Answer
$\color{blue}{M=\dfrac{9d^2}{2\sqrt{x}}}$
Work Step by Step
RECALL:
(1) If $y$ varies directly as $x$, then $y=kx$ where $k$ is the constant of proportionality.
(2) If $y$ varies inversely as $x$, then $y=\dfrac{k}{x}$ where $k$ is the constant of proportionality.
Notice that when the variation is direct, the variable is on the numerator while if the variation is inverse, the variable is in the denominator.
$M$ varies directly with the square of $d$ and inversely with the square root of $x$. This means that $d^2$ will be on the numerator while $\sqrt{x}$ will be in the denominator.
Thus, the equation of the variation is:
$M=k\cdot \frac{d^2}{\sqrt{x}}$
Since $M=24$ when $x=9$ and $d=4$, substituting these into the tentative equation above gives:
$\require{cancel}
M=k\cdot \frac{4^2}{\sqrt{9}}
\\24=k \cdot \frac{16}{3}
\\24=\frac{16}{3}k
\\\frac{3}{16} \cdot 24=\frac{16}{3}k \cdot \frac{3}{16}
\\\frac{3}{\cancel{16}2} \cdot \cancel{24}3=\frac{\cancel{16}}{\cancel{3}}k \cdot \frac{\cancel{3}}{\cancel{16}}
\\\frac{9}{2}=k$
Thus, the equation of the inverse variation is:
$M=\frac{9}{2}\cdot \frac{d^2}{\sqrt{x}}
\\\color{blue}{M=\dfrac{9d^2}{2\sqrt{x}}}$
