It is given that y is inversely proportional to the square of x and that y=48 when x=(1)/(2). Find; (a), the formula for y in terms of x, (b), the values of x when y=3.

Question

It is given that y is inversely proportional to the square of x and that y=48 when x=
`(1)/(2)`.

Find;
(a), the formula for y in terms of x,
(b), the values of x when y=3.

Answer 1

`a. y = 12* (1)/(x^2) \\b. x = 2 , when \ y =3`

Explanation:

`y \ is\ inversely \ proportional \ to \ square \ of \ x \ means , y \ \alpha \ (1)/(x^2)`

`Therefore, y = k * (1)/(x^2)`

Given y = 48, x = 1/2. We will find k.

`y = k * (1)/(x^2)\\\\48 = k * (1)/((1)/(4))}\\\\k = 48 * (1)/(4) =12`

Find x.

`y = k * (1)/(x^2) \\\\3 = 12 * (1)/(x^2)\\\\(3)/(12) = (1)/(x^2)\\\\x^2 = (12)/(3)\\\\x^2 = 4 \\\\x = 2`