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Beer cans are right circular cylinders. My Mathematical Mead, my Polynomial Pilsner, and my Square-Root Stout cans from the Schmidt Brewery, have dimensional units called "brewskies". Using the zero product rule, they have a volume (in cubic brewskies) equal to a solution of the function:
f(x)=-24πx²+3x+x³-72π (where π=pi).
The height divided by the radius of my beer can is equal to the solution of :
(2k+3)^½+(k+1)^½=5.
Do not round π while finding the volume, diameter, and height of my beer can.

  • math -

    v = x^3 - 24πx^2 + 3x - 72π
    = x(x^2+3) - 24π(x^2+3)
    = (x-24π)(x^2+3)
    The only real solution (required when sober) is x=24π

    Now, we need to solve for k:
    √(2k+3) + √(k+1) = 5
    k=3

    so, h/r = 3, meaning h = 3r
    v = 24π = πr^2h = 3πr^3
    24 = 3r^3, so r=2

    I figure you can work out the answers to the questions now...

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