Variable Definition and 1000 Threads

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. A

    Mathematica How to use Switch with variable number of terms?

    Hi, I'd like to use Switch with an integer partition of a number. For example, if n=4, then I define the partition as: monodromyTypes = IntegerPartitions[n]; this gives: monodromyTypes={{4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}}. I'd then like to set up a Switch depending on what the...
  2. G

    Why is entropy a state variable even for irreversible path?

    Hello. The entropy S is a state variable or state function as the integral of dS = dQ/T is a path-independent, provided that the path is reversible process path. However, such a path-independency of the integral breaks down when the path includes irreversible process. So, I guess we can only...
  3. R

    B How Do Variables and Constants Differ in Mathematics?

    There are 2 things taught to us:variables(litersls ) and constants . If we let a value 'a' as a constant ,meaning it would remain unchanged and also it is a set of real numbers . If we take 'x' as a variable, meaning it can change and it is also a set of real nos. For ex. Lim (x>a) x = a...
  4. P

    Variable 100-350VAC output controlled by PLC?

    Hello, I have a strange request from a client. He has a "burn-off" which is used to burn bits of labels that are stuck onto his products, that's a bit vague, but it's all the info I have. The request is that he wants to be able to change the voltage going through the burn-off anywhere between...
  5. Kaura

    Extrema of Two Variable Bounded Function

    Homework Statement Find the maximum and minimum value attained by f(x, y) = x2 + y2 - 2x over a triangular region R with vertices at (0, 0), (2, 0), and (0, 2) Homework Equations partial x = 0 and partial y = 0 at extrema The Attempt at a Solution partial x = 2x - 2 partial y = 2y 2x - 2 =...
  6. J

    Making a 12-24v DC variable power supply

    Homework Statement So, for a school project I have to make a resistance soldering iron. As far as I know, this requires a high current going through high resistance wire (such as stainless steel in my case). I need to make this run from a standard 120v 15A wall outlet. I have figured out so far...
  7. G

    B Cepheid variable stars cause of light variance

    Have been reading about cepheid. Can I just check I've got this? 'When at their hottest (when gravity has squashed them) have more doubly ionised He so star becomes more opaque' Now was just wondering what the main mechanism is here? Because He2+ doesn't have any electrons left to absorb photons...
  8. D

    I Change of variable and Jacobians

    Hi. I realize that Jacobians are not normally used in 1-D but I'm confused as to the following. If I have the following integral ∫a-a f(x)dx and make the change of variable y = -x then dy = -dx and the limits of integration reverse so I end up with ∫-aa f(-y)(-dy) but if I use the Jacobian...
  9. Drako Amorim

    I Limit of a two variable function

    I'm trying to verify that: \lim_{(x,y)\rightarrow (0,0)}\frac{\sin (x^{3}+y^{3})}{x+y^{2}}=0. 0<\sqrt{x^2+y^2}<\delta\rightarrow |\frac{\sin (x^{3}+y^{3})}{x+y^{2}}|<\epsilon 0\leq |\sin (x^{3}+y^{3})|\leq |(x^{3}+y^{3})|\leq |x|x^2+|y|y^2 |\frac{\sin (x^{3}+y^{3})}{x+y^{2}}|\leq \frac{...
  10. L

    MHB Using the Modulus to find a variable - to find co-ordinates

    The co-ordinates of two points are A(4,-1) and B(7, -5) The line L1: 3x+4y−12 = is perpendicular to AB. (a) Find, in terms of k, the distance between the point P (10, k) and the line L2 (b) P(10, k) is on a bisector of the angles between the lines L1 and L2 and L2 :5x+12y−20 =0...
  11. Poetria

    Complex functions with a real variable (graphs)

    Homework Statement How do the values of the following functions move in the complex plane when t (a positive real number) goes to positive infinity? y=t^2 y=1+i*t^2[/B] y=(2+3*i)/t The Attempt at a Solution I thought: y=t^2 - along a part of a line that does not pass through the...
  12. Arman777

