Question

How do you figure this out , what's the answer

Answer 1

$\bf \begin{array}{cccccclllll} \textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\ \textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\ y&=&{{ k}}&\cdot&x \\ && y={{ k }}x \end{array}\\\\ ---------------------------$

$\bf \textit{the houses "h", varies directly, to the square diameter }d^2 \\\\\\ h=kd^2 \\\\\\ \textit{when the diameter is 10, the houses served are 50}\quad \begin{cases} h=50\\ d=10 \end{cases} \\\\\\ 50=10^2k\implies \cfrac{50}{100}=k\implies \cfrac{1}{2}=k\\\\ -----------------------------\\\\ h=\cfrac{1}{2}d^2$

so "k", or the "constant of variation" is 1/2

now $\bf a)\qquad h=\cfrac{1}{2}\cdot 50^2\qquad \qquad b)\qquad 3200=\cfrac{1}{2}\cdot d^2$

for a) get "h", and for "b", solve for "d"