Variable Definition and 1000 Threads

Homework Statement If the probability density function(p.d.f.) of a random variable X is f(x) = 1/6 * e-|x|/3 where x is lying in (-∞,∞) and |-x| = x if x≥0, then what is the p.d.f. of the random variable Z = XY = X*|X| where Y = |X| ? Homework Equations Nothing special. The Attempt at a...

Hi, I am sure there must be something already on here about this kind of thing so if you could point me in that direction that is fine, or to a site anywhere. Basically I have three columns of data, let's say Column A, Column B and Column C. Column A is dependant upon both Columns B & C...

Hello every body, I am simulating a 1 dof spring-mass model in ansys workbench. I need to change the stiffness of spring at every substep based on an "if condition". It means that, in every substep, if a specified condition is satisfied, the stiffness will be changed to a defined value. Also...

Like in the integration, exist a formula to compute the summation by parts, that is: \frac{\Delta }{\Delta x}(f(x)g(x))=\frac{\Delta f}{\Delta x}g+f\frac{\Delta g}{\Delta x}+\frac{\Delta f}{\Delta x}\frac{\Delta g}{\Delta x}\sum \frac{\Delta }{\Delta x}(f(x)g(x))\Delta x = \sum \frac{\Delta...

Hello, my question is a simple one: I am attempting to do problem 2.31 in Griffiths' QM book (latest edition). The question states, "The Dirac Delta function can be thought of as the limiting case of a rectangle of area 1, as the height goes to infinity and the width to zero. Show that the...

I was forced into learning Java. I feel reasonably fluent in C++, so the main problem is with the differences between the way languages are designed. There are no global variables in Java. However, I need one - or at least some equivalent. I have something like a database object that I want...

Homework Statement Find the conditional distribution function and density for the random variable X defined on R given that X is in some interval I = (a,b) where P(X in I) > 0. Assume that the density and distribution for the random variable X is known Homework Equations fX|X\inI =...

Homework Statement |1 0-1-2-8 | -3| |0 0 1 2 7 | 1| |0 0 0 1 -4 | -13| I think that x_{2} is a free variable, so when writing the general solution in a solution set, what would I put for it? Nothing?

Hello, I have a question with regards to solving problems that require knowledge of which variable is dependent and which is independent. Suppose I am presented with the differential equation x^5 y^{(4)} - x^3 y'' + 6y = 0; for this differential equation I am asked to determine if it is linear...

Homework Statement The problem is attached. Homework Equations The Attempt at a Solution I've been trying to take the Log for both sides but the problem is I have (1+0.05X) if I just have e^-0.1 X, I will take Log for both sides and solve it but in this case I have (1+0.05X) too...

Hi all, I'm working on designing a variable inductor using a ferrite core. The basic idea is that I have a large wound inductor on the central arm which I pass a DC-current through, and a smaller, variable inductor on one of the side arms. As you increase the current through the main winding...

I'm having some issues with the rocket equation. I'm deriving the velocity as a function of time for a descending rocket (so the rocket is accelerating upwards in order to slow the descent). The result I should obtain is v=v0+gt+uln(mf/mi) where mf is the final mass, mi is the initial...

I've been relearning c++ and my friend gave me a problem to try and solve programmatically. Here is the set up: There is a pitcher with a gallon of water. The water is being poured out beginning at a rate of 2x milliliters per second. x begins at 1 and increases by 1 over 5 seconds. The...

Suppose we consider the measurement of A\otimes B-A\otimes B'+A'\otimes B+A'\otimes B'at angles 0, 45, 90, 135 degrees. If there exist a non-local variable that determine the result of the pair of result, then one gets for result of measurement 0, 4, -4 Whereas in quantum mechanics, the...

The line with equation y = x + k, where k is a real number, intersects the parabola with equation y = x^2 + x − 2 in two distinct points if I first made the equations equal each other x + k = x^2 + x − 2 0 = x^2 -2 -k From here i thought you use the discriminate a=1 b=o c=-2-k but this...

I have an equation, where acceleration is affected by a driving power and air resistance. The acceleration is given by: a = (2P / m + u^2)^0.5 - (k*p*A*u^2 / 2m) - u I'm trying to make "u" the subject, which is previous velocity, to find at what velocity does acceleration become 0, the...

Hello I am trying to solve this problem: A coin is given with probability 1/3 for head (H) and 2/3 for tail (T). The coin is being drawn N times, where N is a Poisson random variable with E(N)=1. The drawing of the coin and N are independent. Let X be the number of heads (H) in the N draws...

