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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

    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

    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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    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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    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

    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...