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. K

    I Deriving expression as a function of another variable

    I am attempting to understand how I can derive a new expression as a function of another variable in this existing expression. This is a college undergraduate course but I can't recall doing this much before, maybe in high school. I have taken all the way up to ODE's and PDE's. The confusion...
  2. Jehannum

    I Rearranging equation with more than variable instance

    This question is no doubt absurdly simple to many here, but the answer will help me immensely. Say that: c = a ^ 4 Then it's simple to rearrange for a: a = c ^ 0.25 But what if there is more than one term, for example: c = a ^ 4 + a ^ 3 Is it possible to rearrange this to the form: a =...
  3. T

    I Isolating a complex-valued variable

    If ## A, B, ## and ## C## are complex-valued variables, is there an easy way to algebraically solve for ##A## without splitting the variables into their real and imaginary parts? For example: $$ AB^* = 20AB - A^*C + B^*C^* $$ can be isolated for ##A## but only if the real and imaginary parts...
  4. H

    I Multi variable differential

    Hi I understood above differential ## typo. RHS= 2*f ' (x,2z-x) but, what is answer of below equation? is this right? f ' ( g(z),2z-x) * g' (z) + f ' ( g(z),2z-x) *2
  5. baby_1

    Using Cauchy's Tip for Changing Integral Variable Inconsistencies

    Homework Statement I want to change integral variable to jx it means (w=jx) Homework EquationsThe Attempt at a Solution but as you see the bounds of integral are different from the book text , what is my mistake?
  6. T

    MHB Limit of 2 variable function

    I need to find $$\lim_{{(x, y)}\to{(0,0)}} \frac{x^2 - y^2}{\sqrt{x^2 + y^2}}$$ If I plug in zero, I get an indeterminate form. How do I resolve the indeterminate form?
  7. T

    MHB Evaluating limit of 2 variable function

    I have $$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$ If I evaluate the limit along the x-axis, I get $$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$ which evaluates to $1$. If I evaluate the limit along the y-axis, I get $$\lim_{{y}\to{0}} \frac{...
  8. G

    B Understanding Correlations in Non-Realism: The Role of Extra Variables?

    What is the name or term called for this extra variable inside non-realism where it can determine the born rule and correlate spacelike millions of light years away? (counterpart of hidden variable in realism (or counterfactual definiteness))
  9. anorlunda

    A Conjugate variable clarification

    [Mentor's note: forked from https://www.physicsforums.com/threads/conjugate-variable-clarification.878112/] I think the list is very interesting. From https://en.wikipedia.org/wiki/Conjugate_variables The energy of a particle at a certain event is the negative of the derivative of the action...
  10. T

    I Change of variable (2nd order ODE)

    Hi there, I was just trying to perform a change of variable on a differential equation as shown below. The original second order ODE is written in terms of a dependent variable ## \theta ## and independent variable ##q##. I have used the expression ## q = \sqrt{\frac{z\tau'}{LT_R}} ## and...
  11. I

    MATLAB Transforming part of matlab code to Fortran90

    Here are my Fortran codes: program test implicitnone integer*4 nxProjPad, cf, numViews, cc, index, indRad, iv, i, INDEX1, d, n real*4 v4, v5, RSS, S1, F1, gMDL real*4, dimension(:), allocatable :: array, sum, cumsum, transpose, log, SS1, SSs nxProjPad=185 numViews=180...
  12. I

    Normal approximation to Poisson random variable

    Homework Statement Suppose that the number of asbestos particles in a sam- ple of 1 squared centimeter of dust is a Poisson random variable with a mean of 1000. What is the probability that 10 squared cen- timeters of dust contains more than 10,000 particles? Homework Equations E(aX+b) =...
  13. N

    Double integrals with variable upper limit

    How can you compute F(k) = k\int^{\infty}_{0}dy\int^{y}_{0}dx f(kx,y) in C. I know about Python's scipy.integrate.dblquad function but it's just too slow. I have written some Cython code with a 2D gaussian quadrature function in C but it only takes doubles as limits. I think C doesn't have...
  14. Einstein's Cat

    B Exploring Variable Speed of Light Theories

    I was researching variable speed of light theories as alternatives to inflation theory; from Wikipedia I cam across this: "The idea from Moffat and the team Albrecht–Magueijo is that light propagated as much as 60 orders of magnitude faster in the early universe, thus distant regions of the...
  15. F

