college math
posted by Lorie on .
A quantity, W, is directly proportional to x and the square of y and inversely proportional to the cube of z. W3 when x=4,y=2 and z=4. What is the value of w, when x=5, y=5 and z=4. Give answer to three decimal places. Thanks so much!

W = k x√y/z^3
so W=3, x=4,y=2, z=4
3 = k(4√2/64
k = 192/(4√2) = 48/√2
so if x = 5,y=5,z=4
W = (48/√2)(5)(√5)/64
= 15√5/(3√2) or after rationalizing the denominator
= 15√10/8 = appr 5.929