Question

If x varies directly as y²,and if x = 24 when y = 6,find1. x in terms of y2. x when y = 93. y when x = 36

Answer 1

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