Question

If y varies inversely as the square of x, and y=2 when x=4, find y when x=4

Answer 1

y = 2

Explanation:

Given that y varies inversely as the square of x then the equation relating them is

y =
`(k)/(x^2)` ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = yx² = 2 × 4² = 2 × 16 = 32, thus

y =
`(32)/(x^2)` ← equation of variation

When x = 4, then

y =
`(32)/(4^2)` =
`(32)/(16)` = 2