Question Number 152186 by Tawa11 last updated on 26/Aug/21 $$\int\mathrm{x}^{\mathrm{n}} \:\mathrm{cos}\left(\mathrm{nx}\right)\:\mathrm{dx} \\ $$ Answered by mindispower last updated on 26/Aug/21 $${nx}={y} \\ $$$$\Leftrightarrow\frac{\mathrm{1}}{{n}^{{n}+\mathrm{1}} }\int{y}^{{n}} {cos}\left({x}\right){dx}…
Question Number 21112 by Tinkutara last updated on 13/Sep/17 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{bouncing}\:\mathrm{elastically}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{speed}\:\mathrm{1}\:\mathrm{m}/\mathrm{s}\:\mathrm{between}\:\mathrm{walls}\:\mathrm{of}\:\mathrm{a}\:\mathrm{railway} \\ $$$$\mathrm{compartment}\:\mathrm{of}\:\mathrm{size}\:\mathrm{10}\:\mathrm{m}\:\mathrm{in}\:\mathrm{a}\:\mathrm{direction} \\ $$$$\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{walls}.\:\mathrm{The}\:\mathrm{train}\:\mathrm{is} \\ $$$$\mathrm{moving}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{10}\:\mathrm{m}/\mathrm{s} \\ $$$$\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{motion}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{ball}.\:\mathrm{As}\:\mathrm{seen}\:\mathrm{from}\:\mathrm{the}\:\mathrm{ground} \\ $$$$\left({a}\right)\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{motion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball} \\…
Question Number 86646 by Ar Brandon last updated on 30/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Commented by mathmax…
Question Number 21111 by Tinkutara last updated on 13/Sep/17 $$\mathrm{STATEMENT}-\mathrm{1}\::\:{z}_{\mathrm{1}} ^{\mathrm{2}} \:+\:{z}_{\mathrm{2}} ^{\mathrm{2}} \:+\:{z}_{\mathrm{3}} ^{\mathrm{2}} \:+\:{z}_{\mathrm{4}} ^{\mathrm{2}} \:= \\ $$$$\mathrm{0}\:\mathrm{where}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:{z}_{\mathrm{3}} \:\mathrm{and}\:{z}_{\mathrm{4}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{fourth} \\…
Question Number 21109 by Tinkutara last updated on 13/Sep/17 $$\mathrm{STATEMENT}-\mathrm{1}\::\:\mathrm{The}\:\mathrm{locus}\:\mathrm{of}\:{z},\:\mathrm{if} \\ $$$$\mathrm{arg}\left(\frac{{z}\:−\:\mathrm{1}}{{z}\:+\:\mathrm{1}}\right)\:=\:\frac{\pi}{\mathrm{2}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}. \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mid\frac{{z}\:−\:\mathrm{2}}{{z}\:+\:\mathrm{2}}\mid\:=\:\frac{\pi}{\mathrm{2}},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:{z}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}. \\ $$ Commented by youssoufab last updated…
Question Number 21108 by Tinkutara last updated on 13/Sep/17 $$\mathrm{Let}\:{A},\:{B},\:{C}\:\mathrm{be}\:\mathrm{three}\:\mathrm{sets}\:\mathrm{of}\:\mathrm{complex} \\ $$$$\mathrm{numbers}\:\mathrm{as}\:\mathrm{defined}\:\mathrm{below} \\ $$$${A}\:=\:\left\{{z}\::\:\mathrm{Im}\:{z}\:\geqslant\:\mathrm{1}\right\} \\ $$$${B}\:=\:\left\{{z}\::\:\mid{z}\:−\:\mathrm{2}\:−\:{i}\mid\:=\:\mathrm{3}\right\} \\ $$$${C}\:=\:\left\{{z}\::\:\mathrm{Re}\left(\left(\mathrm{1}\:−\:{i}\right){z}\right)\:=\:\sqrt{\mathrm{2}}\right\}. \\ $$$$\mathrm{Let}\:{z}\:\mathrm{be}\:\mathrm{any}\:\mathrm{point}\:\mathrm{in}\:{A}\:\cap\:{B}\:\cap\:{C}\:\mathrm{and}\:\mathrm{let} \\ $$$${w}\:\mathrm{be}\:\mathrm{any}\:\mathrm{point}\:\mathrm{satisfying}\:\mid{w}\:−\:\mathrm{2}\:−\:{i}\mid\:< \\ $$$$\mathrm{3}.\:\mathrm{Then},\:\mid{z}\mid\:−\:\mid{w}\mid\:+\:\mathrm{3}\:\mathrm{lies}\:\mathrm{between} \\…
Question Number 21107 by marin92 last updated on 13/Sep/17 $$\mathrm{Find}\:\mathrm{out}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{nth}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{y}=\mathrm{e}^{\mathrm{msin}^{−\mathrm{1}} \mathrm{x}\:} \:\mathrm{at}\:\mathrm{x}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86643 by mathmax by abdo last updated on 29/Mar/20 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{ch}\left({x}\right)\right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 86640 by niroj last updated on 29/Mar/20 $$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equations}}: \\ $$$$\:\:\left(\boldsymbol{\mathrm{i}}\right).\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\:\boldsymbol{\mathrm{x}}\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:+\:\boldsymbol{\mathrm{y}}\:=\:\:\boldsymbol{\mathrm{log}}\:\boldsymbol{\mathrm{x}}. \\ $$$$\:\:\left(\boldsymbol{\mathrm{ii}}\right).\:\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)^{\mathrm{2}} \:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\:\mathrm{4}\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:+\:\mathrm{6}\boldsymbol{\mathrm{y}}\:=\:\:\boldsymbol{\mathrm{x}}. \\ $$$$\: \\ $$ Answered…
Question Number 152178 by mathdanisur last updated on 26/Aug/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system} \\ $$$$\begin{cases}{\mathrm{y}\sqrt{\mathrm{x}}\:+\:\mathrm{x}\sqrt{\mathrm{y}}\:=\:\mathrm{x}\:+\:\mathrm{y}}\\{\sqrt{\mathrm{x}}\:+\:\sqrt{\mathrm{y}}\:=\:\mathrm{xy}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{other}\:\mathrm{than} \\ $$$$\mathrm{x}\:=\:\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\mathrm{0} \\ $$ Commented by john_santu last updated on 26/Aug/21…