    Exploring the Number of Pi Groups in Dimensional Analysis

    Homework Statement Is the question wrong ? Homework EquationsThe Attempt at a Solution I found that the number of dimension = 6 , primary dimensionof velocity is L / T , which is 2 , number of repeating variable = 2 , so , there are 6-2 = 4 pi group , why the question only gt 3 pi group ?
  16. P

    A Approximation for volatility of random variable

    Hello, could anyone please explain me some logic or derivation behind the approximation: Found it in the Hull Derivatives book without further explanation. Thanks for help
  17. R

    Mass of an annulus with variable mass density

    Hey guys, I just wanted to check if my method for solving this problem is correct. 1. Homework Statement Consider an annulus with inner radius R1 and outer radius R2. The mass density of the annulus is given by σ(r)=C/r, where C is a constant. Calculate the total mass of the annulus. Homework...
  18. O

    I Concrete contrast between local and nonlocal hidden variable

    Can someone concretize the difference between a "hypothetical reality" where hidden variables are local and hidden variables are nonlocal in the following context: Some physical event occurs involving particles A and B (which are/become entangled and will exhibit correlations) at time T and...
  19. RubiksMelia

    Calculating Velocity from a variable force.

    Homework Statement A body of mass 5 kg is acted on by a force in a straight line. The magnitude of the force after t seconds is given by (2t - 3t^2) kg wt. If the body has an initial velocity of 3ms-1 in the same direction as the force, calculate its velocity after 4 seconds. Homework...
  20. T

    I Change of variable - partial derivative

    I am trying to prove that the above is true when performing the change of variable shown. Here is my attempt: What I am not quite understanding is why they choose to isolate the partial derivative of ##z## on the right side (as opposed to the left) that I have in my last line. This ultimately...
  21. S

    MLE of Bivariate Vector Random Variable: Proof & Explanation

    Homework Statement Consider the bivariate vector random variable ##(X,Y)^T## which has the probability density function $$f_{X,Y}(x,y) = \theta xe^{-x(y+\theta)}, \quad x\geq 0, y\geq 0 \; \; \text{and} \; \; \theta > 0.$$ I have shown that the marginal distribution of ##X## is ##f_X(x|\theta)...
  22. W

    Deriving Discharge Expression for Broad Crested Weir Model

    Homework Statement A broad crested weir model is designed to study the discharge per meter of the prototype. Derive an expression for this discharge using the Buckingham Pi theorem. Assume that the overflowing water sheet is thick so that the surface tension and thus viscosity of the fluid can...
  23. evinda

    MHB Integrating by an other variable

    Hello! (Wave) I am looking at a proof where we have: $$\int_{-\infty}^{+\infty} |u|^{\frac{n}{n-1}} dx_1 \leq \left( \int_{-\infty}^{+\infty} |Du| dy_1 \right)^{\frac{1}{n-1}} \left( \prod_{i=2}^n \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} |Du| dx_1 dy_i\right)^{\frac{1}{n-1}}$$...
  24. F

    Rules of choosing repeating variable in Buckingham pi theorem

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  25. N

    Help with variable mass on a slope question

    Homework Statement An armoured car with a mass of 5 tonnes is located on a smooth plane which is inclined at an angle of tan-1 (5/12) to the horizontal as shown in Figure Q3. A missile of mass 15kg is fired horizontally from this armoured car at 650m/s. Determine the velocity with which the...
  26. terryds

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  27. W

    Studying material two variable functions

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  28. Telemachus

    Variable grid mesh in Numerov's method (Fortran)

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  29. I

    Quadratic with variable buried in sqrt?

    Homework Statement 0 = -250*(sqrt(x^2+1)-0.8)^2 + 98.1*x + 59.05 Homework EquationsThe Attempt at a Solution I can't figure out how to solve this equation! After expanding the squared term, I still end up with a sqrt(x^2+1) and I can't figure out how to perform a substitution or something to...
  30. Kirito123

    Independent/dependent variable and modeling equations

    Homework Statement 8. Amelia’s Marina rents rowboats for $12/hour. A cleaning fee of $20 is charged, when the boat is returned. a. Identify the independent and dependent variables, including units, for this scenario.b. Write an equation that models this scenario. c. A nearby marina offers a...
  31. S

    I Integration of 1 variable in 2 different ways.

    I have to do a integration which goes like this: (V-M)(dP/dx)+3P(dV/dx)=0, (where M,P and V are constants). If you integrate with dx, you will get: ∫[(V-M)dP]+∫[3PdV]=0. which ultimately results in the answer M=4V. Now, i can put the first equation in this form also...
  32. S

    A reusable variable: still good to define in the scope that uses it?

