Variable Definition and 1000 Threads

Homework Statement I have the ODE y' = f(\frac{y}{x}) , and I want to re-write this as a separable equation using the change of variable u = \frac{y}{x} The Attempt at a Solution I use the chain rule to write y' = \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx} = \frac{dy}{du}(-\frac{y}{x^2})...

Homework Statement Find k so that the following function is continuous on any interval. j(x) = {k cos(x), x ≤ 0 {10ex − k, 0 < x Homework Equations The Attempt at a Solution I originally thought i had to check if the limits of both parts of the functions...

Hello, I know the value of a field variable in a 3d mapped finite element mesh. Can anyone suggest an effective method/methods to find its gradient throughout the mesh.

I ask this question only to those who read or have this book: If you have Baby Rudin, it would be even better. On the page 34 of the text Conway's Functions of One Complex Variable Vol 1, it proves the Chain Rule but it seems the proof is not valid: It uses sequences to show the limit is...

solve the following equation for z in terms of x and y 3y^{2}+2yz-5z-2x=0 i've spent a lot of time on this question, but i keep getting something along the lines of 0=0 i tried solving for x in temrs of y and z to replace the x but i get 0=0 Homework Statement Homework Equations The Attempt at...

Homework Statement Let f(x)=x/8 be the density of X on [0,4], zero elsewhere. a) Show that f(x) is a valid density and compute E(X) b) Define Y=1/X. Calculate E(Y) c) Determine the density function for Y The Attempt at a Solution a) is just really basic. I've solved that one. b)...

As the title alludes to, I am currently reading about work. One sentence has left me very confused, thought: " Only the magnitude of this variable force changes, not its direction, and the magnitude at any position does not change with time." Could someone possibly help me understand this?

From what I think I understand, a variable is something you input into a function and you get a certain value from it whereas a parameter is something that gives you a different function but 'adjusted'...so the constant C the translates a graph of a function up and down would be a parameter...is...

I just started programming and i don't understand how variables work. First the book defines a as 3 and b as 5 then defines a =a+b. For me who hasnt done programming ever that implies that b=0 but i think second a is different from the first one. Help regarding how variables work in computer

Homework Statement An object starts from position X = 0 and moves along a straight line with its position given by x = 4t^2 - t^3 where t is the time taken to reach position x. Find: i) The time at which the velocity is zero ii) The time at which the acceleration is zero iii) The average...

I have a differential expression that I want to expand to some order around infinity (it's for calculating weak-field limits in GR). I have two functions, B(r) and n(r), and some expression involving them along the lines of n[r] (3 r B'[r]^2 - 4 B[r] (2 B'[r] + r B''[r])) Basically I want...

For my work, I need to solve the following equation for the variable x (if possible): a * (x/1000) = b - x * c Can someone please help me solve it or inform me that it is simply not possible. I'm chemist myself, so solving equations is not exactly my expertise. Thanks in advance!

An object starts from position X = 0 and moves along a straight line with its position given by; X = 20t - 5t^3 where t is the time taken to reach position X. Find; i) The time at which the velocity is zero ii) The time at which the acceleration is zero iii) The average velocity over the...

Homework Statement You run a small business making widgets. You have two employees. Employee A takes two times as long as employee B to make a widget. During each day, both employees working together will make 15 widgets, how many widgets get made by employee A each day? Homework Equations...

The Dirac delta "function" is often given as : δ(x) = ∞ | x = 0 δ(x) = 0 | x \neq 0 and ∫δ(x)f(x)dx = f(0). What about δ(cx)? By u=cx substitution into above integral is, ∫δ(cx)f(x)dx = ∫δ(u)f(u/c)du = 1/c f(0). But intuitively, the graph of δ(cx) is the same as the graph of...

Homework Statement Firstly sorry if this is in the wrong place. I have never submitted a question on this forum about a comp sci question. I got an assignment that asked me to solve for a variable using Bisection of successive approximations. This however is not why I am here as I know you...

I was just wondering if it is possible to find b in this equation? f(x,y)=result. where y=f(a,b). so the I guess f(x,f(a,b))=result. I know the actual value of x,a and result and it is possible to find b in the equation. I also know the function of f(). Please ask me if this...

