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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.

 Jan 22, 2019
 #1
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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

 Jan 22, 2019

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