Variables Definition and 1000 Threads

What variables are maximum at amplitude and equilibrium? What variables are minimum at amplitude and equilibrium? I'm confused about this topic... I know KE is max at equilibrium and PE is max at amplitude.

Solve the following system for x and y in terms of a and b where $ab\ne - 1$ $\left\{{\frac{x+y-1}{x-y+1}=a \atop\frac{y-x+1}{x-y+1}=ab}\right.$ Answer is $x=\frac{a+1}{ab+1}\\y=\frac{a\left(b+1\right)}{\left(ab+1\right)}$ I tried for a hour and? Noticed the denominators were = but?

So It is well known that the 2D solution to the Laplace equation can be obtained by changing to complex coordinates ##u=x+iy## and ##v=x-iy##. This can be extended to n dimensions as long as the complex coordinates chosen also solve the Laplace equation. For example in 3D...

I was reading a book on differential equations when this(taylor expansion of multi variables) happened. Why does it not include derivatives of f in any form? The page of that book is in the file below.

I have a question for determining the limit of a function with two variables. My textbook says that the limit (x,y)->(0,0) of 4xy^2/(x^2+y^2)=0. This is true if we evaluate the limit if it approaches along the x-axis (y=0) or the y-axis (x=0) or any line on the plane y=kx. I am wondering if...

Consider the below recurrence ##T(n) = 2 T(\sqrt(n)) + \log n## substituting ##\log n = m \implies n = 2^m## ##T(2^m) = 2 T(2^{\frac{m}{2}}) + m## substituting ##S(k) = T(2^m)## I'm getting below equation ##S(k) = 2 S(\frac{k}{2}) + m## How can I change 'm' to 'k' in above equation.

In his book, Euler gives the definition of a variable to be : "A variable quantity is an indeterminate or universal quantity, which includes within itself all completely determined values." What does he mean exactly in the last part of the sentence?

[Mentor's note: Moved from a thread about field theories as this is just about the basic meaning of the theorem for ordinary entangled particles]] Suppose that there are photon spin outcomes that are pre existing from entanglement or from local hidden variables. For every detector angle...

Hi, I saw a derivation in a book and I don't see the logical connection. Suppose 1.\ \ a=b \text{ and } 2.\ \ x=y Then 3.\ \ a-b= \lambda (x-y) makes sense to me since 0=\text{Anything}⋅0 However they said "similarly" 4.\ \ a+b= \mu (x+y) , and this I don't understand. To me a+b= 2a...

We have a function: ##\phi'(t',x')##. We want to find: ##\frac{\partial\phi'}{\partial x}##. I know that the answer is: ##\frac{\partial\phi'}{\partial x} = (\frac{\partial\phi'}{\partial t'} \cdot \frac{\partial t'}{\partial x}) + (\frac{\partial\phi'}{\partial x'} \cdot \frac{\partial...

Homework Statement A solid has energy (for one mole): ##U_1 =\frac{S^2}{a_1}+b_1V(V-2V_0)## Write H, F, and G in terms of their proper variables. Homework Equations Maxwell's relations and H=U+PV F=U-TS G=U-TS+PVThe Attempt at a Solution [/B] H, for example: I have tried writing dV as a...

Homework Statement Supposethat X1and X2 are .random variables and that each of them has the uniform distribution on the interval [0, 1]. Find the p.d.f. of Y =X1+X2. Homework Equations Find cdf of Y and then the pdf The Attempt at a Solution the joint pdf would be f(x1,x2)= 1...

I need to get something cleared up. Let's say we have the equation ##x = 1##. For this equation, the solution set is {1}. However, if I do the valid operation of multiplying both sides by x, we get ##x^2 = x##. Now the solution set is {0, 1}. Additionally, if I take the original equation and...

Homework Statement Consider the polynomial ##p(x) = x^4 + ax^3 + bx^2 + cx + d##, where a, b, c, d ∈ ℝ. Given that 1 + i and 1 - 2i are zeroes of p(x), find the values of a, b, c and d. Homework EquationsThe Attempt at a Solution Since 1 + i and 1 - 2i are zeroes, I believe it follows that 1...

Homework Statement I have the joint cdf of two random variables X and Y and they ask me to find the cdf of just Y. I know that you just take the limit of the cdf as x->infinity, but I am just wondering if you can also do this by calculating the joint pdf and then the marginal of Y and then from...

Yes, please help me solve! Explain it very explicitly with equations and not just text. 1) Find the combination of K and L that ensures the maximum profit and find the maximum profit. The profit is given by the following function:where:

I only really need help evaluating the contour integral. I added more detail for completeness. 1. Homework Statement A particle of mass ##m## is constrained to move on the ##x## axis subject to the following potential. V(x)=a \sec^2\left( \frac{x}{l} \right) Find the action angle variables...

