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. S

    Express logarithm in another variable

    The best I can get is: $$\log_{6} 3=m-n+\log_{6} 2$$ Is it possible to get the final answer in terms of ##m## and ##n## only? If yes, I will try to do it again Thanks
  2. PainterGuy

    Random variable and probability density function

    Hi, I was trying to solve the attached problem which shows its solution as well. I cannot understand how and where they are getting the equations 3.69 and 3.69A from. Are they substituting the values of θ₁ and θ₂ into Expression 1 after performing the differentiation to get equations 3.70 and...
  3. PainterGuy

    I Distribution function and random variable

    Hi, I cannot figure out how they got Table 2.1. For example, how come when x=1, F_X(x)=1/2? Could you please help me with it? Hi-resolution copy of the image: https://imagizer.imageshack.com/img923/2951/w9yTCQ.jpg
  4. patric44

    MATLAB Change the value of a variable at each time step in matlab?

    hi guys I am trying to implement the a second order differential equation tat contains a time dependent term, the equation looks something like r'' = -\mu/r^3+(g/g^3-m/m^3) the idea is that i want to calculate 'r' the position vector of a point, that is dependent on vectors g and m, I tired to...
  5. M

    Comp Sci How Does a Boolean Variable Impact Program Functionality in C++?

    #include <iostream> #include <string> #include<iomanip> //prototypes double gettingInfo(double&, double&, double&, bool&, char&); double errorChecking(double&); double calculatingPrice(double&, double&, double&, bool&); double printingReciept(double&, double&, double&,double&); using namespace...
  6. wrobel

    A The equations of variable mass systems

    The equations of variable mass systems are usually deduced from some very informal argument. It is so at least for the books I know. So I tried to construct a formal proof based on the continuous media equations. Criticism, remarks etc are welcomed. Let ##D\subset \mathbb{R}^q## be an open...
  7. A

    A Trend in an approximately exponentially distributed random variable

    I have a series of variables X i where ultimately the variables Xi each follow approximately an exponential distribution with a constant rate. In the beginning, there is a certain long-term trend. Is there a probability model in which Xi depends on the outcome of Xi-1 so that in the long run...
  8. M

    Probability: Prior Distribution for a Continuous Variable

    Hi, I was attempting this problem from the MIT OCW website probability and statistics course. Context: When Jane started class, she warned Jon that she tends to run late. Not just late, but uniformly late. That is, Jane will be late to a random class by ##X## hours, uniformly distributed over...
  9. Tertius

    A Find SEM Tensor from Lagrangian of Temporal Variable

    It seems the field φ(t, xi) could be integrated over all space to form a single temporal variable (which isn't a field anymore, but is just a function of time) as follows: Φ(t) = ∫φ(t, xi)dxi Suppose we then assume a Lagrangian from this temporal variable to be: L1 = -1/2 Φ'(t)2 + 1/2 b2...
  10. archaic

    Solving for a variable in an equation with fractional powers

    I have tried manipulating this to $$1-\frac{8}{(\pi k_B T)^2}\mu^\frac12(\epsilon^\frac32-\mu^\frac32)=0\Leftrightarrow\left[1+\mu^\frac12(\epsilon^\frac32-\mu^\frac32)\right]^{-\frac{8}{(\pi k_B T)^2}}=0$$ but this doesn't seem to lead anywhere. any hints please? the solution is one of these...
  11. Thomas Michael

    I How did the author transform the original equation into the Legendre equation?

