Question

If pp is inversely proportional to the square of qq, and pp is 16 when qq is 9, determine pp when qq is equal to 4.

Answer 1

Given that p is inversely proportional to the square of q, then these two variables are related by the next formula:

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

Substituting with p = 16, and q = 9, and solving for k:

`\begin{gathered} 16=(k)/(9^2) \\ 16=(k)/(81) \\ 16\cdot81=(k)/(81)\cdot81 \\ 1296=k \end{gathered}`

Substituting with k = 1296 and q = 4, we get:

`\begin{gathered} p=(1296)/(4^2) \\ p=(1296)/(16) \\ p=81 \end{gathered}`