Answer:
x = 3
Step-by-step explanation:
y is directly proportional to x²: [tex]y \propto x^2[/tex]
Therefore, [tex]y=kx^2[/tex] for some constant [tex]k[/tex]
Given y = 20 when x = 2
Substitute given values into [tex]y=kx^2[/tex]:
⇒ 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