    I'll give you an example. Let's say I have a snippet of code like while(*s2) { char* c = s1; while(*c++==*s2++); if(!*c) { flag=true; break; } else { flag=false; } } (which is a real snippet of...
  33. F

    Choosing repeating variable in pi Buckingham theorem

    Homework Statement why we can't form the pi group by using repeating variable of (μ, ρ , v) or (D, v , μ ) ? http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/dimension/node9.html http://www.efm.leeds.ac.uk/CIVE/CIVE1400/Section5/dimensional_analysis.htm...
  34. Edison Bias

    I Integral problems with polar coordinates and variable substitution

    H! I wonder how to solve: I=\int_{-\infty}^{\infty}e^{-u^2}\frac{1}{1+Cu} du I have solved: \int_{-\infty}^{\infty}e^{-u^2}du which equals \sqrt{\pi} and I solved it with polar coordinates and variable substitution. Thankful for help! Edison
  35. abdulsulo

    Fortran Taking 1/7 power of a variable

    Hello there. I am trying to take a power of 1/7 of one variable but as a default it gives me 1 similar to if I was taking power of 0. How can I solve this problem. Thanks
  36. H

    B Recast a differential equation with a change of variable

    I obtained an extra factor of ##\frac{1}{l^2}## in the first term on the LHS of (3.34). From (3.33), LHS ##=u^2\frac{d}{d\theta}(\frac{u^2}{m}\frac{du}{d\theta}\frac{dr}{du})-\frac{l^2u^3}{m}## ##=u^2\frac{d}{d\theta}(-\frac{1}{m}\frac{du}{d\theta})-\frac{l^2u^3}{m}##...
  37. topsquark

    MHB PHP Static Variables: Why Doesn't It Reset?

    The code is supposed to generate 0 1 2 My question is this: If we declare $x = 0 in the function then why doesn't it reset to 0 every time we run the function? -Dan
  38. avikarto

    Fortran Modern variable precision and integer multipliers

    I learned Fortran from ancient people who disregard modern standards. As such, my code consists mainly of that older syntax. I am wondering how well this meshes with current Fortran environments, specifically regarding double precision calculations. This comes up mainly because I have been...
  39. D

    MHB Question regarding a probability mass function of a random variable

    Thank you for your time, I really appreciate it I have no idea where to even begin
  40. D

    MHB Continuous random variable question

    A continuous random variable x has the following probability function: f(X)=(X+1)/8 -1<=X<=3 0 Otherwise 1. Find the Pr(X<=2) 2. Find the mean of X
  41. D

    MHB Consider the following probability mass function of a random variable x

    $p(x) ={p}^{x}*{(1-p)}^{1-x}$ for $x=0.1$ $0$ otherwise Where $p$ is such that $0<=p<=1$ Question: Find the mean and variance of $X
  42. Narasoma

    I Hidden Variable Interpretation

    What are advantages and disadvantages of hidden variable interpretation of quantum mechanics?
  43. I

    I Random variable and probability

    Hi! I'm searching for guidance and help since I don't know how to solve this problem. Here it is: a) The two-dimensional random variable (ξ,η) is uniformly distributed over the square K={(x,y): 0≤x≤1 , 0≤y≤1} . Let ζ=√ξ2+η2 me the distance between the origo and the point (ξ,η) . Calculate the...
  44. F

    MHB Understanding Uniform Random Variables: Comparing $X$ and $Y = 1-X$

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  45. U

    Variable Voltage Transformer for Wind Turbine Battery Charging?

    We are trying to build a wind turbine which will charge a battery. Since wind speed varies (which affects the generated current and voltage), we were going to integrate a transformer in. My question is does such a transfomer even exist where the input voltage varies while the output voltage is...
  46. N

    C/C++ C++: Printing output based on variable value

    Print either "Fruit", "Drink", or "Unknown" (followed by a newline) depending on the value of userItem. Print "Unknown" (followed by a newline) if the value of userItem does not match any of the defined options. For example, if userItem is GR_APPLES, output should be: Fruit #include <iostream>...
  47. K

    Standardization of a random variable

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  48. F

    MHB Random Variable over probability space

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  49. C

    High voltage voltage controlled linear variable resistor

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  50. BenR

    Field of variable charge distribution over all space

    Homework Statement A charge distribution has uniform density in the x-y directions and varies with z according to: ρ(z) = ρ0e−|z|/t where ρ0 and t are constants. (a) Find the potential V (z) and the electric field E(z) (b) Sketch them clearly showing their behaviors in the regions |z| ≪ t...
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