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…
Question Number 203919 by Samuel12 last updated on 02/Feb/24 $$\:\: \\ $$ Answered by Mathspace last updated on 02/Feb/24 $$\mathrm{1}={e}^{\mathrm{2}{ik}\pi} \:\:{let}\:{z}={re}^{{i}\theta} \\ $$$${z}^{\mathrm{5}} =\mathrm{1}\:\Leftrightarrow{r}^{\mathrm{5}} {e}^{{i}\mathrm{5}\theta}…
Question Number 203891 by York12 last updated on 02/Feb/24 $$ \\ $$ Answered by sniper237 last updated on 01/Feb/24 $${The}\:{last}\:{factor}\:{should}\:{be}\:\left(\frac{{c}}{{a}+{b}}+\frac{{a}}{{b}+{c}}\right) \\ $$$${If}\:\:{so}\:,\:{Let}\:{named}\:{P}\:{that}\:{product} \\ $$$${Divide}\:{each}\:{factor}\:{by}\:{c},{a},{b}\:{resp} \\…
Question Number 203881 by mr W last updated on 31/Jan/24 Commented by mr W last updated on 31/Jan/24 $${find}\:{the}\:{hatched}\:{area}\:{between}\:{curve} \\ $$$${and}\:{its}\:{tangent}\:{line}. \\ $$ Answered by…
Question Number 203846 by York12 last updated on 30/Jan/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{i}=\mathrm{2}} {\overset{{n}} {\prod}}\left(\frac{{i}^{\mathrm{2}} −\mathrm{1}}{{i}^{\mathrm{2}} }\right) \\ $$ Answered by MM42 last updated on 30/Jan/24 $${p}_{{n}}…