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. E

    Euler - Lagrange Equation(changing variable)

    Create the Euler-Lagrange equation for the following questions (if it's necessary change the variables). Homework Statement $$\tag{1}\int _{y_{1}}^{y2}\dfrac {x^{'}{2}} {\sqrt {x^{'}{2}+x^{2}}}dy$$ $$\tag{2}\int _{x_{1}}^{x_{2}}y^{3/2}ds $$ $$\tag{3} \int \dfrac {y.y'} {1+yy{'}}dx...
  2. F

    Feedback control via ODE variable coefficients?

    If one has a simple variable coefficient process like y'(t) = r(t)*y(t), is there a way to control it to a set point by feedback hitting the variable coefficients in r(t)? I am interested in feedback control of population processes. y'(t) = r*y(t) is simple proportional growth with a...
  3. J

    How to notate a variable that is being held constant

    I remember learning at one point that you can put some sort of symbol on top or near a variable to indicate that it is being held constant. I thought that it was just a bar drawn above the variable but in some cases, it means "the average of." Anyone know what I'm talking about?
  4. H

    Calculating Change and Derivatives for a 2 Variable Function

    Homework Statement f(x,y) = (x-y) / (x+y) Calculate Δf and df for the change of point (3,2) to point (3.2, 2.1) Homework Equations The Attempt at a Solution I guess that I have to use limits, but don't know how to begin with.
  5. maistral

    Differential equations for series variable volume reactions

    How do you make a differential equation for such? Say for example. I have two reactions in series, A → R and R → S going in a gas-phase reaction. If I'm correct, the ODE for the conversion of A is dXA/dt = kA*[(NAo/vo)*(1-XA)/(1+δA*YAo*XA)]*[(vo/NAo)*(1+δA*YAo*XA)]. I don't know now...
  6. R

    Showing tha a random variable is a martingale

    I'm having a bit of a problem proving the second condition for a martingale, the discrete time branching process Z(n)=X(n)/m^n, where m is the mean number of offspring per individual and X(n) is the size of the nth generation. I have E[z(n)]=E[x(n)]/m^n=m^n/m^n (from definition E[X^n]=m^n) =...
  7. K

    What is the variable theta of omega in a series RL cct?

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  8. S

    Variable Dielectric Spherical Capacitor: Calculating Capacitance

    Homework Statement Calculate the capacitance of a spherical capacitor of inner radius A and outer radius B which is filled with a di-electric varying as e=c+dcos^2θ . c and d are constants and θ is the angle made with the z axis.(also known as the polar angle) Homework Equations $C=εA/d$The...
  9. P

    Statistics expectation of discrete variable.

    Hi, Homework Statement How may I find to what number Ʃ(m=1 to ∞) m/2m-1 converges? Further, suppose I know it converges to 4, why would then E(Y), given that P(Y) = 1/2m-1, be equal to 2 (thus asserted the answer) and not 4? Homework Equations The Attempt at a Solution I am...
  10. J

    Center of mass of a slender rod with variable density

    Hi to everybody Homework Statement I´ll show the problem with a picture: Homework Equations L\overline{x}=∫xc ρ dl The Attempt at a Solution Well the total length of the rod is 1 feet, I only need to calculate the integral. The moment xc of a differential element of mass of the rod is...
  11. R

    Computing for any general function whose variable is a gaussian

    If I have a variable X whose gaussian distribution is known and let f be a known function, is there a way to compute f(X) (i.e) the resulting gaussian distribution from this? Is the result actually a gaussian distribution?
  12. Y

    Constant acceleration in a straight line with variable distances

    Homework Statement A particle which moves with a constant acceleration in a straight line passes through the point O, A and B in that order. If the distances OA and AB are 17 m and 35 m respectively and the particle takes the same amount of time , 3 seconds to travel each distance then...
  13. A

    On solving PDE using separating the variable.

    hi.. with refrenence to http://www.math.uah.edu/howell/MAPH/Archives/Old_Notes/PDEs/PDE1.pdf page 7, “Observe” that the only way we can have formula of t only= formula of x only is for both sides to be equal to a single constant. here I do understand that for these to being equal...
  14. C

    Solving for a variable inside the error function?

    i need to solve for a variable inside the error function on excel, is there an opposite function i can use to accomplish this? example: y = sqrt(x-t) -> x = t+y^2 except instead of a sqrt( ) I have erf( ) **this is not a math class so I don't have to get into breaking it down into the...
  15. Jameson

    MHB Transformation of a random variable (exponential)

    Problem: Suppose that $X \text{ ~ Exp}(\lambda)$ and denote its distribution function by $F$. What is the distribution of $Y=F(X)$? My attempt: First off, I'm assuming this is asking for the CDF of $Y$. Sometimes it's not clear what terminology refers to the PDF or the CDF for me. $P[Y \le y]=...
  16. Jameson

    MHB Transformation of random variable (uniform)

    This is something that when I see the work done it makes sense, but I find it difficult to do myself. I'm also aware there is an explicit formula for doing this but that involves Jacobians and a well-defined inverse, so I think it's more intuitive to do it step-by-step. Problem: Suppose $X...
  17. A

    MHB How Does Professor Roberto's Grading System Affect Student Scores?

