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. S

    Isolating a variable when variable is in both sides of equation

    Homework Statement y=(2-x)/(5x) Solving for x=f(y) I can get as far as 5xy=(2-x) Tried 5xy=-1(x+2) All attempts at solving this have given me the wrong answer, and I end up with x on both sides of the equation. Stuck and not sure what to do. Correct answer is x=2/(5y+1) , but I don't...
  2. U

    Tricky to 2 variable line/path integral

    Homework Statement Compute ∫f ds for f(x,y)=\frac {y^3}{x^7} y=\frac {x^4}{4} for 1≤x≤2 Homework Equations ∫f ds= ∫f(c(t))||c'(t)|| ||c'(t)|| is the magnitude of ∇c'(t) The Attempt at a Solution From this... I gathered the following, by saying x=t c(t)= <t,\frac {t^4}{4}> c'(t)= <1, t^3>...
  3. S

    Continuous Functions of One Random Variable

    My problem is as follows (sorry, but the tags were giving me issues. I tried to make it as readable as possible): Let X have the pdf f(x)= θ * e-θx, 0 < x < ∞ Find pdf of Y = ex I've gone about this the way I normally do for these problems. I have G(y) = P(X < ln y) = ∫ θ * e-θx...
  4. Q

    MATLAB Solving a MATLAB Problem with 3 Variable Integration

    dear friends i want to do set of operation in MATLAB but i have a problem: first of all, i want to take 3variable integration from f which is function of x,y,z,m,a but i want to integrate only over x,y,z after that for a special "a" forexample a=0.01 i want to solve the equation.i mean...
  5. J

    Differentiated values are treated just like any other variable, right?

    http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.596257.html One of the steps leads us to A=2x√(r2-x2). The page then says that we could differentiate at this step, but that it would be easier to first square both sides, so as to not have to...
  6. D

    Numerical differentiation with change of variable

    Hi all I am trying to solve for an integral whose integrand is a derivative that has a change of variable inside of it. ∫ (dz/dx) * cos(θ) dθ between 0 and pi. I have a function for z(x), and also know the relation between of x and θ, but what I don't know is how to evaluate such...
  7. U

    MHB Solving Random Variable Work: 0 to Infinity = 0.002?

    Work done so far... Integrating from 0 to infinity and equating it to 1, we get (c/2*10^-3) = 1 c= 2/1000 =0.002 Is it correct? http://www.chegg.com/homework-help/questions-and-answers/-q3136942#
  8. W

    Is a random variable really random or just a function?

    lets say that X is some random variable that takes +1 if rational otherwise -1. at http://tutorial.math.lamar.edu/Classes/CalcI/TheLimit.aspx in example 4, can we consider g(x) as a random variable because it's behaviour is same, right? is random variable really random or just function? I found...
  9. L

    Variance of Continous Random Variable

    I have the continuous random variable Y, defined such that: Y=3X+2 and the PDF of x is zero everywhere but: f(x)=\frac{1}{4}e^{\frac{-x}{4}}, x>0 I correctly got the mean like so: \mu=E(h(x))=\int^{\infty}_{0} h(x)f(x) and evaluated it to be 10. I am unsure as to how I go about...
  10. E

    Integration by parts, more than one variable, and green's identities etc.

    I was wondering if someone can show me or point me to a worked out example using integration by parts for more than one variable (as used in relation to pde's, for example). While I took pdes and calc 3, its been awhile and I don't know if I ever understood how to work out a concrete example...
  11. Jalo

    Parcial derivation of two variable function

    Homework Statement Given the function f(x) defined as: (x^3-y^3)/(x^2+y^2) if (x,y)≠(0,0) 0 if (x,y)=(0,0) Find the parcial derivatives of the function at the point (0,0). Is the function f differentiable? Homework Equations The Attempt at a Solution d/dx [...
  12. F

    Basic random variable question - measure theory approach

    I have always struggled in understanding probability theory, but since coming across the measure theoretic approach it seems so much simpler to grasp. I want to verify I have a couple basic things.So say we have a set χ. Together with a σ-algebra κ on χ, we can call (χ,κ) a measurable space...
  13. M

