Question

If y varies inversely as X^2 and X = 9 when y = 64, how do you find the value of y when x = 4?

Answer 1

`y=324`

Explanation:

`"varies inversely means " 1/"variable"`

`rArr"the initial statement is " yprop1/(x^2)`

`"to convert to an equation, multiply by k, "`
`"the constant of variation"`

`rArry=kxx1/x^2=k/x^2`

`"to find k, use the condition given"`

`y=k/x^2rArrk=x^2y`

`"given " x=9" when " y=64`

`rArrk=9^2xx64=5184`

`rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=5184/x^2)color(white)(2/2)|)))`

`"when x = 4 then"`

`y=5184/16=324`