Question

Let z be inversely proportional to the cube root of y. When y =.064, z =3

Answer 1

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.

$z\propto \dfrac{1}{\sqrt[3]{y}}$

$z=k\dfrac{1}{\sqrt[3]{y}}$              ...(i)

Where, k is the constant of proportionality.

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

$3=k\dfrac{1}{\sqrt[3]{0.064}}$

$3=k\dfrac{1}{0.4}$

$3\times 0.4=k$

$1.2=k$

Therefore, the constant of proportionality is $k=1.2$.

b) From part (a), we have $k=1.2$.

Substituting $k=1.2$ in (i), we get

$z=1.2\dfrac{1}{\sqrt[3]{y}}$

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

$z=1.2\dfrac{1}{\sqrt[3]{0.125}}$

$z=\dfrac{1.2}{0.5}$

$z=2.4$

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