Question 93431
'y' varies directly as 'x' and inversely as 'z^2'.
Hence, {{{y = k(x/z^2)}}} _______ (1)
Now, y = 3 when x = 2 and z = 4, 
Substituting the values of 'x', 'y' and 'z' in (1)
{{{3 = k(2/4^2)}}} 
{{{3 = k/8}}} 
{{{k = 3x8 = 24}}}


So (1) becomes
{{{y = 24(x/z^2)}}} _____ (2)
 

Substituting the values of 'y' and 'z' in (2)
{{{9 = 24(x/4^2)}}}
{{{9 = 24x/16}}}
{{{3 = x/2}}}
{{{x = 3*2 = 6}}}


The reqd. value of 'x' when y = 9 and z = 4 is 6.