Answer
1. x = (2/3)y²
2. x = 54 when y = 9
3. y = 7.35 when x = 36
Explanation
1. x ∝ y²
x = 24, y = 6
x = ky²
24 = k x 6²
24 = 36k
k = 24/36
k = 2/3
∴ x in terms of y is x = (2/3)y²
2. Using x = (2/3)y² to to find x when y = 9, we have
x = (2/3) x 9²
x = 2/3 x 81
x = 2 x 27
x = 54
∴ x = 54 when y = 9
3. Using x = (2/3)y² to to find y when x = 36, we have
36 = (2/3)y²
36 = 2y²/3
2y² = 36 x 3
y² = 108/2
y² = 54
y = √54
y = 7.35
∴ y = 7.35 when x = 36
