Zvaries directly with x and inversely with y^2. when x = 2 and y = 5, z = 8. what is the value of z when x = 4 and y = 9?

Direct variation is  y = kx

Inverse variation is y = k/y

if z varies directly with x, then the equation would be z = kx

if z varies inversely with y^2 then the equation would be z = k/y^2. Combining, these two, we have z = kx/y^2

We use the first set of values to find the constant k:

x = 2, y = 5, z = 8:

8 = 2x/25, k = 100. Now we use the second set of values to find z:

x = 4, y = 9, k = 100 and z is unknown:

z = (4X100)/9^2

z = 400/81--> this is your final final answer.

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