    Professor Roberto has to take an oral examination. The grading scale is as follows: 5: = best and 1: = worst. At most he only gives the note 4. Each student under review is questioned if he is a Lakers fan. The student's grade is based on his answer (is a fan / not a fan) and on the language in...
  18. G

    Function of random variable, limits of integration

    Homework Statement X is uniformly distributed over [-1,1]. Compute the density function f(y) of Y = 2X2 + 1. Homework Equations The Attempt at a Solution FY(Y) = P(Y < y) = P(2X2 + 1 < y) = P(X < +\sqrt{1/2(y-1)} = FX(+\sqrt{1/2(y-1)}) We have that f(x) = 0.5 for -1 < x <...
  19. S

    Effect of electromagnetic damping with variable current

    Hi guys, first time poster. My question is; How would a constant damping provided by an electromagnet affect the damping ratio (and logarithmic decrement) amplitude? And how would increasing the current through the electromagnet affect the damping? So far I've found Biot-Savart's Law which...
  20. M

    Trouble taking 2nd deriv of multi variable

    Homework Statement Use * to show --> Homework Equations The Attempt at a Solution So I've begun by trying to take the 2nd derivative of \frac{\partial z}{\partial r}=\cos\theta\frac{\partial z}{\partial x}+\sin\theta\frac{\partial z}{\partial y} Which gives me this...
  21. Z

    Tricky circuit with variable resistor

    Homework Statement An electric circuit comprises two series resistors A and B, the first of which has a given resistance R_A and the second variable resistance R_B, over which a constant DC voltage U is added. How shall the resistance R_B be selected so that the power P developed in resistor B...
  22. J

    Java Java question: Need some sort of global variable.

    Just wondering if the Java experts here could help me. As part of a project I'm making a function rand9() that returns a pseudo-random number 0 through 9. The problem is that each time it's called I need a certain number to increment so that it can generate a new (not necessarily different)...
  23. F

    Variable amplitude for shaker table

    Hi All, I built this shaker table: and I am now trying to change the amplitude so that it is no longer fixed but instead variable. The frequency I can change but the amplitude is fixed given this design. Does anyone have any suggestions on how to be able to change the amplitude so I can...
  24. C

    Variable Mass:Sand from balloon

    Homework Statement A balloon of mass M contains a bag of sand of initial mass ##m_o##. The balloon experiences a constant upthrust and is initially at rest and in equilibrium: the upthrust compensates exactly for the gravitational force. At time t=0, the sand is released at a constant rate...
  25. Saitama

    Variable Magnetic field bound in a cylindrical region

    Homework Statement There is a uniform but variable magnetic field ##\vec{B}=(B_0 t)(-\hat{k})##, in a cylindrical region, whose boundary is described by ##x^2+y^2=a^2##. ##\displaystyle \int_P^{Q} \vec{E} \cdot \vec{dy}## is (see attachment 1) A)0 B)##\frac{\pi}{4}(B_0 a^2)##...
  26. E

    About taking ODE directly after taking 1 variable calculus

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  27. twoski

    Generating a Random Variable with a Specific Distribution Function

    Homework Statement Give a method for generating a random variable with distribution function F(x) = 1/2(x+x^{2}) 0<x<1 The Attempt at a Solution From what i can tell i am supposed to do something like: Let U be a uniformly distributed random variable over (0,1). U =...
  28. D

    What is the Cumulative Distribution Function for a Continuous Random Variable?

    The cumulative distribution function of a continuous random variable is given as follows: 0 0 ( ) 0 5 5 1 5 X if x x F x if x x           a. Determine and name the density function of . [02] b. Use both and ( ) X F x to find P(X  3) . [05] c. Find the variance of ...
  29. C

    Using dummy variable to integrate (formal solution of rad. trans eqn)

    Homework Statement (Everything here is frequency dependant, but I have left off the v from all the variables to minimise chance of typos - hopefully that is ok but please let me know if not and I will try and retype!) The equation of radiative transfer is dI/dτ = -I + S We guess...
  30. A

    Can You Easily Design a Variable Band Pass Filter in the MHz Range?

