Question

If y is directly proportional to x square and y equal 1/8 when x = 1/2 what is the positive value of x when y it was 9/2?

a) 3/4
b) 3/2
c) 9/4
d) 3​

Answer 1

d

Explanation:

Given y is directly proportional to x² then the equation relating them is

y = kx² ← k is the constant of proportion

To find k use the condition y =
`(1)/(8)` when x =
`(1)/(2)`, then

`(1)/(8)` = k(
`(1)/(2)` )² =
`(1)/(4)` k ( multiply both sides by 8 )

1 = 2k ( divide both sides by 2 )

k =
`(1)/(2)`

y =
`(1)/(2)` x² ← equation of proportion

When y =
`(9)/(2)` , then

`(9)/(2)` =
`(1)/(2)` x² ( multiply both sides by 2 )

9 = x² ( take the square root of both sides )

x = ±
`√(9)` = ± 3

with positive value x = 3 → d