    Two Variable 2nd Order Taylor Series Approximation

    Homework Statement Derive the Derive the two variable second order Taylor series approximation, below, to f(x,y) = x^3 + y^3 – 7xy centred at (a,b) = (6,‐4) f(x,y) ≈ Q(x,y) = f(a,b) + \frac{∂f}{∂x}| (x-a) + \frac{∂f}{∂x}|(y-b) + \frac{1}{2!}[\frac{∂^2f}{∂x^2}| (x-a)^2 + 2\frac{∂^2f}{∂x∂y}\...
  14. V

    Solving for an indicated variable

    Homework Statement http://mathway.com/math_image.aspx?p=tSMB012`SMB02RSMB03SMB02FSMB03mSMB10kSMB02fSMB03SMB02rSMB03?p=67?p=42 We are solving for k. ^click the link. Homework Equations The Attempt at a Solution I know both sides need to be squared... maybe divide t by 2∏...
  15. T

    C/C++ [C++] Basic programming problem, user inputting wrong variable type

    I'm fairly new to programming. I'm doing an undergrad ENG degree and one of my first year mandatory courses is programming. It's my first time ever doing it so I don't know much yet. I'm currently learning C++. I'm in the middle of working on a problem that pretty much involves me making a...
  16. B

    Finding Inverse the Function of multiple variable functions

    I understand that given two functions f:X→Y and g:Y→X, to say that f is the inverse function of g means g o f:X→X is defined by g(f(x))=idx and to say g is the inverse function of f means f o g: Y→Y is defined by f(g(x))=idy I understand how to find inverses of one variable functions and...
  17. L

    Partial derivative with respect to a function, rather than variable?

    Hi all. I've recently started working a lot on my background in math and physics, since this year I began a new masters program which is quite math/physics heavy and I don't have a formal background in either field. I will try to get active on this forum, since I've been luring for some time and...
  18. N

    How to find the expected value of a continuous variable with pdf fy= y^(-2)?

    Homework Statement Find the expected value of a continuous variable y with pdf fy= alpha*y^-2, 0<y<infinity. I know it is the integral from zero to infinity of y*fy, but I don't know where to go from there. I'm then supposed to use the expected value to find the method of moments...
  19. D

    WOrk done by a variable force (in two dimension)

    Homework Statement How to find the work done by a variable force in (two dimension) When F = ax^2 i + b y^3 j If a subject move from (x1,y1) to (x2, y2) Homework Equations F = dW/dr The Attempt at a Solution I tried to solve them separately by x-direction and y-direction, and then I added...
  20. P

    Fortran [Fortran] String variable for output filenames

    This is the troublesome part eLeftOutFile = 'data/ElonL'//fileNameSuffix(0:25)//'.dat' OPEN(754,FILE=eLeftOutFile,STATUS='REPLACE',ACCESS='SEQUENTIAL') First off, fileNameSuffix is a CHARACTER(len=40) just to be safe, I am just cutting it off, since those are the relevant parameters...
  21. A

    MHB Solve Second Order Differential Eq. With Variable Coefficient

    $(1-x^2)y'' - xy' + 4y =2 x \sqrt{1-x^2} $ Hint use the substitution $x =\sin t$ I used it and end with $\cos t y'' + \sin t y' - \frac{\sin t}{\cos t} y' + 4y = 2\sin t |\cos t| $ how to solve this i just want the name of the method
  22. L

    Changing part of a name of a variable in a for loop

    changing part of a name of a variable in a "for" loop hello everyone! let's say i have the equation between two variables: DT10sec= A*T10sec, working in matlab. How can i use a "for" loop to calculate the equation DT20sec= A*T20sec DT30sec= A*T30sec, DT40sec= A*T40sec,... etc How can i...
  23. M

    How to calculate energy used in a variable speed drive

    Homework Statement We'll be running a vsd water pump. We'll be seeing the energy savings of using a vsd, instead of using an AC motor on full load and using a tap to reduce water flow. Sorry for the lack of info. The Attempt at a Solution I'm sure it will have something to do with...
  24. denjay

    Most probable value of a random variable?

