Question Number 20613 by ajfour last updated on 29/Aug/17 Commented by ajfour last updated on 07/Nov/19 $${Find}\:{max}/{min}\:\:{of}\:\left(\alpha+\beta+\gamma\right). \\ $$ Commented by ajfour last updated on…
Question Number 20612 by ajfour last updated on 29/Aug/17 $${Evaluate}\:\int_{\mathrm{0}} ^{\:\:\infty} \int_{\mathrm{0}} ^{\:\:\infty} {e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} {dydx}\:. \\ $$ Answered by ajfour last updated on…
Question Number 151677 by Tawa11 last updated on 22/Aug/21 Answered by Olaf_Thorendsen last updated on 22/Aug/21 $$\mathrm{R}\:=\:\mathrm{1}\Omega+\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{3}\Omega+\mathrm{3}\Omega}+\frac{\mathrm{1}}{\mathrm{3}\Omega+\mathrm{3}\Omega}} \\ $$$$\mathrm{R}\:=\:\mathrm{1}\Omega+\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{6}\Omega}+\frac{\mathrm{1}}{\mathrm{6}\Omega}} \\ $$$$\mathrm{R}\:=\:\mathrm{1}\Omega+\mathrm{3}\Omega\:=\:\mathrm{4}\Omega \\ $$$$\mathrm{I}\:=\:\frac{\mathrm{V}}{\mathrm{R}}\:=\:\frac{\mathrm{12V}}{\mathrm{4}\Omega}\:=\:\mathrm{3A} \\ $$…
Question Number 86142 by jagoll last updated on 27/Mar/20 $$\mathrm{y}'\:.\mathrm{sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:=\:\mathrm{y}\:+\:\mathrm{sin}\:^{\mathrm{3}} \mathrm{t}\: \\ $$$$\mathrm{y}\left(\frac{\pi}{\mathrm{4}}\right)\:=\:\mathrm{0}\: \\ $$ Answered by Kunal12588 last updated on 27/Mar/20 $$\frac{{dy}}{{dt}}=\frac{{y}}{\mathrm{sin}\:{t}\:\mathrm{cos}\:{t}}+\mathrm{sin}\:{t}\:\mathrm{tan}\:{t} \\ $$$$\Rightarrow\frac{{dy}}{{dt}}+\left(−\frac{\mathrm{1}}{\mathrm{sin}\:{t}\:\mathrm{cos}\:{t}}\right){y}=\mathrm{sin}\:{t}\:\mathrm{tan}\:{t}…
Question Number 86140 by Wepa last updated on 27/Mar/20 Commented by Prithwish Sen 1 last updated on 27/Mar/20 $$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2020}} \underset{\boldsymbol{\mathrm{k}}=\mathrm{2}} {\overset{\mathrm{2020}} {\boldsymbol{\sum}}\mathrm{k}}.\mathrm{2}^{\boldsymbol{\mathrm{k}}} \:\:\:\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}}. \\ $$…
Question Number 86141 by TawaTawa1 last updated on 27/Mar/20 $$\mathrm{A}\:\mathrm{number}\:\mathrm{n}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{of}\:\:\mathrm{22}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{remainder}\:\:\mathrm{30}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{33}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{n} \\ $$ Commented by mr W last updated on 27/Mar/20 $${there}\:{is}\:{no}\:{such}\:{number}!…
Question Number 151673 by mathdanisur last updated on 22/Aug/21 Answered by Kamel last updated on 22/Aug/21 $${L}=\underset{{n}\rightarrow+\infty} {{lim}}\underset{{k}={n}} {\overset{\mathrm{2}{n}} {\prod}}\frac{\pi}{\pi−{Arctan}\left(\frac{\mathrm{1}}{{k}}\right)}=\underset{{n}\rightarrow+\infty} {{lim}}\underset{{k}={n}} {\overset{\mathrm{2}{n}} {\prod}}\frac{\pi{k}}{\pi{k}−\mathrm{1}} \\ $$$$\:\:\:=\underset{{n}\rightarrow+\infty}…
Question Number 86138 by jagoll last updated on 27/Mar/20 $$\int\underset{−\mathrm{4}} {\overset{\mathrm{8}} {\:}}\:\frac{\mid\mathrm{x}\mid}{\mathrm{x}}\:\mathrm{dx}\:=\:? \\ $$ Commented by Prithwish Sen 1 last updated on 27/Mar/20 $$\mathrm{l}\underset{\epsilon\rightarrow\mathrm{0}} {\mathrm{t}}\:\left\{\int_{−\mathrm{4}}…
Question Number 20599 by Tinkutara last updated on 28/Aug/17 $$\mathrm{In}\:\mathrm{a}\:\mathrm{rectangle}\:{ABCD},\:{E}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint} \\ $$$$\mathrm{of}\:{AB};\:{F}\:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:{AC}\:\mathrm{such}\:\mathrm{that}\:{BF} \\ $$$$\mathrm{is}\:\mathrm{perpendicular}\:\mathrm{to}\:{AC};\:\mathrm{and}\:{FE} \\ $$$$\mathrm{perpendicular}\:\mathrm{to}\:{BD}.\:\mathrm{Suppose}\:{BC}\:=\:\mathrm{8}\sqrt{\mathrm{3}}. \\ $$$$\mathrm{Find}\:{AB}. \\ $$ Answered by ajfour last updated…
Question Number 86132 by M±th+et£s last updated on 27/Mar/20 $$\int{x}^{\mathrm{3}} \:{sin}\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{6}\right)^{\mathrm{5}} \:{dx} \\ $$ Answered by Kunal12588 last updated on 27/Mar/20 $${I}=\int{x}^{\mathrm{3}} \:{sin}\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{6}\right)^{\mathrm{5}}…