Given:
S varies directly as the 2​/3 power of​ T
So,
[tex]\begin{gathered} S\propto\sqrt[3]{T^2} \\ S=k\cdot\sqrt[3]{T^2} \end{gathered}[/tex]
Where (k) is the constant of proportionality
We will find (k) using the given condition: S=75 when T=125
So,
[tex]\begin{gathered} 75=k\cdot\sqrt[3]{125^2} \\ 75=k\cdot25 \\ \\ k=\frac{75}{25}=3 \end{gathered}[/tex]
So, the relation will be:
[tex]S=3\sqrt[3]{T^2}[/tex]
We will find S when T = 64
So,
[tex]S=3\cdot\sqrt[3]{64^2^{}}=3\cdot16=48[/tex]
so, the answer will be:
[tex]S=48[/tex]
