Variable Definition and 1000 Threads

Suppose that ##F(u,v)=a|u+v|^{r+1}+2b|uv|^{\frac{r+1}{2}}##, where ##a>1, b>0## and ##r\geq3.## How we can show that there exists a positive constant c such that ## F(u,v)\geq c\Big( |u|^{r+1}+|v|^{r+1}\Big). ##

Just need someone to check my work. Thank you for your time. First time doing a 5 input Kmap. Determine the following 5 input Karnaugh map for function f(V,W,Z,Y,Z) determine the minimal SOP equation. NOTE: (WX are the variables associated with the top column, and YZ are the variables...

Homework Statement given f(x,y)=9/(x+y) find a level surface. Homework Equations The Attempt at a Solution g(x,y,z)=f(x,y)-z=0? g(x,y,z)=9/(x+y) -z=0? That answer is wrong. Apparently i must have the following: g(x,y,z)=z(x+y)=9 How do I solve problems like these? Another...

My textbook says that in a voltage divider (voltage source Vin, then a resistor, then another path that leads to Vout, Resistor two, Ground, that it is a bad idea to use variable resistors for BOTH of the resistors (but it is okay if you just do one or the other). Does anybody know why?

It seems to me to follow from the definition of a partial derivative. If f(x,y) = fx + fy, then what else can Δf be other than ∂f/∂x*Δx + ∂f/∂y*Δy? Then in the limiting case, the changes in f, x and y becomes differentials instead. All this seems to be given by the definitions themselves, is...

Hi all, Something has been troubling me. To begin with, I have never been certain about this concept of 'extrinsic' thermodynamic variables. I mean, they don't have to be linear with system size, right? They just need to increase with system size? And also, I have a specific 'example problem'...

Hi, I'm having a bit of a problem with a probability question. The question is Let X be a normal random variable with mean \mu and variance \sigma^{2}. Find E[(X -\mu)^{k}] for all k = 1,2,... I'm not really sure what to do and need some help to confirm how to approach the question...

Hi all, I would like to clarify regarding valid variable names. Well what I fairly understand are the rules regarding names.. What I am unsure about is -- in a test, is there any way to spot a reserved name? For example to make things difficult, trick question, sometimes the question will...

I was stuck on a question and went back to look at an example but couldn't understand the example. It has (y-x)dx +4xy dy = 0 is linear in y because it can be written as 4xy'+y=x First of all what are dx and dy doing in the equation? They look to be from the end of an integral. Second, how did...

Homework Statement The linear mass density in a string is given by μ = μ0[1 + cos(x/R)] where R is a constant. If one averages this density over the large size L it becomes uniform: <μ> = μ0, where <…> means averaging. What is the minimum size L (in terms of R) such that the density can be...

I'm having trouble finding any sources that discuss equations of motion that take into account a changing moment of inertia. Just looking at the scaler case, angular momentum is L = I\omega Then, according to the 2nd law, \tau = \frac{d}{dt}(L) = \dot{I}\omega + I\alpha Is this correct...

Hey, I am an undergraduate physics & astronomy student. I am looking for a good research topic to work on for this semester. I have access to a .5 m telescope in Louisville, Ky (38 deg N), a .5 m telescope, and possibly another with a built in spectroscopy as well as photometry capabilities...

hi PF I read the no-go Kochen theorem using 18 vectors projection (here). One attribute a value to an observable A: v(A) This function is supposed to be linear and verify v(AB) = v(A) v(B) so v(AB - BA) = v(A)v(B) - v(B)v(A) = 0 (v is a real number function) v must assign v(id) = 1 because v(A...

I'm wondering what the difference is between a VFD and servo drive are. I'm pretty familiar with VFDs but not so much with servo drives. From what I read, would the following assumptions be correct? A variable frequency drive without an encoder module will adjust the frequency and amplitude...

We selected X point from interval (-1,2). If X=x, we selected point Y from (-1,x^2). Define the function of density of the random variable Y.

Homework Statement A flatcar of mass ##m_0## starts moving to the right due to a constant horizontal force F. Sand spills on the flatcar from a stationary hopper. The velocity of loading is constant and equal to ##\mu## kg/s. Find the time dependence of the velocity and acceleration of flatcar...

