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.
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...
Hi there.
In the multivariate case it is proven that if
X~Nm(U, S) and Y = a + CX where C is an invertible n x n matrix, and S is the covariance matrix then:
Y ~ Nm(a + CU, CSC')
I am trying to apply this proof to a similar problem.
If we have X1...Xk with Xi ~ Nm(Ui, Si) where i = 1...k...
Homework Statement
Given a random variable X with a known distribution (e.g. a beta distribution), find the distribution of
f(X) = X^2 + X
The Attempt at a Solution
I've tried the normal approaches: the standard transformation theorem; conditioning on X; Laplace transformation, etc...
Homework Statement
That's a graph of Force in Newtons (y axis) vs displacement in meters (x axis) for an object of mass 3.0kg that is moving along the x-axis and initially starts at rest. I am being asked to find the total work done on the object as it moves from x = 0 to x = 7...
Hi all,
Could you please answer my following question related to an exponential random variable? Thank you.
Let X represent the waiting times at a telephone in an office. Assume that X is an exponential random variable with parameter λ: P(X < t) = 1 - e^{-λ*t}
At each time when the...
Homework Statement
A light bulb and a resistor are connected in series to a variable power supply. A student first connects a voltmeter and an ammeter to measure the current through and the voltage across the bulb, as shown in the left circuit. The student varies the power supply voltage and...
Homework Statement
Compute the following sequence (show your work)
(-2)n+3n
÷ (-2)n+1+3n+1
The Attempt at a Solution
(-2)n+3n
÷ (-2)n(-2)+3n3n
After this I don't know what to do. I know that if I can prove that something smaller than this for all n's converges to +∞, this will...
Can a variable star become a non variable one? Or viceversa, can a non variable, as it is (almost) the sun, become quickly (say few thousands of years) a variable one? Is there any record (e.g. in the geological records) which shows that the sun had once a very different luminosity? Has this...
Hello,
I have a really tough time understanding this concept although this isn't anything more complex than a composition of functions.
I have a done example from my book that I am trying to interpret.
p_\xi (x)=\frac{1}{\pi}
for an interval between [0,∏]
The...
I have a system where a cable is pulled down with a load of 100-200 lb. I need a motor that resists this load with a force that can be programmed to be anywhere from 5-30 pounds. I don't want the motor to stop the downward motion, just to offset the magnitude of the force pulling down on the...
A water glass (10 cm diameter at the top, 6 cm diameter at the bottom, 20 cm in height) is being filled at a rate of 50 cm^3/min. Find the rate of change of the height of the water after 5 seconds.
V=(∏* (h/3)) * (R^2 + r^2 +(R*r))
I've been messing around with this for a bit and made a...
Which of the following is an analytic function of the the complex variable z = x+iy in the domain lzl <2 ?
(3+x-iy)^7
[(1+x+iy)^4]*[(7-x-iy)^3]
[(1-2x-iy)^4]*[(3-x-iy)^3]
(x+iy-1)^1/2
Homework Statement
For which parameter \alpha\in\mathbb{R} the function:
f(x, y)= \begin{cases}|x|^\alpha \sin(y),&\mbox{ if } x\ne 0;\\ 0, & \mbox{ if } x=0\end{cases}
is differentiable at the point (0, 0)?
The Attempt at a Solution
For α<0, the function is not continue at (0, 0)...
Homework Statement
If Z has a standard gaussian distribution then what is the distribution of
Z2 and what is its mean?
The Attempt at a Solution
Let T = Z2 Then we can get that
pdf T = e-T/2(1+1/T) x (1/√(2∏T)
I am not sure if this is correct and don't know how to find the...
I learned in school that Median = L + (n/2-cf)*h/f
where L = lower limit of median class
n = no. of observations
cf = cumulative frequency of class preceding the median class,
f = frequency of median class,
h = class size (assuming class size to be equal).
I used to use this formula for...
Hello,
Does anyone know if this makes sense or is usable?
I've only been able to describe it through a graph.
Instead of the x-axis being numbers, being powers of x.
Let me clarify - where normally would be x=0,1,2,3... would now be x^0, x^1, x^2, x^3
and the y-axis would be values of...
Hi all
I'm looking for solving this problem to find the closed form solution if it is possible:
Y=\frac{1}{X}
Where X is uniform random variable > 0
I know the expected value for X which is \overline{X}
is there a method to find the expected value of Y which is \overline{Y} in term of...
Hey,
I have a pdf of a random variable Z given. I am being asked to calculate what the moment generating function of a r.v Y= Z + c will be where c is a constant in ℝ
I tried to calculate it in the following way:
\int^∞_0 e^{(z+c)t} f(z+c)dz where f(z) is an exponential pdf with...
Hi
Shaft A has variable RPM, getting input from some rotating element (say X), ranging from 0 to 2000.
The RPM of X cannot be adjusted or controlled.
A has to transfer the rotation with limiting RPM of upto 400 to Shaft B.
Is there a way to limit the RPM using a mechanism such that at...
Homework Statement
Compute the limits of the following sequence (show your work):
3n+17n+3
4n5n-2
(sorry if it looks funny ... the top line is divided by the bottom line)
The Attempt at a Solution
I was thinking that I should get the exponents the same and add/subtract the...
Homework Statement
This is a problem form my calculus book, which states:
According to the ideal gas law, the pressure, temperature, and volume of a confined gas are related by P=kT/V, where K is a constant. Use differentials to approximate the percentage change in pressure if the temperature...
Homework Statement
(x,y)-->(0,0) y*ln (y2+x2)
Homework Equations
!
The Attempt at a Solution
i've tried polar coordinates i end up with sinθ in it don't know how to proceed
and I've taken several paths like y=0 , x=0 , x=y2 , x=y , x=y3
they all yeild zero
Edit : is it...