    Is there an easy way of designing a band pass filter whose pass band could be varied over a certain band?? The pass band is in MHz range. Thanks
  31. L

    Showing a random Variable has a continuous uniform distribution

    f(x)=1, θ-1/2 ≤ x ≤ θ+1/2 Given that Z=(b-a)(x-θ)+(1/2)(a+b) how would you show that Z has a continuous uniform distribution over the interval (a,b)? Any help would be much appreciated.
  32. Petrus

    MHB Max and min value, multi variable (open sets)

    Calculate max and min value of the function f(x,y)=x^2+y^2-2x-4y+8 in the range defined by the x^2+y^2≤9 Progress: f_x(x,y)=2x-2 f_y(x.y)=2y-4 So I get x=1 and y=2 We got one end point that I don't know what to do with x^2+y^2≤9 If I got this right it should be a elips that x can max be 3,-3 and...
  33. twoski

    Solving Normal Random Variable Equations for P(X(X-1) > 2) and P(|X| > a)

    Homework Statement X is a normal random variable with mean 1, variance 4. 1. Find P( X(X-1) > 2 ) 2. Find a value 'a' for which P(|X| > a ) = .25 The Attempt at a Solution I had no idea how to start 1. For 2, i got this far then got stuck: P(|X| > a) = 1 - P((X-1)/2 <=...
  34. B

    Can you prove the limit of (3/5)^x as x approaches infinity is equal to 0?

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  35. J

    Mips swapping without temp variable

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  36. M

    Limit of Multivariable Function: ln((1+y^2)/(x^2+xy))

    Homework Statement lim(x,y)-(1,0) ln((1+y^2)/(x^2+xy)) Homework Equations The Attempt at a Solution if i just substitude x and y i get ln (1)= 0 so is the limit 0?
  37. C

    Definite integral with variable limits of a multivariable function.

    I have the following integral: \int_0^{f(x,y)}{f' \sin(y-f')df'} Now suppose that f(x,y) = x*y, my question is how do I write the integral in terms of x and y only? Can I do something like this? Since df=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy we can obtain...
  38. V

    Product of random variable with Unif dist and its variance

    First of, I apologize for the vague title, I didn't know how to summarize this issue. Homework Statement Suppose that the interest rate obtained in month i is a random variable Ri with the uniform distribution on [0.01, 0.03], where R1,R2, . . . are independent. A capital of 1 unit...
  39. G

    Factoring in terms of a variable

    Homework Statement ((1/3)(y^3))+(1/y)=.5*ln((x^2)+1) Solve in terms of y Homework Equations The Attempt at a Solution I am in college differential equations, and i just can't solve in terms of y. y teacher wants that...i tried wolfram alpha, etc. How on Earth do you factor this...
  40. D

    Maple Trying to solve an equation but get weird solution with new variable

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  41. A

    MHB Solving for specific variable when solving a recurrence equation

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  42. J

    MHB Finding an explicit solution for this variable

    Hi, I am working on an economics paper, and I find that the following first order condition for my variable of interest (\mu \in [0,1]): \frac{\lambda(1+\mu)}{(1-\mu)}=N-x\frac{(1+\mu)}{\sqrt{\mu}} I would ideally like to provide an explicit solution, but unfortunately, this would amount to...
  43. G

    Multi Variable Optimization Problem

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  44. J

    Exponential Variable and Logarithms

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  45. Y

    System of cross-polynomials of variable degree

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  46. A

    Variable valency explanation and cause

    many transition elements have variable oxidation state like Fe.what is the exact cause for this?they may not obey the octet rule,but what is the reason behind this?Also,elements like nitrogen are not transition elements and still show variable valency.what will be the electronic configuration of...
  47. twoski

    Probability and Poisson Random Variable

    Homework Statement A trial consists of throwing two dice. The result is counted as successful if the sum of the outcomes is 12. What is the probability that the number of successes in 36 such trials is greater than one? What is this probability if we approximate its value using the Poisson...
  48. T

    Isolating a variable in an exponent

    Homework Statement So I had to find out N=Noe-ux Where No=1.5,e is the elementary charge, u=-0.068 and x=0.07 I came to the answer 1.221 Now I need to find x if u =-0.036, N=1.221 and No remains 1.5Homework Equations The Attempt at a Solution I reduce the equation to the following...
  49. N

    Expectation value of a dynamical variable problem.

    Homework Statement Why does the extra phase factor cancel out? Is it because you are multiplying the wave-function with the extra phase factor by its conjugate and if so, why should it matter that the extra phase factor is independent of x? All relevant information, the solution and equation...
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