    Calculating Angular Acceleration and Speed with Variable Force on a Pulley

    Homework Statement A pulley with a rotational inertia of ##10^{-3}\frac {kg} {m^2}## about its axle and a radius of ##10 cm##, is acted on by a force applied tangentially at its rim.The force magnitude varies with time as ##F=0.5t+0.3t^2## , with ##F## in Newtons and ##t## in...
  13. kolleamm

    B Chain rule for variable exponents

    I understand that when you use the chain rule you multiply the exponent by the number in front and then reduce the power by 1. So the derivative of 2x^3 = 6x^2 I'm confused now however on how you would solve something like e^-3x, the answer turns out to be -3e^-3x Am I missing a rule? Why...
  14. HarrisC

    Constant voltage, variable current

    Will my described method allow me to achieve my objective? If so, could you recommend a rheostat that is rated for at least 20A @120VAC that will work for my application? If not, could you describe an alternate method? Objective: Determine the ampacity of various wires at 120VAC Method: Wire a...
  15. mnb96

    I Equivalent definitions of random variable

    Hello, According to the Wikipedia article on random variables: If the above statement is true, then, instead of defining a (real) random variable as a function from a sample space of some probability space to the reals, could we equivalently define it as a subset of ℝ associated with a CDF?
  16. E

    MATLAB How to Set a Variable in Matlab as an Integer Only?

    Is there a function in Matlab that presets the value of a variable as an integer only? For example I will set the variable 'y' as an integer at the very beginning of the code, and whenever the variable gains a new value it automatically returns an integer value. Thank you in advance.
  17. Leo Freeman

    Is this Voltage Variable Capacitor available commercially?

    Is the "Voltage variable capacitor" described in patent US 20070242410 A1 a commercially available component? Has anyone heard of this method of changing the dielectric constant using a biasing voltage? It has been nearly 13 years since the patent was filed, but I've never heard of it. It would...
  18. K

    Work Kinetic energy using variable force

    Homework Statement The position of an object of mass 2 kg is changing as a function of time by the formula x(t) = 4t^3-6t. (a) find the work done by the forces acting on the particle between t=1 and t=3s. (b) What is the object's velocity when the force on it is zero? Homework Equations is...
  19. W

    I Variable displacement hydraulic pumps

    In online examples of variable displacement systems with swash-plate pumps, the input pump & motor are usually of equal size. When the constant RPM input pump is at full tilt (max displacement) the fixed displacement motor is at the same RPM for a 1:1 ratio, and when the pump is at no tilt (no...
  20. cathal84

    Finding length of vector with unknown variable

    Finding length of vector with unknown variable. Purely for study purposes. Find the smallest possible length of the vector →v . Let vector V = (-2/3,b,16/7) Equation for finding length of vector : Sqrt(a^2+b^2+c^2)Question would be quite straight forward had there been no unknown variable but...
  21. Rectifier

    Integration with variable substitution

    Hello, I am having trouble with solving the problem below The problem Find all primitive functions to ## f(x) = \frac{1}{\sqrt{a+x^2}} ##. (Translated to English) The attempt I am starting with substituting ## t= \sqrt{a+x^2} \Rightarrow x = \sqrt{t^2 - a} ## in $$ \int \frac{1}{\sqrt{a+x^2}}...
  22. Z

    If a with respect to b, which is the independent variable?

    Homework Statement My lecture note says that "T-v diagram shows change in specific volume of a substance with respect to temperature.". Is it correct? Homework EquationsThe Attempt at a Solution If a(Specific Volume) "with respect" to b(Temperature), then b(Temperature) should be the...
  23. Daquicker

    Minimal altitude to start a “Suicide Burn” - variable thrust

    Homework Statement I'm trying to calculate the absolute lowest safe altitude above a planet's surface to start firing the thrusters on a simulated lander in order tot just reach vCraft = 0 at the planet's surface. The force the craft's thrusters responsible for desceleration generate is...
  24. Biker

    Electrical circuits with resistors and variable voltage sources

    Homework Statement The following picture illustrate how the current in the circuit changes when you change ##E_2##. Where slope 1 represents the current flowing through ##E_1## and slope 2 represents the current flowing through ##E2## Homework Equations Usual circuit laws :P The Attempt at...
  25. bubblegumandcameras

    Motion under variable acceleration experiment

    Used a mass attached to a dynamic cart via pulley to examine motion under variable acceleration. As the mass was increased, my calculated friction force shows a decrease. I know that friction should increase with larger mass. Any suggestions as to why my calculations show a decrease? Used the...
  26. B

    Is this Variable frequency drive compatible with this motor?

