Answer
a) $M=\frac{345}{\sqrt{t}}$
b) $M= 69$
Work Step by Step
Since $M$ varies inversely with $5\sqrt{t}$, we can write \begin{equation}
M= \frac{k}{5\sqrt{t}},
\end{equation} where $k$ is the constant of proportionality that must be determined.
a) Given that $y= 115$ when $t= 9$, we can use this information to find $k$ as follows: \begin{equation}
\begin{aligned}
115&= \frac{k}{5\sqrt{9}}\\
115\cdot 5\cdot 3&=k\\
\therefore k&=1725.
\end{aligned}
\end{equation} The required equation is
\begin{equation}
\begin{aligned}
M &= \frac{1725}{5\sqrt{t}}\\
&=\frac{345}{\sqrt{t}}.
\end{aligned}
\end{equation} b) Determine $M$ when $t=25$.
\begin{equation}
\begin{aligned}
M&= \frac{345}{\sqrt{25}}\\
&=\frac{345}{5}\\
&= 69.
\end{aligned}
\end{equation} The answer is $M= 69$ when $t= 25$.
