Question Number 140684 by qaz last updated on 11/May/21 $$\int_{\mathrm{0}} ^{\pi} \mathrm{cos}\:^{{n}} \left({x}\right)\centerdot\mathrm{cos}\:\left({nx}\right){dx}=\frac{\pi}{\mathrm{2}^{{n}} } \\ $$ Answered by mnjuly1970 last updated on 11/May/21 $$\:\boldsymbol{\phi}:={Re}\left(\frac{\mathrm{1}}{\mathrm{2}}\:\int_{\mathrm{0}} ^{\:\mathrm{2}\pi}…
Question Number 140687 by mnjuly1970 last updated on 11/May/21 $$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\: \\ $$ Commented by qaz last updated…
Question Number 140680 by bemath last updated on 11/May/21 $$\:\mathrm{log}\:_{\left(\mathrm{x}+\mathrm{2}\right)} \left(\mathrm{7x}^{\mathrm{2}} −\mathrm{x}^{\mathrm{3}} \right)−\mathrm{log}\:_{\frac{\mathrm{1}}{\mathrm{x}+\mathrm{2}}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{3x}\right)\geqslant\:\mathrm{log}\:_{\sqrt{\mathrm{x}+\mathrm{2}}\:} \left(\sqrt{\mathrm{5}−\mathrm{x}}\:\right) \\ $$ Answered by liberty last updated on 11/May/21…
Question Number 75147 by mathocean1 last updated on 07/Dec/19 $$\mathrm{hello} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\frac{\mathrm{5}\pi}{\mathrm{18}}\mathrm{cos}\frac{\mathrm{13}\pi}{\mathrm{18}}=−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\frac{\mathrm{4}\pi}{\mathrm{9}} \\ $$ Answered by MJS last updated on 07/Dec/19 $$\mathrm{sin}\:{a}\:\mathrm{cos}\:{b}\:=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{sin}\:\left({a}−{b}\right)\:+\mathrm{sin}\:\left({a}+{b}\right)\right) \\…
Question Number 140676 by ZiYangLee last updated on 11/May/21 $$\int\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}=? \\ $$ Answered by Dwaipayan Shikari last updated on 11/May/21 $$\int\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}…
Question Number 75141 by chess1 last updated on 07/Dec/19 Commented by chess1 last updated on 08/Dec/19 $$\mathrm{solve}\:\mathrm{please} \\ $$ Commented by chess1 last updated on…
Question Number 9604 by madscientist last updated on 20/Dec/16 $${is}\: \\ $$$$\bigtriangledown×\left(\bigtriangledown×{A}\right)=\bigtriangledown\left(\bigtriangledown\centerdot{A}\right)−\bigtriangledown^{\mathrm{2}} {A} \\ $$$${F}×\left(\bigtriangledown×{A}\right)={F}\left(\bigtriangledown\centerdot{A}\right)−\bigtriangledown^{\mathrm{2}} {A} \\ $$$${the}\:{same}? \\ $$ Terms of Service Privacy Policy…
Question Number 9603 by tawakalitu last updated on 20/Dec/16 $$\mathrm{A}\:\mathrm{regular}\:\mathrm{hexagon}\:\mathrm{has}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{8}\:\mathrm{cm}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{perpendicular}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{two} \\ $$$$\mathrm{opposite}\:\mathrm{faces}. \\ $$ Answered by mrW last updated on 20/Dec/16 $$\mathrm{2}×\frac{\mathrm{8}}{\mathrm{2}}×\sqrt{\mathrm{3}}=\mathrm{8}\sqrt{\mathrm{3}}\:\mathrm{cm} \\…
Question Number 75136 by chess1 last updated on 07/Dec/19 Commented by MJS last updated on 07/Dec/19 $$\frac{\mathrm{1}}{\mathrm{10}} \\ $$ Commented by mathmax by abdo last…
Question Number 9600 by Sopheak last updated on 20/Dec/16 Commented by prakash jain last updated on 20/Dec/16 $${k}^{{th}} \:\mathrm{Term}=\underset{{i}=\mathrm{0}} {\overset{{k}−\mathrm{1}} {\sum}}\mathrm{18}×\left(\mathrm{10}^{\mathrm{2}{i}} \right)=\frac{\mathrm{18}\left(\mathrm{10}^{\mathrm{2}{k}} −\mathrm{1}\right)}{\mathrm{99}} \\ $$$${S}_{{n}}…