Question

The cube root of r varies inversely with the square of s. Which two equations model this relationship?

Answer 1

Answer:

The following two equations model this relationship.

• $\:\sqrt[3]{r}=\:\frac{k}{s^2}$

• $\:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}$  

Step-by-step explanation:

We know that when 'y' varies inversely with 'x', we get the equation

y ∝ 1/x

y = k / x

k = yx

where 'k' is called the 'constant of proportionality'.

In our case, it is given that the cube root of 'r' varies inversely with the square of 's', then

$\sqrt[3]{r}$ ∝ $\frac{1}{s^2}$

$\:\sqrt[3]{r}=\:\frac{k}{s^2}$

or

$\:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}$          ∵ $\sqrt[3]{r}=r^{\frac{1}{3}}$

Therefore, the following two equations model this relationship.

• $\:\sqrt[3]{r}=\:\frac{k}{s^2}$

• $\:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}$