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Question Number 108389 by mathdave last updated on 16/Aug/20

Answered by mbertrand658 last updated on 19/Aug/20

$$\left(a\right)$$$$\mathrm{V}=\frac{1}{3}\pi r^{2}h$$$$h=8.1\Rightarrow r=\frac{2}{3}(8.1)=5.4$$$$\mathrm{V}=\frac{1}{3}\pi {(5.4)}^2(8.1)$$$$\approx \frac{1}{3}\left(\frac{22}{7}\right)(29.16)(8.1)$$$$\approx 247.4{\mathrm{cm}}^3$$$$\left(b\right)$$$$\mathrm{Let}x\mathrm{and}y\mathrm{represent}\mathrm{the}\mathrm{amount}\mathrm{invested}$$$$\mathrm{in}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{firms}.\mathrm{The}\mathrm{total}\mathrm{simple}$$$$\mathrm{interest}\mathrm{earned}\mathrm{between}\mathrm{them}\mathrm{would}$$$$\mathrm{normally}\mathrm{be}\mathrm{found}\mathrm{by}\mathrm{simply}\mathrm{multiplying}$$$$\mathrm{each}\mathrm{by}\mathrm{its}\mathrm{interest}\mathrm{rate}\mathrm{and}\mathrm{adding}\mathrm{the}$$$$\mathrm{results}.\mathrm{However},\mathrm{in}\mathrm{this}\mathrm{case}\mathrm{we}{\mathrm{don}}^{\prime }\mathrm{t}$$$$\mathrm{have}\mathrm{values},\mathrm{only}\mathrm{a}\mathrm{ratio}.{\mathrm{We}}^{\prime }\mathrm{ll}\mathrm{use}\mathrm{that}$$$$\mathrm{ratio}\mathrm{to}\mathrm{form}\mathrm{a}\mathrm{second}\mathrm{equation}\mathrm{that}\mathrm{will}$$$$\mathrm{allow}\mathrm{us}\mathrm{to}\mathrm{solve}\mathrm{the}\mathrm{system}.$$$$$$$$0.08x+0.1y=92000$$$$x=\frac{3}{5}y$$$$0.08\left(\frac{3}{5}y\right)+0.1y=92000$$$$0.048y+0.1y=92000$$$$0.148y=92000$$$$y=621621.621621...$$$$x=\frac{3}{5}(621621.621621...)$$$$x=372972.972972...$$$$$$$$\mathrm{Mr}.\mathrm{Uduh}\mathrm{invested}\mathrm{\$}372,973\mathrm{in}\mathrm{the}\mathrm{first}$$$$\mathrm{account},\mathrm{and}\mathrm{\$}621,622\mathrm{in}\mathrm{the}\mathrm{second}.$$

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