    A problem in this book asks for the most probable value of a random variable x. As far as I know, if a random variable has "most probable value" then it isn't a random variable. The problem is attached. It is the second question in part b. Could the answer be that there is no most probable...
  25. T

    Isolating a function variable

    Homework Statement Im supposed to calculate the value of x for 20*log10(\frac{\sqrt{x^2 +1}}{cos(x)}) = 3 The Attempt at a Solution I start off by dividing by 20 on both sides so I just have the expression with log.. and my idea henceforth is to take the inverse of cosine to...
  26. Jalo

    Existence of a two variable function limit

    Homework Statement In this exercice I'm asked to find out if the limif of the function f(x,y) exists. lim (x,y)→(0,0) sqrt(x*y) / (x^2 - y^2) Homework Equations The Attempt at a Solution I've tried to approach it from different coordinates (y=x, y=0, x=0, y=sqrt(x),...) but I...
  27. Jalo

    Limit of a two variable function

    Homework Statement Hi. I'm trying to solve the limit of the function: lim (x,y)→(0,0)f(x,y) = = lim [SUB](x,y)→(0,0) 3 * x2 / (x2 + y2) Homework Equations The Attempt at a Solution x2 / (x2 + y2) is a limited function. Its image is always between 0 and 1. However I don't...
  28. C

    Using getchar, cant change variable?

    Homework Statement I have some code and I use getchar to read in some input from the user say a5 I have assigned char letter; int number; letter = getchar(); number = getchar(); so that putchar(letter) prints a and putchar(number) prints 5 but when I try ...
  29. A

    Fortran Fortran: opening variable file names

    I am trying to write code so a 2-d array is written to the hard drive (which is later to be read). There are several do loop iterations and I would like the file name to change with every iteration so I get as many files as there are loop iterations. I get one 1-d array that is named A, no...
  30. C

    Solving an equation with variable as denominator?

    Homework Statement The problem initially was a Lagrange multipliers question, and I'm trying to solve for λ. I have an equation in terms of λ alone, but I just can't solve it. I plugged it into Wolfram Alpha and it gave me the λ value in the back of the textbook, but I still don't know how to...
  31. T

    Variable Coefficient PDEs and Continuity of the General Solution

    Variable Coefficient PDEs My homework question: "Find the general solution of ##xu_{x} + 4yu_{y} = 0## in ##{(x,y)\neq(0,0})##; when is this solution continuous at (0,0)?" ##\frac{dx}{dy} = \frac{x}{4y}## ##\frac{dx}{x} = \frac{dy}{4y}## Integrating both sides, we find: ##lnx + c =...
  32. R

    How to solve linear first order variable coefficient systems?

    1. how do i solve X'(t)=A(t)X(t) Homework Equations I know of this equation: x(t) = x_0 \exp\left( \int_{t_0}^t f(\xi) \, d\xi \right) but i think that I'm using it wrong. The Attempt at a Solution i have the following mathematica code: A= x = MatrixExp[Integrate[A, {t, 0, s}]].{1, 0,0,0}...
  33. F

    Change of variable in integral using metric

    What is the formula to evaluate a multi-integral by a change of coordinates using the squareroot of the metric instead of the determinate of the Jacobian? Thanks.
  34. E

    The distribution of function of random variable

    i have this question i do find the distribution like this figure : and i plot the y like this: now i want to find the distribution of y i tried to take the distribution for each interval in Fx(x) like this : but the solution in the book said : who is wrong me or the book...
  35. S

    Conservation of linar momentum - variable mass

    If a railroad car traveling down a straight, frictionless track encounters vertical rain that fills it with additional mass, will the velocity decrease in order for the momentum to be conserved? Will the opposite happen if the water is let out from a hole in the bottom? I cannot see any...
  36. F

    Fortran Problem on reading dataset with variable decimal places as it is using fortran

    Hi all, I have attached my text file(tab delimited). I am planning to read those dataset into real array of (30,38). The dataset has variable decimal places like 312.66, 0, 535.696 ,456122.758. With the following codes, READ(12,*)((X(I,J),I=1,30),J=1,38)...
  37. S

    Statistics-Probability Distribution of Discrete Random Variable

    Homework Statement A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated. What is the probability...
  38. A

    Create Variable Inductance in SPICE

    I'm trying to create a variable inductance in SPICE, specifically in NI Multisim. What I'm trying to do is create a saturable inductor. I need an inductor that changes it's inductance with current. Multisim does have a "virtual" inductor that you can create a inductance function with but I can't...
  39. W

    What is a sequence of random variable?

