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    Tough Olympiad-like Inequalities question

    a, b, c, and d are all positive real numbers. Given that a + b + c + d = 12 abcd = 27 + ab +ac +ad + bc + bd + cd Determine a, b, c, and d. --- The solution says that using AM - GM on the second equation gives abcd (is greater than or equal to) 27 + 6*sqrt of (abcd) From...
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    Stuck on Thermodynamics

    Oooh, I got the answers now. Thanks to you both for the help!
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    Stuck on Thermodynamics

    Thanks sniffer The answer to the first question was 6400 N, but I'm getting something different. Since Volume is 0.039, I should take the cube root of that number to figure out the length of one side of the cube, right? Then to find the area of one of the faces of the cube, I square the...
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    Stuck on Thermodynamics

    These problems are from Giancoli 5th edition (principles with applications) A cubic box of volume 0.039 m^3 is filled with air at atmospheric pressure at 20 celsius. The box is closed and heated to 180 celsius. What is the net force on each side of the box? I first used the ideal gas law...
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    Tricky Integrals

    These are the answers that I got 1) Converges (to 0.5*sqrt (Pi)) 2) Diverges 3) Converges to sqrt (Pi) 4) Converges to 0.25 * sqrt (Pi) Do these look right? Thanks
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    Tricky Integrals

    That's the correct integral, it must diverge.
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    Tricky Integrals

    I am given that e^(-x^2) = 0.5*sqrt(pi), but I couldn't get the integrals into that form through integration by parts - am I doing something wrong? Thanks
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    Tricky Integrals

    All of these integrals have lower bounds of 0 and upper bounds of infinity: Problems 1 and 2 just require me to determine whether it converges or diverges. 3 and 4 actually require a value. 1) e^(-x) * sqrt(x) 2) \frac{x*arctan(x)}{(1+x^4)^(1/3)} 3) e^(-x) / sqrt(x) 4) x^2 * e^[-(x^2)]...
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    BC Calculus help

    Thanks OlderDan, I think I have all three of the problems solved now.
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    BC Calculus help

    Thanks OlderDan, I solved the first two problems, but I'm still having trouble with the third. If I seperate the numbers into a series of fractions, like 1^k over n^k+1 plus 2^k over n^(k+1) plus 3^k over n^(k+1) and end with n^k over n^(k+1), would that give me the answer (which would...
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    Sequences and Series

    Thanks Cyclovenom, I took \frac{sin(1/x)}{1/x} and did the limit as x approaches infinity with L Hopital's rule, but I got 0, so doesn't that make it inconclusive? Thanks
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    Sequences and Series

    I need to determine whether Sigma [sin(1/x)] for x=1 to x=infinity converges or diverges. I have a feeling that it diverges, but I don't know how to prove it. Thanks
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    3(x)^1/2 = (x)^1/2 help

    You should first square each side to get rid of the square root, giving you: 9x = x And x = 0 should be your only answer
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    BC Calculus help

    Sorry I'm not very good at using latex, but here's my shot. 1. Let f(x) = sqrt (1+2x) - 1 - sqrt (x). Find some a where a is positive, such that lim of \frac{f(x)}{x^a} as x approaches 0 from the right is finite and non zero. I know the problem requires the use of L'Hopital's rule, but I...
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    Steam Engine/Rotation Problem

    Thanks, I solved the steam engine one and got (pi*10^-5)/0.27 as the angular acceleration
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    Steam Engine/Rotation Problem

    Hi, I came across this problem when browsing through a AP Physics B book (the answer was not in there). Can anyone help me? Heron of Alexandria invented the steam jet engine in the first century A.D. One of his many inventions, the one shown below was invented for amusement but employs...
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