    My senior design adviser told me that the VFD must be the same brand as the motor that is being used, I'm not sure I believe this. I plan on using a GS1 series AC drive, here is a link; https://www.automationdirect.com/adc/Overview/Catalog/Drives/GS1_(120_-z-_230_VAC_V-z-Hz_Control) Here is a...
  27. R

    Continuous random variable transformation and marginals

    On the attachment, I was told my joint pdf was right, but the support was NOT 0<y1y2<1 0<y2<1, so maybe it's right now? Obviously B and C are incorrect, too, since they don't integrate to 1. I'm probably making just a few simple mistakes. Thanks in advance!
  28. P

    Changing Independent Variable in the Bessel Equation

    Homework Statement Given the bessel equation $$x^2\frac{d^2y}{dx^2} + x\frac{dy}{dx} -(1-x)y=0$$ show that when changing the variable to ##u = 2\sqrt{x}## the equation becomes $$u^2\frac{d^2y}{du^2}+u\frac{dy}{du}+(u^2-4)y = 0$$ Homework Equations The Attempt at a Solution ##u=2\sqrt{x}##...
  29. L

    A Ortogonality of two variable functions

    In functional analysis functions ##f## and ##g## are orthogonal on the interval ##[a,b]## if \int^b_a f(x)g(x)dx=0 But what if we have functions of two variables ##f(x,y)## and ##g(x,y)## that are orthogonal on the interval ##[a,b]##. Is there some definitions \int^b_a f(x,z)g(z,y)dz=0?
  30. 1

    I Convert 2 variables into 1 representative variable

    I need help to convert 2 variables A,B into 1 representative variable C, which is used to filter A,B: Below is an example with C=A+B, which makes Set 2 the highest value: Set 1: A=65, B=75, C=140; Set 2: A=50, B=100, C=150; Set 3: A=54, B=90, C=144; Set 4: A=72, B=72, C=144; Set 5: A=71, B=73...
  31. K

    B Dividing an equation by a variable

    Hello guys, I am confused about when we can multiply and divide by the variable. I know the if zero is hidden as a factor then we can not divide or multiply. eg. x/2x+1=0 are we allowed to divide both side 2x+1. Although zero is hidden value of x, there are no other ways to solve this...
  32. merricksdad

    Find the center of mass of a cone with variable density....

    Homework Statement Find the center of mass of an inverted cone of height 1.5 m, if the cone's density at the point (x, y) is ρ(y)=y2 kg/m. Homework Equations The formula given for this problem is rcm=1/M * ∫rdm, where M is total mass, r is position, and m is mass. The Attempt at a Solution...
  33. N

    Stargazing How do we know how bright a cepheid variable star is?

    Most of us know what that we can judge the distance of an object such as a car headlight by how bright that headlight is. The things is we know how bright car headligjts are from 1 foot away so that seems pretty obvious. A Cepheid variables brightness is commonly used to measure the distance...
  34. K

    Variable Amplitude Fatigue Analysis - Super Confused on how

    Hey everyone I'd be really grateful if anyone could help me out here, been going round in circles for two weeks now and I need to get going soon. Jumping right to the point, here's my problem: We are currently working on a student project and designing a Wind Turbine for future opensource use...
  35. MacLaddy

    How can I safely vary the current to a variable torque DC motor for my project?

    I have recently learned that in order to vary torque output from a DC motor, I need to vary the input current. A project I am working on requires that I have a DC motor that will be backdriven while providing resistance to a lever. A max torque of about 10 lbft will be provided from the lever...
  36. J

    B Variable focal length TV / screen

    Recently I have had a lot of eye strain from excessive computer use. The problem is because your eye lenses re stuck in a fixed position. I wanted to know if it would be possible to make a screen that is 1m away look like it is 4m away for example. Would it be possible by making the screen out...
  37. MeaningfromForm

    Super small electronic variable resistor -- Exists?

