Question

2. The volume of gas in a container at a constant temperature varies inversely as the pressure.
(a) If the volume is 26 cubic centimeters at a pressure of 6 pounds, write an equation to represent this relationship.
Show work!! (3 points)
(b) Use your equation from part a to find the volume of a gas that has a pressure of 17. Round your answer to the
nearest hundredth if necessary. Show work!! (2 points work, 1-point answer)

Answer 1

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

$\stackrel{\textit{\boxed{v}olume varies inverse as the \boxed{p}ressure}}{v = \cfrac{k}{p}}\qquad \textit{we also know that} \begin{cases} v = \stackrel{cm^3}{26}\\ p=\stackrel{lbs}{6} \end{cases} \\\\\\ 26=\cfrac{k}{6}\implies 156=k~\hfill \underset{\textit{part a)}}{\boxed{v = \cfrac{156}{p}}} \\\\\\ \textit{when p = 17, what is "v"?}\qquad v = \cfrac{156}{17}\implies v = 9\frac{3}{17}\implies \underset{\textit{part b)}}{v\approx 9.18~cm^3}$