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. B

    How do I know when to factor out a variable?

    Take the equation for gamma. I know how to get from step 1 to gamma. How would I do that if I have not have seen the instructions? There are many ways to factor step 1 without getting the same values of ## gamma = \frac 1 {\sqrt {1 - \frac {v^2} {c^2}}} ## step 1 = Speaking of factoring and...
  2. M

    Adding a variable to a Lagrangian

    Would the following: $$ L = m(\vec{\dot r + \vec v})$$ (constant velocity added to above eq.) lead to equivalent euler-lagrange equations due to the fact that the ratio of T and V is unaffected by an increase in constant velocity? And would this be an example of energy conservation?
  3. Jonathanos

    Courses Complex Analysis Courses or Complex Variable Courses?

    Hello, My university offers a couple Complex Analysis courses, among them there is one with the following description: Introduction to complex variables: "substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply principles to physical...
  4. W

    I Taylor series and variable substitutions

    I'm currently typing up some notes on topics since I have free time right now, and this question popped into my head. Given a problem as follows: Find the first five terms of the Taylor series about some ##x_0## and describe the largest interval containing ##x_0## in which they are analytic...
  5. F

    Understanding the PMF of a Random Variable: A Brief Overview

    I am new to the topic so I do need your help here. Thanks in advance
  6. F

    How to operate a Variable DC source

    Hello, I am experimenting with DC variable power supply and want to make sure I am using it correctly. My understanding is that it can output a variable DC voltage by turning the voltage know CW. The current-limit knob, as far as I know, is only there to set the maximum current that we would...
  7. E

    B How do we interpret a random variable?

    I've read that we can define a random variable on a probability space ##(\Omega, F, P)## such that it is a function that maps elements of the sample space to a measurable space - for instance, the reals - i.e. ##X: \Omega \rightarrow \mathbb{R}##. That being said, it's often treated (at least...
  8. Adesh

    Confusion about the independent variable of function in magnetostaics.

    When we calculate the curl of magnetic field, that is the curl of Biot-Savart equation for magnetic field. Please consider these . The working of last equation $$ \nabla \times \mathbf {B} = \frac...
  9. A

    Motor / transformer variable frequency control

    few questions 1) is it true that for a 50 or 60hz induction motor maximum torque is achieved from 0hz up to design hz and if an VFD is used and frequency is increased above 50 or 60hz like 100hz the rpm will increase but the available torque will decrease? Is the reason behind this the fact...
  10. nima_kheradhoosh

    How can I apply a variable phase shift to an AC signal generated by a VFD?

    Hey fellas, I’m trying to apply a variable phase shift (0 to 180 degrees) on an AC signal generated from a Variable Frequency Drive (VFD). The frequency is variable and ranged between 10 and 50 Hz. the voltage amplitude is also variable between 10-50Volts (this shouldn’t be a problem I suppose)...
  11. A

    A Third and fourth central moment of a random variable

    My question is as follows. In the attached paper a formula is given on page 272 for the expectation of Tn (formula 23) and for the variance of Tn (formula 24). Now I would like to know what the formulas look like for Tn 's third and fourth central moment.
  12. karush

    MHB 004- USMA(WP) entrance exam question independent variable

    ok not sure what forum this was supposed to go in,,so... If the independent variable of $W(\theta)=2\theta^2$ is restricted to values in the interval [2,6] What is the interval of all possible values of the dependents variable?
  13. R

    Change of variable in a double integral

    Hi everyone, I tried to solve the last part of the question, I substituted back the expression of x and y into the equation of the ellipse, I got that r=1 or r=-1. But got no idea how to find the boundary for theta, I got a guess that, It should be from zero to pi. But got no reason why to...
  14. G

    MHB Calculating Total Cost with Variable n: C = 7500 + 8n

    C = 7500 + 8n
  15. R

    Engineering Find the Minimal SOP Using a 5 Variable K-Map

    My concern is that, when I tried checking my work, it doesn't match up with what's found on Logic Friday, a program I tried using to minimize the function.
  16. SoulOfSword_

    How Do You Find Extragalactic Cepheid Variable Databases?

    Hi Guys! I've been working on my EE in IB Physics and I'm looking at how redshift of Cepheid Variables changes based on distance. I've been looking for astrophysics databases that include cepheid variables for a while now, but I can't find any. Is there any you guys can suggest or know of? Any...
  17. E

    Rocket moving through a cloud of dust, variable mass problem

    The first way to solve this is to just say, by conservation of momentum, that M_{0}v_{0}=(M_{0}+Apx)\frac{v_0}{2} where Apx is the mass of dust the rocket comes into contact with in a distance x. For the second method, by considering the change of momentum of the dust in 1 second, we know the...
  18. F

    I Distribution of a sample random variable

    $X_1, X_2, ..., X_{15}$ are independently to each other and follow $N (7, 3^2)$ what distribution the following statistics follow$T = \frac{(\bar{X}− 7)}{\sqrt{s^2/15}}$i know this follow t distribution $t_(n-1) =t_{14}$but how do i find what distribution $T^2$ follows, can i just multiply it?$T...
  19. nomadreid

    I Quantum state variable for entangled system

    (This question is on the elementary side...) In the Schrödinger picture, the state is dependent on time. If you have a state composed of several particles, generally you can break them up, with each one depending on local time. But in an entangled system, say of two particles, you can no longer...
  20. CheesyPeeps

    Force on side of tank filled with liquid of variable specific weight

    Homework Statement: An open tank with a rectangular side 1 m wide and 4 m high is filled with a liquid of variable specific weight, γ, with γ = 50 + 2y (N/m3), where y is measured vertically downward from the free surface. Find the magnitude of the force on the side of the tank. Homework...
  21. Math Amateur

    MHB Diiferentiability of Functions of a Complex Variable .... Markushevich, Theorem 7.1 .... ....

