Question Number 141368 by bemath last updated on 18/May/21 $${A}\:{closed}\:{cylindrical}\:{can}\:{be}\:{is}\:{to}\:{hold} \\ $$$$\mathrm{1}\:{liters}\:{of}\:{liquid}\:.\:{How}\:{should}\:{we}\: \\ $$$${choose}\:{the}\:{height}\:{and}\:{radius}\: \\ $$$${to}\:{minimize}\:{the}\:{amount}\:{of} \\ $$$${material}\:{needed}\:{to}\:{manufacture} \\ $$$${the}\:{can}\:?\: \\ $$ Answered by TheSupreme…
Question Number 141365 by bemath last updated on 18/May/21 $$\:\mathrm{log}\:_{\frac{\mathrm{9}}{\mathrm{4}}} \left(\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{…}}}}\right)\:=? \\ $$ Answered by EDWIN88 last updated on 18/May/21 $$\mathrm{let}\:\mathcal{E}\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\:\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\:\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\:\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\ldots}}}} \\ $$$$\Rightarrow\:\mathcal{E}\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\:\sqrt{\mathrm{6}−\mathcal{E}}\: \\ $$$$\Rightarrow\:\mathcal{E}^{\mathrm{2}}…
Question Number 75830 by Master last updated on 18/Dec/19 Commented by Master last updated on 18/Dec/19 $$\mathrm{sir}\:\mathrm{mind}\:\mathrm{is}\:\mathrm{power}\:,\:\mathrm{sir}\:\mathrm{mathmax}\:\mathrm{plz} \\ $$ Commented by turbo msup by abdo…
Question Number 10294 by Tawakalitu ayo mi last updated on 02/Feb/17 $$\mathrm{A}\:\mathrm{student}\:\mathrm{needs}\:\mathrm{at}\:\mathrm{least}\:\mathrm{three}\:\mathrm{notebooks}\:\mathrm{and} \\ $$$$\mathrm{three}\:\mathrm{pencils}.\:\mathrm{Notebooks}\:\mathrm{cost}\:#\mathrm{60}\:\mathrm{and}\:\mathrm{pencil} \\ $$$$#\mathrm{36}\:\mathrm{and}\:\mathrm{the}\:\mathrm{student}\:\mathrm{has}\:#\mathrm{360}\:\mathrm{to}\:\mathrm{spend}.\:\mathrm{The} \\ $$$$\mathrm{student}\:\mathrm{decides}\:\mathrm{to}\:\mathrm{spend}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{possible} \\ $$$$\mathrm{of}\:\mathrm{his}\:#\mathrm{360}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{he}\:\mathrm{spend}\:\mathrm{his}\:\mathrm{money} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Does}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ways}\:\mathrm{give}\:\mathrm{him}\:\mathrm{change}\:??? \\…
Question Number 141367 by cesarL last updated on 18/May/21 $$\int\left(\sqrt{{cosx}\centerdot{senx}}\right){dx} \\ $$ Answered by MJS_new last updated on 18/May/21 $$\mathrm{if}\:\mathrm{sen}\:{x}\:=\mathrm{sin}\:{x} \\ $$$$\int\sqrt{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}\:{dx}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\int\sqrt{\mathrm{sin}\:\mathrm{2}{x}}\:{dx}= \\ $$$$\:\:\:\:\:\left[{t}={x}−\frac{\pi}{\mathrm{4}}\:\rightarrow\:{dx}={dt}\right] \\…
Question Number 75828 by 21042004 last updated on 18/Dec/19 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{10}^{{n}} } \\ $$ Commented by mathmax by abdo last updated on 18/Dec/19 $$\sum_{{n}=\mathrm{1}}…
Question Number 75826 by liki last updated on 18/Dec/19 Commented by liki last updated on 18/Dec/19 $$…{plz}\:{help}\:{me}\:{part}\:\left({c}\right). \\ $$ Answered by mr W last updated…
Question Number 141360 by cesarL last updated on 17/May/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \sqrt{{cosxsenx}}{dx} \\ $$ Commented by iloveisrael last updated on 18/May/21 $${qn}\:\mathrm{141367} \\ $$ Terms…
Question Number 10290 by konen last updated on 02/Feb/17 $$\mathrm{3}×\mathrm{3}!+\mathrm{4}×\mathrm{4}!+…+\mathrm{12}×\mathrm{12}!=? \\ $$ Answered by ridwan balatif last updated on 02/Feb/17 $$\mathrm{3}×\mathrm{3}!+\mathrm{4}×\mathrm{4}!+…+\mathrm{12}×\mathrm{12}! \\ $$$$\left(\mathrm{4}−\mathrm{1}\right)×\mathrm{3}!+\left(\mathrm{5}−\mathrm{1}\right)×\mathrm{4}!+\left(\mathrm{6}−\mathrm{1}\right)×\mathrm{5}!+…+\left(\mathrm{13}−\mathrm{1}\right)×\mathrm{12}! \\ $$$$\mathrm{4}×\mathrm{3}!−\mathrm{1}×\mathrm{3}!+\mathrm{5}×\mathrm{4}!−\mathrm{1}×\mathrm{4}!+\mathrm{6}×\mathrm{5}!−\mathrm{1}×\mathrm{5}!+…+\mathrm{13}×\mathrm{12}!−\mathrm{1}×\mathrm{12}!…
Question Number 10289 by konen last updated on 02/Feb/17 $$\frac{\mathrm{9}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}}+\mathrm{3}=\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}\Rightarrow\Sigma\mathrm{x}=? \\ $$$$ \\ $$ Answered by ridwan balatif last updated on 02/Feb/17 $$\frac{\mathrm{9}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}}+\mathrm{3}=\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}…