(n-1) + • • • + a0 and also in the form fix) = b(n)X^(n) + b(n-1)X^(n-1) + • • • + b0 Prove that a(i)=b(i) for all i=0,1,2,...,n-1,n Homework Equations 3. The...

Can somebody confirm if this is correct? I'm trying to use a wye-delta transformation on capacitors to solve for equivalent capacitance, but to be super-precise, I want to put capacitance in terms of resistance. I = C*(dV/dt) V = IR, so I = V/R V/R = C*(dV/dt) (V*dt) = R*C* dV Integrate both...

Homework Statement , relevant equations, and the attempt at a solution are all in the attached file. I was reading through Invitation to Discrete Mathematics and attempted to solve an exercise that involved a proof. I've typeset everything in LaTeX and made a PDF out of it so that it does not...

Hello friends (I hope :biggrin:), For a maths project I am working on, I need to be able to prove the equation for an elliptical orbit, related to Kepler's first law: and p = a(1-e2) (or should be as p can be replaced by that value) Where: r = distance from sun to any point on the orbit p =...

Homework Statement Let σ : Z_11 → Z_11 be given by σ([a]) = [5a + 3]). Prove that σ is bijective. Homework EquationsThe Attempt at a Solution I am just wondering if I can treat σ as a normal function and prove that is bijective by using the definitions of one to one and onto.

Homework Statement Let X be a set and R ⊂ X × X. Assume R is an equivalence relation and a function. Prove that R = I_X, the identity function. Homework EquationsThe Attempt at a Solution Proof We know that R has to be reflexive, so for all elements b in X, bRb but b can't be related to any...

I had a thought about electric fields created by charges Look at this picture: Point ##B## is at the half the distance between ##q## and ##2q##. What I am trying to prove/disprove That there might be actually a point (##A##) near of charge ##2q## that might have an electric field stronger than...

In "The Theoretical Minimum" of Susskind (p.98) it says that if we take any two basisvectors |i \rangle and |j \rangle of any orthonormal basis, and we take any linear time-development operator U, that the inner product between U(t)|i \rangle and U(t)|j \rangle should be 1 if |i \rangle=|j...

Homework Statement Prove the following: Let V be a vector space and assume there is an integer n such that if (v1, . . . , vk) is a linearly independent sequence from V then k ≤ n. Prove is (v1, . . . , vk) is a maximal linearly independent sequence from V then (v1, . . . , vk) spans V and is...

Homework Statement Prove the following theorem: Let (v1, . . . , vk) be a sequence of vectors from a vector space V . Prove that the sequence if linearly dependent if and only if for some j, 1 ≤ j ≤ k, vj is a linear combination of (v1, . . . , vk) − (vj ). Homework EquationsThe Attempt at a...

Homework Statement I'm doing quite a strict proof in school. Where we should proof something and use mathematical language and symbols. Homework Equations The Attempt at a Solution To proof what I have to proof I need to draw some help lines. As for instance the "red" one I did from A to B...

In Charles Murray's book Real Smart: Four Simple Truths For Bringing America's Schools Back To Reality, Murray writes about the postmodernists in literary criticism. His description really gets my interest. I think it would be interesting and perhaps amusing (I have a strange sense of humor)...

Homework Statement z1, z2 are complex numbers. If z1z2 =/= -1 and |z1| = |z2| = 1 then number : z1 + z2 ________ 1 + z1z2 is real. Homework EquationsThe Attempt at a Solution z1 = (a+bi), z2 = (c+di)[/B] Should i use this extended form or is there a shorter...

Homework Statement Let X = {1, 2, 3, 4, 5, 6}. Determine the number of relations on X which are reflexive and anti-symmetric Homework EquationsThe Attempt at a Solution This problem looks a little bit hard. Approach: consider R={(x,x),... } If there is just one pair in the relation in the...