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. 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. Calculus Problem: Blowing Up a Spherical Balloon

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. Electron in a time variable magnetic field

TL;DR Summary: Find acceleration of electron in dB/dt >0 Hello. Here is a problem that i'm not so sure about: Inside a solenoid there is a time-dipendent magnetic field B, so we have dB/dt = b (constant). We want to know the acceleration of an electron: a) placed in the center of the solenoid...
4. Voltage Variation w/ Variable Resistor: Correct?

In this figure, I suppose the maximum voltage is when R2=1kohm and the minimum voltage is when R2=0kohm, which means R2 is a variable resistor. Is the way I think is correct or not? Please give me suggestions. Thank you.
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. 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. I Linear Model with independent categorical variable

Hello, I have been pondering on the following: we have data for blood pressure BP (response variable) and data about age and gender (categorical variable with two levels). We can build two linear regression models: $$BP=b_0+b_1 age+b_2 gender$$ $$BP=b_0+b_1 age$$ The first model does not take...
8. 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. JS Variable Hygiene: Preventing Global Var Access

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. Comp Sci Assigning a variable using a unary operator

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. A Boundary conditions for variable length bar

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. Adjustment of Variable Resistance in an automobile battery

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. 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. Sound Varieties: Rules for Varying Ranges

It seems that a sound (eg aa, ah, ih...) has a variable range of sound.I know that the before is affected by the follow, eg ''d" in do and did are different. Are there any other rules for the variation range?
15. Am vs Fm variable capacitor receiver, what is the difference?

What is the difference between a variable capacitor in a AM receiver and a variable capacitor in a FM receiver? I understand that Am is amplitude modulation and that the signal is carried over a changing amplitude and that the frequency is constant. And the opposite in FM signals. And a variable...
16. Variable mass, uniform body, force -- pulling a massive rope

So i got some equations but i think i am missing something, my main doubt is what is the relation between dx / dt and v(o) [ here] . Workings in attachment
17. Help with random variable linear estimation

Hi all, I have a problem on linear estimation that I would like help on. This is related to Wiener filtering. Problem: I attempted part (a), but not too sure on the answer. As for unconstrained case in part (b), I don't know how to find the autocorrelation function, I applied the definition...
18. Is the Work Done by a Variable Force Non-Conservative?

Can anyone tell me if my answer is wrong ?!
19. Mathematica Loop with variable nesting depth and variable count at each level

In Mathematica, how can we have "M" levels of nested loops, with each loop (level) going from 1 to Counts=##\{N_1, N_2, ... N_M\}## respectively, where the value of M and the elements of Counts are computed beforehand?
20. A How to check if a function doesn't depend on a variable?

Hello! I have some experimental data points ##(z_i,dz_i)## and I know that in the most general case this variable can be written in terms of 2 other variables as ##z_i = ay_i+bx_i##. Beside ##z_i## I can also measure, for each point, ##x_i## (we can assume that the uncertainty in ##x_i## is...
21. Kinematics of movement subject to a variable acceleration

Can someone guide me how can I find time ?! I don't have any idea. This is a part of a question in Classical Dynamics.
22. 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...
23. I Algebra equation with variable as exponent

This equation takes a present value (PV) to find mortgage payments, PMT: Alternatively, switching V for PV and T for PMT: V/T = r(1-r^n)/(1-r) What is an algebraic method to solve for "r"? Can it not be solved for? I realize I can just find out "r" by trial by error in Excel using the PMT...
24. A Is it possible for variable speed of light in a vacuum?

<unacceptable reference deleted> As our universe is expanding, that is, our vacuum is becoming more and more sparse, I believe it is possible that some key characterics of our vacuum is also variable.
25. I Random variable vs Random Process

Hello, When flipping a fair coin 4 times, the two possible outcomes for each flip are either H or T with the same probability ##P(H)=P(T)=0.5##. Why are the 4 outcomes to be considered as the realizations of 4 different random variables and not as different realizations of the same random...
26. Finding constant related to random variable

Var (Y) = a2 . Var (X) (6.96)2 = a2 . (8.7)2 a = Β± 0.8 But the answer key states that the value of a is only 0.8 Why a = -0.8 is rejected? Thanks
27. Fortran How do I create a pointer to an element of an array with a variable index?

program main implicit none real,dimension(3),target::x=[0,4,5] real,pointer::y call point_to_biggest(x,y) !print *,y ! For testing purposes; to be unmuted only when y points to something contains subroutine point_to_biggest(array,ptr) implicit none...

29. F

Change of variable for Jacobian: is there a method?

Hello, This problem comes just prior to introducing change of variables with Jacobian. Given the following region in the x-y plane, I have to choose (with justification) the correct change of variables associated, for ##u\in [0,2]## and ##v \in [0,1]##. The correct choice here is a), but I do...
30. Static variable in static method - how to use?

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...
31. How to Calculate Variable Force on a Particle with Varying Coordinates?

##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.

39. Variable pitch spring calculations

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kβ is changing as well, is there an equation I can use to calculate the new...

41. Assigning variable values "on the fly" within expressions

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?
42. 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:
43. Continuous joint random variable

(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...
44. Find the distance CD in the given complex variable question

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...
45. MHB Multiple choice test : random variable

Hey! π 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...
46. MHB Game : random variable for net profit

Hey! π You participate in the following game : You toss a fair coin until heads falls, but no more than three times. You have to pay $1$ euro for each throw. If your head falls, you win $3$ euros. The random variable $X$ describes your net profit (profit minus stake). Give the values that $X$...
47. Mathematica Use a rule variable for AxesStyle->20

How to use a variable rule, e.g. axs = AxesStyle->20 , to set the AxesStyle ? The code in the summary gives this error: "Options expected (instead of axs) beyond position 2 in Plot[x x,{x,0,10}, axs]. An option must be a rule or a list of rules." Isn't that "axs" a legit rule?
48. 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...
49. A Array variable of envelope function (parameter representation)

Hi, I have a question regarding the envelope function in parameter representation. Let an array of curves in cartesian coordinates be given in parameter representation, with curve parameter π‘ and array variable π π₯=π₯(π‘,π) π¦=π¦(π‘,π) Condition for envelope is: π/ππ‘ π₯(π‘,π) π/ππ π¦(π‘,π)=π/ππ...
50. I A coordinate representing rotation about a variable axis and ##T##

If a system is represented by a set of generalized coordinates ##q_i## in which one coordinate say ##\theta## is such that ##d \theta## represents a rotation of the system about a fixed axis( an axis whose orientation remains fixed in space) then the kinetic energy ##T## shouldn't depend on it...