Homework Statement Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from radiation spectra. I am having trouble finding information on how to calculate and propagate errors when the quantities in my equations are not independent...

Homework Statement Consider two random variables X and Y with joint PMF given by: PXY(k,L) = 1/(2k+l), for k,l = 1,2,3,... A) Show that X and Y are independent and find the marginal PMFs of X and Y B) Find P(X2 + Y2 ≤ 10) Homework Equations P(A)∩P(B)/P(B) = P(A|B) P(A|B) = P(A) if independent...

Homework Statement I need to find the absolute extrema of the function in the specified region f(x, y) = x^2 + xy R = {(x,y): |x|<=2, |y|<=1}The Attempt at a Solution The first partial derivatives are fx(x,y) = 2x+y and fy(x,y) = x They are both 0 only when x and y are both 0. So...

Homework Statement The wave equation for ψ(t, x) in 3D is ##\frac{\partial ^2 \psi}{\partial t^2}## - Δ ##\psi =0## Let ϒ(x) satisfy Δϒ = λϒ where λ<0. The x is in bold presumably to indicate it is in 3D, so represents also y and z? Show there is a solution of the form ψ(t, x) = sin(ωt)ϒ(x)...

Homework Statement The wave equation for ψ=ψ(t,x,y) is given by ##\frac{\partial ^2 \phi}{\partial t^2} - \frac{\partial ^2 \phi}{\partial x^2} - \frac{\partial ^2 \phi}{\partial y^2}## Use separation of variables to separate the equation into 3 ODEs for T, X and Y. Use the separation...

I just wanted to check something. The equation ∂2φ / ∂x2 + ∂2φ / ∂y2 = sin(xy) Was given as an example of a separable equation. I can't separate it, and I found online that to use separation of variables the equation should be linear, which this isn't? Is there a way of separating this?

A rock is dropped from a cliff of height h. At the same time a rock is thrown straight up from the bottom with an initial velocity. Assuming they meet, at what time will they meet. V1 = 0 A = -9.82 Thats all you have across both rocks... is this even possible. You probably have to do some...

Umm from memory I used to use...that triangle: 1 1 1 1 2 1 1 3 3 1 Fibonachii was it? Pathetic I can't even remember the name. To factorise...or was it expand...polynomials...anyway, I don't think that's elevant here. My question is; I had an...

Variable; A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable. [mathsisfun.com] Q. Why is it called the variable? This seems to me to imply that its value varies. In the above example it seems to me to simply be the unknown...

I am searching for a site that enables me to plot a function of multiple variables in 3D form. Say f(x1,x2,x3,x4) and I wish to plot this function as a 3D graph for x1 and x2 where x3 and x4 are kept constant.

Hi I'm having a few conceptual difficulties with random variables and I was hoping someone could clear up a few things for me: 1) Firstly, what exactly do we mean when we say that two random variables X and Y are equal. I understand what identically distributed means, but my difficulty is with...

This question arose as I was studying mathematical modeling in fluid mechanics. It was posted to math.stackexchange, but there a was a lack of response, probably due to the applied nature of the problem. One form of the Buckingham Pi Theorem says that for nn variables with kk dimensions, the...

Hello! I'm in the process of simplifying an equation at the moment. The question I have is: How do you select the variables when building an equation? For instance if I'm trying to explain "fastest observed velocity of matter" which letter or symbol do I use? Is there a list somewhere I'm...

Homework Statement A potential satisfies ##\nabla^2 Φ = 0## in the 2d slab ## -\inf < x < \inf ##, ##-b < y < b ##, with boundary conditions ## Φ(x, +b) = +V_s(x)## on the top and ##Φ(x, b) = -V_s(x)## on the bottom, where[/B] ##V_s (x)= -V_0 for -a<x<0## ##V_s (x)=+V_0 for 0<x<a## (a) what...

Homework Statement You are the chief of the Angry Birds (Google it, if you don’t know the reference...it’s not important). You can shoot red birds from a catapult, and they will fly as projectiles under the effect of gravity. Gravity points downwards and has magnitude g = 9.80 m/s2 . Your goal...

Homework Statement Find the domain and range of the following function: f(x, y) = ln(x+y) Homework EquationsThe Attempt at a Solution I know that the natural log ln(x) is only defined when x>0, so does that mean that ln(x+y) is only defined when x+y>0? Also, would the range just be all positive...