Homework Statement I'm working through Mahajan's Street-fighting Mathematics for fun, and am a bit puzzled about the following problem: The Attempt at a Solution It's mostly the first part that's tripping me up. I could use the substitution tan\theta=x and solve both integrals...

Hi everybody, I try to figure out connections and differences between random variables (RV), random processes (RP), and sample spaces and have confusions on some ideas you may want to help me. All sources I searched says that RP assigns each element of a sample space to a time function. I want...

The Question: Find the value of r such that v = xr is a solution of xd2v/dx2 + (x+4)\frac{dv}{dx} + 3v = 0 My Solution: After finding the 1st and 2nd derivative of v and substituting into the equation to equat to zero and look for r, I get the answer r =-3. I also get a root that is...

Homework Statement The changing variable formula in partial derivative f(u,v) x=x(u,v) y=y(u,v) (∂f/∂x)y = (∂f/∂u)v(∂u/∂x)y + (∂f/∂v)u(∂v/∂x)y I khow the how chain rule works, but I don't know why in the (∂f/∂u) v is constant and in the (∂u/∂x) y is constant Homework Equations The...

An interesting and well presented new paper by Kumar and Xu: "Observational constraints on a cosmological model with variable equation of state parameters for matter and dark energy" http://arxiv.org/abs/1207.5582 The idea of a variable equation of state for matter and dark energy is not...

I have an ode function which is of the form: function [output]=Fun[input1,input2,input3] which is solving a set of non-linear differential equations. input1 and 3 are fixed but input2 is a variable. Say: input1=3; % a constant input3=20; input2=[2 4 6 8]; function Fun is being...

Can I use excel to make an equation for 4 variables (x,y,z,w) e.g a,b,c,d,3,f,g,h,i, would be constants w = ax + by + cz + dx^2 + ey^2 + fz^2 + gxy + hyz + iyz What are these equations called ? What literature can I study to better understand the procedure of making these tye of...

Homework Statement An oscillating LC circuit is designed to operate with a maximum current of 31 mA. The inductance is fixed at 42 mH, and the frequency is changed by means of a variable capacitor C. (a) If the highest voltage that the capacitor can handle is 50 V, can the circuit be operated...

Typical VC: http://goo.gl/Z4Dbg I have that guy there or one very similar. My question is how does one hook this up to the inductor? Forget, for now, the rest of the circuit. How do these two piece fit together? The bottom feet (there are two on each side) I assume take the positive...

Homework Statement http://img12.imageshack.us/img12/1176/img20120713190506.jpg Homework Equations V_{C}' = dv/dt I_{L}' = di/dt The Attempt at a Solution I did KCL at the centre node: I_{L} + i_{2} = \frac{V_{C}'}{5} (Vc'/5 is basically the current coming from the capacitor...

Homework Statement Suppose X is a discrete random variable whose probability generating function is G(z) = z^2 * exp(4z-4) Homework Equations No idea The Attempt at a Solution I'm thinking that due to the exponent on the z term, that the exp(4z-4) would be the P[X=3] =...

Homework Statement In the electric circuit shown in the figure, when the value of the variable resistor R3 is 25Ω, the current which flows into the power supply is 2A. Moreover, when the value of the variable resistor R3 is 5Ω a current of 1A flows into the resistance R2. Q1.Find the value of...

Homework Statement First, there's a slender rod with length L that has a mass per unit length that varies with distance from the left end, where x=0, according to dm/dx = yx where y has units of kg/m^2. (a) Calculate the total mass of the rod in terms of y and L (Which I've already done and...

Homework Statement A line charge in the x directio has a variable charge density given by the equation λ=4 λnot((1-x)/2L), where λnot is a constant. The rod has a length of L. i)What is the net charge of the rod? Hint-the net charge is calculated by integrating the charge density with respect...