    Hi I couldn't find of these exist anywhere. Is there a component that is a variable resistor that adjusts based solely on receiving an up/down signal? And maintains its state on powerdown? I don't want this solution to involve any type of software, just a hardware solution. Looking for...
  38. Automata-Theory

    A Particle Moving Along a Ring with Variable Potential

    Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...
  39. victorhugo

    Independent variable question i'm not getting

    I know that D is definitely a dependent variable, but I don't see how the others are dependent on anything else... The correct answer is A btw. Please explain to me how B and C are dependent variables considering the investigation is to "determine and compare the heat of combustion of three...
  40. Kernul

    Line orthogonal to a plane with variable parameter

    Homework Statement I have to find for which values of the real parameter ##b## the following plane is orthogonal to the following line: ##\pi : 5x + (2b - 1)y - (1 + 8b)z + 3 = 0## ##s : \begin{cases} x + z - 4 = 0 \\ x - 3y + z + 2 \end{cases}## Homework EquationsThe Attempt at a Solution For...
  41. L

    I 2° order linear, homogeneous, variable coefficients

    sin(x) * y''(x) + 2cos(x) * y(x) = 0 y(0) = 0 y'(0) = 1 how do I solve it? (I know the solution because I have created the diff. equation starting from a simple function). -- lightarrow
  42. S

    How do you solve the problem of a rocket with variable mass?

    Homework Statement Rockets are propelled by the momentum of the exhaust gases expelled from the tail. Since these gases arise from the reaction of the fuels carried in the rocket, the mass of the rocket is not constant, but decreases as the fuel is expended. Show that for a Rocket starting...
  43. T

    Changing coefficient when an independent variable is added?

    Homework Statement (b) (10 points) Estimate the equation income = β0 + β1female. Interpret theβ1 coefficient. How does β1 compare to your difference in means in part a? (c) (10 points) Estimate income as a linear function of highest grade and female. Report results. How does the coefficient on...
  44. TheSodesa

    Probability for a binomially distributed variable X

    Homework Statement Let ##X \sim Bin(n, p)## where ##n=20## and ##p=0.1##. Calculate ##P(|X-\mu| \leq \sigma)##. Give your answer up to three decimal places. Homework Equations For a binomially distributed random variable, using moment generating functions we have: \begin{equation} \mu= E(X) =...
  45. C

    Comp Sci Fortran variable value changing randomly

    This isn't really a question for which the template is useful.. Can anyone explain to me why the value of the variable 'seed' in location 1 is different from the value in location 2? The only thing happening in between is the defining of the varaible v(1) using the real function. I don't see...
  46. E

    Variable Mass System: Calculate Speed of Truck

    Homework Statement A pickup truck is driving at night through the rain. He drives onto a frozen lake. He immediately turns off his engine to save fuel (it wouldn't help anyway on frictionless ice) and let's the truck coast (move under no power). Unfortunately, the rain is accumulating in the...
  47. A

    B Calculating error when constant is divided by variable

    Hello everyone, I have a very simple question but for some reason, I couldn't find the exact answer to it on the internet. Let's say we have a formula y = k/x where k is constant and x and y are variables. Assume that I am given the absolute uncertainty in x how should I calculate the...
  48. P

    Linear Optimization Conversion (nested free variable)

    Homework Statement (This is a mock-up) Given maximize(x,y) Ax + | x - y | s.t. x + By - C >= 0 y >= 0 A, B, and C are some coefficients. Homework Equations Linearizing absolute expressions: z = | x |; where z >= x, z >= -x Linearizing free variables: let x = x+ - x-; where x+, x- >= 0...
  49. KonaGorrila

    MATLAB How to get the last variable of a for loop in MATLAB

    Aloha guys, I am just having trouble getting MatLab to output only the last variable of my "for loop." If anyone can help all I am looking for is an example of notation. p.s. I have done this before just not in a while and will continue to look through my old scripts and functions. just not in...
  50. W

    Limit of x as it approaches a variable

    1. Problem statement Q. Use limit to find the instantaneous velocity at time t if the postition is p(t) at time t. p(t) = t + (1/t) at x = t 2. Homework Equations (Sorry dashes are in there to keep everything where it should be. I don't know how to make fractions in this and it was...
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