Question Number 133346 by bramlexs22 last updated on 21/Feb/21 $$\:\mathrm{Find}\:\mathrm{modulus}\:\mathrm{and}\:\mathrm{argumen}\:\mathrm{of}\: \\ $$$$\:\mathrm{z}\:=\:\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{4}} \left(\sqrt{\mathrm{3}}+{i}\right)^{\mathrm{7}} }{\left(\mathrm{1}+{i}\sqrt{\mathrm{2}}\right)^{\mathrm{8}} \left(−\mathrm{1}−{i}\sqrt{\mathrm{3}}\right)^{\mathrm{12}} } \\ $$ Answered by mathmax by abdo last updated…
Question Number 133321 by 777316 last updated on 21/Feb/21 $${Find}\:{x}\:: \\ $$$${sin}\left(\mathrm{3}{x}\right)−{sin}\left(\mathrm{2}{x}\right)−\mathrm{2}{sin}\left({x}\right)\:=\:\sqrt{\mathrm{3}}{cos}\left({x}\right) \\ $$ Commented by bramlexs22 last updated on 21/Feb/21 $$\mathrm{x}=\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$$$\mathrm{sin}\:\left(\mathrm{3}×\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{sin}\:\left(\mathrm{2}×\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{2sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)= \\…
Question Number 2234 by madscientist last updated on 10/Nov/15 $${in}\:{quantum}\:{physics}\:{is}\:{this}\:{a}\:{true}\: \\ $$$${statement}?\:{h}={h}\:{bar} \\ $$$$\frac{{d}}{{dt}}\langle\psi\left({t}\right)\mid\psi\left({t}\right)\rangle=\mathrm{0} \\ $$$$\frac{{d}}{{dt}}\langle\psi\left({t}\right)\mid\psi\left({t}\right)=\int\psi^{\ast} \left({t}\right)\psi\left({t}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\int\frac{{d}\psi^{\ast} }{{dt}}\psi{dx}+\int\psi^{\ast} {H}\psi{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=−\frac{\mathrm{1}}{{ih}}\int\left({H}\psi\right)^{\ast} \psi{dx}+\frac{\mathrm{1}}{{ih}}\int\psi^{\ast} {H}\psi{dx}…
Question Number 67745 by Enock last updated on 31/Aug/19 $${solve}\:{the}\:{system}\:{of}\:{equations\begin{cases}{\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}={y}}\\{\mid{y}−\mathrm{3}\mid=\mathrm{4}{x}−\mathrm{12}}\end{cases}} \\ $$ Answered by Rasheed.Sindhi last updated on 31/Aug/19 $$\begin{cases}{\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}={y}\Rightarrow{y}\geqslant\mathrm{4}}\\{\mid{y}−\mathrm{3}\mid=\mathrm{4}{x}−\mathrm{12}\Rightarrow\mathrm{4}{x}−\mathrm{12}\geqslant\mathrm{1}\Rightarrow{x}\geqslant\frac{\mathrm{13}}{\mathrm{4}}}\end{cases} \\ $$$$\left(\mathrm{i}\right)\rightarrow\left(\mathrm{ii}\right): \\ $$$$\Rightarrow\mid\:\left(\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}\right)−\mathrm{3}\:\mid=\mathrm{4}{x}−\mathrm{12} \\…
Question Number 2191 by lakshaysethi039 last updated on 07/Nov/15 $${Find}\:{the}\:{number}\:{of}\:{quadratic}\:{equations}\:{having}\:{real}\:{roots} \\ $$$${and}\:{which}\:{do}\:{not}\:{change}\:{by}\:{squaring}\:{their}\:{roots}. \\ $$$$ \\ $$ Answered by prakash jain last updated on 07/Nov/15 $$\mathrm{Eq}:\:{ax}^{\mathrm{2}}…
Question Number 133264 by Dwaipayan Shikari last updated on 20/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sinn}}{{n}^{\mathrm{3}} } \\ $$ Commented by Dwaipayan Shikari last updated on 20/Feb/21 $${I}\:{have}\:{found}\:\frac{\mathrm{1}}{\mathrm{12}}−\frac{\pi}{\mathrm{4}}+\frac{\pi^{\mathrm{2}}…
Question Number 2172 by 123456 last updated on 06/Nov/15 $${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\frac{\partial{f}}{\partial{x}}=\frac{\partial{f}}{\partial{y}} \\ $$$${f}\left({x},{y}\right)=?? \\ $$ Answered by prakash jain last updated on 06/Nov/15…
Question Number 67697 by Rasheed.Sindhi last updated on 30/Aug/19 $$\Cup\mathrm{si}\Cap\mathrm{g}\:\mathrm{ChineseRemainderTheorm} \\ $$$$\partial\mathrm{etermine}\:\mathrm{polynomial}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{such}\:\mathrm{that} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{8}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv−\mathrm{24}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{6}\left(\mathrm{mod}\:\mathrm{x}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{2}\right) \\ $$$$ \\…
Question Number 67686 by Rio Michael last updated on 30/Aug/19 $${given}\:{that}\:{the}\:{roots}\:{of}\:{the}\:{equation}\:\:\mathrm{4}{x}^{\mathrm{2}} \:+\:\mathrm{6}{x}\:+\:\mathrm{9}\:=\mathrm{0}\:{are}\:\:\lambda\:{and}\:\delta\:\:{where}\: \\ $$$$\:\lambda\:=\:\left(\mathrm{1}\:+\:\alpha^{\mathrm{2}} \:+\beta^{\mathrm{2}} \right)\:\:{and}\:\:\delta\:=\:\alpha^{\mathrm{3}} \:+\:\beta^{\mathrm{3}} \\ $$$${find}\:{an}\:{equation}\:{whose}\:{roots}\:{are}\: \\ $$$$\:\:\frac{\mathrm{1}}{\alpha\lambda}\:{and}\:\:\frac{\mathrm{1}}{\beta\delta} \\ $$ Commented by…
Question Number 67688 by Rio Michael last updated on 30/Aug/19 $${A}\:{relation}\:\mathbb{R}\:{defined}\:{by}\:\:\:_{\left({x},{y}\right)} {R}_{\left({u},{v}\right)} \:\Leftrightarrow\:\:{v}^{\mathrm{2}} −{y}^{\mathrm{2}} \:=\:{u}^{\mathrm{2}} −{x}^{\mathrm{2}} \\ $$$${show}\:{that}\:{R}\:{is}\:{an}\:{equivalent}\:{Relation}. \\ $$ Commented by Prithwish sen last…