Question

If p is inversely proportional to the square of q and p is 13 when q is 4, what is p when q is 2?

Answer 1

52

Explanation:

Here it's given that p is inversely proportional to the square of q. We can write this mathematically as ,

`\longrightarrow p \propto (1)/(q^2)`

Let k be the constant of proportionalality .

`\longrightarrow p = (k)/(q^2)`

Again it's given that when p is 13 , q is 4 . On substituting this in the above equation we can find out the value of k , as ;

`\longrightarrow 13 =(k)/(4^2)`

Solve out for k ,

`\longrightarrow k = 13 (16)`

Multiply ,

`\longrightarrow k = 208`

Again when the value of q is 2 , we need to find out the value of p . So ,

`\longrightarrow p =(k)/(q^2)`

Substitute ,

`\longrightarrow p =(208)/(2^2)\\`

`\longrightarrow p = (208)/(4)`

Simplify,

`\longrightarrow p = 52`

This is the required answer.