Question

Assume that y varies inversely with x. If y=1/3 when x=1/2, find y when x=1/4.

Answer 1

y =
`(2)/(3)`

Explanation:

Given that y varies inversely with x then the equation relating them is

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

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

`(1)/(3)` =
`(k)/((1)/(2) )` = 2k ( divide both sides by 2 )

k =
`(1)/(6)`

y =
`(1)/(6x)` ← equation of variation

When x =
`(1)/(4)` , then

y =
`(1)/(6((1)/(4)) )` =
`(1)/((3)/(2) )` =
`(2)/(3)`