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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}\:…

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Question Number 123947 by Dwaipayan Shikari last updated on 29/Nov/20 $$\frac{\mathrm{9}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{9}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }.\frac{\mathrm{18}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{18}^{\mathrm{2}} −\mathrm{0}^{\mathrm{2}} }.\frac{\mathrm{27}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{27}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }.\frac{\mathrm{36}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{36}^{\mathrm{2}}…

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Question Number 58358 by Mahmoud A.R last updated on 22/Apr/19 $${knowing}\:{that}:\: \\ $$$${cos}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}} }{\left(\mathrm{2}{n}\right)!}\:\:\:\: \\ $$$${sin}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}\:+\mathrm{1}\right)!} \\ $$$${prof}\:{that}:\:{cos}\left({x}+{y}\right)=\:{cos}\left({x}\right){cos}\left({y}\right)−{sin}\left({x}\right){sin}\left({y}\right)…