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Question-58675

Question Number 58675 by ajfour last updated on 27/Apr/19 Commented by ajfour last updated on 27/Apr/19 $$\mathrm{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{square};\:\mathrm{while},\:\mathrm{PQM}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{sector}.\:\mathrm{Find}\:\mathrm{in}\:\mathrm{what}\:\mathrm{proportion} \\ $$$$\mathrm{are}\:\mathrm{radii}\:\mathrm{b},\:\mathrm{r},\:\mathrm{g}\:\left(\mathrm{blue},\:\mathrm{red},\:\mathrm{green}\right. \\ $$$$\left.\mathrm{respectively}\right). \\ $$…

Question-189710

Question Number 189710 by Mastermind last updated on 20/Mar/23 Answered by aleks041103 last updated on 20/Mar/23 $${V}\left(\mathrm{12}\right)={V}\left(\mathrm{21}\right)−{V}\left(\mathrm{21}−\mathrm{15}\right)={V}\left(\mathrm{21}\right)−{V}\left(\mathrm{6}\right) \\ $$$${V}\left(\mathrm{12}\right)=\mathrm{2}{V}\left(\mathrm{6}\right) \\ $$$$\Rightarrow\frac{\mathrm{3}}{\mathrm{2}}{V}\left(\mathrm{12}\right)={V}\left(\mathrm{21}\right)\Rightarrow{V}\left(\mathrm{12}\right)=\frac{\mathrm{2}}{\mathrm{3}}{V}\left(\mathrm{21}\right) \\ $$$$\Rightarrow{the}\:{water}\:{is}\:\frac{\mathrm{2}}{\mathrm{3}}\:{of}\:{the}\:{bottle} \\ $$$$\boldsymbol{{Note}}\:\mathrm{1}:\:{V}\left({x}\right)\:{is}\:{the}\:{volume}\:{of}\:{water}\:{for}\:…