Question

if p inversely proportional to the square of q and p is 25 when q is 3 determine p when q is equal to 5

Answer 1

When two values are inversely proportional, it is true that

$\begin{gathered} y=\frac{k}{x} \\ \text{ Where }k\text{ is the constant of proportionality} \end{gathered}$

Then, transcribing the given statement into the mathematical language you have

$p=\frac{k}{q^2}$$\begin{gathered} 25=\frac{k}{3^2} \\ \text{ because } \\ p=25 \\ q=3 \end{gathered}$

Now, you can solve for k

$\begin{gathered} 25=\frac{k}{3^2} \\ 25=\frac{k}{9} \\ \text{ Multiply by 9 into both sides of the equation} \\ 25\cdot9=\frac{k}{9}\cdot9 \\ 225=k \end{gathered}$

Finally, since you already have the value of k you can determine the value of p

$\begin{gathered} p=\frac{k}{q^2} \\ p=\frac{225}{5^2} \\ p=\frac{225}{25} \\ p=9 \end{gathered}$

Therefore, the value of p is 9 when q is equal to 5.