Question

The pair of values below is from an inverse variation. Find the missing value.(6,10) (8 y)

Answer 1

`\qquad \qquad \textit{inverse proportional variation}\\\\\textit{\underline{y} varies inversely with \underline{x}}~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill }\\\\\textit{\underline{x} varies inversely with }\underline{z^5}~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill }\\\\[-0.35em]\rule{34em}{0.25pt}`

`\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} x=6\\ y=10 \end{cases}\implies 10=\cfrac{k}{6} \\\\\\ 60=k\qquad therefore\qquad \boxed{y=\cfrac{60}{x}} \\\\\\ \textit{when x = 8, what is`