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

Sagot :

[tex]\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}[/tex]

[tex]\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 "y"?}\qquad y=\cfrac{60}{8}\implies y=\cfrac{15}{2}[/tex]

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