    I am reading the book: "Theory of Functions of a Complex Variable" by A. I. Markushevich (Part 1) ... I need some help with an aspect of the proof of Theorem 7.1 ...The statement of Theorem 7.1 reads as follows: At the start of the above proof by Markushevich we read the following: "If f(z)...
  22. S

    Finding truth value of each propositional variable.

    Note: ^ represents and. V represents or ~ represents not T represents True F represents False My solution... I started by substituting T in all variables... [p^(qVr)]^ ~r [T^(TVT)] ^ ~T (T^T) ^ F T^F F The answer is p = True q = True r = False
  23. Math Amateur

    MHB Verify Gamelin's Remark: Complex Square and Square Root Functions

    I am reading Theodore W. Gamelin's book: "Complex Analysis" ... I am focused on Chapter 1: The Complex Plane and Elementary Functions ... I am currently reading Chapter 1, Section 4: The Square and Square Root Functions ... and need some help in verifying a remark by Gamelin ... ... The...
  24. M

    MHB Cdf, expectation, and variance of a random continuous variable

    Given the probability density function f(x) = b[1-(4x/10-6/10)^2] for 1.5 < x <4. and f(x) = 0 elsewhere. 1. What is the value of b such that f(x) becomes a valid density function 2. What is the cumulative distribution function F(x) of f(x) 3. What is the Expectation of X, E[X] 4. What is...
  25. WMDhamnekar

    MHB Transformation of random variable

    Hello, A discrete random variable X takes values $x_1,...,x_n$ each with probability $\frac1n$. Let Y=g(X) where g is an arbitrary real-valued function. I want to express the probability function of Y(pY(y)=P{Y=y}) in terms of g and the $x_i$ How can I answer this question? If any member...
  26. BiGyElLoWhAt

    How to store ping results into an array or variable using a batch file

    I don't know much about batch, but what I want is to execute a command such as ping google.com -n 200 and store all 200 ping latency results to a variable. The default results (avg max min %lost) isn't enough for me to tell if I can do what I need to do. I would like to calculate the average...
  27. X

    Determining the optimal resistance of a variable resistor

    Let ##R## denote resistance of standard resistor and ##R_v## the resistance of the variable resistor. I know that ##I = \frac{V}{(R_v + R)}##. Now I also know that ##P = I^2 R_v##represents the power dissipated by the variable resistor and that I need to maximise ##P##. The problem I am having...
  28. W

    I Variable mass F=ma versus Rocket F=ma

    In the book by Tipler & Mosca, the section on F=ma for variable mass derives the following equation: ##\mathbf{F}_{ext}+\frac{dM}{dt} \mathbf{v}_{rel}=M\frac{d\mathbf{v}}{dt}## where ##\mathbf{F}_ext## is the external force on the system as a whole (ie not just the variable mass sub-system...
  29. J

    A Which is the quantized variable in quantum gravity?

    In Quantum Mechanics, the position (or momentum) variable is quantized. I define "quantization" as promoting a variable into a probability distribution. For example, with the double slit experiment, the classical assumption that the position/path of a particle is "unique" cannot explain...
  30. N

    I Variable transformation for a multivariate normal distribution

    Hello. I would like to draw (sample) several random vectors x from a n-dimensional multivariate normal distribution. For this purpose I want to use C++ and the GNU Scientific Library function gsl_ran_multivariate_gaussian ...
  31. Protea Grandiceps

    I X variable in damping force equation for damped oscillation?

    Hi, for ease of reference this posting is segmented into : 1. Background 2. Focus 3. Question 1. Background: Regarding (one, linear, second-order, homogeneous, ordinary, differential) equation describing the force in a non-driven, damped oscillation: F = m.a = -k.x - b.v F =...
  32. uzi kiko

    A Estimate the source of a variable when there are several distributions

    Hello everyone In my study, I inject a different amount of fluid in each experiment, such as 1 ml, 2 ml..., and test the change in the general dielectric properties of the solution. Now that I have done much (over 100) measurements for each injection in a specific volume, one can see that for...
  33. I

    Use a variable substitution to get into a Bessel equation form?

    Hello, For my homework I am supposed to get- into the form of a Bessel equation using variable substitution. I am just not sure what substitution to use. Thanks in advance.
  34. Suppaman

    B Is time a true variable in the scheme of things?

