Question 12122
z is proportional to {{{(x/y^2)}}}


so, the equivalent equation is {{{z = k(x/y^2)}}}, where k is the constant of proportionality.


we need to know the value of k. To do this, we need to know x,y and z, which we do... so:


{{{1/4 = (6k)/8^2}}}
{{{1/4 = (6k)/64}}}
--> 6k = 64/4
--> 6k = 16
--> k = 16/6
--> k = 8/3


so, the equation is {{{z = (8x)/(3y^2)}}}


Right, now for the question to find z when x=9 and y=2.


{{{z = (8x)/(3y^2)}}}
--> {{{z = (8*9)/(3*2^2)}}}
--> {{{z = (8*9)/(3*4)}}} and now simplify these fractions to give...
--> {{{z = (2*3)/(1*1)}}} 
--> z = 6


jon.