Question Number 99869 by bachamohamed last updated on 23/Jun/20 $$\:\boldsymbol{{tng}}\frac{\boldsymbol{\pi}}{\mathrm{9}}\:\:+\:\mathrm{4}\boldsymbol{{sin}}\frac{\boldsymbol{\pi}}{\mathrm{9}}\:=\sqrt{\mathrm{3}} \\ $$ Answered by smridha last updated on 23/Jun/20 $$\frac{\boldsymbol{{sin}}\left(\frac{\boldsymbol{\pi}}{\mathrm{9}}\right)+\mathrm{2}\boldsymbol{{sin}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\mathrm{9}}\right)}{\boldsymbol{{cos}}\left(\frac{\boldsymbol{\pi}}{\mathrm{9}}\right)}=\frac{\boldsymbol{{sin}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\mathrm{9}}\right)+\boldsymbol{{cos}}\left(\frac{\boldsymbol{\pi}}{\mathrm{18}}\right)}{\boldsymbol{{cos}}\left(\frac{\boldsymbol{\pi}}{\mathrm{9}}\right)}\:\: \\ $$$$=\frac{\boldsymbol{{sin}}\left(\frac{\mathrm{4}\boldsymbol{\pi}}{\mathrm{9}}\right)+\boldsymbol{{sin}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\mathrm{9}}\right)}{\boldsymbol{{cos}}\left(\frac{\boldsymbol{\pi}}{\mathrm{9}}\right)}=\frac{\mathrm{2}.\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}.\boldsymbol{{cos}}\left(\frac{\boldsymbol{\pi}}{\mathrm{9}}\right)}{\boldsymbol{{cos}}\left(\frac{\boldsymbol{\pi}}{\mathrm{9}}\right)}=\sqrt{\mathrm{3}} \\ $$ Answered…
Question Number 165381 by mathlove last updated on 31/Jan/22 Commented by MJS_new last updated on 02/Feb/22 $$\mathrm{we}\:\mathrm{have}\:\mathrm{only}\:\mathrm{one}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{2}\:\mathrm{unknowns} \\ $$$$\Rightarrow\:\mathrm{no}\:\mathrm{unique}\:\mathrm{solution}. \\ $$ Answered by mahdipoor last…
Question Number 99846 by bachamohamed last updated on 23/Jun/20 $$\:\:\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{m}}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}!}\right)^{\left(\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}\right)^{………\left(\frac{\mathrm{1}}{\boldsymbol{{n}}!}−\frac{\mathrm{1}}{\left(\boldsymbol{{n}}+\mathrm{1}\right)!}\right)} } =? \\ $$ Commented by Dwaipayan Shikari last updated on 23/Jun/20 $${Ans}=\mathrm{1} \\…
Question Number 34307 by prof Abdo imad last updated on 03/May/18 $${let}\:{give}\:{A}_{{n}} =\:\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\frac{\alpha}{{n}}}\\{−\frac{\alpha}{{n}}\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} ^{{n}} \:\:\:\:. \\ $$ Commented by math khazana by…
Question Number 34305 by abdo mathsup 649 cc last updated on 03/May/18 $$\left.{let}\right]\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{0}\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\mathrm{1}\:\right. \\ $$$$\left.\mathrm{1}\right){find}\:{the}\:{caractetistic}\:{polynom}\:{of}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{A}^{{n}} \\ $$ Commented by prof Abdo…
Question Number 165375 by mathlove last updated on 31/Jan/22 Answered by Rasheed.Sindhi last updated on 31/Jan/22 $$\underset{−} {{a}+{b}+{c}=\mathrm{7}\:\wedge\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{9}\:\wedge\:{abc}=\mathrm{5}\:\:\:\:} \\ $$$$\left({a}+{b}+{c}\right)^{\mathrm{2}} =\left(\mathrm{7}\right)^{\mathrm{2}} \\…
Question Number 165364 by mathlove last updated on 31/Jan/22 Answered by Ar Brandon last updated on 31/Jan/22 $${S}=\frac{\mathrm{1}}{\mathrm{1}+{e}^{−\mathrm{99}} }+\frac{\mathrm{1}}{\mathrm{1}+{e}^{−\mathrm{98}} }+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{1}+{e}^{\mathrm{98}} }+\frac{\mathrm{1}}{\mathrm{1}+{e}^{\mathrm{99}} } \\ $$$$\:\:\:\:=\frac{{e}^{\mathrm{99}} }{\mathrm{1}+{e}^{\mathrm{99}}…
Question Number 99827 by MWSuSon last updated on 23/Jun/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{days}\:\mathrm{after}\:\mathrm{12}/\mathrm{7}/\mathrm{1941} \\ $$$$\left(\mathrm{pearl}\:\mathrm{harbour}\:\mathrm{bombed}\right)\:\mathrm{was}\:\mathrm{9}/\mathrm{11}/\mathrm{2001} \\ $$$$\left(\mathrm{the}\:\mathrm{september}\:\mathrm{11}\:\mathrm{terrorist}\:\mathrm{attack}?\right. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help},\:\mathrm{i}'\mathrm{m}\:\mathrm{having}\:\mathrm{27175days},\: \\ $$$$\mathrm{which}\:\mathrm{apparently}\:\mathrm{isn}'\mathrm{t}\:\mathrm{correct}. \\ $$ Terms of Service…
Question Number 165362 by HongKing last updated on 31/Jan/22 Answered by aleks041103 last updated on 01/Feb/22 $${if}\:{gcd}\left({a},{b}\right)=\mathrm{1}\:{and}\:{b}>{a},\:{then}: \\ $$$${for}\:\forall{r}=\mathrm{0},\mathrm{1},\mathrm{2},…,{b}−\mathrm{1},\:\exists{k}\in\mathbb{N}\:{such}\:{that} \\ $$$${ka}\equiv{r}\left({mod}\:{b}\right). \\ $$$$ \\ $$$${In}\:{our}\:{case},\:{gcd}\left(\mathrm{19},\mathrm{360}\right)=\mathrm{1}…
Question Number 165355 by Ari last updated on 31/Jan/22 Answered by Ar Brandon last updated on 31/Jan/22 $$\begin{cases}{{x}+{y}−{z}=\mathrm{170}}\\{{z}+{y}−{x}=\mathrm{130}}\end{cases}\:\:\Rightarrow\mathrm{2}{y}=\mathrm{300}\Rightarrow{y}=\mathrm{150} \\ $$ Terms of Service Privacy Policy…