Question Number 107617 by mathdave last updated on 11/Aug/20 Answered by Ar Brandon last updated on 11/Aug/20 $$\mathrm{I}=\int\mathrm{sec}^{\mathrm{3}} \mathrm{xtan}^{\mathrm{3}} \mathrm{xdx} \\ $$$$\:\:=\int\mathrm{sec}^{\mathrm{2}} \mathrm{x}\left(\mathrm{sec}^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)\mathrm{secxtanxdx} \\…
Question Number 107609 by mathdave last updated on 11/Aug/20 Answered by mr W last updated on 11/Aug/20 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}+\mathrm{4}} \\ $$$$=\underset{{k}=\mathrm{5}} {\overset{{n}+\mathrm{4}} {\sum}}\frac{\mathrm{1}}{{k}} \\…
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Question Number 107589 by mathdave last updated on 11/Aug/20 Answered by Ar Brandon last updated on 11/Aug/20 $$\mathcal{I}=\int\left(\frac{\mathrm{x}+\mathrm{6}}{\mathrm{x}+\mathrm{8}}\right)^{\mathrm{6}} \mathrm{dx}=\int\left(\mathrm{1}−\frac{\mathrm{2}}{\mathrm{x}+\mathrm{8}}\right)^{\mathrm{6}} \mathrm{dx} \\ $$$$\:\:\:=\int\left\{\mathrm{1}−\frac{\mathrm{12}}{\mathrm{x}+\mathrm{8}}+\frac{\mathrm{60}}{\left(\mathrm{x}+\mathrm{8}\right)^{\mathrm{2}} }−\frac{\mathrm{160}}{\left(\mathrm{x}+\mathrm{8}\right)^{\mathrm{3}} }+\frac{\mathrm{240}}{\left(\mathrm{x}+\mathrm{8}\right)^{\mathrm{4}} }−\frac{\mathrm{192}}{\left(\mathrm{x}+\mathrm{8}\right)^{\mathrm{5}}…
Question Number 173116 by ali009 last updated on 06/Jul/22 $${let}\:{w}={e}^{{i}\pi/\mathrm{4}} =\left(\mathrm{1}+{i}\right)/\sqrt{\mathrm{2}\:}\:{show}\:{that}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{i}}{erf}\left({wx}\sqrt{\frac{\pi}{\mathrm{2}}}\right)=\int_{\mathrm{0}} ^{{x}} {e}^{−{i}\:{t}^{\mathrm{2}} \:\pi/\mathrm{2}} \:{dt}={c}\left({x}\right)−{is}\left({x}\right) \\ $$ Commented by ali009 last updated on…
Question Number 107586 by Tinku Tara last updated on 11/Aug/20 $$\mathrm{App}\:\mathrm{Updates}:\:\mathrm{v2}.\mathrm{135} \\ $$$$\bullet\:\mathrm{fix}\:\mathrm{for}\:\mathrm{background}\:\mathrm{color}\:\mathrm{problems} \\ $$$$\bullet\:\mathrm{new}\:\mathrm{drawing}\:\mathrm{tools}\:\mathrm{added}\:\mathrm{in} \\ $$$$\:\:\:\mathrm{build}\:\mathrm{and}\:\mathrm{edit}\:\mathrm{menu} \\ $$$$\:\:\:\mathrm{add}\:\mathrm{equality}\:\mathrm{marker}\:\mathrm{to}\:\mathrm{line}\:\mathrm{etc} \\ $$$$\bullet\:\mathrm{A}\:\mathrm{new}\:\mathrm{drawling}\:\mathrm{tool}\:\mathrm{to}\:\mathrm{draw} \\ $$$$\:\:\:\:\mathrm{smooth}\:\mathrm{curves}. \\ $$…
Question Number 107571 by ZiYangLee last updated on 11/Aug/20 $${G}\mathrm{iven}\:\mathrm{0}<\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}},\:\mathrm{0}<\mathrm{y}\leqslant\frac{\pi}{\mathrm{2}}, \\ $$$$\mathrm{Let}\:{z}_{\mathrm{1}} =\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{y}}+\frac{\mathrm{cos}\:{y}}{\mathrm{sin}\:{x}}\:{i}\:,\mathrm{and}\:\mid{z}_{\mathrm{1}} \mid=\mathrm{2}\:; \\ $$$$\mathrm{If}\:{z}_{\mathrm{2}} =\sqrt{{x}}+\sqrt{{y}\:}{i}\:,\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mid{z}_{\mathrm{1}} −{z}_{\mathrm{2}} \mid. \\ $$ Terms of…
Question Number 42029 by jasno91 last updated on 17/Aug/18 Answered by MJS last updated on 17/Aug/18 $$\mathrm{6}\:\mathrm{persons}\:\mathrm{pay}\:\mathrm{1800}\:\mathrm{for}\:\mathrm{the}\:\mathrm{rail} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{taxi}\:\mathrm{isn}'\mathrm{t}\:\mathrm{cheaper}\:\mathrm{for}\:\mathrm{6}\:\mathrm{than}\:\mathrm{for}\:\mathrm{8}\:\mathrm{persons} \\ $$$$\mathrm{they}\:\mathrm{pay}\:\mathrm{2400}\:\mathrm{for}\:\mathrm{the}\:\mathrm{taxi} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{taxi}\:\mathrm{is}\:\frac{\mathrm{12}}{\mathrm{8}}×\mathrm{6}=\mathrm{9}\:\mathrm{for}\:\mathrm{6}\:\mathrm{persons}\:\mathrm{they}\:\mathrm{pay} \\ $$$$\mathrm{1800}\:\mathrm{for}\:\mathrm{the}\:\mathrm{taxi}…
Question Number 42007 by jasno91 last updated on 16/Aug/18 Answered by MJS last updated on 16/Aug/18 $$\mathrm{lcm}\left(\mathrm{3}{x},\:\mathrm{4}{x}\right)=\mathrm{12}{x}=\mathrm{180} \\ $$$${x}=\frac{\mathrm{180}}{\mathrm{12}}=\mathrm{15} \\ $$$$\mathrm{3}{x}=\mathrm{45}=\mathrm{3}^{\mathrm{2}} \mathrm{5}^{\mathrm{1}} \\ $$$$\mathrm{4}{x}=\mathrm{60}=\mathrm{2}^{\mathrm{2}} \mathrm{3}^{\mathrm{1}}…
Question Number 173061 by mathocean1 last updated on 06/Jul/22 $${Calculate}\:{and}\:{factorize}\:{for}\:{m}\:\in\:\mathbb{R},\: \\ $$$${The}\:{caracteristic}\:{polynom}\:{of} \\ $$$${A}=\begin{pmatrix}{−\mathrm{2}−{m}}&{\:\:\:\mathrm{5}+{m}}&{\:\:\:\:\:{m}}\\{\:\:\:\:\:\:\:\:\mathrm{5}}&{−\mathrm{2}−{m}}&{\:\:−{m}}\\{\:\:\:\:−\mathrm{5}}&{\:\:\:\:\:\:\mathrm{5}}&{\:\:\:\:\:\:\mathrm{3}}\end{pmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com