$\qquad \qquad \textit{direct proportional variation}\\\\\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill }\\\\\textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill }\\\\[-0.35em]~\dotfill$

$\stackrel{\textit{"th" varies directly with "p"}}{th=kp}\qquad \textit{we also know that} \begin{cases} th=1.8\\ p=350 \end{cases} \\\\\\ 1.8=k(350) \implies \cfrac{9}{5}=350k\implies \cfrac{9}{1750}=k~\hfill \boxed{th=\cfrac{9}{1750}k} \\\\\\ \textit{when p = 84, what is "th"?}\qquad th=\cfrac{9}{1750}(84)\implies th=\cfrac{54}{135}\implies th=0.432$

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2 years ago