Question

Y is inversely proportional to the square of x. If Y = 9 when x = 3, then what is y, when x is 6?

Answer 1

y =
`(9)/(4)`

Explanation:

given Y is inversely proportional to x² then the equation relating them is

Y =
`(k)/(x^2)` ← k is the constant of proportionality

to find k use the condition if Y = 9 when x = 3 , then

9 =
`(k)/(3^2)` =
`(k)/(9)` ( multiply both sides by 9 )

81 = k

Y =
`(81)/(x^2)` ← equation of proportion

when x = 6 , then

Y =
`(81)/(6^2)` =
`(81)/(36)` =
`(9)/(4)`