math
posted by Jeremie .
Beer cans are right circular cylinders. My Mathematical Mead, my Polynomial Pilsner, and my SquareRoot 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+x³72π (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.

v = x^3  24πx^2 + 3x  72π
= x(x^2+3)  24π(x^2+3)
= (x24π)(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...