Question

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

Answer 1

Answer:

x = 3

Step-by-step 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