What is Variable: Definition and 1000 Discussions

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.

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  1. D

    How to Calculate Interest in a Variable Interest Account?

    Is there a simple formula to find the amount of money in an account given a situation like this... You deposit x into the account Each year you get interest Year one the interest is 1% Year two the interest is 2% Year three the interest if 3% and so on Is it possible to get a simple general...
  2. T

    PDF of a continuous random variable

    Homework Statement Let X denote a continuous random variable with probability density function f(x) = kx3/15 for 1≤X≤2. Determine the value of the constant k. Homework Equations I'm not sure if this is right but I think ∫kx3/15 dx=1 with the parameters being between 2 and 1, The Attempt at a...
  3. I

    Distribution of a Function of a Random Variable

    Homework Statement If X is uniformly distributed over (0,1), find the PDF of Y = |X| and Z = e^X Focusing on the |X| one Homework Equations Derivative of CDF is the PDF The Attempt at a Solution So I start by writing down the CDF of X, Fx(x): 0 for x <0 x for 0 ≤ x ≤ 1 1 for x ≥ 1 And I...
  4. I

    Expectation of Continuous Random Variable [word problem]

    Homework Statement Here's the problem with the solution provided: Homework Equations Fundamental Theorem of Calculus (FToC) The Attempt at a Solution So I understand everything up to where I need to take the derivative of the integral(s). Couple of things I know is that the derivative of...
  5. bananabandana

    Two variable function, single integral

    Homework Statement Evaluate: I(y)= \int^{\frac{\pi}{2}}_{0} \frac{1}{y+cos(x)} \ dx if y > 1 Homework EquationsThe Attempt at a Solution I've never seen an integral like this before. I can see it has the form: \int^{a}_{b} f(x,y) dx I clearly can't treat it as one half of an exact...
  6. Thinkor

    Evidence for Variable Speed of Gravity in Coordinate Spacetime

    Although the speed of light is constant in GR, within coordinate spacetime the speed of light varies. For example, light travels more slowly near a black hole than in remote space. The same is theoretically true of the speed of gravity. But is there any supporting empirical evidence?
  7. T

    Representing a function of one variable in terms of a sequence of gaussians

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  8. GreenAce92

    Variable strength electric motor

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  9. B

    Integration - Change of Variable

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  10. blair chiasson

    I have a problem with variable forces

    Homework Statement A force F has components F sub x = axy-by^2, F sub y= -axy+bx^2 where a= 2N/m^2 & b=4N/m^2 Calculate the work done on an object of mass 4kg if it is moved on a closed path from (x,y) values of (0,1) to (4,1), to (4,3) to (0,3) and back to (0,1). all coordinates are in metres...
  11. T

    Would someone be able to isolate v?

    Homework Statement So I have a group lab for physics, but I need some alg/trig help isolating v for a derived equation. I've tried many times to to get v0 by itself but when I check the equation with the values that I have for each variable I always get the wrong answer. ∆y =...
  12. B

    MHB Definite integral on elliptic integral where modulus is function of variable

    How to prove: $\int_{0}^{\frac{\pi }{2}} {\frac{\sin \theta}{\sqrt{Z^2+(R+h \tan \theta)^2}} K[k(\theta)]}=\frac{\pi }{2\sqrt{R^2 + (h+Z)^2}} $ where \[ k(\theta)=\sqrt\frac{4Rh \tan \theta}{Z^2+(R+h \tan \theta)^2}\] and $ K[k(\theta)] $ is the complete elliptic integral of the first kind...
  13. S

    MHB Random Variable Transformation

    We have a r.v. X with p.d.f. = sqrt(θ/πx)*exp(-xθ) , x>0 and θ a positive parameter. We are required to show that 2 θX has a x^2 distribution with 1 d.f. and deduce that, if x_1,……,x_n are independent r.v. with this p.d.f., then 2θ∑_(i=1)^n▒x_ι has a chi-squared distribution with n...
  14. T

    Fourier transform of function of a complex variable

    Can anyone point me to some material on applying the Fourier transform to the case of an analytic function of one complex variable? I've tried to generalize it myself, but I want to see if I'm overlooking some important things. I've started by writing the analytic function with u + iv where u...
  15. PattyCake

    What is the Velocity of a Block Released from a Compressed Spring?

