Question Number 19349 by Tinkutara last updated on 10/Aug/17 $$\mathrm{Prove}\:\mathrm{that}\:\mid{z}_{\mathrm{1}} \:+\:{z}_{\mathrm{2}} \:+\:{z}_{\mathrm{3}} \:+\:….\:+\:{z}_{{n}} \mid\:\leqslant \\ $$$$\mid{z}_{\mathrm{1}} \mid\:+\:\mid{z}_{\mathrm{2}} \mid\:+\:\mid{z}_{\mathrm{3}} \mid\:+\:….\:+\:\mid{z}_{{n}} \mid \\ $$ Commented by Tinkutara…
Question Number 19345 by tawa tawa last updated on 10/Aug/17 $$\mathrm{A}\:\mathrm{thin}\:\mathrm{bi}\:−\:\mathrm{convex}\:\mathrm{lens}\:\mathrm{rest}\:\mathrm{on}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{mirror}\:.\:\:\mathrm{it}\:\mathrm{is}\:\mathrm{found}\:\mathrm{that}\:\mathrm{a}\:\mathrm{point} \\ $$$$\mathrm{objects}\:\mathrm{placed}\:\mathrm{20cm}\:\mathrm{above}\:\mathrm{the}\:\mathrm{object}\:\mathrm{coincide}\:\mathrm{with}\:\mathrm{it}\:\mathrm{own}\:\mathrm{image}. \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{position}\:\mathrm{and}\:\mathrm{nature}\:\mathrm{of}\:\mathrm{the}\:\mathrm{image}\:\mathrm{when}\:\mathrm{the}\:\mathrm{object}\:\mathrm{is}\:\mathrm{placed} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{8cm}\:\:\mathrm{and}\:\:\left(\mathrm{ii}\right)\:\mathrm{12}\:\:\:\:\mathrm{from}\:\mathrm{the}\:\mathrm{lens}\:\mathrm{mirror}\:\mathrm{combinatiom} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 150418 by ajfour last updated on 12/Aug/21 Commented by ajfour last updated on 12/Aug/21 $${For}\:{tetrahedron}\:{edge}\:{a}, \\ $$$${and}\:{sphere}\:{radius}\:{r},\:{find}\: \\ $$$${fractional}\:{volume}\:{of}\:{sphere}\: \\ $$$${within}\:{the}\:{tetrahedron}. \\ $$$${f}=\begin{cases}{{g}_{\mathrm{1}}…
Question Number 150413 by saly last updated on 12/Aug/21 Commented by MJS_new last updated on 12/Aug/21 $$\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{we}\:\mathrm{must}\:\mathrm{take}\:\mathrm{the}\:\mathrm{long}\:\mathrm{way}\:\mathrm{home}… \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\mathrm{arctan}\:{r}\:=−\frac{\mathrm{i}}{\mathrm{2}}\left(\mathrm{ln}\:\left(\mathrm{1}+\mathrm{i}{r}\right)\:−\mathrm{ln}\:\left(\mathrm{1}−\mathrm{i}{r}\right)\right) \\ $$$$\Rightarrow \\ $$$$\int\mathrm{arctan}\:\mathrm{sin}\:{x}\:{dx}=…
Question Number 84879 by sahnaz last updated on 17/Mar/20 $$\mathrm{e}^{\int\frac{\mathrm{2dx}}{\mathrm{xlnx}}} \\ $$ Commented by jagoll last updated on 17/Mar/20 $$\int\:\frac{\mathrm{2dx}}{\mathrm{x}\:\mathrm{lnx}}\:=\:\int\:\frac{\mathrm{2d}\left(\mathrm{lnx}\right)}{\mathrm{lnx}}\:=\:\int\:\mathrm{2}\frac{\mathrm{du}}{\mathrm{u}} \\ $$$$=\:\mathrm{2}\:\mathrm{ln}\:\mathrm{u}\:+\:\mathrm{c}\:,\:\left[\mathrm{u}\:=\:\mathrm{ln}\:\mathrm{x}\:\right] \\ $$$$=\:\mathrm{2ln}\left(\mathrm{lnx}\right)\:+\:\mathrm{2lnC}\:=\:\mathrm{2ln}\left(\mathrm{Clnx}\right) \\…
Question Number 19341 by tawa tawa last updated on 09/Aug/17 Commented by tawa tawa last updated on 09/Aug/17 $$\left(\mathrm{1}\right)\:\mathrm{Using}\:\mathrm{Stoke}'\mathrm{s}\:\mathrm{theorem},\:\mathrm{find}\:\:\oint\:\:\mathrm{y}^{\mathrm{2}} \mathrm{dx}\:+\:\mathrm{z}^{\mathrm{2}} \mathrm{dy}\:+\:\mathrm{x}^{\mathrm{2}} \mathrm{dz}\:,\:\:\mathrm{where}\:\:\Gamma\:\mathrm{is}\:\mathrm{the}\:\mathrm{closed} \\ $$$$\mathrm{curve}\:\:\mathrm{A}\rightarrow\mathrm{B}\rightarrow\mathrm{C}\rightarrow\mathrm{A}\:\:\mathrm{and}\:\:\mathrm{A}\:=\:\left(\mathrm{1},\:\mathrm{0},\:\mathrm{0}\right),\:\:\mathrm{B}\:=\:\left(\mathrm{0},\:\mathrm{0},\:\mathrm{1}\right),\:\:\mathrm{C}\left(\mathrm{0},\:\mathrm{1},\:\mathrm{0}\right). \\…
Question Number 150410 by ajfour last updated on 12/Aug/21 Commented by ajfour last updated on 12/Aug/21 $${If}\:{length}\:{of}\:{cylinder}\:{and} \\ $$$${both}\:{width}\:{and}\:{length}\:{of} \\ $$$${wedge}\:{are}\:{equal},\:{and}\:{that} \\ $$$${their}\:{material}\:{densities} \\ $$$${are}\:{even}\:{equal},\:{and}\:{their}…
Question Number 84873 by john santu last updated on 17/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\left(\frac{\mathrm{x}!}{\mathrm{x}}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}} \\ $$ Commented by john santu last updated on 17/Mar/20 $$\mathrm{yes}.\:\mathrm{i}\:\mathrm{agree}\:\mathrm{sir}…
Question Number 150405 by liberty last updated on 12/Aug/21 Answered by EDWIN88 last updated on 12/Aug/21 Answered by ajfour last updated on 12/Aug/21 Commented by…
Question Number 150404 by mathdanisur last updated on 12/Aug/21 $$\Omega\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{log}\left(\mathrm{x}\right)}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on 12/Aug/21 $$\Omega\left({a}\right)=\int_{\mathrm{0}}…