Variables Definition and 1000 Threads

Homework Statement I'm doing a research project in which there's a survey given to respondents from 3 different groups of education(high school vs university etc) related to STD contraction rates. On the survey there's a question asking how many STD's they have contracted over their lifetime...

I'm having some difficulty setting up a problem. I'm trying to model the temperature of a thermistor connected to a constant current source. The thermistor's resistance varies with temperature, so with a fixed current, I would expect to see the thermistor's temperature to oscillate with time...

Suppose X ~ U[ 0, pi ] What is the distribution of Y=sinX. I have a solution in my notes however I don,t understand the following the second transition: F_Y(y) = P(Y \leq y) = P(X \leq \arcsin(y)) + P(X \geq \pi - \arcsin(y)) = ... Where the P(X \geq \pi - \arcsin(y)) comes from?

Hey guys, Can anyone help me out with these questions? The first one has a positive initial value. Separation of variables and integrating gave me: |y+3| = k√[(t^2) + 1)] Ultimately, I got k= √5 and thus y=√5√[(t^2) + 1)] - 3. Also, for the second one, I used a similar process, found...

I've been thinking about the Central Limit Theorem and by my understanding it states that the sum of randomly distributed variables follows approximately a normal distribution. My question is if you have, say, 100 uniformly distributed variables that range from 0 to 10, their sum has to be...

Write the restrictions on the variables for the following equation. Keeping in mind the restrictions, solve the equation 5/x=(10/3x)+4 Here is what I did, but I'm not sure if it's right. (3x)(5/x)=(3x)[(10/3x)+4] 15=(3x)(10/3x)+(3x)4 15=10+12x 5=12x x=5/12 But I don't know what to do...

I'm reading up on interpretations of quantum theory, and I just came across Bell's theorem, which is confusing me. My main concern is this: Why would quantum mechanics predict something different than hidden variables? I hope that question is coherent enough. I'm not sure if I'm using the...

I know the formula for a change of variables in a double integral using Jacobians. $$ \iint_{S}\,dx\,dy = \iint_{S'}\left\lvert J(u,v) \right\rvert\,du\,dv $$ where ## S' ## is the preimage of ## S ## under the mapping $$ x = f(u,v),~ y = g(u,v) $$ and ## J(u,v) ## is the Jacobian of the mapping...

Hi there! The question is: if I have to prove that a function is a change of variable it is sufficient to prove that the function is a diffeomorphism? i.e. prove that the function is bijective, differentiable, and its inverse is differentiable? Thanks!

Homework Statement Use the power series for e^z and the def. of sin(z) to check that sum ((-1)^k z^(2 k+1))/((2 k+1)!) Homework Equations The Attempt at a Solution I apologize, but I am not particularly good with latex. Therefore, I attached a picture of my solution thus far...

Homework Statement Trying to make sense of my notes... "A polynomial in n variables on an n-dimensional F-vector space V is a formal sum of the form: p(x)= ∑(C_i)x^β" so basically can somebody help me understand how polynomials represent vector spaces? Whatever degree the polynomial is...

I am trying to solve 3 non-linear system of 3 variables using the Newton-raphson method in matlab. Here are the 3 non-linear equations: \begin{equation} c[\alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I \alpha =0 \end{equation} \begin{equation} s[\lambda_b c P_C +\lambda_r (1-q)]- \lambda_b c P_C =0...

I am trying to solve 3 non-linear system of 3 variables using the Newton-raphson method in matlab. Here are the three equations: \begin{equation} c[\alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I \alpha =0 \end{equation} \begin{equation} s[\lambda_b c P_C +\lambda_r (1-q)]- \lambda_b c P_C =0 \end{equation}...

Hello, I have a tricky chain rule question, I think understanding it is more difficult than solving. For the function z=f(x,y) it is given that: f_{y}(0,-3)=-2 and \[f_{x}(0,-3)=3\] so for the function \[g(x,y)=f(2\cdot ln(x+y),x^{4}-3y^{2})\] choose the correct answer: (1)...

This problem: A random variable X has expected value E(X) = 6.2 and variance Var(X) = 0.8. Calculate the expected value of g(X) where g(x) = 7x + 2. Do I just plug in numbers here? I've never seen this kind of problem before.

If given three points ##P_0 = (x_0, y_0)##, ##P_1 = (x_1, y_1)## and ##P_2 = (x_2, y_2)##, the polynomial function ##f(x)## that intersect those points is ##f(x) = a_2 x^2 + a_1 x^1 + a_0 x^0##. where: ## \begin{bmatrix} a_0\\ a_1\\ a_2\\ \end{bmatrix} = \begin{bmatrix} x_0^0 & x_1^0 & x_2^0...