    Hi all, I am really confused about the random variables Toss a coin three times, so the set of possible outcomes is Ω={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Define the random variables X = Total number of heads, Y = Total number of tails In symbol, X(HHH)=3...
  40. P

    Transformation of random variable

    Hi there, I am currently reading Rohatgi's book "An introduction to probabilty and statistics" (http://books.google.de/books?id=IMbVyKoZRh8C&lpg=PP1&hl=de&pg=PA62#v=onepage&q&f=true). My questions concerns the "technique" of finding the PDF of a transformed random varibale Y by a function...
  41. fluidistic

    Probability density of a new variable

    Homework Statement Let X be a continuous random variable with parameters \langle x \rangle and \sigma. Calculate the probability density of the variable Y=exp(X). Calculate the mean and the variance of Y. Homework Equations Reichl's 2nd edition book page 180: P_Y(y)=\sum...
  42. P

    Dynamic behaviour of a rotatable airfoil, at constant and variable flow field

    Homework Statement While I was learning about drag and lift on airfloils, I imagined a special airfoil which is fixed at a certain elevation and cannot move vertically (y axis) but can be rotated around its axis (z). Let's assume the direction of the flow to be the x axis. I try to predict...
  43. C

    Left & Right Limits Of A Function (Finding Values Of A Variable)

    Homework Statement Homework Equations Only ones I know that are relevant are the equations shown in the question (for the left and right limits). The Attempt at a Solution The difficulty that I am having right not is comprehending what is really being asked from the question. From...
  44. J

    Division of Chi Squared Random Variables

    Hey guys, I have a quick question. Suppose X is a chi squared random variable with n degrees of freedom and Y is another independent chi squared random variable with n degrees of freedom. Is X/Y ~ 1 ? Intuitively, it makes sense to me but I'm not too sure.
  45. fluidistic

    Characteristic function of a continuous random variable

    Homework Statement I must calculate the characteristic function as well as the first moments and cumulants of the continuous random variable f_X (x)=\frac{1}{\pi } \frac{c}{x^2+c^2} which is basically a kind of Lorentzian.Homework Equations The characteristic function is simply a Fourier...
  46. A

    Nature of stationary points three variable functions

    Homework Statement Find and characterise the stationary points for F(x,y,z) = x2 + xy + y2 - 2z2 +3x -2y +z The Attempt at a Solution I found fx, fy, fz and let them equal to 0. Solving gives me the critical point (-8/3,7/3,14). From here I'm not sure how to determine the nature...
  47. J

    Change of Variable for a Vector from Rectangular to Cylindrical

    Homework Statement 1.21 Express in cylindrical components: (a) the vector from C(3, 2,−7) to D(−1, −4, 2); (b) a unit vector at D directed toward C; (c) a unit vector at D directed toward the origin. I just want to know (a). And the solution from the book is attached, too...
  48. E

    Variable shift positive clamper

    for the given circuit and waveform , i am not getting how output for ωt < π is Vs + E1 ? given Vs is input and equal to Vm Sinωt
  49. D

    ODE Change of Variable: Solving Separable Equations with u = y/x

    Homework Statement I have the ODE y' = f(\frac{y}{x}) , and I want to re-write this as a separable equation using the change of variable u = \frac{y}{x} The Attempt at a Solution I use the chain rule to write y' = \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx} = \frac{dy}{du}(-\frac{y}{x^2})...
  50. P

    Find the variable to make the function continuous

    Homework Statement Find k so that the following function is continuous on any interval. j(x) = {k cos(x), x ≤ 0 {10ex − k, 0 < x Homework Equations The Attempt at a Solution I originally thought i had to check if the limits of both parts of the functions...
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