Question Number 159480 by ZiYangLee last updated on 17/Nov/21 Commented by bobhans last updated on 18/Nov/21 $$\:\begin{cases}{\mathrm{z}=\mathrm{cos}\:\theta\:+\mathrm{i}\:\mathrm{sin}\:\theta}\\{\frac{\mathrm{1}}{\mathrm{z}}=\mathrm{cos}\:\theta−\mathrm{i}\:\mathrm{sin}\:\theta}\end{cases}\:;\:\begin{cases}{\mathrm{z}^{\mathrm{6}} =\mathrm{cos}\:\mathrm{6}\theta+\mathrm{i}\:\mathrm{sin}\:\mathrm{6}\theta}\\{\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{6}} }=\mathrm{cos}\:\mathrm{6}\theta−\mathrm{i}\:\mathrm{sin}\:\mathrm{6}\theta}\end{cases} \\ $$$$\:\mathrm{z}^{\mathrm{6}} +\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{6}} }\:=\:\mathrm{2cos}\:\mathrm{6}\theta \\ $$$$\Rightarrow\left(\mathrm{z}^{\mathrm{3}}…
Question Number 159469 by 0731619 last updated on 17/Nov/21 Commented by cortano last updated on 17/Nov/21 $$\:\sqrt{{x}}\:=\:{u}\:{and}\:\sqrt{{y}}\:=\:{v}\: \\ $$$$\:\begin{cases}{{u}^{\mathrm{3}} +{v}^{\mathrm{3}} \:=\:\mathrm{35}}\\{{u}^{\mathrm{2}} \:{v}+\:{uv}^{\mathrm{2}} \:=\:\mathrm{30}}\end{cases} \\ $$$$\:\begin{cases}{{u}^{\mathrm{3}}…
Question Number 159433 by joki last updated on 17/Nov/21 $$\frac{\mathrm{5x}^{\mathrm{2}} −\mathrm{15x}−\mathrm{11}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} }\:\mathrm{fractio}\:\mathrm{partil} \\ $$$$ \\ $$ Commented by cortano last updated on 17/Nov/21 $$\:\frac{\mathrm{5}{x}^{\mathrm{2}} −\mathrm{15}{x}−\mathrm{11}}{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{2}\right)^{\mathrm{2}}…
Question Number 159428 by mkam last updated on 16/Nov/21 $$\frac{{dy}}{{dx}}={cos}\left({x}+{y}\right)+{sin}\left({x}+{y}\right) \\ $$ Answered by mr W last updated on 16/Nov/21 $${let}\:{u}={x}+{y} \\ $$$$\frac{{du}}{{dx}}=\mathrm{1}+\frac{{dy}}{{dx}} \\ $$$$\frac{{du}}{{dx}}−\mathrm{1}=\mathrm{cos}\:{u}+\mathrm{sin}\:{u}=\sqrt{\mathrm{2}}\mathrm{sin}\:\left({u}+\frac{\pi}{\mathrm{4}}\right)…
Question Number 159431 by ghakhan88 last updated on 16/Nov/21 Answered by mr W last updated on 17/Nov/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\int_{\mathrm{0}} ^{{x}} \frac{{t}^{\mu−\mathrm{1}} }{{x}^{\mu} }{u}\left({t}\right){dt} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 93843 by naka3546 last updated on 15/May/20 $${Use}\:\:{Horner}\:\:{to}\:\:{solve}\:{it}\:. \\ $$$$\:\:\left({a}^{\mathrm{2}} −\mathrm{5}{ab}−\mathrm{3}{b}^{\mathrm{2}} \right)\::\:\left({a}−{b}\right) \\ $$$${find}\:\:{the}\:\:{remainder}\:\:. \\ $$ Answered by i jagooll last updated on…
Question Number 93836 by oustmuchiya@gmail.com last updated on 15/May/20 $${If}\:{cos}\alpha+{cos}\beta+{cos}\gamma=\mathrm{0}\:=\:{sin}\alpha+{sin}\beta+{sin}\gamma,\:{prove}\:{that} \\ $$$$\left(\mathrm{i}\right)\:{cos}\mathrm{3}\alpha+{cos}\mathrm{3}\beta+{cos}\gamma\:=\:\mathrm{3}{cos}\left({a}+\beta+\gamma\right) \\ $$$$\left(\mathrm{ii}\right)\:{sin}\mathrm{3}\alpha+{sin}\mathrm{3}\beta+{sin}\gamma\:=\:\mathrm{3}{sin}\left(\alpha+\beta+\gamma\right) \\ $$$$\left(\mathrm{iii}\right)\:{cos}\mathrm{2}\alpha+{cos}\mathrm{2}\beta+{cos}\mathrm{2}\gamma\:=\:\mathrm{0} \\ $$$$\left(\mathrm{iv}\right)\:{sin}\mathrm{2}\alpha+{sin}\mathrm{2}\beta+{sin}\mathrm{2}\gamma\:=\:\mathrm{0} \\ $$$$\left(\mathrm{Hints}:\:\mathrm{T}{ake}\:{a}=\mathrm{cis}\:\alpha,\:\mathrm{b}=\mathrm{cis}\:\beta,\:\mathrm{c}=\mathrm{cis}\:\gamma,\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{0}\:\Rightarrow\:\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} =\mathrm{3abc}\right. \\ $$$$\left.\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}+\frac{\mathrm{1}}{\mathrm{c}}=\mathrm{0}\:\Rightarrow\:\mathrm{a}^{\mathrm{2}}…
Question Number 93827 by oustmuchiya@gmail.com last updated on 15/May/20 $${simplify}:\:\frac{\left({cos}\alpha+\boldsymbol{\mathrm{i}}{sin}\alpha\right)^{\mathrm{3}} }{\left({sin}\beta+\boldsymbol{\mathrm{i}}{cos}\beta\right)^{\mathrm{4}} } \\ $$ Commented by PRITHWISH SEN 2 last updated on 15/May/20 $$\frac{\mathrm{e}^{\boldsymbol{\mathrm{i}}\mathrm{3}\boldsymbol{\alpha}} }{\mathrm{e}^{\boldsymbol{\mathrm{i}}\mathrm{4}\left(\frac{\pi}{\mathrm{2}}−\beta\right)}…
Question Number 28293 by mondodotto@gmail.com last updated on 23/Jan/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159358 by ZiYangLee last updated on 16/Nov/21 $$\mathrm{List}\:\mathrm{all}\:\mathrm{the}\:\mathrm{assymptotes}. \\ $$$$\mathrm{List}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{and}\:\mathrm{the}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{intercepts} \\ $$$$\mathrm{of}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)=\:\frac{{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{x}−\mathrm{4}}{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}} \\ $$ Terms of Service Privacy…