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# help

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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