Let z be inversely proportional to the cube root of y. When y =.064, z =3 a) Find the constant of proportionality k.
b) Find the value of z when y = 0.125.​

Given:

z be inversely proportional to the cube root of y.

When y =0.064, then z =3.

To find:

a) The constant of proportionality k.

b) The value of z when y = 0.125.​

Solution:

a) It is given that, z be inversely proportional to the cube root of y.

             ...(i)

Where, k is the constant of proportionality.

We have, z=3 when y=0.064. Putting these values in (i), we get

Therefore, the constant of proportionality is .

b) From part (a), we have .

Substituting in (i), we get

We need to find the value of z when y = 0.125.​ Putting y=0.125, we get

Therefore, the value of z when y = 0.125 is 2.4.

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