Question

‘y’ is inversely proportion to the square of x and x = 4 when y = 2. Find the value of x when

y = 4.

Answer 1

x = 2√2

Explanation:

If is inversely proportional to x², then:

`y \propto (1)/(x^2) \implies y=(k)/(x^2) \quad \textsf{(for some constant k)}`

Given:

• x = 4 when y = 2

Substitute the given values into the found equation and solve for k:

`\implies 2=(k)/(4^2)`

`\implies 2=(k)/(16)`

`\implies k=32`

Therefore:

`y=(32)/(x^2)`

To find the value of x when y = 4, substitute y = 4 into the found equation and solve for x:

`\implies 4=(32)/(x^2)`

`\implies x^2=(32)/(4)`

`\implies x^2=8`

`\implies x=√(8)`

`\implies x=√(4 \cdot 2)`

`\implies x=√(4) √(2)`

`\implies x=2√(2)`