Homework Statement I just need to know how to access an arraylist that was created in a class (call it Company). In class CompanyTest, I need to access a list of employees that was created in Company. This is Company class: public ArrayList<Employee> list = new ArrayList<Employee>()...

the problem is as follows: [1-(12*x*(y^2))]*(dy/dx)=y^3 we need to solve this equation such as x=5 & y=2 by regarding y as the independent variable. Here is my work for the first attempt: Step 1)separation & integration Step 2)ln(x)= (-1/(2y^2))-12ln(y)+C...

Dear all, I have a question about the variable substitution in Langevin equation and Fokker-Planck equation and this has bothered me a lot. The general Langevin equation is: $$\frac{dx}{dt}=u(x)+\sqrt{2 D(x)}\eta(t)$$ and the corresponding Fokker-Planck equation is thus: $$\frac{\partial...

Hi Maybe I don't see the wood because of all the trees, but: You have a second derivative \frac{\mathrm{d}^2}{\mathrm{d}x^2} e^{-ax} \cdot u(ax) Now you make the variable transformation w=ax How to express \frac{\mathrm{d}^2}{\mathrm{d}w^2} Thanks Greetings

Homework Statement A racing car of mass 20000kg accelerates with a driving force of 480(t-10)^2 Newtons until it reaches its maximum speed after 10 seconds. Find its maximum speed, and the distance it travels in reaching this speed. The Attempt at a Solution Again, I can't seem to...

EDIT: Oh and I forgot that $p_Y(y) = 0$ otherwise.

Homework Statement A car of mass 1200kg is at rest on a level road. Two people push it, producing a total force given by (240-12t) Newtons, where t is the time in seconds, until this becomes zero after 20 seconds. How fast is the car then moving, and how far does it move while it is being...

You are given a random exponential variable X: f(x) = λ exp(-λ x). Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X: Y = IP(X), Z = FP(X). Which is the following conditional probability: P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

I want to calculate \int_a^b \frac{1}{\sqrt{2 \pi \sigma^2}} e^{(-(x-\mu)/\sigma^2)} log_2 (1 + e^{-x}) dx

Homework Statement An open-topped railway wagon of mass M is rolling freely along straight level frictionless track at a constant velocity v0. At time t=0 the wagon enters a heavy rain shower and starts to collect rainwater. The rain falls vertically. As a consequence the wagons mass increases...

Homework Statement A 2kg bucket containing 10kg of water is hanging from a vertical ideal spring of force constant 125N/m and oscillating up and down with amplitude 3cm. Suddenly the bucket springs a leak in the bottom such that water drops out of the bucket at a steady rate of 2g/s...

Hi, I have a random variable X with some zero-mean distribution. I have a function Y of this r.v. given by something complicated Y=(a+X)^\frac{2}{3} Is there an explicit way of finding the distribution of Y or even its mean? Thanks

hello! I am interested to know if a tube can be created that with some kind of mechanism, its diameter will increase on demand the range of the diameter should start at the smallest possible (0.01 mm or less if possible, even if the walls of the tube virtually concur) and increase up to...

Homework Statement So I came across the integral \int^{1}_{0}x\sqrt{1-x^2} and I tried to solve it in two ways using the change of variables theorem for integration, however both ways are supposed to give me the same result, but they differ in the sign and I cannot find what I am doing...

Hi Iknow that if we have delta function of one variables function, then we can write it as: \delta (f(x)) = \sum \frac{\delta(x-x0)}{f'(x0)} but how we can write a function of two variables: \delta (f(x,y))

what is log of z=X+JY? Thanks

Hello all, I have a 3 phase Variable frequence drive that requires an input voltage of 380-480VAC. I would like to test what would happen if I apply 300VAC to the drive. I have access to 208V and 440V. Is there anything I can do to obtain 300V? I have thought about a variable power supply...

Hi All, I need to train an HMM using data with sequences of variable length (5 - 500 symbols per input sequence). From what I've seen thus far, all (or most) trainings are perfirmed on data-sets of a fixed size, although there is no explicit demand for this in the HMM structure. So...

Homework Statement http://img716.imageshack.us/img716/7453/28042782.jpg The Attempt at a Solution What I do not understand is how the Jacobian suddenly gets inverted when doing the integral, I have looked over my other tutorial problems for similar solutions and I do not recall doing...