    A 1.2 kg block is held against a spring of force constant 1.0 x 10^4 N/m, compressing it a distance of 0.15m. How fast is the block moving after it is released and the spring pushes it away?
  16. B

    How to find the coefficient of friction in a rotor-ride?

    Homework Statement I have no values at all, so it's just going to be the variables in the relevant equations. I need to define mu using those variables. A carousel is moving in a circle at velocity v and has a radius r. It is moving fast enough that each person with mass m is pinned against the...
  17. teroenza

    Mathematica Mathematica Globally Define Variable as Real

    I want to write a line of code at the top of my .nb and have Mathematica treat the specified variables as real only. I've tried using "Assumptions" and "Assuming", but it just won't work. I still get back answers where the entire expression is returned inside the Re[ ] command, like it is...
  18. S

    MHB Probability function (p.f) of a random variable

    If one has a Bernoulli random variable W that is derived from a Variable T (Poisson λ), by the following rules W = (if T=0 then W=1 and if T>0 then W=0), I am having trouble finding the pf for W. Any suggestions about how to proceed forward?
  19. S

    MHB Find the image of a two variable function

    So on my first course of Algebra in university I have been asked to find the image of the following function: f : Z x Z -> Z, f(x, y) = x2 - y2 In high school I worked only with single variable functions and I could have found the image by drawing its graph, using limits or using some specific...
  20. Q

    Calculators TI-89 how to save result of an embedded funtion to a variable

    Hello, I do a lot math and physics work, (predominantly advanced fundamental theories), and have consistently been hindered by a particular issue when it comes to a few of my defined functions. I feel like it would be a kind of "order of execution" issue with a simple solution, but though I've...
  21. M

    MATLAB [Matlab] How to use inputdlg string variable in text file?

    I am trying to display the input that I enter into the dialog box from "inputdlg" function into a text file. This is what I've so far: prompt={['What is your name?']}; title = 'Name Machine'; answer = inputdlg(prompt, title); name = answer{1}; fileID = fopen('NameMachineFive.txt', 'w')...
  22. I

    Finding the value of a variable in a matrix

    Homework Statement Given :  x+y+5z = 2   x+2y+7z = 1   2x−y+4z = a . a) Determine the value of a which will make the given system have many solutions. Explain your answer. b) Choose a value of a which will make the given system have NO solutions. Explain your answer. c) Is it possible...
  23. I

    C/C++ "Understanding the C++ For Loop Variable [i]"

    ok so i realized my problem with c++ is that i don't really understand for loops. well it's not exactly the loop itself but i don't understand the loop variable [i]. what is for EXACTLY? why is it needed? why can't you just use the other variable you are using? why does this extra variable need...
  24. H

    Unraveling Diffraction: Understanding Variable Relationships

    I'm having trouble understanding the relationships between various variables at play in diffraction. Say you have diffraction with one slit, two slits, and a grating as shown below. So 1) The Amplitude of each peak is directly proportional to the intensity of the incoming waves. This makes...
  25. W

    Sampling - the variable of X

    Homework Statement A bag contains a large number of coins comprises of 1 cent and 5 cents coins in the ration of 1:3 find the man and variance of the values of coins.. i have attached the sample ans here. i don't understand why the value of '2' is used?? why not '5' ...for me '5' represent 5...
  26. evinda

    MHB Does the variable take these values?

    Hello! (Wave) If we have the following for loop: for (i=8^{n-1}; i<8^n; i+=1) (where $n$ is an integer) does $i$ take the values $8^{n-1}, 8^{n-1}+1, \dots, 8^n-1$, or am I wrong? (Thinking)
  27. R

    Unit Circle and Quantum Predictions [hidden variable model agrees with QM?]