This question is from the parametric equations chapter of my calc book. I am given x =\frac{1}{\sqrt{t+1}} and y = \frac{t}{t+1}, for (x> -1) Solving the x(t) for t, we get \frac{1- x^{2}}{x^{2}} Eliminating the parameters by substitution, we get y = 1 - x^{2} for (x > 0) My question is...

Homework Statement A couple is expecting the arrival of a new boy. They are deciding on a name from the list S = { Steve, Stanley, Joseph, Elija }. Let X(ω) = first letter in name. Find Pr(X = S). Homework Equations The Attempt at a Solution Ok the answer is 2/3. How is it 2/3...

Simple C programming problem, variable "stuck" at initialised value Hello! This is most likely an error in my code but I just can't see what it is! I am new to C programming and maybe I have just been staring at it for so long that I can't see the obvious error. I was playing around with a...

Homework Statement ind the absolute minimum value of the function f(x,y) = 6 + 3xy -2x- 4y on the set D. D is bounded by the parabola y=x^2 and y=4 Homework Equations Partial derivatives and a theorem where if F is continuous on a closed bounded set in R(2) then F has an abs. max and...

Knowing that the limits of integration of a any function, for example: \int_{-\infty}^{+\infty}\delta (x)dx=1 I know that's correct call your primitive through the limit superior as a variable, so H(x)=\int_{-\infty}^{x}\delta (x)dx But, and if I want to describe your primitive through the...

What sort of company would I contact to have something like this made? I am looking to have made a Variable DC power supply capable of outputting up to 300-400 amps and up to 30v(and as little as well below 1 into the decimal region). Preferably as small as possible. My only requirements for...

Homework Statement Evaluate the following integral with a change of variable of your choice. \int_0^{1} \int_y^{y+2} \sqrt{(x-y)}dxdy The Attempt at a Solution I'm supposed to choose a u and v that will simplify the integral, but I have no idea how to even start this. I tried...

Homework Statement Let F: X x Y -> Z. We say F is continuous in each variable separately if for each ##b \in Y## the function h: X -> Z, h(x) = F(x,b), and for each ##a \in X##, the function g: Y -> Z, g(y) = F(a,y) is continuous. Show that if F is continuous, then F is continuous in each...

I don't have any big programs. I just write programs to get me through my math classes. But I want to have the output look pretty. Like one program I have is for my finance class. prompt p if p = 1 then Prompt b,r,n,t r/100→x b/(1+x/n)^(n*t)→l disp l else Prompt b,r,n,t r/100 →...

For example, let's say there was an block infinitely long in the x and y direction and in the z direction bounded by positive and negative a. I am trying to find the charge of a imaginary partition infinitely long in the x and y direction and in the z direction bounded by positive and...

Hello, I have some data that I am looking into correlation factors (Pearson). Let's say I have two data sets: X and Y. I have Graph X vs. Y then graph 1/X vs. Y. The reciprocal (1/X) yields a more linear relationship. Why does this occur? Thanks in advance!

hi guys, i am going to machine aluminum using EDM die sinking to study the MRR, TWR and Surface finish. i have read many papers where "One Variable at a Time Approach is used" but do not understand how the input parameters are chosen or i can choose them randomly? thanks

While doing work, I always see notation like: F(x) = ∫0xf(t)dt - first equation F(x) = ∫1xf(t)dt What is the exact reasoning we always use the upper limit? What is the lower limit was a variable? From FTC 2, the answer for the first equation is F(x) - F(0) right yet is written as F(x) when...

Homework Statement This is an Optimization Problem, find the maximum value. P(R)=(E^2*R)/(R+r)^2 Homework Equations P'(R)=? The Attempt at a Solution I have the solution to this problem, and I can solve it, I just don't understand some parts. I tend to think that the...

Homework Statement A box with one corner at the origin and the opposite corner at (a,b,c). The density is:##\rho=\rho_o\frac{z^2}{c^2}## Homework Equations ##r_{cm}=\frac{\int\vec{r}dm}{\int dm}## The Attempt at a Solution I calculated the mass...

Brand spanking new to the forum. Registered just to ask this question... We have a machine at work that has the following parameters: tempurature pressure time This machine machine processes a prodcut that has two properties: quantity stiffnes shade (Not really sure if the shade...

Homework Statement Water vapor condense in a raindrop with rate μ units of mass per time. The raindrop starts with 0 velocity with initial mass $$ M_0 $$ and falls horizontally. Find the space it traverses as a function of time (g is given).Homework Equations ∂m/ ∂t= μ The Attempt at a...

