Question Number 98640 by IE last updated on 15/Jun/20 Commented by IE last updated on 15/Jun/20 $$\mathrm{please}\:\mathrm{help}.\:\mathrm{topology} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 98638 by Ar Brandon last updated on 15/Jun/20 $$\mathrm{Le}\:\mathrm{plan}\:\mathrm{complexe}\:\mathrm{est}\:\mathrm{rapport}\acute {\mathrm{e}}\:\grave {\mathrm{a}}\:\mathrm{un}\:\mathrm{rep}\grave {\mathrm{e}re} \\ $$$$\mathrm{orthornorme}\:\mathrm{directe}\:\left(\mathrm{0},\overset{\rightarrow} {\mathrm{e}}_{\mathrm{1}} ,\overset{\rightarrow} {\mathrm{e}}_{\mathrm{2}} \right).\:\mathcal{O}\mathrm{n}\:\mathrm{note}\:\mathrm{A}\:\mathrm{et}\:\mathrm{B}\:\mathrm{les} \\ $$$$\mathrm{points}\:\mathrm{d}'\mathrm{affixes}\:\mathrm{respectives}\:\boldsymbol{\mathrm{i}},\:\mathrm{et}\:\mathrm{2}\boldsymbol{\mathrm{i}}.\:\mathrm{Soit}\:\mathrm{f},\:\mathrm{l}'\mathrm{application} \\ $$$$\mathrm{du}\:\mathrm{plan}\:\mathrm{priv}\acute {\mathrm{e}}\:\mathrm{de}\:\mathrm{A}\:\mathrm{dans}\:\mathrm{lui}-\mathrm{m}\hat…
Question Number 33096 by 7991 last updated on 10/Apr/18 $${z}\:{and}\:{w}\:\in\:\mathbb{C} \\ $$$${proof}\:\mid\mid{z}\mid−\mid{w}\mid\mid\:\leqslant\:\mid{z}−{w}\mid\:{and}\:\mid{z}\mid−\mid{w}\mid\leqslant\:\mid{z}+{w}\mid \\ $$ Answered by MJS last updated on 10/Apr/18 $${z}={x}+{y}\mathrm{i} \\ $$$${w}={u}+{v}\mathrm{i} \\…
Question Number 33095 by 7991 last updated on 10/Apr/18 $${z}={x}+{yi}\:\in\:\mathbb{C} \\ $$$$\overset{−} {{z}}={x}−{y}\:\in\:\mathbb{C} \\ $$$${proof}\:\mid{z}\mid^{\mathrm{2}} =\mid{z}^{\mathrm{2}} \mid={z}\overset{−} {{z}},\:{so}\:{z}\neq\mathrm{0}\:\rightarrow\frac{\mathrm{1}}{{z}}=\frac{\overset{−} {{z}}}{\mid{z}\mid^{\mathrm{2}} } \\ $$ Answered by Rasheed.Sindhi…
Question Number 98620 by MWSuSon last updated on 15/Jun/20 $$\boldsymbol{{how}}\:\boldsymbol{{do}}\:\boldsymbol{{i}}\:\boldsymbol{{make}}\:\boldsymbol{{use}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{function}} \\ $$$$\boldsymbol{{gamma}}\left(\boldsymbol{{n}}\right). \\ $$$$\boldsymbol{{example}},\:\boldsymbol{{gamma}}\left(\boldsymbol{{n}}\right)=\underset{\mathrm{0}} {\overset{\infty} {\int}}\boldsymbol{{x}}^{\boldsymbol{{n}}−\mathrm{1}} \boldsymbol{{e}}^{−\boldsymbol{{x}}} \boldsymbol{{dx}}? \\ $$$$\boldsymbol{{instead}}\:\boldsymbol{{of}}\:\boldsymbol{{typing}}\:\boldsymbol{{gamma}}\left(\boldsymbol{{n}}\right). \\ $$$$\boldsymbol{{i}}\:\boldsymbol{{can}}'\boldsymbol{{t}}\:\boldsymbol{{find}}\:\boldsymbol{{it}}\:\boldsymbol{{in}}\:\boldsymbol{{the}}\:\boldsymbol{{app}}. \\ $$ Answered…
Question Number 33005 by Rio Mike last updated on 09/Apr/18 $$\:{Given}\:{that}\: \\ $$$$\:\:\:{y}=\:\frac{{sin}\:{x}}{\mathrm{1}\:+\:{cos}\:{x}}\:{find}\:\frac{{dy}}{{dx}} \\ $$$${Evaluate}\: \\ $$$$\:\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \left({x}\:+\:\mathrm{4}\right){dx} \\ $$ Commented by abdo imad…
Question Number 33004 by Rio Mike last updated on 09/Apr/18 $${how}\:{do}\:{i}\:{solve}\: \\ $$$$\:\:\:\:{for}\:{x}\: \\ $$$$\left.{a}\right)\:\mathrm{2}^{\mathrm{3}−{x}} +\mathrm{2}^{{x}} =\:\mathrm{6} \\ $$$$\left.{b}\right)\:\left({log}_{\mathrm{3}} {x}\right)^{\mathrm{2}} \:−\:\mathrm{6}\left({log}_{\mathrm{3}} {x}\right)\:+\:\mathrm{9}=\mathrm{0} \\ $$ Commented…
Question Number 98468 by mr W last updated on 14/Jun/20 Commented by mr W last updated on 14/Jun/20 $${he}\:{created}\:{the}\:{most}\:{beautiful}\:{questions}, \\ $$$${he}\:{gave}\:{the}\:{most}\:{ingenious}\:{solutions}, \\ $$$${he}\:{made}\:{the}\:{most}\:{perfect}\:{diagrams}, \\ $$$$…..…
Question Number 98443 by Ar Brandon last updated on 14/Jun/20 $$\mathcal{G}\mathrm{iven}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{U}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{defined}\:\mathrm{by}\:\mathrm{U}_{\mathrm{0}} =\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{U}_{\mathrm{n}+\mathrm{1}} =\mathrm{f}\left(\mathrm{U}_{\mathrm{n}} \right)\:\mathrm{where}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$$$\mathcal{S}\mathrm{how}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\mathrm{0}<\mathrm{U}_{\mathrm{n}} \leqslant\frac{\mathrm{1}}{\mathrm{n}} \\…
Question Number 32869 by Rio Mike last updated on 04/Apr/18 $${A}=\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{1}\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}\:;{h}\:\mathrm{and}\:{k}\:\mathrm{are}\:\mathrm{numbers}\:\mathrm{so} \\ $$$$\mathrm{that}\:\mathrm{A}^{\mathrm{2}} ={hA}\:+\:{kI},\mathrm{where}\:\mathrm{I}=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{h}\:\mathrm{and}\:{k}. \\ $$ Commented by abdo mathsup last updated on…