Homework Statement A square is made up of four plates with a potential of zero on the top and bottom plates at (x,L/2) and (x,-L/2), and a potential of cos(πy/L)+cos(3πy/L). Find the potential and electric fields inside the square. The Attempt at a Solution I start with...

Does anyone know any very simple to operate (intuitive) software for graphing polynomials in two variables. If the software allows you to plot two polynomials simultaneously then all the better ... Be a bonus if it allowed the finding of zeros also ... Peter

## \int_{0}^{∞}\int_{0}^{∞} \frac{x^2+y^2}{1+(x^2-y^2)^2} e^{-2xy} dxdy ## ##u= x^2-y^2## ##v=2xy##I tried to find the jacobian and the area elements, I found it to be ## dA = \frac{1}{v} du dv ## I'm having problem finding the limits of u & v and getting rid of ##x^{2}+y^{2}##.

I am just getting into C++ and I would like to ask you guys for some help regarding transferring variables form one function to another. Is there any way I can declare a variable such that it can be referenced and changed throughout all the programs functions? Thanks.

Does QM uncertainty cause/explain the Second Law of Thermodynamics? If so is entropy the contribution of hidden variables, to our classical world? How about negentropy? http://arxiv.org/abs/quant-ph/0605031 Irreversibility in Collapse-Free Quantum Dynamics and the Second Law of Thermodynamics...

I need to show that the following expression, $$a^3b-a^3c+a^3z+a^3x+a^3y-a^2bx+a^2by+a^2cx-a^2cy-a^2zx+a^2zy-a^2x^2+a^2y^2-abcz-abcx-aczx-acx^2+b^2c^2+2bc^2x+c^2x^2-b^2c-2bcx-cx^2,$$ is positive given that: $1.$ $\ a,b,c,x,y,z$ are positive real numbers $2. \ \ a>b+x$ $3. \ \ c<b+y$ I...

U = A a² V = 2 A a b W = A b² u = 2 A a c + B a v = 2 A b c + B b w = A c² + B c + C I'd like to solve this system for A, B, C, a, b, c. Is it possible!?

So the thing I have issues with in this problem is that it's about 2 particles traveling relative to each other. Been going though the basics of relativity, relativistic lengths, times, kinetic energy, work and force. But this problem states two particles and I'm not sure how to approach it. The...

Sorry for the disturbance, So I have been looking (without success) for a way to define a variable within an implicit function in Java. What I really mean by this is I have the equation: In this function my program will give me all of the values except for px. I have tried rearranging the...

this is the gyroscope I am talking about: the variables are: -the angular velocity of the disk -the angular velocity of precession -the amount of force "applied" by the disk upward or downward

This is not really a homework or anything, just found myself hitting a wall when doodling around. If I have an integral like ##\int_{-1}^{0} x(x^2-1) dx## and I introduce a new variable: ##u = x^2## How do I calculate the limits of the new integral? In this case the upper limit is obviously 0...

I want to evaluate \displaystyle\lim_{(x,y)\to(-1,0)}\frac{y^4(x+1)}{|x+1|^3+2|y|^3} With some help, I was able to prove that the limit is 0, using Hölder's inequality. Like this: \left(|x+1|^3\right)^{1/5}\left(\frac{1}{2}|y|^3\right)^{4/5}\leq\frac{1}{5}|x+1|^3+\frac{4}{5}\frac{1}{2}|y|^3...

1. Given, x + yi = tan^-1 ((exp(a + bi)). Prove that tan(2x) = -cos(b) / sinh(a)Homework Equations I have derived. tan(x + yi) = i*tan(x)*tanh(y) / 1 - i*tan(x)*tanh(y) tan(2x) = 2tanx / 1 - tan^2 (x) Exp(a+bi) = exp(a) *(cos(b) + i*sin(b))[/B]3. My attempt: By...

Hi everyone - I guess this will be a very basic question for you guys, but I'm no statistician and I need your advice, please. At work (drug discovery, medicinal chemistry) we often get a lot of data, and we expect to find correlations between them. I'm afraid we're not always as good as we...

Say I have a basic slingshot (like an elastic band attached to a 'Y' shaped stick), what variables do I need to consider when calculating its ability to launch an object into the air? So for example, say I load a mass, m, into a slingshot, pull the elastic band back x metres, and then release...

Dear all, I'd like to know what is the place/use of complex variables (and complex analysis) in classical mechanics. By the way, is there any? Thanks for your help. Best regards!

Homework Statement This is a theoretical question from my homework. We did a lab in class where we were using motion to see how kinetic friction is affected by different variables. We found the acceleration of a sliding wooden block (sliding on another wooded block), and then used that...