EDIT: If you're reading this and are still learning algebra basics, IGNORE this. I made a wrong assumption, thanks to MarkFL for pointing that out! So far, I was led by my own assumptions to believe that this: a1 $$\frac{1}{5} + \frac{y}{2} = 7$$ could be turned into this: a2 $$\frac{2}{10} +...

Assume X is a random variable under a probability space in which the sample space ?= {a,b,c,d,e}. Then if I am told that: X({a}) = 1 X({b}) = 2 X({c}) = 3 X({d}) = 4 X({e}) = 5 And that: P({a}) = P({c}) = P({e}) = 1/10 P({b}) = P({d}) = 7/20 Find the C.D.F of X, the density of X...

How do we know that the work-energy theorem holds for variable mass systems? Or rather, since I'm sure that we can at least know it to be true experimentally, what is the mathematical basis for the work-energy theorem? I know for fixed mass systems, a rather simple derivation comes from...

Hello, I have an issue with the problem below. I have a series connection of two variable capacitances C_{1}(t) and C_{2}(t). I want to establish the differential equation between the current i and voltage V on the ports of the series connection. The capacitance of the series connection of...

Homework Statement A narrow beam of light passes through a slab obliquely and is then received by an eye. The index of refraction of the material in the slab fluctuates slowly with time. How will it appear to the eye? Homework Equations The Attempt at a Solution Let a point object be kept at...

Hi, I have a quick question. Let R and S be two independent exponentially distributed random variables with rates λ and μ. How would I compute P{S < t < S + R}? I am a little bit confused because of the variables on either side of the inequalities. I have tried conditioning on both S and R...

Given the following ODE \[ \left(\frac{du}{dx}\right)^2 = \mu u^2 - \frac{2\alpha}{\sigma + 2}u^{\sigma + 2} - \frac{\gamma}{\sigma + 1}u^{2(\sigma + 1)} \] How do I obtain \[ u(x) = \left(\frac{A}{B + \cosh(Dx)}\right)^{1/\sigma} \] where \(A = \frac{(2 + \sigma)B\mu}{\alpha}\), \(B =...

I've been following a few derivations for quantities in classical mechanics of rotating systems, and one of the integrals is transformed in a way I've never seen before. For angle theta, angular velocity omega and angular acceleration alpha: Intuitively I can see that they've 'just' swapped...

import java.util.Scanner; import java.io.FileNotFoundException; import java.io.FileReader; import java.io.IOException; import java.io.PrintWriter; public class CountryPopulationReverse{ public static void main(String args[])throws FileNotFoundException { //Variable...

If you have the equation \frac{dx}{dt}=4(x^2+1) I sometimes get confused if i should should subtract 4(x^2+1) from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but...

I know this is a very elementary question, but I suddenly realized in calculus that I don't really know precisely what the definition of a variable and constant was. I know what people tend to call constants and variables in something like: ax + by = c, where you'd call x and y a variable...

Homework Statement The problem is given in the picture attached. However we are given the equation of a 4 dimensional shape with certain choice given to explain the shape in that dimension. Homework Equations Equations of different shape such as: sphere: √(x^2+y^2+z^2) = r...

Homework Statement A cube is falling from a height of 200 m (initial velocity =0) , it reaches it's terminal velocity . Given that :its mass is 100 kg , cross sectional area 40 cm2 and coefficient of drag 2. Putting only weight and drag in consideration , calculate its terminal velocity and...

Prove that for any two numbers x,y we have [(x^2 + y^2)/2] >= x + y - 1 Solution) For any number a we have have a^2 > 0. So, (x-1)^2 + (y-1)^2 >= 0 And if we solve this we get the solution.I don't get the red part.

Homework Statement Let X_1, X_2 have the joint pdf h(x_1, x_2) = 8x_1x_2, 0<x_1<x_2<1 , zero elsewhere. Find the joint pdf of Y_1=X_1/X_2 and Y_2=X_2. Homework Equations p_Y(y_1,y_2)=p_X[w_1(y_1,y_2),w_2(y_1,y_2)] where w_i is the inverse of y_1=u_1(x_1,x_2) The Attempt at a Solution We can...

Homework Statement \frac{\partial f}{\partial t},\frac{\partial f}{\partial x} where f=f(x,t,\frac{dx}{dt}) Homework Equations The Attempt at a Solution I think it's impossible to consider it as a simple partial derivative.