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. S

    Variable pulley distance - tensioner force help needed

    Greetings, lurked for a long time, but I need some help here so I joined up. Please have some patience with me if I miss any important information. I am working on a belted pulley drive system where the driveN pulley will move relative to the driveR while in the stopped state. An outside...
  2. J

    Solving equation involving a variable and its logarithm

    Can you suggest a general analytical solution to the following equation \ln(x^{3/2})-bx-c=0 where x is real positive variable and b and c are real positive constants.
  3. S

    Variable Mass and Steady Leakage: Finding the Velocity of a Cart with Calculus

    A cart has a load of 100 kg sand at start and it is pulled by a steady resultant force of 100N starting from rest. A hole in the cart causes steady leakage of 1kg/s. Find velocity v of the cart after 50s of motion. What I know about this is that, we have to use calculus. dF =(dM /dT) *(dV/dT)...
  4. S

    How Does Mass Leakage Affect the Velocity of a Cart?

    A cart has a load of 100 kg sand at start and it is pulled by a steady resultant force of 100N starting from rest. A hole in the cart causes steady leakage of 1kg/s. Find velocity v of the cart after 50s of motion.
  5. P

    Calculus of variations: multiple variables, functions of one variable

    Simply put, can you find the function which extremizes the integral J[f]=\iint L\left(x,y,f(x),f(y),f'(x),f'(y)\right) \,dx \,dy Where ##f## is the function to be extremized, and ##x## and ##y## are independent variables? A result seems possible by using the usual calculus of variation...
  6. M

    Integration by trigonometric change of variable

    Homework Statement I'm trying to solve ##\int\sqrt{a^2 - x^2}## by using the substitution ##x = asin\theta## Homework Equations ##x = asin\theta The Attempt at a Solution ##y = \int\sqrt{a^2 - a^2cos^2\theta}## ##y = a\int\cos\theta## ##y = a^2\int\cos(\theta)^2## ##y = (a^2)/2 *...
  7. M

    How to Derive the Lorentz Factor from Pythagoras?

    Hey guys, this is a little silly question but it bothers me. I am not a math genius (yet i hope) and I am still in elementary school so there's a lot to learn. But i just read about the lorenz factor in this example he basically used pythagoras of this light clock in a train, so it started of as...
  8. M

    Lead-lag test for discrete variable vs continuous variable

    Let's say I'm applying electrical currents to a certain part of a human test subject and measuring certain deflections in his heart readings during this period. Before I increase the electrical currents, which could be dangerous, I'm interested to see if the changes in electrical currents are...
  9. M

    Integer solutions for multiple variable equations

    Obviously it will take some brute-force. But how do I minimize the brute-force needed (optimize)? I know one can solve Diophantine equations and quadratic Diophantine equations. But what if I have something like 10 (any number) of variables? (what if there are no squares, what if there are...
  10. C

    Green's function in n-dim, but with one independent variable.

    Suppose we have some partial differential equation for a scalar ##f## $$Df = \rho$$ taking values in ##\mathbb{R}^n##, and further suppose that the differential equation is completely independent of the variable ##y:=x^n## so that the differential operator ##D## only contains derivatives with...
  11. M

    Resistance Variable Cross Section

    Homework Statement The question asks for resistance R of a disk with radius r and fixed width w, whose cross sectional area is variable. Unlike in the picture below, the resistor is not connected to the circuit on the flat ends, but on the cylindrical sides. Homework Equations...
  12. S

    MHB Studying for a Test with Variable Answers

    This technically might not belong here, mods, put it in it's proper place if not. So I'm studying for a test on Monday. Not a big deal, we use webassign, you may commence with the horrified gasps and groans, I know. So here's my odd little situation. I get a problem like this one Integral...
  13. Ravi Mohan

