Question

Write a function that models the variation. x = 1/3, y = 1/5, and r = 3 when z = 1/2. z varies directly with x and inversely with the product of r^2 and y.

Answer 1

z varies directly with x
so, let z = kx (k is some constant)
now, since when z = 1/2, x = 1/3
we get, 1/2 = k/3, so k = 3/2
so, we get z = 3x/2

z varies inversely with the product of r^2 and y
so, z = c/(y * r^2) (c is some constant)
again, when z = 1/2, y = 1/5 and r = 3
so, we get, 1/2 = c/(9/5), so c = 9/10
so, we get z = 9/(10*y*r^2)

the above two functions model the variations

does this make sense ?
hopefully this is right!