Variables Definition and 1000 Threads

What's the best approach to solving the partial-fraction decomposition of the following expression? $$\frac{1}{(a-y)(b-y)}$$ The expression is not of the following forms: But I know the solution is $$= \frac{1}{(a-b)(y-a)}-\frac{1}{(a-b)(y-b)}$$

Hello! (Smirk) Suppose that we have an algorithm of the form: Algorithm(NODE *P){ static int s=0; Algorithm(P->RC); ...... Algorithm(P->LC); ...... s++; } where P is the root of a binary tree, for example this one: When we call the function Algorithm(a), s will get the value...

Hi If the function ##f(x,y)## is independently continuous in ##x## and ##y##, i.e. f(x+d_x,y) = f(x,y) + \Delta_xd_x + O(d_x^2) and f(x,y+d_y) = f(x,y) + \Delta_yd_y + O(d_y^2) for some finite ##\Delta_x##, ##\Delta_y##, and small ##\delta_x##, ##\delta_x##, does it mean that it is continuous...

An example: A car that senses if you have your seat belt on and the door is closed I can declare: D - for door S - for seat belt D is 1 is door is open, 0 if door is closed S is 1 if seat belt is on, 0 if it's off This is all very straight forward and can be implemented with combinational...

Homework Statement Assume uniform acceleration. The projectile is released at a height 1m above the ground traveling at angle 60 above the horizontal. It hits the ground 60m away from the launch position. Calculate acceleration of the particle in acceleration phase.[/B]Homework Equations...

So I've started reading Landau's classical mechanics text and I'm at the part where L(v'2) = L(v2 + 2v⋅ε +ε2) and he says to expand it out in powers of ε to get L(v'2) = L(v2) + ∂L/∂(v2) * 2v⋅ε where v and ε are vectors. Can someone explain how this result is obtained in more detail?

Homework Statement If ##X\sim\mathcal{U}(-1,1)## and ##Y = X^2##, is it possible to determine to ##cov(X, Y)##? Homework Equations \begin{align} f_x &= \begin{cases} 1/2, & -1<x<1\\ 0, & \text{otherwise} \end{cases}\\ f_y &= \begin{cases} 1/\sqrt{y}, & 0<x<1\\ 0, & \text{otherwise} \end{cases}...

So the TI-89 can solve ODEs and the arbitrary constants show up as @1, @2, @3, etc. Every time I put in a new ODE it uses the next constants @4,@5 etc. How do I clear them to get back to @1,@2 again? There used to be a sub forum here on math software etc. but I cannot find it now so I posted...

Homework Statement Hello guys! I have a dimensional analysis problem where water is draining from a open topped tank and in a certain amount of time,t it drops from h1 to h2. and I need to find a bunch (6) of variables which apply to this problem. I have some but I am not sure about the other...

The question gives the code for MATLAB to solve Hill equation with 5 different values of distance x, which will generate 5 plots on same axis. But the plots will be Force versus time. The question ask you to interpret the relationship between X and F(t). How do I know this plot represents...

1. A spring of spring constant k is attached to a support at the bottom of a ramp that makes an angle θ with the horizontal. A block of inertia m is pressed against the free end of the spring until the spring is compressed a distance d from its relaxed length. Call this position A. The block is...

Homework Statement Given x^2 - xy + y^2 = 4(x+y-4) where x, y both are real then the number of pairs (x, y) satisfying the equation will be (A) Only one (B) Two (C) Three (D) No pair Homework EquationsThe Attempt at a Solution The equation can be written as (x-2)^2 + (y-2)^2 + 8 = xy on...

Is Complex Analysis and Complex Variables the same thing? Is Complex Analysis pure or applied math? Is Complex Variables pure or applied math? What's the prerequisite of Complex Analysis and Complex Variables? Are they useful for the field of computer science?

Homework Statement I need to find q in terms of f and p. Homework Equations I am dealing with this equation at the moment: 1/p + 1/q = 1/f. The Attempt at a Solution I think I should isolate the q, so that I have the variables p and f on one side of the equals sign, and q on the other side of...

As most people interested in mathematics know, iterations of rational functions of complex variable can be used to produce fractals such as the Mandelbrot set... What about iterating functions whose domain is a noncommutative ring? A ring can be a vector space of any dimensionality (or can...

Hi! I am looking for a very rigorous book on some of the topics covered in Calculus of Multiple Variables. My University uses the last part of Adams "Calculus: a complete course" and I found the presentation therein more fit for people needing to know enough to perform the calculations than for...

hey all, I'm stumped so I thought I'd try posting here. I am in the early stages of design of a vehicle where we have a rough approximation of weight, no idea what gear ratios or power/torque to use yet, but have an acceleration requirement. I am trying to graphically model the relationship...

