Question

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

Answer 1

a and b it was right on the test

Explanation:

Answer 2

The following two equations model this relationship.

• 
  `\:\sqrt[3]{r}=\:(k)/(s^2)`

• 
  `\:\:s^2\:r^{(1)/(3)}=\:(k)/(s^2)`

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}` ∝
`(1)/(s^2)`

`\:\sqrt[3]{r}=\:(k)/(s^2)`

or

`\:\:s^2\:r^{(1)/(3)}=\:(k)/(s^2)` ∵
`\sqrt[3]{r}=r^{(1)/(3)}`

Therefore, the following two equations model this relationship.

• 
  `\:\sqrt[3]{r}=\:(k)/(s^2)`

• 
  `\:\:s^2\:r^{(1)/(3)}=\:(k)/(s^2)`