Write a general formula to describe the variation: the square of T varies directly with the cube of a and inversely with the square of​ d; ...

Hello!

Because `T^2` is directly proportional to `a^3,` then `a^3` must be at the numerator. `T^2` is inversely proportional to `d^2` means `d^2` is at the denominator. Also it may be multiplied by any constant `C.`

So the general formula for `T^2` is `T^2 = C*a^3/d^2.`  It is given that for `a=3` and `d=2` must be `T=5.` We can find `C` from this:

`5^2 = C*3^3/2^2,` so `C = (25*4)/27 = 100/27`  and  `T^2 = 100/27 * a^3/d^2.`

And if we want a formula for `T,` not `T^2,` it is

`T = +- sqrt(C)*a^(3/2)/d = +- 10/(3sqrt(3)) *a^(3/2)/d =+- (10 sqrt(3))/(9) *a^(3/2)/d.`