Question

If pp is inversely proportional to the square of qq, and pp is 10 when qq is 10, determine pp when qq is equal to 5.

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)`

where k is some constant.

Substituting with p = 10 and q = 10, and solving for k:

`\begin{gathered} 10=(k)/(10^2) \\ 10=(k)/(100) \\ 10\cdot100=(k)/(100)\cdot100 \\ 1000=k \end{gathered}`

Substituting with q = 5 and k = 1000, we get:

`\begin{gathered} p=(1000)/(5^2) \\ p=(1000)/(25) \\ p=40 \end{gathered}`