Recent content by tickle_monste

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    How much input maps to output?

    Given a polynomial abcdefg, there are 8 possible inputs and thus 8 possible outputs, and I have 8 equations describing each possible output. They are: p(000) = 0 p(100) = a p(010) = b p(001) = c p(110) = a+b+d p(101) = a+c+e p(011) = b+c+f p(111) = a+b+c+d+e+f+g Given a polynomial abcdefg and...
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    How much input maps to output?

    Homework Statement I have polynomials of the form: x1 + x2 + x3 + x1x2 + x1x3 + x2x3 + x1x2x3 The x's can be a combination of 1s and 0s, so all the possible inputs could be written as strings: 000, 100, 010, 001, 110, 101, 011, 111 The polynomials can also have coefficients a...g, so...
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    Positive charge of NAD+ molecule

    Why is the positive charge of the NAD+ molecule located on the nitrogen in the nicotinamide group? This nitrogen has 4 bonds attached to it, but nitrogen only has 3 holes in its valence shell, so wouldn't this make a negative charge on this nitrogen?
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    People leaving and entering city

    ([SIZE="2"]Moderator's note: thread moved from "Differential Equations") By natural increase, a city, whose population is 40,000, will double in 50 years. There is a net addition of 400 persons per year because of people leaving and moving into the city. Estimate its population in 10 years. My...
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    Solve ODE Dilution Problem: 400-400e

    I forgot to preview my original post, hence the horrible LaTeX job. But no matter, I've figured out the problem in my solution. I'll restate the problem since my first attempt is next to illegible: 200 gal fresh water, brine with 2lb/gal flows in @ 2 gal/min, and the mix flows out at the same...
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    Solve ODE Dilution Problem: 400-400e

    A tank initially contains 200 gal of fresh water with 0 lbs of salt. Brine whose salt concentration is 2lb/gal flow in at 2 gal/min and the mix flows out at the same rate. x = salt content, t = time. So I figure that dx = 4dt - 2xdt/200 or dx = (400 - x).01dt dx/(400-x) = .01dt \int0x...
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    Eigenvalue of 3D rotation matrix

    It was pretty cool to stumble upon Euler's formula as the eigenvalues of the rotation matrix. det(Rot - kI) = (cos t - k)2 + sin2t =k2-2(cos t)k + cos2t + sin2t =k2-2(cos t)k + 1 k = {2cos t +/- \sqrt{4cos^2(t) - 4}}/2 k = cos t +/- \sqrt{cos^2(t) - 1} k = cos t +/- \sqrt{cos^2(t) - cos^2t -...
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    Is i squared equal to -1 or +1?

    sqrt(-a)=sqrt[i2a] sqrt[i2a]*sqrt[i2b] = (i*i)sqrt[a]sqrt[b]= -(sqrt[ab])
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    Proving the Equivalence of Solving Equations and Finding Functions

    My wording of the problem was poor, I forgot to account for multiple independent solutions. So, here it is, better worded: Finding a solution of Q in the equation is equivalent to finding a function f, such that when f is substituted for Q in the equation, the equation will reduce to an...
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    Proving the Equivalence of Solving Equations and Finding Functions

    I've got a proof but I'll wait a couple days to post mine to give you guys a chance to take a crack at it. Prove that: For all equations E(A1, ... , An), solving for Ai is equivalent to finding the function f(A1..A(i-1),A(i+1)...An), such that when f is substituted in E in place of Ai, E...
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    Change of variables in heat equation

    Wow, I really should've been able to do that myself. Thanks a lot though, that's a big help
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    Change of variables in heat equation

    dTB/dt = -k(TB-TM). TM is held constant. (TB-TM) = Q, so: dTB/Q = -kdt. How would I change this equation so that instead of integrating wrt to TB, I can instead integrate wrt Q?
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    Solving Dilution Problem with Water Level Change & Brine Addition

    Actually on second thought I'm not quite sure what you're trying to specify with z'. What exactly are you differentiating Z with respect to?
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