Question

If pp is inversely proportional to the square of qq, and pp is 22 when qq is 8, determine pp when qq is equal to 4.

Answer 1

Given that p is inversely proportional to the square of q that implies:

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

Remove the sign of proportionality and put a proportionality constant k such that:

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

Given that when q is 8 then p is 22. So,

`22=(k)/(8^2)\Rightarrow k=22*64=1408`

Put k = 1408 and q = 4 in the equation to find the value of p:

`p=(1408)/(4^2)=(1408)/(16)=88`

Thus, the answer is 88.