Question

Suppose that S varies directly as the 2/3 power of T, and that S=75 when T=125. Find S when T=64.

Answer 1

Given:

S varies directly as the 2​/3 power of​ T

So,

`\begin{gathered} S\propto\sqrt[3]{T^2} \\ S=k\cdot\sqrt[3]{T^2} \end{gathered}`

Where (k) is the constant of proportionality

We will find (k) using the given condition: S=75 when T=125

So,

`\begin{gathered} 75=k\cdot\sqrt[3]{125^2} \\ 75=k\cdot25 \\ \\ k=(75)/(25)=3 \end{gathered}`

So, the relation will be:

`S=3\sqrt[3]{T^2}`

We will find S when T = 64

So,

`S=3\cdot\sqrt[3]{64^2^{}}=3\cdot16=48`

so, the answer will be:

`S=48`