    Probability distribution of a stochastic variable

    I am studying an article which involves stochastic variables http://www.rmki.kfki.hu/~diosi/prints/1985pla112p288.pdf. The author defines a probability distribution of a stochastic potential V by a generator functional G[h] = \left<exp\left(i\int...
  14. M

    350W PMA: Looking for a Variable Load Solution

    Hi, I'm currently working on my end of the year project for my studies. I have a DC motor mechanically linked to a wind turbine PMA. My aim is to control the speed of this motor (using PWM) to simulate different types of winds. My problem lies on the generator side. I need a load to...
  15. U

    Multiple variable prediction interval

    Hey! I'm working with some regression related stuff at the moment and i'd need some help with multiple variable prediction interval. Prediction interval for a single variable can be calculated using PI = \hat{\beta_0}+\hat{\beta_1}x_i \pm t^* s_e \sqrt{1+\frac{1}{n} +...
  16. R

    Variable capacitor q factor for fm radio jammer

    i'm building fm radio jammer for project for my ee class in physics department. a circuit is here. http://www.circuitstoday.com/fm-radio-jammer i bought the components, soldered on PCB. it hasn't worked. an oscilloscope shows sine oscillation even if there is no L and C for tank circuit...
  17. T

    Variable gear ratio [Worm gear - Worm Wheel]

    Hello fellow PF members, This is my first post. I am wondering if there is a mechanism that alters the gear ratio in worm gear-worm wheel setup.. Something like a variable pitch worm gear that can be used instantaneously to alter the gear ratios. If not for worm gear, is there anything in...
  18. K

    Proportionality with more than one variable?

    if x is direct, indirect or exponentially propotional to A and as well as B can we write x=kAB ? if we write the equation seperately, we have x=k1A, x=k2B when combined, x2=(k1k2)1/2 (AB)2 then x=k3(AB)1/2 to see the real complicate example EX.1 trypsinogen is converted to trypsin in...
  19. D

    Understanding Variable Loads in Circuits: Solutions & Verification

    Homework Statement Question 1: For the circuit below, determine what happens at maximum resistance when varying the 10K (decade box) variable load. Question 2:Explain the answer to the previous question, in terms of voltage compliance of the current source. Question 3:What causes detectable...
  20. A

    C Programming: acos() not accepting variable

    The following function acos() does not accept any variables. I have included the math.h header. For example i = 1; acos(i/2); // This should be equal to 60
  21. I

    Partial derivatives, change of variable

    Given V=xf(u) and u = \frac{y}{x} How do you show that: x^2 \frac{\partial^2V}{\partial x^2} + 2xy\frac{\partial^2V}{\partial x\partial y} + y^2 \frac{\partial^2V}{\partial y^2}= 0 My main problem is that I am not sure how to express V in terms of a total differential, because it is a...
  22. N

    Solving 2nd order PDE of single variable

    I've been getting pretty rusty in terms of derivation in recent years. Encountered this problem which I can't derive the steps despite knowing the solution. \frac{\partial^2 u}{\partial r^2} + \frac{\partial u}{\partial r}\left(\beta + \frac{1}{r}\right)+\frac{\beta}{r}u=0 Known...
  23. L

    Solve for a variable inside a summation

    I need to solve the equation for x, where a is a known constant and . The bs are known too. What i need to do is sto find for which xs I'll have a specific value of a, eg a=0.5, i.e. solve for x and substitute the a. I believe that the result will be a group of xs and not a single...
  24. S

    MHB Solve Integral w/ Change of Variable Technique

    How would I apply the change of variable technique to solve the integral \int x\frac{2x}{1000^2}e^{-(x/1000)^2}dx w/ out the x I used u=(x/1000)^2 , and du=2x/1000^2 Now, I am calculating E(x), and now sure how to deal w/ the extra x. Thanks for any help!
  25. D

    Integration substiuition of new variable

    Homework Statement for this question, my ans is pi/2 not pi/4 . can anybody please check where's the mistake? Homework Equations The Attempt at a Solution
  26. D

    MHB Solving Change of Variables Problem with T(u,v) - Can You Help?

