Question Number 127888 by A8;15: last updated on 02/Jan/21 Answered by mindispower last updated on 02/Jan/21 $${x}={sh}\left({t}\right) \\ $$$$\Rightarrow{dx}={ch}\left({t}\right){dt} \\ $$$$\Leftrightarrow\int_{\mathrm{0}} ^{\infty} {sin}\left({ch}\left({t}\right)\right){cos}\left({sh}\left({t}\right)\right){dt}..=\Omega \\ $$$$\Lambda=\int_{\mathrm{0}}…
Question Number 127889 by A8;15: last updated on 02/Jan/21 Answered by mindispower last updated on 02/Jan/21 $$=\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{1}}{\mathrm{5}^{{n}} {n}} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}−{x}}=\underset{{n}\geqslant\mathrm{0}} {\sum}{x}^{{n}} \\ $$$$\Rightarrow\int_{\mathrm{0}} ^{{t}}…
Question Number 127882 by zakirullah last updated on 02/Jan/21 Commented by mr W last updated on 03/Jan/21 $${please}\:{pay}\:{attention}\:{when}\:{typing}! \\ $$$$\left(\mathrm{111}\right)\mathrm{8}\:{is}\:{misleading},\:{since}\:{you} \\ $$$${meant}\:\left(\mathrm{111}\right)_{\mathrm{8}} . \\ $$…
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Question Number 127861 by naka3546 last updated on 02/Jan/21 $${How}\:\:{many}\:\:{natural}\:\:{numbers}\:\:{n}\:\leqslant\:\mathrm{2020}\:{such}\:\:{that} \\ $$$$\left({n}\:+\:\mathrm{3}\right)!\:\:{is}\:\:{divisible}\:\:{by}\:\:\mathrm{2}^{{n}} \:? \\ $$ Answered by floor(10²Eta[1]) last updated on 03/Jan/21 $$\mathrm{2}^{\mathrm{n}} \mid\left(\mathrm{n}+\mathrm{3}\right)!\Rightarrow\mathrm{k}\geqslant\mathrm{n} \\…
Question Number 62308 by aliesam last updated on 19/Jun/19 Commented by maxmathsup by imad last updated on 20/Jun/19 $${x}^{\mathrm{2}} −\mathrm{2}{x}\:\:+\mathrm{2}\:=\mathrm{0}\:\rightarrow\Delta^{'} \:=\mathrm{1}−\mathrm{2}\:=−\mathrm{1}\:={i}^{\mathrm{2}} \:\Rightarrow\alpha\:=\mathrm{1}+{i}\:\:{and}\:\beta\:=\mathrm{1}−{i}\:=\overset{−} {\alpha}\:\Rightarrow \\ $$$$\alpha^{{n}}…
Question Number 62289 by naka3546 last updated on 19/Jun/19 Answered by MJS last updated on 19/Jun/19 $$\mathrm{we}\:\mathrm{have} \\ $$$${A}_{\mathrm{1}} =\mathrm{3}=\frac{\mathrm{1}}{\mathrm{2}}×{a}×{x}\:\Rightarrow\:{x}=\frac{\mathrm{6}}{{a}} \\ $$$${A}_{\mathrm{2}} =\mathrm{5}=\frac{\mathrm{1}}{\mathrm{2}}×{b}×{y}\:\Rightarrow\:{y}=\frac{\mathrm{10}}{{b}} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{triangle}\:=\:{c}…
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Question Number 62273 by alphaprime last updated on 18/Jun/19 $${Mr}.\:{Rasheed}.{Sindhi}\: \\ $$$${I}\:{sense}\:{you}'{re}\:{much}\:{engaged}\:{in}\:{making}\: \\ $$$${olympiad}\:{contents}\:{these}\:{days}\:,\:{I}\:{wish}\: \\ $$$${that}\:{you}\:{join}\:{my}\:{workspace}\:{concerning}\:{that}\:{same}. \\ $$ Commented by Rasheed.Sindhi last updated on 20/Jun/19…
Question Number 62265 by azizullah last updated on 18/Jun/19 Commented by tanmay last updated on 18/Jun/19 $${question}\:{is}\:{not}\:{clear}… \\ $$ Answered by MJS last updated on…