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    How to think about entropy microstates/macrostates for a gas in a box

    I'm trying to relate an analogy from Brian Greene about entropy microstates/macrostates to the real world. In the analogy, you have 100 coins that you flip. The microstate is which particular coins landed heads up. The macrostate is the total number of coins that are heads up. So a low entropy...
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    I Is there a reason eigenvalues of operators correspond to measurements?

    Given a wave function \Psi which is an eigenstate of a Hermitian operator \hat{Q}, we can measure a definite value of the observable corresponding to \hat{Q}, and the value of this observable is the eigenvalue Q of the eigenstate $$ \hat{Q}\Psi = Q\Psi $$ My question is whether it's a postulate...
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    Formula for the expected value of a function

    The formula for the expected value of a continuous random variable is E(x) = \int_{-\infty}^{\infty} x\cdot f(x). This leads me to believe that the expected value of a function g(x) is E(x) = \int_{-\infty}^{\infty} g(x)\cdot f(g(x)). However, the correct formula is E(x) =...
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    Finding the domain of integration in spherical coordinate of a shifted cylinder

    So I've done some problems where a sphere intersects with a cylinder and I needed to find the volume of the intersected region using triple integrals. For example, if I needed to find the domain of integration for the intersection of the sphere $$x^2+y^2+z^2=a^2$$ and the cylinder...
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    Combinations proof

    Thanks, but I'm still not sure what to do from here. I'm not sure how to deal with the sum, I guess. EDIT: I guess I kind of get it now. For the summand, if we keep changing i then we're finding the number of ways to choose 2k elements from n-1 elements by choosing them from each sized set. So...
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    Combinations proof

    Homework Statement Prove that for any positive integer n, k, $$\binom{n}{2k+1}=\sum_{i=1}^n{\binom{i-1}{k}\binom{n-i}{k}}$$ Homework Equations $$\binom{n}{k}=\frac{n!}{(n-k)!k!}$$ The Attempt at a Solution I'm looking for a starting point. I've been given a hint that says, But I don't know...
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    Electric Field for a cylinder without using Gauss's law?

    I recently learned how to calculate the field from a cylinder (inside and outside the cylinder) using Gauss's law. I was wondering how I would be able to derive the same formula without using Gauss's law (just for practice). My idea is that you would need to integrate the electric field from...
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    Why doesn't this diff eq. have two solutions?

    Say you have the diff eq. x'=2x(x-13); x(0)=20. After separating and integrating we get, ln|(x-13)/x|=26t+C From here, we raise e to the power of each side to get rid of the natural log. Does this get rid of the absolute value signs? If so, why? If not, why is there only one solution (as...
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    Software for typing programming papers

    The syntax is only highlighted in Notepad++, copying it to another program like Word removes the formatting.
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    Software for typing programming papers

    Just like there's LaTeX for writing math papers and LaTeX editors to parse it, is there anything for writing papers in programming? Specifically a nice way to automatically format code.
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    Given a random number from 0-3, return a random number from 0-6

    I thought division might be involved, resulting in non-integers. What's the difference? I thought if something was random, the probability for each result would be the same (uniform). I'll try it out, see if I can come up with anything. If anyone else has any other ideas, please share them...
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    Why does grounding protect you from electricity?

    But I recently saw someone attach a wristband to their hand which was connected to a conducting pad which was connected to ground. After doing this he said it was safe to work with an electronic component sitting on the pad. So if only the electronic component needed to be grounded, he could...
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    Given a random number from 0-3, return a random number from 0-6

    Well the relationship is that after being given this random number from 0-3, you need to perform mathematical operations (functions such as floor and ceiling are allowed) to arrive at a new number from 0-6. Now if you performed these same steps for the random input number many times, you would...
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    Given a random number from 0-3, return a random number from 0-6

    This is actually for a program, but the challenging part is really the math. So you're given a number 0, 1, 2, or 3 and the probability of getting each is the same. Now given this random number, I need to output a number 0, 1, 2, 3, 4, 5, or 6 but the probability of getting each number needs to...
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    Why does grounding protect you from electricity?

