Variable Definition and 1000 Threads

How to solve a equation of this kind T' = a*(T^4 - r^4) + b*(T^4 - s^4) + P*(1 - η(T)) The above equation is driving me nuts... the 'η' is a function of T(Temperature) the efficiency and initial value of T is known. Say at t = 0 T is 298 Need help! Please! I need to find the...

My problem At temperature 5 degrees the Y=1.00228594 for X=435 and Y=1.000986038 for X=449 and Y=0.999760292 for X=463 At temperature 7 degrees the Y=1.002094781 for X=435 and Y=1.00079709 for X=449 and Y=0.999573015 for X =463 For a new temperature of 9.6 degrees how to find the Y...

Hi, I am trying to understand how to predict the distribution of a variable that is a combination of other random variables. For example, how should I determine the distribution of Variable A, which is the sum of Variable X and Variable Y? Variable X has a normal distribution and Variable...

I am wondering if I can find a decomposition of Y that is absolutely continuous nto two i.i.d. random variables X' and X'' such that Y=X'-X'', where X' is also Lebesgue measure with an almost everywhere positive density w.r.t to the Lebesge mesure. My main intent is to come up with two i.i.d...

The following values are tonnes of a specific animal feed for a specific consumer. Jan - 13.97 Feb - 12 Mar - 11 Apr - 5.87 May - 10 Jun - 13.95 Jul - 15.96 Are these variables best described as "quantitative ratio variables" and why? If not what would be the most accurate class...

Hello, I've got an extremely limited background in electronics, so I'd like to ask for some advice regarding this circuit: I found the diagram online, It's supposed to allow variable control of a load up to 1500w at 120v, using an ordinary light dimmer and a 600V / 40A triac. After...

Homework Statement I just don't understand how one chooses a free variable when using Gaussian elimination and back substitution to solve linear equations Homework Equations The Attempt at a Solution One particular example here is provided (already in row echelon form) -2...

Suppose you start with a system of N particles identified by position vectors r_1, r_2, \ldots, r_N and masses \mu_1, \mu_2, \ldots, \mu_N. Then (quantum mechanically) the kinetic energy operator for this system is given by (assuming \hbar = 1) T = \sum_{i = 1}^N -\frac{\Delta_i}{2\mu_i}...

There are plenty example of functions are random variables from my class note. I only interested of thinking up functions are not random variables. If you know functions are not random variables please please reply this post. This class is about set theory, probability measure, Borel...

Homework Statement The problem is labeled Variable Acceleration. The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared and is given (in SI units) by the expression Ax = -3.00 Vx^2. If the marble enters this fluid with a speed of 1.50 m/s, how long...

Dear All I would like to calculate work done on the system by variable force & distance at each point. Kindly let me know to the formula how to calculate work in excel sheet (because I'm having huge data) I have attached my copy of data for your reference. Kindly advice. Many...

Let $f:B(0,2)\to B(0,2)$ be an analytic function so that $f(1)=0.$ Prove that for all $z\in B(0,2)$ is $\left| \dfrac{f(z)}{z} \right|\le \left| \dfrac{2(z-1)}{4-z} \right|.$ What's the trick here? I don't see it.

Hi, I'm working on a problem that i would like your input on. I have a solution but i would like to see how others would approach it since my solution is more of a hypothesis until we continue with the testing phase. In the most basic form, this project can be described as a hanging container...

Homework Statement Which of the following formulas is valid if the angular acceleration of an object is not constant? Explain your reasoning in each case. (a) v = rω; (b) atan = r\alpha; (c) ω = ω0 + \alphat; (d) arad = rω2; (e) K = 0.5Iω2. Homework Equations The Attempt at a...

I have an inductor in a design that is one half of an air coupled RF transformer. The operating frequency is 50 MHz. The purpose is to provide power to the load side. It is for all intents and purposes an RF to DC power supply design over some gap. The primary is the fed radiator inductor, a...

Homework Statement Rewrite this in terms of f, f, ∂f/∂x, and x: ∂f(x,y)/∂(%Δx) = ∂f(x,y)/∂(d log(x) ) Homework Equations ∂(%Δf(x,y))/∂(%Δx) = ∂logf(x,y)/∂log(x)= ∂f(x,y)/∂x*x/f(x,y). ∂f(x,y)/∂log(x)=x∂f(x,y)/∂x The Attempt at a Solution I found that (%Δx) can be written as...