    I would like to reopen a discussion on assertions made by David Mermin such as: “There is no conceivable way to assign such instruction sets to the particles from one run to the next that can account for the fact that in all runs taken together, without regard to how the switches are set, the...
  28. SSGD

    Variable Set Distribution - Buckingham Pi Theorum

    Background: I am trying to write a program for Buckingham Pi Groups. I need to find a way to list all the input varialbes as different sets. For example if I have 4 variables [V D p u] and I want to distribute them 3 ways I get 4 sets. Number of Sets = Binomial(Number of Variables...
  29. D

    MHB Second moment of the Poisson random variable

    With a Poission random variable, we know that \(E[X] = var(X) = \lambda\). By definition of the variance, we can the second moment to be \[ var(x) = E[X^2] - E^2[X]\Rightarrow E[X^2] = var(X) + E^2[X] = \lambda(1 + \lambda). \] The characteristic equation for the Poisson distribution is...
  30. S

    Mass in Equilibrium with Variable Length Cable

    Homework Statement Consider the diagram below. A 1000 kg block being suspended in equilibrium by cables c and a. Cable c is on a pulley which can vary the length of the cable. Write the constraints of equilibrium. Find the tension in each cable based on varying lengths of cable c between 1.2 m...
  31. H

    Variable low speed motor, how much can I vary it?

    I'm looking at getting a motor to drive a micrometer. It's on an interferometer mirror for the curious. I'll need around 1RPM or so, but I want to be able to vary the speed, because I'm pretty unsure about how fast I'll need it to go for my experiment to work. I'm thinking a range of like 1/4 to...
  32. J

    Double integral change of variable polar coordinates question

    Homework Statement evaluate the double integral of cosh(6x^2+10y^2) dxdy by making the change of variables x=rcos(theta)/sqrt(3) and y=rsin(theta)/sqrt(5) let D be the region enclosed by the ellipse 3x^2+5y^2=1 and the line x=0 where x>0. Homework EquationsThe Attempt at a Solution first I...
  33. I

    C/C++ C++ Loop Variable: What & Why?

    what is the purpose of a loop variable (i)? how is it useful?
  34. A

    Help me factorize a quadratic equation in a complex variable

    The equation is: (appears while solving a trigonometric integral using residue theorem) 2Z2+iZ2-6Z+2-i =(2+i)Z2-6Z+(2-i) The roots are: Z1=(2-i) and Z2=(2-i)/5 I can't write the equation in factored form. If I simply write it like this: {z-(2-i)}{5z-(2-i)} It doesn't give the same...
  35. B

    Finding the PMF of a function of a discrete random variable

    The discrete random variable K has the following PMF: p(k) = { 1/6 if k=0 2/6 if k=1 3/6 if k=2 0 otherwise } Let Y = 1/(1+K), find the PMF of Y My attempt: So, I am really confused about what this is asking. I took...
  36. A

    While loop - Variable not changing in C

    I am not sure if this is supposed to go in the homework forum or not since it is more of an off physics topic so sorry if it is incorrect. I have a programming assignment for class and I am having a lot of trouble with a while loop. For this part of the program I have to prompt the user to...
  37. M

    Solving Questions with Variable Mass: Seeking Guidance

    Hello everyone. I've been struggling with how to deal or solve questions that include variable masses. Considering the method I usually try to solve with, it either gets me lost or just makes things complicated and doesn't work often to me. :P I was wondering if you guys could help me out...
  38. C

    Fluid dynamics - find distribution of a conserved variable

    I accidentally posted this to the "Calculus & Beyond" forum when I meant to post it to the physics forum. If someone can tell me how to move this post, I will get rid of it here! Homework Statement Consider a property, for example temperature θ, that is conserved during advection (i.e. Dθ/Dt =...
  39. N

