A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates.
This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:
Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks.
Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.Many, possibly most, stars have at least some variation in luminosity: the energy output of our Sun, for example, varies by about 0.1% over an 11-year solar cycle.
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...
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...
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...
I'm in a probability theory class and I feel like I'm missing something fundamental between random variables and their distribution functions. I was given the following questions:
1)Let θ be uniformly dist. on [0,1]. For each dist. function F, define G(y) = sup{x:F(x)≤y}. Prove G(θ) has the...
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.
the random variable X and Y have a joint PDF given by:
$f_{x,y}(x,y) = \frac{1}{10}$, $(x,y)\in[-1,1] * [-2,2] \cup [1,2] * [-1,1]$
a) find the conditional PDF for $f_{y|x}(x,y)$ and $f_{x|y}(xy)$
and
b) find E[X|Y], E[X] and Var[X|Y]. Use these to calculate var(X)
for part a) I am unsure...
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...
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 Schrodinger equation, Ψ is called wave function, which is not observable, while Ψ·Ψ* is the probability, which is observable.
can we rewirte the Schrodinger 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...
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...
The problem:
Let \mu_{n} = \frac{1}{n} for n \in \mathbb{N}. Let X_{n} \; \mathtt{\sim} \; \textrm{ Poisson}\left( \lambda_{n} \right).
Let Y_{n} = n X_{n}. Show that Y_{n} \xrightarrow{P} 0 .
Work I've done:
I've shown that X_{n} \xrightarrow{P} 0 by showing that \mathbb{P} \left(...
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
Given X=ZU+Y
where
(i) U,X,Y, and Z are random variables
(ii) U~N(0,1)
(iii) U is independent of Z and Y
(iv) f(z) = \frac{3}{4} z2 if 1 \leq z \leq 2 , f(z)=0 otherwise
(v) fY|Z=z(y) = ze-zy (i.e. Y depends conditionally on...
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...
I have a queueing system.
The probability Generating Function of the number of packets in the queue (queue length) is given by
Q_G(z)=\frac{e^{\lambda T(z-1)}(1-z^{-1})(1-\lambda T)}{1-z^{-1}e^{\lambda T(z-1)}}.
I need to find the PGF of a conditional quantity.
X=(Q_G|Q_G>0)
i.e. to say in...
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...