    Here's the problem: I'm having trouble using T(u,v) to figure out how to find the region that transforms into the the given region, R. Can anyone help? Thank you!
  27. H

    The main problem with Hidden Variable Theory

    The major problem I have with hidden variable theories is this: Even if you find hidden variable solutions which would render quantum physics unnecessary, you'd still be left with the ultraviolet catastrophe problem. You can use holographic principle, alternate realities, determinism or any...
  28. D

    Seperate variable and integration

    Homework Statement for this Q and t are variables, 10 and surd k are constant, is my working correct? Homework Equations The Attempt at a Solution
  29. A

    What method should I use to solve variable mass problems in physics?

    I'm a little confused about these. Sometimes I have seen solutions where F=d(mv)/dt=mdv/dt+vdm/dt is used and solved as a differential equation. An example is this: A water drap falls through a cloud. It has initial mass m which increases at a constant rate km as it falls. Show that it's...
  30. A

    Isolating variable confounded by cursed reciprocals

    Homework Statement Given 1) xy = 1 2) x(t^2)-y = (t^3)-1/t Express x in t, y in t 2. The attempt at a solutionx/t = [(tx+1)(td-1)] / [(t^2)-1] but I still can't separate t and x, driving me mad it is. Also subtracted 1) from 2) to obtain (t^2)x - (t^3) +1/t -1/x = 0 but no progress...
  31. C

    Second order system of odes with variable coefficients

    Hi, I have looked everywhere. Can someone please point me in the right direction for solving a system of ODEs with variable coefficients? I managed to solve such system with constant coefficients.
  32. ETBunce

    MHB Non-linear function with two unknown constants and one variable

    Am am presented with the problem: h(t) = c - (d - 4t)^2 At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above, in which c and d are positive constants. If the ball reached...
  33. C

    Variable coefficient 2nd order DE

    Homework Statement This an example from Boyce+DiPrima's text on ODEs. Original problem is to solve 2t2y''+3ty'-y=0, given that y1=1/t is a solution. But I'm stuck at the part where I'm to solve 2tv''-v'=0, v being the second unknown solution. The Attempt at a Solution In the text...
  34. Barioth

    MHB Finding Limit of Multi Variable Function Using Squeeze Law

    Let f(x,y)= \frac{x^3+y^3}{x^2-y} if x^2 is not equal to y and 0 otherwise. I need to find the limit when (x,y)->(0,0) I'm sure the limit exist and is equal to 0, I was unable to conclude switching to polar coordinate so I wana use "the squeeze law" I only have to evaluate f(x,y)=...
  35. M

    How do you solve a non-linear ODE involving a variable mass dust particle?

    Homework Statement At time t=0 a dust particle of mass m_0 starts to fall from rest through a cloud. Its mass grows exponentially with the distance fallen, so that after falling through a distance x its mass is m_0exp[αx] where α is constant. Show that at time t the velocity of the particle...
  36. mishima

    Which Variable Star Has the Longest Period?

    Hi, what is the name of the variable star with the longest period? I know Mira variables are in general the longest, but which particular star has the longest period? Thanks.
  37. C

    Solving for a variable in an equation that involves vectors

    Homework Statement I have the equation: \mathbf{F}_{2,1} = \frac{Q_1 Q_2}{4 \pi \varepsilon_0 {r_{2,1}}^2}\hat{r}_{2,1} (standard electric force equation for 2 charges) I know the value of everything except Q2 and have to find it. The vectors each have 3 components. Normally in an...
  38. I

    Delta/epsilon two variable limit

    Homework Statement In calculus 1, honestly, I never understood this as it just doesn't make sense. Now in multivariable calculus, it still doesn't make sense. After all these engineering, math, and science classes, I still cannot figure these problems out, and it pisses me off! I would...
  39. Monsterboy

