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. MatinSAR

    Find ##b-a## which satisfies following limit

    ## \lim_{x \rightarrow 1} {\frac {x-2} {x^3+ax+b}} = -\infty## The limit is equal to ##\frac {-1} {1+a+b}## . so I can say that ## a+b = -1 ##. But I cannot find another equation to find both ##b-a##.
  2. I

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  3. M

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  4. Lay1

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  5. M

    C/C++ Variable defined in scope gives error depending on scope

    Hi PF! The following runs if lines 5 and 11 are commented, but fails otherwise. Can someone explain what's happening here? Something with scope but I'm very lost. Thanks in advance! #include <iostream> int main() { { int* i = new int; { int b = 5; i...
  6. F

    I Sample space, outcome, event, random variable, probability...

    Hello, I am solid on the following concepts but less certain on the correct understanding of what a random variable is... Random Experiment: an experiment that has an uncertain outcome. Trials: how many times we sequentially repeat a random experiment. Sample space ##S##: the set of ALL...
  7. F

    I Linear Model with independent categorical variable

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  8. ananonanunes

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    This is what I did: $$\lim_ {(x,y) \rightarrow (1,0)} {\frac {g(x)(x-1)^2y}{2(x-1)^4+y^2}}=\lim_ {(x,y) \rightarrow (1,0)} {g(x)y\frac {(x-1)^2}{2(x-1)^4+y^2}}$$ I know that ##\lim_ {(x,y) \rightarrow (1,0)} {g(x)y}=0## and that ##\frac {(x-1)^2}{2(x-1)^4+y^2}## is limited because ##0\leq...
  9. DaveC426913

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    To skip the humble-bragging, jump down past the screenshots and descriptions to "Anyway"... For my client, I made this one-page vanillaJS app that shows a heat map of counties serviced by their three professions (if they add a fourth I'm screwed): The Niagara county is serviced by one PNSW...
  10. C

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  11. H

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    Suppose I'm looking at a bar of length L(t) in 1D and I have the conservation of mass: \frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x}(\rho u)=0 In order to make things easier, I make the change of variable x'=x/L(t) so that in this frame of reference, the length remains constant...
  12. S

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    How is the load (variable resistance) adjusted in an automobile battery? Mechanically (potentiometer, rheostat) or electronically (digital potentiometer) or are both configurations possible.Can the load in a automobile battery be a three terminal divider (potentiometer) or is it almost always...
  13. M

    Engineering How to implement a transfer function in Simulink with variable coefficients?

    The implementations for the two filters in simulink are as follow: For the first filter: For the second one: The obtained results have values of 10^-12, while the expected results should be between 10^-3 - 10. Since it's the first time when I try t implement a tf with variable coefficients I...
  14. F

    Sound Varieties: Rules for Varying Ranges

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  15. sol47739

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  16. Spector989

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  17. A

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  18. S

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  19. K

    A How to check if a function doesn't depend on a variable?

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  20. MatinSAR

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  21. F

    I Variable Normalization for different variable ranges....

    Hello, On the topic of feature scaling: I am wondering if normalization needs to be used all the time or only in some particular circumstances. Normalization means transforming/remapping the range of a variable with values ##[x_0,x_f]## to the range ##[0,1]##. For example, let's consider a...
  22. adamaero

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  23. K

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  24. F

    I Random variable vs Random Process

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  25. S

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  26. Eclair_de_XII

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  27. F

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  28. bikashdaga

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    I wanted to declare a local variable inside a static method main(). My code looks like this - class Operator { static int a; public static void input() { Scanner in=new Scanner(System.in); System.out.println("Enter the number:"); a=in.nextInt(); //this is...
  29. rudransh verma

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    ##W=-k(y\hat i+ x\hat j)d##. I am not getting the coordinate of particle correctly so that I can find the value of d. Also the force is varying.
  30. A

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  31. rudransh verma

    B Work energy theorem by variable force

    Its Good to be Back! From Resnik, Fundamentals of physics: Consider a particle of mass m, moving along an x-axis and acted on by a net force F(x) that is directed along that axis. The work done on the particle by this force as the particle moves from position ##x_i## to position ##x_f## is given...
  32. marcophys

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    Hello everyone :) I'm struggling to wrap my head around recalculating a data set based upon median. The data set represents a fixed distribution pattern of population to income group. There is no data available for 'population to income group' at differing medians, hence we accept the...
  33. T

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    v(20)=288000 m/s=80000km/h a=(80 000-0)/(20 -0)=4000 m*s^(-2) F=m*a=0.0005*80 000 which doesn't fit any answers
  34. shivajikobardan

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  35. shivajikobardan

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  36. J

    I Integral-form change of variable in differential equation

    I have the following differential equation, which is the general Sturm-Liouville problem, $$ \dfrac{d}{dx} \left[ p(x) \dfrac{d\varphi}{dx} \right] + \left[ \lambda w(x) - q(x) \right] \varphi(x) = 0\ , $$ and I want to perform the change of variable $$ x \rightarrow y = \int_a^x \sqrt{\lambda...
  37. M

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  38. S

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    I've used this kind of thing often in JavaScript and Mathematica. z = ((a=3) +( b=2) )**2 + 1/a +1/b I'm currently learning Julia, and it doesn't seem to be supported. What is this syntax called?
  39. M

    MHB Understanding Random Variable Mapping and Probability Functions

    Hey! :giggle: What does it mean to give the mapping for a random variable? Do we have to give the outcome space and the probability function? Does it hold that $X: ( \Omega, P)\mapsto \mathbb{R}$ ? :unsure:
  40. docnet

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    (a) $$\int_0^1\int_0^1x+cy^2 dxdy=\int_0^1 [\frac{x^2}{2}+cxy^2]_0^1dy= \int_0^1\frac{1}{2}+cy^2 dy=[\frac{y}{2}+\frac{cy^3}{3}]_0^1=\frac{1}{2}+\frac{c}{3}=1$$ $$\Rightarrow c=\frac{3}{2}$$ (b) The marginal pdf of X is $$f_X(a)=\int_0^1 f_{X,Y}(a,b)db=\int_0^1 x+\frac{3}{2}y^2...
  41. chwala

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    This is the problem; Note that i am conversant with the above steps shown in the solution, having said that i realized that we could also borrow from the understanding of gradient and straight lines in finding the distance ##CD##... it follows that the equation of ##BA= -1.5x-0.5##, implying...
  42. M

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    Hey! 😊 A multiple choice test consists of 10 questions. For every question there are five possible answers, of which exactly one is correct. A test candidate answers all questions by chance. (a) Give a suitable random variable with value range and probability distribution in order to work on...
  43. M

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  44. S

    Mathematica Use a rule variable for AxesStyle->20

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  45. K

    I An equation invariant under change of variable

    It's said that the below equation is invariant under a substitution of ##-\theta## for ##\theta## , ##\frac{d^{2} u}{d \theta^{2}}+u=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right)## I can't understand this how this is so. It's supposed to be obvious but I can't see it. Please help...
  46. M

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  47. K

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