Question

Y is directly proportional to x^2. If y=20 when x=2 find x when y=45

Answer 1

x = 3

Explanation:

y is directly proportional to x²:
`y \propto x^2`

Therefore,
`y=kx^2` for some constant
`k`

Given y = 20 when x = 2

Substitute given values into
`y=kx^2`:

⇒ 20 = k · 2²

⇒ 20 = 4k

⇒ k = 20 ÷ 4 = 5

Therefore, equation is y = 5x²

Substitute y = 45 into the equation and solve for x:

⇒ 45 = 5x²

⇒ x² = 45 ÷ 5 = 9

⇒ x = √9 = 3