Question

Y varies 1/x², when X=2, Y=1. Find the values of X when Y=4/9.​

Answer 1

x = ± 3

Explanation:

given y varies as
`(1)/(x^2)` , then

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

to find k use the condition x = 2 , y = 1

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

4 = k

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

when y =
`(4)/(9)` , then

`(4)/(9)` =
`(4)/(x^2)` ( cross- multiply )

4x² = 36 ( divide both sides by 4 )

x² = 9 ( take square root of both sides )

x = ±
`√(9)` = ± 3