Homework Statement Show that if X is a bounded random variable, then E(X) exists.Homework Equations The Attempt at a Solution I am having trouble of finding out where to begin this proof.This is what I got so far: Suppose X is bounded. Then there exists two numbers a and b such that P(X > b)...

Hi, I'm trying to find an analytical solution (if one exists) to the 1d diffusion equation with variable diffusivity κ(x); \partial_t u(x,t) = \partial_x[\kappa(x) \partial_x u(x,t)] Could someone point me in the right direction to solve this if its possible to do so analytically. I've...

Homework Statement In manufacture of nitric acid, ammonia and prehated air are mixed to form a gas containing 10 mole %NH3 at 650 C. If ammonia enters the gas blending unit at 25C at a rate o 520kg/? and heat is lost from the mixer to its surroundings at a rate of 7 kW, determine the...

Homework Statement A Normally distributed random variable with mean μ has a probability density function given by _ρ_...*...((-ρ2(x-μ)2)/2δ) √2∏δ|...e^ Homework Equations Its standard deviation is given by: A)ρ2/δ B)δ/ρ C)√δ|/ρ D)ρ/√δ| E)√δ|/2ρ The Attempt at a Solution...

Hi guys, I need to find the moment generating function for X ~ N (0,1) and then also the MGF for X2 . I know how to do the first part but I'm unsure for X2. do i use the identity that if Y = aX then MY(t) = E(eY(t)) = E(e(t)aX) or do i just square 2pi-1/2e x2/2 and then solve as...

Hi, I've been muddling over this problem for a few days. I thought there would be a simple approach, but I'm having trouble reaching a solution. Here is the rundown: We have a 2D projectile launcher. It hurls an object from the origin (0,0) at some initial velocity with magnitude V_i at angle...

Homework Statement Hi! In an assignment I have reached an integral that has the form: \int\frac{A+Bx+Cx^2}{Dx+Ex^2} where A-E are constants, the integration variable is x and the limits are 0 to 1. I'm supposed to remove the singularity at x=0 by substitution. A-E have values but they're...

Hi guys. Please help me with this. Consider the Mapping: w = 1/(z-j) questions:(1) Write z as a function of w. (2) Express X and Y in terms of u and v. (3) Find and describe the image of the line x = 1 under this mapping. Homework...

Matrices- Variable in Matrices-Help! 1-19-12 I need help. I have a homework question that I have tried to solve. The matrix in the attachment has no inverse. Explain how you can determine the value of x. Then find x. I tried cross multiplying. 3*2/3=4x 6/3=4x 2=4x x=2/4 x=1/2

I want to design build and overall engineer a variable pitch turbocharger. This will go a long way in regulating both the hot and compressor sides flow rates, a larger turbo can essentially be used in smaller applications, and vice-versa. I want to use the VNT or VGT type turbos for my testbed.

As you can probably guess by my last few posts, I'm looking into resonance right now. I thought it would be interesting to make a device that could hit a specific resonant frequency, maybe even smash an object. Sure, people have done it, but...fun :) Anyhow, I was looking on how to make one...

There are plots that compare the expectation value E(a,b) of (i) a hidden variable theory (ii) quantum mechanics For example here: 1. Talk given by Alain Aspect, video at 2m28s 2. PF Thread: The Unfair Sampling Assumption & Bell Tests For the hidden variable theory the expectation...

Hey, there's this thing I can't wrap my head around. Let's say we have a negative binomial variable x, with parameters p and r. That is, x is the number of failures we get before the rth sucess, while looking at random bernolli variables with sucsess rate p. It can be shown that...

Hi All, I am trying to solve a set of coupled non-linear algebraic equations. I'm doing this using the LinearSolve fcn of mathematica and an implementation of the Newton-Raphson method. One of the issues I'm having is that I need to tell mathematica that one of these variables,let's say x...

I'm having a bit of trouble understanding a probability distribution of 2 variables. Take for example taking n cards from a deck, and seeing what is the probability of getting X queens and say Y aces (with replacement). This involves the binomial distribution. The probabilities for the...

I've been fooling around with the Fibonacci sequence for some time and I thought it would be interesting to see what would happen if I made the coefficients in a three variable system of equations follow that sequence. The results are intriguing and enigmatic. I discovered the following...

Homework Statement Say you have: EQ1: y1''*t+y1'*t+y2=0 and EQ2: y2''*t+y2'*t+y1=0 y1(0)=0,y1'(0)=0,y2(0)=0,y2'(0)=0 Homework Equations The Attempt at a Solution I can get it so far, but having both y1 and y2 really gives me fits: Eq1: Y1(-2s-1)+dY1/ds(-s2-s)=-Y2...

