Question

Y is inversely proportional to the square root of x if y=3 when x=25 find y when x is 9

Answer 1

`y=5`

Explanation:

`\textsf{If }y \textsf{ is \underline{inversely proportional} to the square root of }x, \textsf{ then}:`

`y \propto(1)/(√(x)) \implies y=(k)/(√(x))\quad \textsf{(where k is some constant)}`

`\textsf{When }x=25, y = 3:`

`\implies 3=(k)/(√(25))`

`\implies 3=(k)/(5)`

`\implies k=15`

Inputting the found value of k into the equation:

`\implies y=(15)/(√(x))`

To find the value of y when x is 9, substitute x = 9 into the found equation:

`\implies y=(15)/(√(9))`

`\implies y=(15)/(3)`

`\implies y=5`