If t varies inversely as the cube of z, the the equation relating t and z is expressed as
t = k/z^3
where
k is the proportionality constant
If t varies directly as the square of r, then the equation relating them is
t = kr^2
This is combined variation The formula relating all the variables would be
t = kr^2/z^3
From the information given,
t = 4, z = 3 and r = 6
By substituting these values into the formula,
4 = k * 6^2/3^3
4 = 36k/27 = 4k/3
By cross multiplying,
4 * 3 = 4k
k = (4 * 3)/4
k = 3
Thus, the formula is
t = 3r^2/z^3
When z = 6 and r = 9, we have
t = 3 * 9^2/6^3
t = 243/216
t = 1.125