    I'm reading "Differential Equations with Applications and Historical Notes" by George F. Simmons and I am confused about something on pages 431-432 He has the second order ordinary differential equation $$\frac {d^2v} {d\phi^2} + \frac {\cos(\phi)} {\sin(\phi)} \frac {dv} {d\phi} + n(n+1)v = 0...
  12. tommy7

    Mechanical device trigger with variable time delay (100-500ms)

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  13. Cosmin1337

    Single phase universal motor, variable frequency

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  14. Yalanhar

    Calculate work done by variable force

    Is my solution correct? $$ F(t) = at + b $$$$W=\int_t F(t)dr, ~~~~~~~~~ ~~dr = v(t)dt$$$$W=\int_t F(t)\cdot v(t) dt$$ $$ f = \frac{dp}{dt}$$ therefore $$v(t) = \frac{1}{m}(at^2/2+bt)$$then $$W = \int_t \frac{at+b}{m}\cdot\left(\frac{at^2}{2}+bt\right)dt$$ $$W = \frac{1}{m}\int_t...
  15. P

    Engineering Current variable given through junction crossing

    I'm supposed to solve this using nodal analysis. No biggie! I'm just not sure how to handle ia. I've never seen a current indicated in a junction crossing. I searched the web and my textbook and found zilch. I asked a GSI and was informed it is indeed written where is supposed to be. Within the...
  16. Arman777

    I Error propagation of a variable for an integral

    I have an integral that depends on two parameters ##a\pm\delta a## and ##b\pm \delta b##. I am doing this integral numerically and no python function can calculate the integral with uncertainties. So I have calculated the integral for each min, max values of a and b. As a result I have obtained...
  17. F

    B Choosing which variable is the dependent or independent variable

    Hello, I am review some basics. In the case of two variables like ##t## and ##C##, which represent the time in year and the cost in $ of a product respectively, we can graphically represent this pair of variables on a Cartesian plane. The horizonal axis is generally assigned the variable ##t##...
  18. V

    Synchronous generator variable speed and constant excitation

    The question is regarding an electrically excited synchronous generator. Consider that this generator is not connected to the grid and thus not locked with the grid frequency. This generator is spinning at variable speed and gets constant and similar excitation current meaning that the...
  19. F

    Variable, Data Type and Array Data Structures

    Hello, In Python and other programming languages, data can be of different types: integer, float, string, Boolean. On the other hand, Data structures are containers of data items which can (or not) have the same data type. A variable, when created, has: a) name (a piece of data stored in...
  20. U

    MHB Expectation of Conditional Expression for Exponentially Distributed RV

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  21. A

    A Creating a Variable Bend in a Function with Preserved Properties

    I have the following function: $$y = s-1 + exp (-ln (-1 / (s-1)) x)$$ with 0 < s < 1. For ##x = 0## you have ##y = s## and for ##x = 1## you have ##y = 0##. The function has a fixed bend, but now I want to make the bend variable, while the two properties, that for ##x = 0## you have ##y = s##...
  22. Arman777

    I Proving an identity for a free variable

    Let us suppose we have a function such that $$z = e^{1/ab} - 1$$ Where we have two free parameters, a and b. Q1) Can we say that as ##b \rightarrow \infty##, ##z = 0##? Or, since ##a## is a free parameter, there is always some value for ##a## such that ##z \neq 0## for ##b \rightarrow...
  23. Y

    Question on static int variable

    I don't understand this header file in the book. In line 4, it declares static int objectCount; I tried to put static int objectCount = 0; it won't compile, I tried putting in the next line objectCount = 0; it doesn't work. I tried putting in line 6, it doesn't work. Being declare in private...
  24. U

    MHB How to find PDF and Expected value of max(x,0), for a random variable x

    Let $a,b,c, \tau$ be positive constants and $x$ is an exponentially distributed variable with parameter $\lambda = 1$, i.e. $x\sim\exp(1)$. \begin{equation} E = \tau\Big[a\frac{1+a}{1+e^{-bx+c}} - 1 \Big]^+ \end{equation} where $[z]^+ = \max(z,0)$ How can I find The PDF for $E$ The...
  25. L

    I Sure way to convert variable integral to infinite integral?

