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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    I'm struggling with section a. This is my calculation: The expression remains depend on the variable t, while in the answer is a concrete number:
  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

    Find limit of multi variable function

    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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    int a[]={12,34,55,76,89,23}; int n=5; while(n>1){ a[n]=a[--n];} for(int i=0;i<6;i++){ printf("%d\t",a[i]); } Mentor note: Please use code tags in future posts. I've added them to this code. The above code should shift the element values to the right of each array cell, but after running...
  11. H

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  12. S

    Adjustment of Variable Resistance in an automobile battery

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  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

    Help with random variable linear estimation

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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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  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

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    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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    Hi, does anyone know how to calculate the current spring constant of a variable pitch spring when under compression. Since some of its coils get inactive when compressed the stiffness is increasing and consequently β€œk” is changing as well, is there an equation I can use to calculate the new...
  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

    MHB Multiple choice test : random variable

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  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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