Suppose that \(y^3\) varies inversely with \(\sqrt[3]{z}\). If y=2 when z=1, find the value of z when y=4. Express your answer in simplest fractional form.

Guest Jan 22, 2019

#1**+1 **

y^3 = k/(cubrt(z))

2^3 = k /(cubrt(1) results in

k = 8

y^3 = 8/(cubrt(z))

When y = 4 find z

4^3 = 8 /(cubrt z)

8/4^3 = cubrt z

8 / 64 = cubrt z

1/8 = cubrt z cube both sides of the equation to find 'z'

1 / 512 = z When y = 4

ElectricPavlov Jan 22, 2019