z is jointly proportional to the cube of x and the square of y. If z=212 when x=3 and y=2, find z when x=2 and y=5.

Answer 1

z = k•x^3•y^2; this is what jointly proportional means -- k is an unknown constant of proportionality.

Condition is (x0, y0, z0) = (3, 2, 212); we are given a triplet of values that make the equation above true.

Plugging in and solving for k: 212 = k•(3^3)(2^2) => k = [212/(27*4)].

So now we have the full specification of our expression for z => z = [212/(27*4)]•x^3•y^2.

and for any pair, (x, y), we can calculate z.

If (x,y) = (2,5) then z = k•x^3•y^2 = [212/(27*4)]•2^3•5^2 .

I expected a prettier answer!