So I'm currently taking electricity and magnetism and I'm expected to know how to perform a separation of variables on laplace equation in 2 dimensions.I have taken Zero differntial equations courses and I literally have no freaking idea what's going on. The book I use doesn't spend any time...

Homework Statement Solve: \frac{d^{2}y}{dx^{2}} + \omega^{2}y = 0 Show that the general solution can be written in the form: y(x) = A\sin(\omega x + \alpha) Where A and alpha are arbitrary constants Homework EquationsThe Attempt at a Solution I know that I will need to change variables for...

Here is a picture of the problem. Can anyone give me some hints on the problem? I've looked in my textbook, but I don't know what "s" means. I found stuff on the parametric vector form, and it gives me the equation x = su + tv, but I don't see any "t"'s in this problem. I first tried...

Hi, I am having a hard time understanding why the Addition Rule for two Random Variables holds even when the random variables are dependent. Essentially: why is E(X+Y) = E(X) + E(Y) when X and Y are dependent random variable? Given the two variables are dependent, if X happens to take on a...

Hi :) I need to program several nested 'for' loops which differs only in index of their variables inside. So I need to convert this: for i1 = 1000:-d:0 for i2 = (1000-(d*i1):-d:0 ... for in = (1000-(d*in-1):-d:0 some function containing all index variables like: b=(i1*A( :,2), i2*A( :,3), ...

My friends and I are in our first senior-level physics course at the University of Alabama in Huntsville, Introductory E&M. At the moment, we're working on using separation of variables to calculate electric potentials inside different objects given certain boundary conditions. One, however, is...

Hi all I am doing this question right now and I don't even know how to start it up. I know that it's in relation to a sum of a random number of random variables, but I don't know how to continue on from that. I've read my textbook and it states some definition for an MGF which is: $M_{y}(t) =...

Homework Statement Determine the minimum mean square error for the joint PMF. You will need to evaluate ##E_{X, Y}[(Y - 14/11\cdot X - 1/11)^2]##. Homework EquationsThe Attempt at a Solution The answer is ##\frac{3}{22}##, but when I work it out, I get ##\frac{203}{484}##. From my values, I...

Homework Statement [/B] Sun Tyrant: 25, 28, 25, 28, 29, 24, 28, 24, 24, 28, 30, 24, 22, 27 Sun Acrid: 29, 31, 29, 26, 28, 22, 25, 29, 29, 27, 28, 23, 26, 29 Laminatekist: 25, 26, 26, 26, 26, 28, 27, 26, 25, 28, 24, 28, 27, 25 This data set shows the number of raisins in each of 14 boxes of...

i am a 50 year old man, lovingly arguing with my 12 year old niece who has an algebra word problem. we're stumped (I'M stumped) -- and would love to get some help. CAN YOU PLEASE HELP ME SOLVE THIS "2 VARIABLE" PROBLEM ASAP (need it by 6am pacific time on 10/7/14). thanks! PROBLEM: Ashlee...

Homework Statement Let X and Y be independent exponential random variables with parameters a and b. Calculate E(X|X+Y). Homework EquationsThe Attempt at a Solution I'm pretty sure I have it, just want to make sure. Joint density for X and Y is abe^(-ax)e^(-by) for x,y>0. Let Z=X and W=X+Y so...

The question looks like this. Let $f(x, y)$ = 0 if $y\leq 0$ or $y\geq x^4$, and $f(x, y)$ = 1 if $0 < y < x^4 $. (a) Show that $f$ is discontinuous at (0, 0) (b) Show that $f$ is discontinuous on two entire curves. In regarding (a), I know $f(x, y)$ is discontinuous on certain...

The question looks like this. Let ##f(x, y)## = 0 if y\leq 0 or y\geq x^4, and f(x, y) = 1 if 0 < y < x^4 . (a) show that f(x, y) \rightarrow 0 as (x, y) \rightarrow (0, 0) along any path through (0, 0) of the form y = mx^a with a < 4. (b) Despite part (a), show that f is discontinuous at (0...

In the lagrangian formalism, we treat the position ##q## and the velocity ##\dot q## as dependent variables and talk about configuration space, which is just the space of positions. In the hamiltonian formalism we talk about canonical positions and momenta, and we consider them independent. Is...

