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Please-how-did-z-a-r-became-z-a-re-i-

Question Number 195848 by pete last updated on 11/Aug/23 $$\mathrm{Please}\:\mathrm{how}\:\mathrm{did}\:\mid\mathrm{z}−\mathrm{a}\mid=\mathrm{r}\:\mathrm{became}\: \\ $$$$\mathrm{z}=\:\mathrm{a}\:+\:\mathrm{re}^{\mathrm{i}\theta} ? \\ $$ Answered by Frix last updated on 11/Aug/23 $$\mid{z}−{a}\mid={r}\:\Rightarrow\:{z}−{a}={r}\mathrm{e}^{\mathrm{i}\theta} \\ $$$$\mathrm{This}\:\mathrm{step}\:\mathrm{is}\:\mathrm{always}\:\mathrm{true},\:\mathrm{even}\:\mathrm{for}\:{z}−{a}\in\mathbb{R}…

3-12-1-3-3-1-3-x-1-3-y-1-3-z-1-3-x-y-z-N-x-y-z-mr-W-please-help-me-and-other-my-friends-please-help-me-

Question Number 195813 by jabarsing last updated on 11/Aug/23 $$\begin{cases}{\mathrm{3}\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{12}}−\sqrt[{\mathrm{3}}]{\mathrm{3}}}\:\:=\:\sqrt[{\mathrm{3}}]{{x}}\:+\:\sqrt[{\mathrm{3}}]{{y}}\:−\sqrt[{\mathrm{3}}]{{z}}}\\{{x},{y},{z}\:\in\:{N}}\end{cases}\:\Rightarrow\:{x},{y},{z}\:=? \\ $$$${mr}.{W}\:{please}\:{help}\:{me} \\ $$$${and}\:{other}\:{my}\:{friends}\:{please}\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

1-0-pi-2-x-2-sin-2-x-dx-1-2-2-0-pi-2-x-tan-x-

Question Number 195846 by mnjuly1970 last updated on 11/Aug/23 $$ \\ $$$$\:\:\:\:\:\:\begin{cases}{\:\:\:\Omega_{\mathrm{1}} \:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{x}^{\:\mathrm{2}} }{{sin}^{\:\mathrm{2}} \left({x}\right)}\:{dx}\:}\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\frac{\Omega_{\mathrm{1}} }{\Omega_{\:\mathrm{2}} }\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\\{\:\:\Omega_{\:\mathrm{2}} =\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{x}}{{tan}\left({x}\right)}\:{dx}}\end{cases} \\ $$$$ \\…

Question-195772

Question Number 195772 by dimentri last updated on 10/Aug/23 $$\:\:\:\:\cancel{\underline{\underbrace{ }}}\:\cancel{ } \\ $$ Answered by MM42 last updated on 10/Aug/23 $${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{3}}} \:\:\frac{{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}\:−\mathrm{2}{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}×{sin}\frac{\mathrm{3}{x}}{\mathrm{2}}}{\mathrm{4}{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}{sin}\frac{\mathrm{3}{x}}{\mathrm{2}}{cos}\mathrm{3}{x}} \\ $$$$={lim}_{{x}\rightarrow\frac{\pi}{\mathrm{3}}}…