    I accept that time can pass at different rates depending on if the applied motion or gravity (both a parameter in some formula) and as a result time passes at a different rate. However, this seems to imply that we have some control over how slow time may pass. So, if that is just a fact of the...
  35. A

    A Can we create a random variable using QED effects?

    Quantum Electrodynamics (QED) has some observable effects such as the lamb shift, which is mainly caused by the vacuum polarization and the electron self-energy. These effects contribute to the "smearing" of the electron in an unpredictable manner, other than the uncertainty we already have...
  36. Eucliwood

    Work done on an object given a variable mass

    I was just doing some review on my physics lecture and I stumble on the idea of what if there was an object hanging and the cord mass is also included in the weight and it's displaced upward without having velocity nor time hypothetically and the cord change mass. I tried solving it by W = fΔx...
  37. R

    Choosing Free Variable for Generalized Eigenvector

    As you can see from my eigenvalues, here I've got a repeated roots problem. I'm wondering if it matters which variable I can choose to be the free variable when I'm solving for the generalized eigenvector. I think both are equally valid but they look different from one another and I'd like to...
  38. user366312

    A Question about the Poisson distributed of random variable

    The following is related to Poisson process: $$P(N_1=2, N_4=6) = P(N_1=2, N_4-N_1=4) = P(N_1=2) \cdot P(N_3=4)$$ Why is $$(N_3=4)=(N_4-N_1=4)$$? Can anyone explain?
  39. W

    I Continuous variable entanglement

    Hi all, I have learned the very basics of entanglement (discrete, 2 particle systems) and was hoping that someone can recommend introductory (undergrad-level) material for continuous-variable, 2 particle entanglement. Stuff I have found online so far (like this...
  40. E

    A variable mass problem with friction

    Homework Statement A water tank with a total mass of m0 is moving on a horizontal road with a coefficient of friction equals to μ. At t=0 water starts to come out of the tank with a velocity equal to u0 in relation to the tank. Each second the mass of water that comes out is λ. Find the...
  41. E

    Why Is Momentum Conserved in a Variable Mass System Like a Sand-Laden Cart?

    Homework Statement A cart with no motor moves on a plane. At t=0 it has a mass equal to m0 and some velocity. Each second sand with a mass of α comes out of the cart with a velocity of 0 in relation to the plane. What is the equation of motion of the cart? Answer: dV/dt=αv(t)/(m0-αt) Homework...
  42. Ranku

    I Variable Dark Energy: Would P Remain Constant?

    If dark energy density were to vary with time, in the equation of state w = p/ρ, would p remain constant and only ρ vary?
  43. DrClaude

    Mortgages: fixed vs variable rates

    I don't know how things are changing globally, but over here the bank rates are slowly going up. In conjunction, I've been reading articles from my bank that say that it would be a good time to go from a variable-rate mortgage (where the rate is adjusted every 3 months) to a fixed-rate mortgage...
  44. CivilSigma

    Find the PDF in terms of another variable

    Homework Statement For $$f_x(x)=4x^3 ; 0 \leq x \leq 1$$ Find the PDF for $$ Y < y=x^2$$ The Attempt at a Solution So, we take the domain on x to be: $$0\leq x \leq \sqrt y$$ and integrate: $$ \int_0^{\sqrt y} f_x(x) dx = \int_0^{\sqrt y} 4x^3 dx$$ Do we integrate with respect to x or y...
  45. R

    Finding formulas for the variable "a" and summations

    Homework Statement Can someone explain how to get from step 5 to step 6. I'm not seeing the link. Thanks in advance! Homework EquationsThe Attempt at a Solution
  46. Ottodomus

    Fortran Help with a warning: Uninitialized Variable

    Hi, I am trying to run this program and I am having a warning: "warning 298 - value X has been used without being given an initial value" Here is my code: [moderator: code tags added] real :: x real :: arcsin complex :: I = ( 0.0 , 1.0 ) print *, ' Enter the value of x ' if ( abs ( x ) >= 1...
  47. jk22

    B Usage of variable in integration

    When solving differential equations the following scripture can arise, for example: $$\int \frac{df}{\sqrt{\sin(\theta)^2-f^2}}$$ If the change of variable ##f=\sin(\theta)\sin(u)## Is performed, do the letters ##f,\theta## shall be considered independent or is...
  48. N

    Partial Differential Equation with variable coefficients

    Homework Statement This question relates to a very large project I have been assigned in a course on mathematical methods in structural engineering. I have to solve the following equation, in a specific way: (17) Now we have to assume the following solution: (18) It wants me insert...
  49. A

    Variable induced surface charge density on a sphere

    Homework Statement Homework Equations While solving this problem at r >>a ,the corresponding potential due to the dipole is kpcosθ/r2(potential due a dipole) where k is the electrostatic constt. ...(1) If σ(θ) is the surface charge density induced due to external electric field. then the...
  50. R

    I Using PCA for variable reduction

    In the textbook “Principal Component Analysis” Jolliffe (§9.2) suggests the following method for variable reduction: “When the variables fall into well-defined clusters, there will be one high-variance PC and, except in the case of 'single-variable' clusters, one or more low-variance PCs...
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