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=(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=(k)/(q^2)`
`\begin{gathered} 25=(k)/(3^2) \\ \text{ because } \\ p=25 \\ q=3 \end{gathered}`

Now, you can solve for k

`\begin{gathered} 25=(k)/(3^2) \\ 25=(k)/(9) \\ \text{ Multiply by 9 into both sides of the equation} \\ 25\cdot9=(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=(k)/(q^2) \\ p=(225)/(5^2) \\ p=(225)/(25) \\ p=9 \end{gathered}`

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