SOLUTION: Thank you in advance for your help! The question is: Suppose z varies directly as x and inversely as the square of y. If z= 1/4 when x =6 and y =8, find z when x =9 and y =2.

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z is proportional to

so, the equivalent equation is , 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:



--> 6k = 64/4
--> 6k = 16
--> k = 16/6
--> k = 8/3

so, the equation is

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


-->
--> and now simplify these fractions to give...
-->
--> z = 6

jon.