    Solution of diffusion equation with three independent variable (r,z,t)

    Hi, I want to solve the following diffusion equation: (d/dt) C(r,z,t)=D*∇^2 C(r,z,t) where C is the concentartion and D is the coefficient of diffusivity (constant) with initial condition C(r,z,0)=C0 (constant) and boundary condition dc/dr=0 at r=0; (dc/dz) at z=-L equal to (dc/dz)...
  40. I

    C/C++ Using Constant Variables in C++ for Shipping Cost Calculation

    i don't even understand this... Given shipWeight in pounds, compute the cost to ship a package and assign to shipCost. Shipping involves a flat fee of 75 cents, plus 25 cents per pound. Declare and use a const named COST_PER_POUND. Sample program: #include <iostream> using namespace std; int...
  41. D

    MATLAB Matlab estimate PDF from random variable X

    How do I estimate the pdf from a random variable \(X\) where \(X = U_1 - U_2\) and \(U_i\) are uniform random variables? In the code below, I used unifrnd(-5, 5, 1000, 1) which generated a 1000x1 vector of uniform random number between -5 and 5. How do I estimate the PDF for X? rng; X =...
  42. I

    Boat slowing down with variable acceleration

    A motor boat of mass m moves on the surface of a lake at a speed0v. At the moment 0t= the engine is shut down. Assuming the resistance of water to be proportional to the speed of the boat, F=−rv, find a) the time interval after which the boat stops; b) the speed of the boat as a function of...
  43. kini.Amith

    Eigenvalues containing the variable x

    Homework Statement The wave function ψ(x)=Ae-b2x2/2 where A and b are real constants, is a normalized eigenfunction of the schrodinger eqn for a free particle of mass m and energy E. Then find the value of E Homework Equations The Attempt at a Solution Substituting the wave...
  44. S

    Integration involving continuous random variable

    Homework Statement please refer to the question, i can't figure out which part i did wrongly. i 'd been looking at this repeatedly , yet i can't find my mistake. thanks for the help! the correct ans is below the question. where the c= 283/5700 , q = 179/5700 Homework Equations The...
  45. mesa

    Is the use of the term 'general form' correct for variable functions?

    For certain types of functions I have been using the term 'general form' as a way of stating that some function of some variable(s) is true for more than one value of the variable (usually an infinite number). Here is a simple example, 1=cos(2∏x) There have been (at times) where the use of...
  46. mesa

    How does one express a function of a single variable and a constant?

    How would someone go about writing a general expression for a function of a single variable and a constant? For example, if we have a function of two variables 'x' and 'y' we can use f(x,y). If we had a function of 'x' and the constant '∏' is it acceptable to write it as f(x,π)?
  47. N

    Definite Double Integral of a single variable

    Homework Statement This isn't actually homework. I was messing around in my notebook trying something when I ended up writing something to the effect of this: dT = \frac{V^{2}}{R(1+α dT)}dQ R(1+α dT) dT = V^{2}dQ Where α and V are constants. Now, I'm fairly sure what I had done made...
  48. Z

    Transformation of variable (what happens with the area?)

    Homework Statement Dear friends, let U and V independent variables that are both defined on [-∏, ∏] and are uniformly distributed. If x = cos(U + V) and y = sin(U-V), what is the area where the variables X and Y are defined? Homework Equations U + V = arccos(x) U - V = arcsin(y) For a test...
  49. S

    Variable pulley distance - tensioner force help needed

    Greetings, lurked for a long time, but I need some help here so I joined up. Please have some patience with me if I miss any important information. I am working on a belted pulley drive system where the driveN pulley will move relative to the driveR while in the stopped state. An outside...
  50. J

    Solving equation involving a variable and its logarithm

    Can you suggest a general analytical solution to the following equation \ln(x^{3/2})-bx-c=0 where x is real positive variable and b and c are real positive constants.
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