    Sometimes I would like to transform an integral ##F(x) = \int_{a}^{x}f(s)ds## into an infinite integral of the form ##F(x) = \int_{0}^{\infty}f(g(u),x)du##. Is there some kind of change of variables that can guarantee this conversion on the boundaries and still give me a function of ##x##, at...
  26. S

    Find minimum value of f(x) in terms of variable a

    (1) For ##x>a## ##f(x)=x^2+x-a+1 \rightarrow## minimum value obtained when ##x=-\frac{1}{2}## Minimum value of ##f(x)=\frac{3}{4} -a## (2) For ##x<a## ##f(x)=x^2-x+a+1 \rightarrow## minimum value obtained when ##x=\frac{1}{2}## Minimum value of ##f(x)=\frac{3}{4}+a## But the teacher said...
  27. Hamiltonian

    B Basic doubts in vector and multi variable calculus

    If say we have a scalar function ##T(x,y,z)## (say the temperature in a room). then the rate at which T changes in a particular direction is given by the above equation) say You move in the ##Y##direction then ##T## does not change in the ##x## and ##z## directions hence ##dT = \frac{\partial...
  28. H

    I Principal Component Analysis with dependent variable?

    So I found a paper, https://www.sciencedirect.com/science/article/pii/S0022231314006048?via%3Dihub which concerns a property of a compound called "Quantum Yield", which is a result of various factors (independent variables). The authors are trying to figure out what factors affect the quantum...
  29. A

    A capacitor of variable capacitance

    Using: $$i(t)=\frac{U}{R}.e^{-\frac{t}{RC}} As the power is constant, then the current will be constant, so: t/RC is constant I don't know how to proceed anymore. I think you should use some derivative, but I'm still very new to that part, so how can I proceed?
  30. W

    I Superdeterminism and the hidden variable

    Bell's superdetermimism seems to imply that there is a hidden variable. Please correct me if I am wrong but that seems like classical physics.
  31. M

    I Failure rate for a uniformly distributed variable

    Hi, I have this question: If random variable T is uniformly distributed over [a, b] , what is its failure rate? Please help
  32. robotman

    Potential Energy associated with a Variable Force

    Don't really know what they want from me
  33. archaic

    Calculating a mean related to a continuous random variable

    I am not sure about how to approach this. Since the volume is uniformly distributed, the mean volume is ##(5.7+5.1)/2=5.4##, which is less than ##5.5##. From this, I could say that, on average, the producer won't spend any extra dollars. But then I thought that maybe I should interpret this as...
  34. F

    Why is a temporary directory created when using the Python library matplotlib?

    Hello, I am getting better at using the command line in Windows. I understand that the "set" command at the prompt shows all the various environment variables, PATH variable included, and I see many directories listed in the PATH. However, when I access the environment variables through the...
  35. T

    Integral of (xsin(t))....Two Variables in Single Variable Calc Integral

    I was told this problem could simply be solved with calc-1 techniques, so I'm tempted to say we could do d/dx(x∫(limits: 0,x) sin(t) dt. Then it's a simple product rule: d/dx (x) * ∫(0,x) sint dt + x * d/dx(∫ (0,x) sin (t) dt) = 1 - cos(x) + x*sin(x). However, I wonder if we have to allow that...
  36. J

    I Expected value of a variable and its reciprocal

    If E(X1)>E(X2), does it mean that E(1/X1)<E(1/X2)? Thanks!
  37. AN630078

    Kinematics Motion with Variable Acceleration

    The displacement of the particle is; s= ∫v dt s= ∫4-3t^2 dt s=4t-t^3+c When the particle is at the Origin, t=0; 0=4(0)-(0)^3+c c=0 So this becomes; s=4t-t^3 The particle next passes through the origin when; 4t-t^3=0 Factor out the common term -t; -t(t^2-4)=0 Rewrite t^2-4 as t^2-2^2 and factor...
  38. K

