Question

If y varies inversely as x and y = 8 when x = 4, find y when x = 16?

Answer 1

`y=2`

Explanation:

The statement is expressed as `yprop1/x`

`"inverse means " 1/"variable"`

To convert to an equation introduce k, the constant of variation.

`y=kxx1/x`

`rArry=k/x`

To find k use the given condition that y = 8 when x = 4

`8=k/4rArrk=4xx8=32`

`rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=32/x)color(white)(2/2)|)))`

`x=16toy=32/16`

`rArry=2" when " x=16`