Recent content by hb1547

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    Conditional probability of several events? (sports-related)

    I'm casually working on determining the probability of a team in a given sport (let's say football) reaching at least a certain level in a season. There are two main parts to this: How many games they won in the season, and how far they got in the playoffs. I'd like to assign one final number...
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    Trying to understand the oscillation of electrons in the magnetic fiel

    Yes, but what is the physics behind the reduction in the parallel component? Why does it reduce? I found this, which explains it well in terms of a dipole, but perhaps there's an explanation in terms of just the particle?
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    Trying to understand the oscillation of electrons in the magnetic fiel

    Yes, this makes sense, and I know I can think of it either as purely magnetic (Earth's frame) or as an electric field (electron's frame). I thought the electron's frame would be easier but it hasn't been. Then to me it seems that perhaps the converging of the magnetic field lines might help...
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    Trying to understand the oscillation of electrons in the magnetic fiel

    Working on understanding the physics of how an electron oscillates along the Earth's magnetic field. I understand that an electron will spiral around the magnetic field line, that's easy to tell from the Lorentz force. What I don't understand is what causes the oscillation. My best guess is...
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    A continuous function having an inverse <=> conditions on a derivative?

    Sorry for the poorly-worded title. I help tutor kids with pre-calculus, and they're working inverse functions now. They use the "horizontal line test" to see if a function will have an inverse or not by seeing visually if it's one-to-one. I was thinking about what that might imply. If a...
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    Covariance between x and f(x)?

    Homework Statement As part of an assignment, I have to determine propagated error of some function: f(x,t) I did it first with x & t being completely uncorrelated, but now I'm given x as a function of t, x(t), and have to do the same. Homework Equations I know the linear approximation for...
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    How to evaluate this integral to get pi^2/6:

    Anyone else have any input?
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    How to evaluate this integral to get pi^2/6:

    \int_0^\infty \frac{u}{e^u - 1} I know that this integral is \frac{\pi^2}{6}, just from having seen it before, but I'm not really sure if I can evaluate it directly to show that. I know that: \zeta(x) = \frac{1}{\Gamma(x)} \int_0^\infty \frac{u^{x-1}}{e^u -1} du Does the value...
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    Proving that 'volume' and 'surface' of hypersphere go to 0 as n -> infinity?

    Homework Statement I'm supposed to find the equations of a hypersphere in n-dimensions (meaning the set of points within the radius R), as well as of its surface (the set of points at exactly radius R). I've already found the equations, and now need to show that both go to zero as n goes to...
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    Perturbation with equations of motion for air resistance

    Homework Statement "A ball is tossed upwards with speed V_0. Air resistance is -mkv^2 and there's gravity too. Find the the time it takes the ball to reach the maximum height. Do not solve the equation of motion exactly. Use the perturbation method on the equation of motion. Solve the equation...
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    Estimate mass of neutrino given distance & KE

    Homework Statement A supernova 1.54\times10^21 m away sends out neutrinos, and a detector on Earth detects two, ten seconds apart. The first one (A) that comes has a kinetic energy of 30 MeV, the second (B) has a kinetic energy of 10 MeV. Using this, I'm supposed to come up with an upper...
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    Finding total energy as a function of the Fermi Energy

    OH I get it -- that clears it up a lot. Thanks! I was able to get it from there, I really appreciate the help!
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    Finding total energy as a function of the Fermi Energy

    Hmm actually I'm still having some trouble with this one. I get why you can integrate from 0 to E_{Fermi}, yet I'm not following when you plug in the equation for E_{Fermi}. Did you do it before or after integrating? If before, I keep getting to an integral I can't solve: \int_{0}^{E_{F}} \...
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    Finding total energy as a function of the Fermi Energy

    Yeah this is the Harris problem haha. So I plug in the Fermi energy equation for E in the top, as well as N(E)_{FD} and D(E)? Sounds good, I'll try it and see where it gets me. Thanks, I was just leaving the term as E and it wasn't working too well
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    Finding total energy as a function of the Fermi Energy

    Homework Statement "The numerator of this fraction: \overline{E}=\frac{\int \! E N(E)D(E)dE}{\int \! N(E)D(E)dE} (N(E) is the number of particles in an energy state, D(E) is the density of states) is the total (as opposed to the average particle) energy, which we'll call U_{total} here...
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