Question

HELP ASAP PLZ

A student is given that y varies directly with x^2 and that x = 2 when y = 8. Correct the student’s claim that x = 3 when y = 9 then. Explain your reasoning.

Answer 1

see explanation

Explanation:

Given that y varies directly with x² then the equation relation them is

y = kx² ← k is the constant of variation

To find k use the condition x = 2 when y = 8

k =
`(y)/(x^(2) )` =
`(8)/(4)` = 2

y = 2x² ← equation of variation

When y = 9, then

2x² = 9 ( divide both sides by 2 )

x² =
`(9)/(2)` = 4.5 ( take the square root of both sides )

x =
`√(4.5)` ≈ 2.12 ≠ 3