Answer
$\color{blue}{y=\dfrac{4wx^2}{z}}$
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 jointly as $w$ and the square of $x$ and inversely as $z$.
Thus, the equation of the variation is $y=\dfrac{kwx^2}{z}$.
To find the value of $k$, substitute the given values to obtain:
$$y=\dfrac{kwx^2}{z}
\\49=\dfrac{k\cdot3\cdot 7^2}{12}
\\49=\dfrac{3k\cdot 49}{12}
\\49=\dfrac{147k}{12}
\\\frac{12}{147} \cdot 49=\frac{147k}{12} \cdot \frac{12}{147}
\\4=k$$
Thus, the equation of the variation is: $\color{blue}{y=\dfrac{4wx^2}{z}}$.
