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Category: Algebra

Let-F-be-Field-of-characteristic-0-L-i-i-1-2-be-two-algebraic-extension-of-F-and-L-1-L-2-be-a-field-in-F-where-F-is-the-algebraic-closure-of-F-defined-by-l-1-l-2-l-i-L-i-i-1-2-

Question Number 214098 by issac last updated on 28/Nov/24 $$\mathrm{Let}\:{F}\:\mathrm{be}\:\:\mathrm{Field}\:\mathrm{of}\:\mathrm{characteristic}\:\mathrm{0} \\ $$$${L}_{{i}} \:\left({i}=\mathrm{1},\mathrm{2}\right)\:\mathrm{be}\:\mathrm{two}\:\mathrm{algebraic}\:\mathrm{extension} \\ $$$$\mathrm{of}\:{F}\:,\:\mathrm{and}\:{L}_{\mathrm{1}} {L}_{\mathrm{2}} \:\mathrm{be}\:\mathrm{a}\:\mathrm{field}\:\mathrm{in}\:\bar {{F}}\: \\ $$$$\left(\mathrm{where}\:\bar {{F}}\:\:\mathrm{is}\:\mathrm{the}\:\mathrm{algebraic}\:\mathrm{closure}\:\:\mathrm{of}\:{F}\right) \\ $$$$\mathrm{defined}\:\mathrm{by}\:\left\{{l}_{\mathrm{1}} {l}_{\mathrm{2}} \mid{l}_{{i}}…

determiner-l-equation-de-la-parabole-represente-par-la-courbe-ci-dessous-avec-y-3-

Question Number 214061 by a.lgnaoui last updated on 25/Nov/24 $$\mathrm{determiner}\:\mathrm{l}\:\mathrm{equation}\:\mathrm{de}\:\mathrm{la}\:\mathrm{parabole} \\ $$$$\mathrm{represente}\:\mathrm{par}\:\mathrm{la}\:\mathrm{courbe}\:\mathrm{ci}−\mathrm{dessous} \\ $$$$\mathrm{avec}\:\boldsymbol{\mathrm{y}}=−\mathrm{3} \\ $$ Commented by a.lgnaoui last updated on 25/Nov/24 Terms of…

Question-214059

Question Number 214059 by RoseAli last updated on 25/Nov/24 Answered by a.lgnaoui last updated on 25/Nov/24 $$\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{5}\right)\:=\mathrm{0}\:\:\:\: \\ $$$$\: \\ $$$$\begin{cases}{\mathrm{x}_{\mathrm{1}} \:\:\:\:=\left\{\frac{\mathrm{10}}{\mathrm{10}}\:\:,\frac{−\mathrm{10}}{−\mathrm{10}}\right\}}\\{\mathrm{x}_{\mathrm{2}} \:\:\:=\left\{\frac{\mathrm{50}}{\mathrm{10}}\:\:\:\:,\frac{−\mathrm{50}}{−\mathrm{10}}\:\:\:\right\}\:\:}\end{cases} \\ $$$$\boldsymbol{\mathrm{S}}=\left\{\frac{−\mathrm{50}}{−\mathrm{10}}\:;\:\:\frac{−\mathrm{10}}{−\mathrm{10}}\:\:;\:\frac{+\mathrm{10}}{+\mathrm{10}}\:;\:\frac{+\mathrm{50}}{+\mathrm{10}}\right\}…

evaluate-0-pi-e-sin-2-u-du-i-use-Feynman-s-trick-to-solve-integral-0-pi-e-sin-2-u-du-I-I-t-0-pi-e-tsin-2-u-du-I-1-t-0-pi-sin-2-u-e-tsin-2-u-du-0-

Question Number 214051 by issac last updated on 25/Nov/24 $$\mathrm{evaluate}\:\int_{\mathrm{0}} ^{\:\pi} \:{e}^{\mathrm{sin}^{\mathrm{2}} \left({u}\right)} \mathrm{d}{u}…\: \\ $$$$\mathrm{i}\:\mathrm{use}\:\mathrm{Feynman}'\mathrm{s}\:\mathrm{trick}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{integral} \\ $$$$\int_{\mathrm{0}} ^{\:\pi} \:{e}^{\mathrm{sin}^{\mathrm{2}} \left({u}\right)} \mathrm{d}{u}={I} \\ $$$${I}\left({t}\right)=\int_{\mathrm{0}} ^{\:\pi}…

Question-214030

Question Number 214030 by RoseAli last updated on 24/Nov/24 Answered by A5T last updated on 24/Nov/24 $${x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}=\mathrm{0} \\ $$$$\Rightarrow\left({x}+\mathrm{1}\right)^{\mathrm{2}} \equiv\mathrm{6}\left({mod}\:\mathrm{10}\right) \\ $$$$\Rightarrow{x}=\mathrm{3},\mathrm{5} \\ $$…

find-all-solutions-of-the-equation-x-2-x-in-each-of-the-rings-Z-2-Z-3-and-Z-6-

Question Number 214001 by RoseAli last updated on 24/Nov/24 $$\mathrm{find}\:\mathrm{all}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} ={x}\:\mathrm{in}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rings}\: \\ $$$${Z}_{\mathrm{2}} \: \\ $$$${Z}_{\mathrm{3}} \\ $$$$\mathrm{and}\:\mathrm{Z}_{\mathrm{6}} \\ $$ Answered by TonyCWX08 last updated…