The three non-linear equations are given by \begin{equation} c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0 \end{equation} \begin{equation} s[2.001 *c + 835(1-q)]-2.001*c =0 \end{equation} \begin{equation} q[2.73 + (5.98*10^{10})c]-(5.98 *10^{10})c =0 \end{equation} Using the...

Homework Statement Show z(x,y) = cos(xy) is a solution of (∂z/∂x)y + (∂z/dy)x = (x+y) ( (∂2z/∂x∂y) + xyz) (question also attached if it makes it clearer) The Attempt at a Solution ∂z= (∂z/∂x)ydx + (∂z/dy)xdy ∂z/∂x = -ysin(xy) ∂z/∂y = -xsin(xy) what does it mean show it...

Hi, I've been running into a problem lately where I have a system of equations that needs to be solved or I need to do some other sort of matrix algebra, but the components of the matrix that I am trying to perform row operations on have unknowns in them. Specifically, I was working with a...

Homework Statement Use the change of variables ##u=x+y## and ##y=uv## to solve: \int_0^1\int_0^{1-x}e^{\frac{y}{x+y}}dydx Homework Equations The Attempt at a Solution So I got as far as: \int\int{}ue^vdvdu. But I just can't find the region of integration in terms of ##u## and ##v##.

Hi! I'm taking my first course in statistics and am hoping to get some intuition for this set of problems... Suppose I have a bowl of marbles that each weighs m_{marble}=0.01 kg. For each marble I swallow, there is a chance p=0.53 that it adds m_{marble} to my weight, and chance 1-p that...

I am writing a paper and I was using 'o' for a variable. Then I decided that it looked too much like '0', and thought I might use capital omega. How do I know when I should and should not use Greek letters? Thanks

Let L: R3 -> R3 be L(x)= \begin{pmatrix} x1+x2\\ x1-x2\\ 3x1+2x2 \end{pmatrix} find a matrix A such that L(x)=Ax for all x in R2 From what I understand I need to find the transition matrix from the elementary to L(x). However it is'nt a square matrix and it has variables instead of numbers...

Homework Statement Suggest a substitution/transformation that will simplify the following integral and find their jacobians: \int\int_{R}x\sin(6x+7y)-3y\sin(6x+7y)dA Homework Equations [ tex ] \int\int_{R}x\sin(6x+7y)-3y\sin(6x+7y)dA [ / tex ] The Attempt at a Solution This topic is...

For example the surface (x,y,x²+y²), can for example surfaces be considered as one abstract 'vector' in some abstract 'vector'-space? The ' ' because surfaces might not be a vector space. For surfaces we can exceptionally define normal vectors at every point.

Homework Statement these are on the picture Homework Equations transformation, jacobian The Attempt at a Solution I don't know how to enter the equation, so i uploaded the picture.. is it alright? I think I solved it somehow, but not quite sure if it is right... please tell me if there's a...

If a polynomial of 1 variable, for example: P(x) = ax²+bx+c, can be written as P(x) = a(x-x1)(x-x2), so a polynomial of 2 variables like: Q(x,y) = ax²+bxy+cy²+dx+ey+f can be written of another form?

Homework Statement find the solution to: \frac{\partial^{2}u}{\partial x \partial y} = 0 \frac{\partial^{2}u}{\partial x^{2}} = 0 \frac{\partial^{2}u}{\partial y^{2}} = 0 Homework Equations theorem of integration The Attempt at a Solution now from a previous question I...

Homework Statement if z = x2 + 2y2 , x = r cos θ , y = r sin θ , find the partial derivative [SIZE="4"]\left(\frac{\partial z}{\partial \theta}\right)_{x} Homework Equations z = x2 + 2y2 x = r cos θ y = r sin θ The Attempt at a Solution The textbook says that the equation...

Why is it assumed that the method of separation of variables works when the boundary conditions of some boundary valued problem are homogeneous? What is the reasoning behind it?

Homework Statement hello i need a pdf or a homepage where i can get all symbols (variables ) for Laser questions for example λ=Wavelength v=frequency ω=Beam waist Q= quality factor etc. i have a problem understanding some questions because i don't know which symbol they...

My question is on using a form of the single variable Noether's theorem to remember the multiple variable version. Noether's theorem, for functionals of a single independent variable, can be translated into saying that, because \mathcal{L} is invariant, we have \mathcal{L}(x,y_i,y_i')dx =...

suppose you have two random variables X and Y which are independent, we want to form a new random variable Z=XY, if f(x) and f(y) are density functions of X and Y respectively what is the density function of Z? I tried taking logs and applying convolution, but it did not really work

Homework Statement A uniform rod of length l has an initial (at time t = 0) temperature distribution given by u(x, 0) = sin(\frac{πx}{l}), 0 \leq x \leq l. The temperature u(x, t) satisfies the classical one-dimensional diffusion equation, ut = kuxx The ends of the rod are...

