Question Number 75598 by A8;15: last updated on 13/Dec/19 Commented by mr W last updated on 13/Dec/19 $${please}\:{see}\:{Q}#\mathrm{74970} \\ $$ Terms of Service Privacy Policy…
Question Number 141132 by mnjuly1970 last updated on 16/May/21 $$\:\:\: \\ $$$$\:…{mathematical}\:…{analysis}… \\ $$$$\:\:\:\:{prove}\:\:{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}^{{n}} } }\:\right)\:\overset{?} {=}\:\mathrm{2}\:\:\: \\ $$$$\:\:\:\:\:\:…… \\ $$…
Question Number 10062 by ridwan balatif last updated on 22/Jan/17 Commented by ridwan balatif last updated on 22/Jan/17 $$\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{of}\:\mathrm{the}\:\mathrm{division}\:\mathrm{20}^{\mathrm{2017}} +\mathrm{1}^{\mathrm{2017}} +\mathrm{17}^{\mathrm{2017}} +\mathrm{72}^{\mathrm{2017}} \:\mathrm{by}\:\mathrm{2017} \\ $$…
Question Number 141135 by bobhans last updated on 16/May/21 $$\:\:\:\:\:\:\:{Find}\:{the}\:{minimum}\:{of}\: \\ $$$$\:\:\:\:\:\:\frac{\mathrm{12}}{{x}}\:+\:\frac{\mathrm{18}}{{y}}\:+\:{xy}\:{for}\:{all}\: \\ $$$$\:\:\:\:\:\:{positive}\:{number}\:{x}\:\&\:{y}\:. \\ $$ Answered by mitica last updated on 16/May/21 $$\frac{\mathrm{12}}{{x}}+\frac{\mathrm{18}}{{y}}+{xy}\geqslant\mathrm{3}\sqrt[{\mathrm{3}}]{\frac{\mathrm{12}}{{x}}\centerdot\frac{\mathrm{18}}{{y}}\centerdot{xy}}=\mathrm{18} \\…
Question Number 141134 by mnjuly1970 last updated on 16/May/21 $$\:\:\:\:\: \\ $$$$\:\:\:{prove}\:{that}:: \\ $$$$\:\:\Phi:=\underset{{m},{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{m}^{\mathrm{2}} +{n}^{\mathrm{2}} }=\:\frac{\pi^{\mathrm{2}} }{\mathrm{24}}+\frac{\pi{ln}\left(\mathrm{2}\right)}{\mathrm{8}} \\ $$$$ \\ $$ Answered…
Question Number 75597 by aliesam last updated on 13/Dec/19 Commented by mathmax by abdo last updated on 13/Dec/19 $${let}\:{f}\left({x}\right)=\frac{\left({cosx}\right)^{\frac{\mathrm{1}}{{m}}} −\left({cosx}\right)^{\frac{\mathrm{1}}{{n}}} }{{x}^{\mathrm{2}} }\:\:{we}\:{have} \\ $$$${cosx}\:\sim\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:\Rightarrow\left({cosx}\right)^{\frac{\mathrm{1}}{{m}}}…
Question Number 141129 by bobhans last updated on 16/May/21 $${For}\:{what}\:{values}\:{of}\:\lambda\:{are}\:{the} \\ $$$${vectors}\:\lambda\hat {{i}}\:+\:\mathrm{2}\hat {{j}}\:+\:\hat {{k}}\:,\:\mathrm{3}\hat {{i}}\:+\mathrm{4}\hat {{j}}\:+\lambda\hat {{k}}\: \\ $$$$,\:\hat {{j}}\:+\:\hat {{k}}\:\:{coplanar}\: \\ $$ Answered…
Question Number 75593 by ajfour last updated on 13/Dec/19 $${u}^{\mathrm{3}} +{v}^{\mathrm{3}} ={a}\:,\:\:{s}^{\mathrm{3}} +{m}^{\mathrm{3}} ={b}\:, \\ $$$${uv}=\left({s}+{m}\right)^{\mathrm{2}} \:,\:\:{sm}=\left({u}+{v}\right)^{\mathrm{2}} \:. \\ $$$${Find}\:{u},{v},{s},{m}\:\:{in}\:{terms}\:{of}\:{a},{b}. \\ $$ Answered by behi83417@gmail.com…
Question Number 10056 by Tawakalitu ayo mi last updated on 22/Jan/17 $$\mathrm{Infrared}\:\mathrm{rays}\:\mathrm{of}\:\mathrm{frequency}\:\mathrm{1}.\mathrm{0}\:×\:\mathrm{10}^{\mathrm{13}} \:\mathrm{Hz} \\ $$$$\mathrm{have}\:\mathrm{a}\:\mathrm{wavelength}\:\mathrm{of}\:\mathrm{3}.\mathrm{0}\:×\:\mathrm{10}^{−\mathrm{5}} \:\mathrm{m}\:\mathrm{in}\:\mathrm{a}\:\mathrm{vacuum}. \\ $$$$\mathrm{The}\:\mathrm{wavelenth}\:\mathrm{of}\:\mathrm{X}\:\mathrm{rays}\:\mathrm{of}\:\mathrm{frequency} \\ $$$$\mathrm{5}.\mathrm{0}\:×\:\mathrm{10}^{\mathrm{16}} \:\mathrm{Hz}\:\mathrm{in}\:\mathrm{a}\:\mathrm{vacuum}\:\mathrm{will}\:\mathrm{be}\:? \\ $$ Answered by…
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