    Variable specific impulse magnetoplasma rocket(VASIMR)

    Hi, I was reading about VASIMR ,my knowledge in rocket science is very limited ,i was able to understand how plasma is produced and used for propulsion but i didn't understand how specific impulse is varied and why is it not possible for other (ion)thrusters or even chemical ones to vary the...
  40. S

    Solving Three Variable Equations: Finding x, y, and z

    Homework Statement find (x,y,z) Homework Equations 3x - 4y + 7z = 0,-------------->first equation 2x - y - 2z = 0,---------------->second equation 3x3 - y3 + z3 = 18.---->third equation The Attempt at a Solution on subtracting first two equations i get x - 3y + 9z = 0 using this if i...
  41. R

    Can HMMs accommodate variable time delays in observations?

    Hello All, I'm building a HMM for some data where there are two different time delays. Specifically, I collect data in consecutive traces, such that the time delay between each data point within a trace is approximately fixed, and the time delay between each trace is approximately fixed, but...
  42. V

    MATLAB Minimizing a function in one variable in Matlab

    This problem was originally a multi objective problem but using scalarization it can be transformed to the following: Min: -p'*x + u*x'*V*x subject to 1*x=1 -u is the risk aversion index that I wish to vary from .1 to 100 -V is a (4x4) variance covariance matrix -p is the (4x1) expected...
  43. H

    I want to make a variable watt device

    i was looking at an e-cig and wondering how it regulates watts. would it be viable to make your own? for those of you who don't know they run off of a 18650 3.7v battery that powers a coil. the coil is in the ballpark of .3 - 3.5 ohms. how do i get 30 watts of regulated power and jam it...
  44. D

    Shifting integration variable when determing population densities

    Hi, I'm hoping someone can enlighten me on this as I'm a little bit fuzzy on the reasoning: Say I have a space-time dependent field B_{a} that interacts with fermions such that it affects their energy dispersion. It appears in the energies in the form...
  45. D

    Complex Circle Equation with random variable attached to Z.

    Homework Statement |zi - 3| = Pi Homework Equations Well, it clearly has to do with a circle but I do not believe there is a general equation for what I am asking about. The Attempt at a Solution There is no general solution not trying to solve anything. I want to know exactly...
  46. S

    Random variable conv. in prob. to c. How to find c?

    Homework Statement Let ##Y_1,...Y_n## be independent standard normal random variables. What is the distribution of ##\displaystyle\sum_{i=1}^n{Y_i}^2## ? Let ##W_n=\displaystyle\frac{1}{n}\sum_{i=1}^n {Y_i}^2##. Does ##W_n\xrightarrow{p}c## for some constant ##c##? If so, what is the...
  47. R

    MHB Transform Random Var CDF to Standard Normal: F(x)=1-exp(-sqrt x)

    How to transform a random variable CDF to a standard normal Given F(x) = 1- exp (-sqrt x), for x greater that 0 Thanks.
  48. B

    Is there a Leibnitz theorem for sums with variable limits?

    Is there a "Leibnitz theorem" for sums with variable limits? Wikipedia says that if we want to differentiate integrals where the variable is in the limit and in the integrand, we can use Leibnitz theorem: But what if I need to integrate a function defined like this:\Sigma_{I(x)}[f(x,t)]...
  49. H

    Isolating a variable gives me endless loop

    Coming in here with the following question, when I see what kind of stuff you normally tackle, is very embarrassing! But... I simply am too rusty for this stuff, it seems. This is NOT homework. This is something I need to do in a game I'm working on. I end up in and endless loop when trying...
  50. M

    Can a Variable Inertia Flywheel Maintain Constant Speed?

    Hello, My question is: how much energy is needed for changing inertia of flywheel? example: on rotary shaft we have linear actuator which is moving some object (mass). by that movement, radius of flywheel is changing. ...if there is energy input to flywheel, mass is moving away form...
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