Why are y and y' treated as independent variables, while they are not? Another slightly related question: if ' = d/dt then df'/dg' = df/dg because f' = df/dg g', but if we differentiate f' to g' we implicitly assume that df/dg is independent of g', is it?

Hey! :o I have a question.. (Wasntme) When we have the following boundary value problem: $$u_{xx}+u_{yy}=0, 0<x<a, 0<y<b (1)$$ $$u_x(0,y)=u_x(a,y)=0, 0<y<b$$ $$u(x,0)=x, u_y(x,b)=0, 0<x<a$$using the method of separation of variables, the solution would be of the form $u(x,y)=X(x) \cdot Y(y)$...

Here is the question: I have posted a link there so the OP can view my work.

Homework Statement If X is a random variable uniformly distributed over (0,1), and a, b are constants, what can you say about the random variable aX + b? What about X^2? Homework Equations For uniformity of notation, let f(x) = probability density function of x F(a) = distribution function...

Hi, I need some clarification on exactly which critical points are saddle points. The definition I am finding everywhere is that "A saddle point is a stationary point that is neither a local minimum nor a local maximum." My question is: what kind of minimum and maximum is the above definition...

Hello I am trying to solve this integral 25-9x^2-25y^2/9 dydx integrating from 0 to sqrt(9-9x^2/25) and the limits of the second integration are 0 to 5. I can find tutorials on how to find the definite double integral of a single variable, but not for two variables. Any clues? edit: so far...

Homework Statement A grandfather clock has a pendulum that consists of a thin brass disk of radius r and mass m that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in...

Why variables (RHS) in directly proportionality are always multiplied. Suppose the Newton 2nd law ##{F}\propto{m}## ##{F}\propto{a}## ##{F}\propto{m*a}##

Homework Statement Handle all possible exceptions for a program that takes two int number from the user and print sum. Homework Equations The Attempt at a Solution import java.util.Scanner; public class Task1 { }

f(x,y) = ln(9 - x2 - y2) Domain I got: (x, y) in R2 such that x2 + y2 < 9 How do I find the range from the domain? Wouldn't it be all positive numbers of ln such that it is less than ln(9)? Answer says less than or equal to 9, I don't get why. Any input is appreciated!

Suppose we have a function ##F:\mathbb{R}_+\to\mathbb{R}_+## such that ##\frac{F(y)}{y}## is decreasing. Let ##x## and ##y## be some ##\mathbb{R}_+##-valued random variables. Would ##\mathbb{E}x\leq\mathbb{E}y## imply that ##\mathbb{E}F(x)\leq\mathbb{E}F(y)##?

Homework Statement I hate to upload the whole problem, but I am trying to evaluate an indefinite integral, and I can follow the solution until right near the end. The example says that for a point on C_R|e^{-3z}|=e^{-3y}\leq 1. I don't understand how they can say this. Below is the question...

Simplify 1) Simplify and state any restrictions on the variables: $$\frac{3a-6}{a+2} ÷ \frac{a-2}{a+2} $$ This is what I did. Can someone tell me what I did wrong? Thanks. $$\frac{3a-6}{a+2} ⋅ \frac{a+2}{a-2} $$ $$\frac{3a^2-12}{a^2-4}$$ $$\frac{(3a+6)(a-2)}{(a+2)(a-2)}$$...

Simplify and state any restrictions on the variables: $$\frac{2(x+1)}{3} ⋅ \frac{x-1}{6(x+1)} $$ This is what I did, which is wrong (according to the textbook). $$\frac{2}{3} ⋅ \frac{x-1}{6}$$ $$\frac{2x-2}{18}$$ $$\frac{2(x-1)}{18}$$ Can someone tell me what I've done wrong? Also, how...

I'm not really sure where to put this, it's from an MCR3U course(Advanced Functions): Simplify and state the restrictions on the variables. a) (3x)2/4xy * 16y/36x I got as far as = 12xy2/36x2y = Xy2/3x2y = 3x-1y but I don't really know how to state the restrictions. Thanks in advance.

I need to define some "general" variables in Mathematica 8, and I wonder if this can be done the following way. Say ta[n] and tb[m] are my variables, in turn depending on n and m. I want to define a function, for example E[ta[n]_ , tb[m]_ ] := Cos[ ta[n] ] + Sin [tb[m] ] (just a simple...