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Question Number 125760 by snipers237 last updated on 13/Dec/20 $${Let}\:{n}\geqslant\mathrm{1}\:{and}\:{integer},\:{P}_{{n}} \left({X}\right)=\left(\mathrm{1}+{X}\right)^{{n}} −\left(\mathrm{1}−{X}\right)^{{n}} \: \\ $$$$\left.\mathrm{1}\right)\:{Factorize}\:{P}_{{n}} \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:{S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left[\mathrm{4}+{cotan}^{\mathrm{2}} \left(\frac{{k}\pi}{\mathrm{2}{n}+\mathrm{1}}\right)\:\right] \\ $$ Answered by…
Question Number 125758 by ZiYangLee last updated on 13/Dec/20 $$\Delta\mathrm{ABC}\:\mathrm{have}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10}\:\mathrm{13}\:\mathrm{13} \\ $$$$\mathrm{while}\:\Delta\mathrm{PQR}\:\mathrm{have}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{length} \\ $$$$\mathrm{13}\:\mathrm{13}\:\mathrm{24}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{Area}\:\mathrm{of}\:\Delta\mathrm{ABC}\::\:\mathrm{Area} \\ $$$$\mathrm{of}\:\Delta\mathrm{PQR}. \\ $$ Answered by mr W last…
Question Number 60219 by ANTARES VY last updated on 19/May/19 $$\boldsymbol{\mathrm{C}}=\frac{\mathrm{2}\boldsymbol{\pi\varepsilon\varepsilon}_{\mathrm{0}} \boldsymbol{\mathrm{L}}}{\boldsymbol{\mathrm{ln}}\left(\frac{\boldsymbol{\mathrm{R}}_{\mathrm{2}} }{\boldsymbol{\mathrm{R}}_{\mathrm{1}} }\right)}. \\ $$$$\boldsymbol{\mathrm{prove}}. \\ $$ Commented by ANTARES VY last updated on…
Question Number 60212 by peter frank last updated on 18/May/19 Commented by maxmathsup by imad last updated on 19/May/19 $${we}\:{have}\:\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} \:+\mathrm{2}{x}−\mathrm{4}\:=\mathrm{3}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} \:+\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{2}{x}−\mathrm{4}…
Question Number 191283 by Shrinava last updated on 22/Apr/23 Answered by amin96 last updated on 22/Apr/23 $$\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{problem}}\:\boldsymbol{\mathrm{new}}\:\boldsymbol{\mathrm{RMM}}\:\boldsymbol{\mathrm{problem}} \\ $$$$\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{my}}\:\boldsymbol{\mathrm{instagram}}\:\boldsymbol{\mathrm{page}}\: \\ $$$$ \\ $$@mathematics.azerbaijan Terms of…
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Question Number 191276 by Mingma last updated on 22/Apr/23 Answered by mr W last updated on 22/Apr/23 $$\frac{{c}}{{a}}=\frac{{a}+{b}}{{b}−{a}} \\ $$$$\Rightarrow{c}=\frac{{a}\left({a}+{b}\right)}{{b}−{a}} \\ $$ Commented by Mingma…
Question Number 125743 by MathSh last updated on 13/Dec/20 $$\boldsymbol{{x}}\:;\:\boldsymbol{{y}}\:;\:\boldsymbol{{z}}\:\rightarrow\:\boldsymbol{{simple}}\:\boldsymbol{{numbers}}\:, \\ $$$$\boldsymbol{{y}}<\boldsymbol{{x}}<\boldsymbol{{z}}\:, \\ $$$$\boldsymbol{{y}}+\boldsymbol{{x}}+\boldsymbol{{z}}=\mathrm{68}\:, \\ $$$$\boldsymbol{{y}}\:\centerdot\:\boldsymbol{{x}}\:+\:\boldsymbol{{x}}\:\centerdot\:\boldsymbol{{z}}\:+\:\boldsymbol{{z}}\:\centerdot\:\boldsymbol{{y}}\:=\:\mathrm{1121}\:, \\ $$$$\boldsymbol{{y}}\:\centerdot\:\boldsymbol{{x}}\:=\:? \\ $$ Commented by MJS_new last updated…
Question Number 191278 by Mingma last updated on 22/Apr/23 Answered by a.lgnaoui last updated on 23/Apr/23 $$\mathrm{chaque}\:\mathrm{heptagone}\:\mathrm{a}\:\mathrm{7}\:\mathrm{triangles}\:\mathrm{isoceles}\:\mathrm{de}\:\mathrm{somet}\:\mathrm{O} \\ $$$$\mathrm{d}\:\mathrm{angle}\:\boldsymbol{\theta}=\frac{\mathrm{2}\pi}{\mathrm{7}}\:\:\mathrm{de}\:\mathrm{cote}\:\boldsymbol{\mathrm{x}}\:\:\mathrm{avec}\:\:\:\:\boldsymbol{\mathrm{x}}\mathrm{sin}\:\frac{\boldsymbol{\theta}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{xsin}\:\frac{\pi}{\mathrm{7}}=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\mathrm{x}=\frac{\mathrm{1}}{\mathrm{2sin}\:\frac{\pi}{\mathrm{7}}} \\ $$$$\:\mathrm{du}\:\mathrm{rayon}\:\mathrm{du}\:\mathrm{cercle}\:\mathrm{circonscrit}\:\boldsymbol{\mathrm{r}}=\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{s}}=\boldsymbol{\mathrm{y}}.\boldsymbol{\mathrm{x}}\:\:\:;\:\:\:\:\:\:\:\:\left[\:\boldsymbol{\mathrm{y}}^{\mathrm{2}}…