[tex]\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}\\\\
---------------------------\\\\[/tex]
[tex]\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[/tex]
so "k", or the "constant of variation" is 1/2
now [tex]\bf a)\qquad h=\cfrac{1}{2}\cdot 50^2\qquad \qquad b)\qquad 3200=\cfrac{1}{2}\cdot d^2[/tex]
for a) get "h", and for "b", solve for "d"
