Answer
$\color{blue}{y=\dfrac{6x}{wz^2}}$
Work Step by Step
RECALL:
(1) When $y$ varies directly as $x$, the equation of the variation is $y=kx$ .
(2) When $y$ varies inversely as $x$, the equation of the variation is $y=\frac{k}{x}$.
(3) When $y$ varies jointly as $x$ and $z$, the equation of the variation is $y=kxz$.
$y$ varies directly as $x$ and inversely as $w$ and the square of $z$.
Thus, the equation of the variation is $y=\dfrac{kx}{wz^2}$.
To find the value of $k$, substitute the given values to obtain:
$$y=\dfrac{kx}{wz^2}
\\4.5=\dfrac{k\cdot15}{5\cdot2^2}
\\4.5=\dfrac{15k}{5\cdot 4}
\\4.5=\dfrac{15k}{20}
\\\frac{20}{15} \cdot 4.5=\frac{15k}{20} \cdot \frac{20}{15}
\\6=k$$
Thus, the equation of the variation is: $\color{blue}{y=\dfrac{6x}{wz^2}}$.