Hello, the question I have arises from the 4th Edition of the book "Advanced Engineering Mathematics" written by K.A. Stroud. For those who owns the book, it is the example #2 starting at page 379. More precisely, the example is separated into two parts but the first one is very straight...

We know that in Schrödinger equation, Ψ is called wave function, which is not observable, while Ψ·Ψ* is the probability, which is observable. can we rewirte the Schrödinger equation to a form without Ψ but only Ψ·Ψ*? because I think, in this way can I figure out all conservations in the...

We have the following trapezoid: The question is to find the length of the fourth side when the area of trapezoid is maximized. I realize we will not be able to find a numerical value for the fourth side due to the given information (rather, lack thereof). So we are essentially going have...

Homework Statement I'm wondering how to find the inverse function of some f(x,y)? Homework Equations The Attempt at a Solution

Hello, This will probably sound like a HW question, but it's not. There is a certain phone system that I can use to call someone. There is an outgoing charge per call and a per minute charge. The per minute charge is $ 7/18 The outgoing call charge is $299/90 Say I have $50 on the...

Hey guys, I have a question for you... how would one go about solving an equation like this... or this... This came across my mind the other day. I was wondering how to solve that equation if the function is of t-1, instead of t. Obviously, if it was f(t), the solution would be Ce^t, but I was...

Homework Statement 1/x - 1/a = 1/b Solve for x Homework Equations The Attempt at a Solution I used to be able to do this in high school, but now I am 43! Normally, I would just cross-multiply and solve for x, to get the x out of the denominator, but you cannot...

Homework Statement I don't understand case 1. In case 2 that is normal integration , isn't? Then why case 1 can simply ignore the r ? I don't think r is constant. Homework Equations The Attempt at a Solution Please guide. Thanks

Homework Statement What's the expected value of this problem (random variable)? X: represent the result of dice number 1 - result of dice number 2 example dice 1 first roll = 2; second roll = 3 dice 2 first roll = 1; second roll = 2 X = 2+3 -(1+2) = 2 what's the expected value...

Hi, I'm an economics graduate student doing some work on a nested logit model. I am trying to generate random variables that follow the following CDF: F(x_1, x_2) =\textrm{exp}[ -(e^{-2x_1}+e^{-2x_2}) ^{1/2}] (This is an extreme-value distribution) With a single random variable, I...

Homework Statement Let F: x^2 + y^2 - z^2 + 2xy - 1 = 0 and G: x^3 + y^3 - 5y - 4 = 0. Calculate dz/dx. Note: This is NOT the partial derivative ∂z/∂x. I do not need help in taking the derivative of many polynomials. What I need help in is setting up a Jacobian determinant to evaluate this...

Who first studied variable speed of light? --- Einstein Variable speed of light is a hypothesis that states that the speed of light, usually denoted by c, may be a function of space and time. Einstein's first mentioned a variable speed of light in 1907, and he reconsidered the idea more...

Homework Statement A man wants to travel to four cities (A,B,C,D) but he has such a bad memory that he can't remember the cities that visited, therefore, if he travel to city A he can choose between (B,C,D) and if he then travel to B he can choose between (A,C,D). Find v, If v it's the...

Hello all, In the equation V= apd/Ln(pd)+b as described by Paschens law regarding breakdown voltage, I was wondering what the "L" and the "n" stood for. Example of what I'm looking for: p stands for pressure. Thanks.

Hello folks, I'm being tricked by the pesky friction force again. I know that static friction acts just to put everything in equilibrium as long as its magnitude doesn't exceed a certain value. That is ok. But when there are other adjustable force such as TENSION and NORMAL, (which in this...

Hey forum I need to ask for a link to a page for Variable density or preferably an explanation from someone who can describe it simply. I am trying to teach myself about the function of Qubits and have run into probability density functions and cannot find a good reference on what exactly...

If X is a continuous random variable and g is a continuous function defined on X (Ω), then Y = g(X ) is a continuous random variable. Prove or disprove it.

If X is a random variable distributed uniformly in [0, Y], where Y is geometric with mean alpha. i) Is this definition valid for uniform distribution ? ii) If it is valid, what is the pdf of the transformation Y-X?