    Let's saying you're working with something that has electricity running through it. If you ground yourself by touch something metal, aren't you making it easier for charge to flow through you through the metal, so a greater charge would flow through you? And if you didn't touch something metal...
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    Time it takes for an electron and proton to collide

    It's a positron not a proton, so the mass is the same.
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    Integrating factor for first order linear equations uniqueness theorem

    Thanks, that makes sense. One thing I don't understand in the link you gave me is on page four, they state w(t)=y1(t0)-y2(t0)=y0-y0. Why are the intial values of those two functions the same, if we assumed that the two functions would be different?
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    Integrating factor for first order linear equations uniqueness theorem

    My book stated the following theorem: If the functions P(x) and Q(x) are continuous on the open interval I containing the point x0, then the initial value problem dy/dx + P(x)y = Q(x), y(x0)=y0 has a unique solution y(x) on I, given by the formula y=1/I(x)\intI(x)Q(x)dx where I(x) is the...
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    Time it takes for an electron and proton to collide

    I don't know, acceleration is changing. Let say we have F=kq1q2/r2=ma. Since this problem is symmetrical, I was thinking the two particles would meet in the middle, so each would travel a distance of R/2. So I could divide by m and integrate twice to find the position function, and set that...
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    Time it takes for an electron and proton to collide

    Homework Statement An electron and positron have mass me and separation R and are initially at rest. Find the time T it takes for them to collide. Homework Equations F=kq1q2/R2 The Attempt at a Solution My problem is that the force is not constant. Do I integrate the force then...
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    Negative sign in coulomb's law/centripetal motion question

    Homework Statement I had a question in my physics class today that was relatively easy but what I was confused about was a misplaced negative sign. "An electron is rotating around a proton at a distance R. The mass of the electron is me and the charge is -e. Find the period." Homework...
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    Sunglasses + Plane Window = Colors?

    They did. In fact, I took some videos and pictures while in flight (often when electronic devices were supposed to be off; aren't I rebellious :P). The taking these videos was often accompanied by akward stares from the other passengers... I'm back home now and won't be flying for a long time so...
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    Sunglasses + Plane Window = Colors?

    So in short what's going on is the stress in the glass polarizes the light once and the stress in the sunglasses polarizes it again causing the spectrum of colors. Right? It's cool seeing things I learned in school appear in the most unexpected places.
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    Sunglasses + Plane Window = Colors?

    I'll give that a try. That makes sense, but I saw all of the colors in all orientations, and I think I should only be seeing one at a time... Why would you need another polarizer? And on my side of the window? That would be my glasses wouldn't it? We only skimmed that in my physics class...
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    Sunglasses + Plane Window = Colors?

    Well don't polarized glasses change the amount of light passing through based on the orientation? I tested it out and it seemed like the same amount of light now matter how I looked through them... Also, why would polarized glasses show colors based on strains in the window? Unless the...
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    Sunglasses + Plane Window = Colors?

    I was on a plane the other day and it was bright outside so I put on my sunglasses and looked outside and saw a spectrum of colors. Just looking through the window or just looking through the glasses didn't produce the colors. Any idea what's going on?
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    Intensity of single slit and double slit

    After looking at the graphs of single slit and double slit interference of intensity vs. angle, it seems that the intensity drops off very steeply with single slit interference but doesn't drop off at all with double slit interference patterns. Why is that?
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    VSEPR question

    The question is: Which species has exactly five pairs of electrons around the central atom? (A) ClF5 (B) SF4 (C) SF5– (D) XeF4 The answer is B. Can someone explain why? I'm not too good with these geometries that use the d-orbital.
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    How to determine which molecule has the highest melting point?

    The question is: Which substance has the highest melting point? (A) CO (B) CO2 (C) SiO2 (D) P2O5 The answer is C but I don't know why (you obviously can't look up the values). I need to be able to figure these types of questions out regardless of the...
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    The Second Ace Paradox

    Ok, I've figured out the math behind the original question, but the difference between the first and second set of questions Hurkyl posted has intrigued me and confused me. Why does the second question "add no new information"? With the first set of questions, you know that the person has at...
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