If `x prop y^(2)` and y =4 when x =8 , if x =32 , then the positive value of y is

Options

A. 4
B. 8
C. 16
D. 32

Explanation

`x prop y^(2), therefore x=k.y^(2)` (where k=non -zero constant )…….(i)
As per question , y =4 when x =8
`therefore` from (1) we get , 8 =k.`4^(2) ` or , 8 =16k or k=`(8)/(16)=1/2`
`therefore` x =`1/2y^(2)` [from (1)]…….(2)
Now ,putting x =32 in (2) we get , 32 =`1/2y^(2)`
or , `Y^(2)`=64 or , y=`sqrt(64)=pm8`.
`therefore` y =8 (taking positive value )
`therefore` (b) is correct.