    MHB Ix1 + x2 + x3 + x4 = 12 with at least one variable equal or greater than 5

    So i got this problem in which there is a system with natural variables x1 + x2 + x3 + x4 = 12 and there is at least one variable that is equal or greater than 5 and i would like to know all the possibilities for this system. Aprecciate.
  39. U

    I Unclear step in "Change of variable in a multiple integral" proof

    I'm studying the proof of this theorem (Zorich, Mathematical Analysis II, 1st ed., pag.136): which as the main idea uses the fact that a diffeomorphism between two open sets can always be locally decomposed in a composition of elementary ones. As a remark, an elementary diffeomorphism...
  40. Kaguro

    Engineering What to Do When Input Voltage is Variable? | 5-20mA Range Explained

    This is a very confusing situation for me. If the input voltage were constant, then I would be able to understand that by varying load resistance, I can change the current through it, such that the drop across the load = Vz = 6.8V. But the input voltage is also not constant. So what am I to...
  41. R

    Variable friction on an inclined plane and maximum velocity

    This problem was from the chapter on Work and Energy so, I thought of using the principle of conservation of mechanical energy. Clearly, the potential energy of the block decreases by mgh (assuming the block has mass m). This energy should have been converted to kinetic energy, but it clearly...
  42. S

    MHB Single Variable Calculus Summary Rulesheet

    Students see my 20+ page calculus bundle on limits, derivatives and integrals and their applications. The summary notes are cleanly written, have background math grid paper, and summarize all major concepts, formulas, and procedures from calculus books. Please tell me what you think and if this...
  43. G

    MHB Finding minimum value of function with two variable

    I have a formula for cost calculation that contain x and y two variable. I have to find the value of (x,y) where that formula will gives minimum value as cost should not be equal to zero, it has some minimum value. I took 1st partial derivative with respect to x and then with y and found the...
  44. J

    MHB Finding the Unique Solution of a Polar System with Variable Radius?

    Hello! Brand new to the forums, hopefully someone here can help me out. Paths start out at the edge of a circle and "flow" along a polar equation that determines phi based off the initial phi (phi0) and a variable radius (ie. as your radius grows, your phi is changing). Hopefully this image...
  45. S

    A Fractional Calculus - Variable order derivatives and integrals

    Does anyone know any good research on this topic? I'm basically looking for information on what would be solving integral and differential equations in which the unknown you need to solve for is the level of a integral or derivative in the equation. For example F'1/2(u)+F'x(u)=F'1/3(u) where the...
  46. Boltzman Oscillation

    Engineering Variable Gain Amplifier Analysis help

    I need to find A_v, I want to relate Vin to Vout. To do this I did KVL on the major loop: $$V_{DD} = I_D*R_D + V_{SD1} - V_{SD2} - I_D*R_D$$ Since M1 = M2 then everything would cancel out and I would just get V_dd = 0 which is probably wrong. This is assuming V_sd1 = V_sd2, is that correct?
  47. mertcan

    A Solution to a differential equation with variable coefficients

    Hi, I really struggled to dig valuable things out of internet and books related to high order homogeneous differential equation with variable coefficients but I have nothing. All methods I see involves given solution and try to find others(like reduction of order method), even for second order...
  48. P

    A Translating/encoding a continuous variable model into a qubit model

    I've read these two pages that discuss going from qubit to continuous variable - https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 . I'm curious if anyone knows some papers that discuss going the other way around? I.e. qubitizing a continuous variable model? Any insight...
  49. E

    Can anyone explain this derivation of the variable mass equation?

    This question stems from one of the recent homework threads. I'm familiar with the derivation given here regarding mass accretion and ejection, where the general idea is to define a system around body and all of the incoming/leaving mass so that we can once again apply NII to the whole thing. I...
  50. D

    Simple pendulum of variable mass

    Hello, I've got to rationally analice the form of the solutions for the equations of motion of a simple pendulum with a varying mass hanging from its thread of length ##l## (being this length constant). I approached this with lagrangian mechanics, asumming the positive ##y## direction is...
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