15+1/2=0.60(20x)

Create the Euler-Lagrange equation for the following questions (if it's necessary change the variables). Homework Statement $$\tag{1}\int _{y_{1}}^{y2}\dfrac {x^{'}{2}} {\sqrt {x^{'}{2}+x^{2}}}dy$$ $$\tag{2}\int _{x_{1}}^{x_{2}}y^{3/2}ds $$ $$\tag{3} \int \dfrac {y.y'} {1+yy{'}}dx...

If one has a simple variable coefficient process like y'(t) = r(t)*y(t), is there a way to control it to a set point by feedback hitting the variable coefficients in r(t)? I am interested in feedback control of population processes. y'(t) = r*y(t) is simple proportional growth with a...

I remember learning at one point that you can put some sort of symbol on top or near a variable to indicate that it is being held constant. I thought that it was just a bar drawn above the variable but in some cases, it means "the average of." Anyone know what I'm talking about?

Homework Statement f(x,y) = (x-y) / (x+y) Calculate Δf and df for the change of point (3,2) to point (3.2, 2.1) Homework Equations The Attempt at a Solution I guess that I have to use limits, but don't know how to begin with.

How do you make a differential equation for such? Say for example. I have two reactions in series, A → R and R → S going in a gas-phase reaction. If I'm correct, the ODE for the conversion of A is dXA/dt = kA*[(NAo/vo)*(1-XA)/(1+δA*YAo*XA)]*[(vo/NAo)*(1+δA*YAo*XA)]. I don't know now...

I'm having a bit of a problem proving the second condition for a martingale, the discrete time branching process Z(n)=X(n)/m^n, where m is the mean number of offspring per individual and X(n) is the size of the nth generation. I have E[z(n)]=E[x(n)]/m^n=m^n/m^n (from definition E[X^n]=m^n) =...

What is the variable "theta of omega" in a series RL cct? Homework Statement Hi I'm not looking for a complete solution to this problem. My question concerns just one specific part of the solution to part A: why is tan θ(ω) = ωL/R? and what θ(ω) represent? how does it relate to the...

Homework Statement Calculate the capacitance of a spherical capacitor of inner radius A and outer radius B which is filled with a di-electric varying as e=c+dcos^2θ . c and d are constants and θ is the angle made with the z axis.(also known as the polar angle) Homework Equations $C=εA/d$The...

Hi, Homework Statement How may I find to what number Ʃ(m=1 to ∞) m/2m-1 converges? Further, suppose I know it converges to 4, why would then E(Y), given that P(Y) = 1/2m-1, be equal to 2 (thus asserted the answer) and not 4? Homework Equations The Attempt at a Solution I am...

Hi to everybody Homework Statement I´ll show the problem with a picture: Homework Equations L\overline{x}=∫xc ρ dl The Attempt at a Solution Well the total length of the rod is 1 feet, I only need to calculate the integral. The moment xc of a differential element of mass of the rod is...

If I have a variable X whose gaussian distribution is known and let f be a known function, is there a way to compute f(X) (i.e) the resulting gaussian distribution from this? Is the result actually a gaussian distribution?

Homework Statement A particle which moves with a constant acceleration in a straight line passes through the point O, A and B in that order. If the distances OA and AB are 17 m and 35 m respectively and the particle takes the same amount of time , 3 seconds to travel each distance then...

hi.. with refrenence to http://www.math.uah.edu/howell/MAPH/Archives/Old_Notes/PDEs/PDE1.pdf page 7, “Observe” that the only way we can have formula of t only= formula of x only is for both sides to be equal to a single constant. here I do understand that for these to being equal...

i need to solve for a variable inside the error function on excel, is there an opposite function i can use to accomplish this? example: y = sqrt(x-t) -> x = t+y^2 except instead of a sqrt( ) I have erf( ) **this is not a math class so I don't have to get into breaking it down into the...

Problem: Suppose that $X \text{ ~ Exp}(\lambda)$ and denote its distribution function by $F$. What is the distribution of $Y=F(X)$? My attempt: First off, I'm assuming this is asking for the CDF of $Y$. Sometimes it's not clear what terminology refers to the PDF or the CDF for me. $P[Y \le y]=...