smc

$x$ varies directly to $\frac{y}{z^2}$ (The inverse variation of y and the square of z) We can write the expression $x=\frac{ky}{z^2}$ Now we plug in the values of $x=10$ when $y=4$ and $z=14$. This gives us $k=490$ We can use this to find the value of $x$ when $y=4$ and $z=14$ $x=\frac{490\cdot 4}{14^2}$ Simplifying this we get, $\boxed{160}$