Question

The value of q varies directly withp2,andq=16whenp=2.What is the value of q whenp=12?

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \textit{q varies directly with p}^2\qquad q=kp^2 \\\\\\ \textit{we also know that } \begin{cases} q=16\\ p=2 \end{cases}\implies 16=k2^2\implies \cfrac{16}{2^2}=k \\\\\\ 4=k\qquad therefore\qquad \boxed{q=4p^2} \\\\\\ \textit{when p = 12, what is \underline{q}?}\qquad q=4(12^2)$