Answer
$a=\frac{7}{4}$
Work Step by Step
To find out the solution we need to follow the four-step procedure:
Step (1). As $a$ varies directly as $b$ and inversely as ${{c}^{2}}$ varies, we have
$a=k\frac{b}{{{c}^{2}}}$
Here $k$ is a constant.
Step (2).
Substitute $b=9$ , $c=6$ and $a=7$ in $a=k\frac{b}{{{c}^{2}}}$ to find the value of k.
$\begin{align}
& 7=k\frac{9}{{{6}^{2}}} \\
& k=\frac{7\times 36}{9} \\
& k=28 \\
\end{align}$
Step (3). Substitute $k=28$ in the equation $a=k\frac{b}{{{c}^{2}}}$
$a=\left( 28 \right)\frac{b}{{{c}^{2}}}$
Step (4). Substitute $b=4\,\text{ and }\,c=8$ to get:
$\begin{align}
& a=28\times \frac{4}{{{8}^{2}}} \\
& a=\frac{28\times 4}{64} \\
& a=\frac{7}{4} \\
\end{align}$
