Question Number 204055 by hardmath last updated on 05/Feb/24 $$\mathrm{y}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{arctg}\:\left(\mathrm{x}^{\mathrm{4}} \right) \\ $$$$\mathrm{find}:\:\:\mathrm{y}^{'} \:=\:? \\ $$ Answered by AST last updated on 05/Feb/24 $${y}^{'} =\frac{\mathrm{2}}{\mathrm{3}}\left[\frac{{d}}{{dx}}{tan}^{−\mathrm{1}}…
Question Number 204082 by depressiveshrek last updated on 05/Feb/24 $$\sqrt{\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }+{x}}{{x}}}−\sqrt{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }−{x}^{\mathrm{2}} }=\mathrm{5} \\ $$ Commented by Frix last updated on 05/Feb/24 $${x}=\frac{\mathrm{6}}{\:\sqrt{\mathrm{119}}}…
Question Number 204041 by hardmath last updated on 04/Feb/24 $$\mathrm{Find}:\:\:\:\begin{vmatrix}{\mathrm{1}}&{\mathrm{7}}&{−\mathrm{1}}\\{\mathrm{9}}&{−\mathrm{3}}&{\mathrm{5}}\\{−\mathrm{1}}&{\mathrm{5}}&{\mathrm{3}}\end{vmatrix}=\:? \\ $$ Answered by AST last updated on 04/Feb/24 $$=\mathrm{1}\begin{vmatrix}{−\mathrm{3}}&{\mathrm{5}}\\{\mathrm{5}}&{\mathrm{3}}\end{vmatrix}−\mathrm{7}\begin{vmatrix}{\mathrm{9}}&{\mathrm{5}}\\{−\mathrm{1}}&{\mathrm{3}}\end{vmatrix}−\mathrm{1}\begin{vmatrix}{\mathrm{9}}&{−\mathrm{3}}\\{−\mathrm{1}}&{\mathrm{5}}\end{vmatrix} \\ $$$$=−\mathrm{9}−\mathrm{25}−\mathrm{7}\left(\mathrm{27}+\mathrm{5}\right)−\mathrm{1}\left(\mathrm{45}−\mathrm{3}\right)=−\mathrm{300} \\ $$ Answered…
Question Number 204039 by hardmath last updated on 04/Feb/24 $$\begin{vmatrix}{\mathrm{1}}&{\mathrm{7}}&{−\mathrm{1}}\\{\mathrm{9}}&{−\mathrm{3}}&{\boldsymbol{\mathrm{x}}}\\{−\mathrm{1}}&{\mathrm{5}}&{\mathrm{3}}\end{vmatrix}=\:\mathrm{0}\:\:\:\Rightarrow\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by AST last updated on 04/Feb/24 $$\mathrm{1}\left(−\mathrm{9}−\mathrm{5}{x}\right)−\mathrm{7}\left(\mathrm{27}+{x}\right)−\mathrm{1}\left(\mathrm{45}−\mathrm{3}\right)=\mathrm{0} \\ $$$$\Rightarrow−\mathrm{9}−\mathrm{5}{x}−\mathrm{189}−\mathrm{7}{x}−\mathrm{42}=\mathrm{0}\Rightarrow\mathrm{12}{x}=−\mathrm{240} \\ $$$$\Rightarrow{x}=−\mathrm{20} \\…
Question Number 204038 by hardmath last updated on 04/Feb/24 $$\mathrm{y}\:=\:\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}\right)\:\centerdot\:\mathrm{3}^{\boldsymbol{\mathrm{x}}} \\ $$$$\Rightarrow\:\mathrm{y}^{'} \:=\:? \\ $$ Answered by AST last updated on 04/Feb/24 $${y}^{'} =\mathrm{3}^{{x}+\mathrm{1}}…
Question Number 204018 by mnjuly1970 last updated on 04/Feb/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:{Aut}\:\left(\mathbb{Z}\:\right)=\:? \\ $$$$\:\:\:\:\:\:\:{where}\:,\:{Aut}\:\left({G}\:\right)=\:\left\{\:{f}\:\mid\:{f}\::{G}\:\underset{{G}\:{is}\:{a}\:{group}} {\overset{{f}\:{is}\:{a}\:{isomorphism}} {\rightarrow}}\:{G}\right\} \\ $$ Answered by witcher3 last updated on 04/Feb/24…
Question Number 204019 by mnjuly1970 last updated on 04/Feb/24 $$ \\ $$$$\:\:\:\:\:{G}\:{is}\:{a}\:{group}\:: \\ $$$$\:\:\:\:\:{prove}\:{that}\::\:\:\frac{{G}}{{Z}\:\left({G}\:\right)}\:\cong\:{Inn}\left({G}\:\right) \\ $$$$\:\:\:\:{Where}\:,\:{Inn}\left({G}\right)=\:\left\{{f}\:\mid\:{f}:\:{G}\:\overset{{f}\:{is}\:{an}\:{Automorphism}} {\rightarrow}\:{G}\right\} \\ $$$$ \\ $$ Commented by mokys last…
Question Number 203995 by 0977460907 last updated on 03/Feb/24 $$\mathrm{3}{x}+\mathrm{4}{x}=\mathrm{5} \\ $$ Answered by SonGoku last updated on 03/Feb/24 $$\: \\ $$$${x}\left(\mathrm{3}+\mathrm{4}\right)=\mathrm{5} \\ $$$${x}\left(\mathrm{7}\right)=\mathrm{5} \\…
Question Number 204005 by hardmath last updated on 03/Feb/24 $$\mathrm{Find}: \\ $$$$\mathrm{cos44}°\:−\:\mathrm{cos84}°\:+\:\mathrm{ctg45}°\:=\:? \\ $$ Commented by Frix last updated on 04/Feb/24 $$\mathrm{We}\:\mathrm{cannot}\:\mathrm{get}\:\mathrm{an}\:\mathrm{expression}\:\mathrm{for}\:\mathrm{cos}\:\mathrm{44}°. \\ $$ Answered…
Question Number 203975 by witcher3 last updated on 03/Feb/24 $$\mathrm{Let}\:\mathrm{P}\in\mathbb{C}\left[\mathrm{X}\right] \\ $$$$\mathrm{p}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{p}^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{1} \\ $$$$\mathrm{p}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\mathrm{determin}\:\mathrm{all}\:\mathrm{polynom}\: \\ $$ Commented by Rasheed.Sindhi last updated…