Going over my Lecture Notes my Lecturer as Started with Show that a Gaussian Distribution Corresponds to a CTS random variable. Then she has i) Taken the f(x) = [p.d.f] and shown a) f(x) >= 0 for all x member of real numbers. b) Integral over all real numbers = 1 ii) Found the M.G.F then...

Evening gents, I am somewhat of a novice with electronics, but nonetheless am working on a temp. controlled computer fan but I've run into some trouble and need some help! My basic layout is a thermistor implemented as a voltage divider (with a resistor of course) which feeds into an amp...

The STL containers have a lot of member types, so I assume they must be there for declaring variables of those types. However, I can't discern how exactly it is that I'm supposed to use those member types to declare a variable. For example:map<int, char> t; t::key_type u; // I want this to...

It is easy to integrate the delta function of real variable. But when the argument of the delta function is complex, I get stuck. For example, how to calculate the integral below, where u is a complex constant: \int_{ - \infty }^{ + \infty } {f\left( x \right)\delta \left( {ux}...

Homework Statement A random variable X has probability generating function gX(s) = (5-4s2)-1 Calculate P(X=3) and P(X=4) Homework Equations The Attempt at a Solution Ehh don't really know where to go with one... I know: gX(s) = E(sx) = Ʃ p(X=k)(sk) Nit sure how to proceed.. Any help would...

Homework Statement a) Let X1, X2, ...XN be a collection of independent Bernoulli random variables. What is the distribution of Y = \sumNi = 1 Xi b) Show E(Y) = np Homework Equations Bernoulli equations f(x) = px(1-p)1-x The Attempt at a Solution a)X1 + X2 + ... + XN = p...

Time variable of space-time at the end of universe... As universe is continuously expanding at the accelerating speed...expansion of the universe causes Redshift...the whole universe is made up of the tiny particles and the material. Because of this all the material particles of the universe...

Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...

Homework Statement A multi plate variable capacitor has 4 pair of plates. The plates, when closed, are separated in air by 0.01mm and a capacitance range of 10 to 400pF. a) Estimate the required radius R of each plate. b) The capacitor is set to maximum 400pF and is charged to 10V...

Determine constant c so that random variable will have a t distribution? Homework Statement Suppose that five random variables x1, x2, x3, x4, x5 are independent and have normal distribution N(0,1). Determine a constant c such that the random variable c*(x1+x2)/\sqrt{x_3^2 + x_4^2 +...

Almost two months ago I posted the following question: I probably wasn't specific enough in my question to really get the answer I wanted. So I now ask, "Can an integral that is a variable of itself be solved analytically?"

Let f: X \rightarrow \mathbb{R}. The definition given for upper semicontinuity at a point a is for any positive \epsilon there is a positive \delta such that if |x - a| < \delta then f(x) < f(a) + \epsilon. My understanding is, for ordinary continuity at the point a then the inequality...

Homework Statement lim(x,y)->(0,0) x2y / 2x3-y3 Homework Equations The Attempt at a Solution I found lim f(x,0)=0 and lim f(0,y)=0.So i assume limit exists and equals 0? I would like to get some tips on how to solve this type of problems?Do I always find f(x,0) and f(0,y)?Because I...

1. Person is climbing a mountain with rope attached to rock on a flat surface above for support. The slope has an incline angle of 50 degrees. The rock is on frictionless ground, and the mass of the rope can be ignored. The person (100 kg) is 3 meters from the flat surface, the rock (700 kg) is...

Homework Statement Solid cylinder: H=0.14m, R=0.05m. Mass density ∂=900-(900r/0.05), where r is distance from axis of the cylinder. A string of negligible mass and length 0.85m is wound around the cylinder, which is set spinning by a horizontal pull on the string with F=2.5N. The cylinder...

I have an equation with two variables x and y. I wish to plot a function in 3d (let's say cosine) with x and y as parameters. I know the plot3d command in Maple is as follows: plot3d(cos(x+y),x=-1..1, y =-1..1); My question is this: how would I modify the increment values of x and y which...

i want to solve the following differential equation: y''(x) - A*y'(x) - B*exp(-C*A*x)*y(x) = M*exp(-N*x) A,B,C,M,N are constants. -is there any solution of the above equation (except series solution)? -is there any proper substitution that can turn the variable coefficient into constant...