Hiya! I am a beginner in programming and I am now having a java course in college... In the first few lessons, we are taught that programming involves declaration of variables and variables are classified into several categories (e.g. int, float, boolean, double, etc.). I wonder why we have to...

Homework Statement If f(x) = mx^3 + gx^2 - x + 3 is divided by x - 1, the remainder is 3. If f(x) is divided by x + 3, the remainder is -1. What are the values of m and g? Homework Equations Remainder Theorum/Factor Theorum The Attempt at a Solution Here is what I did...

Homework Statement A standard procedure for finding an approximate mean and variance of a function of a variable is to use a Taylor Expansion for the function about the mean of the variable. Suppose the variable is y, and that its mean and standard deviation are "u" and "o". f(y) = f(u) +...

Homework Statement Let ##X_k## be iid uniform discrete on ##\{0,...,9\}##. Find the distribution of ##\sum\limits_{k=1}^{\infty} \frac{X_k}{10^k}##Homework Equations The Attempt at a Solution I've tried a lot of things, I've tried decomposing ##X_k## into 10 bernoulli trials, I've tried using...

General formula of a line is ax+b=0 Similarly can we have a general formula of a circle ?

The double slit experiment is not known to violate any Bell inequality, and thus may have a local hidden variables description. Does Bohm-Dirac theory provide a local hidden variables description for the double slit? Are there other local hidden variables descriptions for the double slit? (If...

Hi guys, I have a system of six equations and thirteen variables. I would like to reduce it to seven free parameters. I used Reduce to solve it but it is taking really long (one full day and no output yet) and I think there must be a better way. Here is my code Y = {{y1}, {y2}, {y3}} T =...

In Quantum Mechanics, why do the dynamical variables become operators? What is the justification or motivation, if any exist?

I've posted a method below. I'm experimenting with local variable declarations in java. Actually, a compiler error in eclipse has made me reconsider what I understand about local variables. Why can't the local variable, String final, be created inside my if statement? Why, instead, would...

Homework Statement A coffee shop sell tea and coffee. The number of cups of coffee sold in a minute can be assumed to be a random poisson variable with mean = 1.5 . The number of cups of tea sold can be assumed to be an independent random variable with mean = 0.5. Calculate the probablity...

For discrete variables, a POVM on a system can be thought of as a projective measurement on the system coupled to an apparatus. This is called the Naimark extension. Is this also true for continuous variables? http://arxiv.org/abs/1110.6815 (Theorem 4, p10)

$$(2xy-3y)dx-({x}^{2}-x)dy=0$$ ans. $$xy(x-3)=C$$ ty

Simply put, can you find the function which extremizes the integral J[f]=\iint L\left(x,y,f(x),f(y),f'(x),f'(y)\right) \,dx \,dy Where ##f## is the function to be extremized, and ##x## and ##y## are independent variables? A result seems possible by using the usual calculus of variation...

I am curious how legitimate a solution Separation of Variables tends to give. I've been working problems out of Griffith's book on Electromagnetism, and am often uneasy as to the way things are done. I have two specific issues. The first, is that in spherical it is often necessary to remove...

Hi there, I'm having some difficulty in understanding how the change of variables by considering a retarded time frame can be obtained for this particular eqn I have. Say I have this original equation, \frac{\partial A}{\partial z} + \beta_1 \frac{\partial A}{\partial t}+ \frac{i...

Homework Statement Write the Laplace equation \dfrac {\partial ^{2}F} {\partial x^{2}}+\dfrac {\partial ^{2}F} {\partial y^{2}}=0 in terms of polar coordinates. Homework Equations r=\sqrt {x^{2}+y^{2}} \theta =\tan ^{-1}(\frac{y}{x}) \dfrac {\partial r} {\partial x}=\cos \theta \dfrac...

Dear All, I am a starter to machine learning and i am currently confused about the following problem: what is the result of P(X|Y)P(Y|Z)? In my book, it is written to be P(X|Z). But I don't think it is correct since P(X|Z)= P(X|Y,Z)P(Y|Z) But clearly P(X|Y)=/= P(X|Y,Z) Assuming...

Homework Statement Solve the equations sin(x+2y)=1/2 , cos(2x-y)=1/ sqrt(2) Homework Equations The Attempt at a Solution I tried getting a generic solution for both the first and second equation. How do I further proceed? By simultaneously solving? I so, how? 2x-y=2m*pi + or...

I have around 550 asymmetrical sigmoid curves fitted to a function with 4 varying coefficients. Each of these curves represent strength as a function of time and temperature for a different compound. Each compound is made up of varying substances at varying concentrations. Overall, I have 550...