Question

The cube root of our varies inversely with the square of S which to equations model this relationship?

Answer 1

The question states as follows;

"The cube root of r varies inversely with the square of s."

The general form of an inverse relationship is shown below;

`y=(k)/(x)`

Substituting the variables, we would now have;

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

Therefore, the third option is correct.

Also;

`\begin{gathered} \sqrt[3]{r}=(k)/(s^2) \\ \text{Observe that}_{} \\ \sqrt[3]{r}=r^{(1)/(3)} \end{gathered}`

Therefore, we can alo have the expression;

`\begin{gathered} r^{(1)/(3)}=(k)/(s^2) \\ \text{Cross multiply, and we'll have;} \\ s^2r^{(1)/(3)}=k \end{gathered}`

The fifth option is also correct.

ANSWER:

The third and fifth options are both correct models of the inverse relationship given.