Question Number 199771 by Rupesh123 last updated on 09/Nov/23 Answered by AST last updated on 09/Nov/23 $$\frac{{sin}\left(\mathrm{4}{x}\right)=\mathrm{2}{sin}\left(\mathrm{2}{x}\right){cos}\left(\mathrm{2}{x}\right)}{{a}}=\frac{{sin}\left(\mathrm{2}{x}\right)}{{b}} \\ $$$$\Rightarrow{cos}\left(\mathrm{2}{x}\right)=\frac{{a}}{\mathrm{2}{b}}=\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}\Rightarrow{cos}^{\mathrm{2}} {x}=\frac{{a}+\mathrm{2}{b}}{\mathrm{4}{b}} \\ $$$$\frac{{sin}\left(\mathrm{2}{x}\right)=\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right)}{{b}}=\frac{{sin}\left({x}\right)}{{c}}\Rightarrow{cos}\left({x}\right)=\frac{{b}}{\mathrm{2}{c}} \\ $$$$\Rightarrow\frac{{a}+\mathrm{2}{b}}{{b}}=\frac{{b}^{\mathrm{2}}…
Question Number 199766 by cortano12 last updated on 09/Nov/23 Answered by mr W last updated on 09/Nov/23 Commented by mr W last updated on 09/Nov/23…
Question Number 199821 by a.lgnaoui last updated on 09/Nov/23 $$\mathrm{ABFE}\:\:\mathrm{Care} \\ $$$$\mathrm{determiner}\:\boldsymbol{\mathrm{x}}\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\mathrm{a}\:\mathrm{etb} \\ $$$$\mathrm{BC}=\boldsymbol{\mathrm{a}}\:\:\:\:\:\:\mathrm{DE}=\:\boldsymbol{\mathrm{b}} \\ $$ Commented by a.lgnaoui last updated on 09/Nov/23 Commented by…
Question Number 199817 by ajfour last updated on 09/Nov/23 Answered by ajfour last updated on 09/Nov/23 $$\left\{{a}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \theta\right)−\frac{\mathrm{sin}\:\theta}{\mathrm{2}\left(\mathrm{1}+\mathrm{sin}\:\theta\right)}\right\}^{\mathrm{2}} \\ $$$$\:\:\:={a}\left\{{a}+\frac{\mathrm{sin}\:\theta}{\mathrm{2cos}\:\theta\left(\mathrm{1}+\mathrm{sin}\:\theta\right)}\right\} \\ $$$${b}=\frac{\mathrm{sin}\:\theta}{\mathrm{2cos}\:\theta\left(\mathrm{1}+\mathrm{sin}\:\theta\right)} \\ $$…
Question Number 199781 by cortano12 last updated on 09/Nov/23 $$\:\:\: \\ $$ Answered by qaz last updated on 09/Nov/23 $${f}\left({x}\right)=\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{2}{x}\right)}{{x}\left(\mathrm{1}−{x}\right)}−{f}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right) \\ $$$$=\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{2}{x}\right)}{{x}\left(\mathrm{1}−{x}\right)}−\left(\frac{\mathrm{2}\left(\mathrm{1}−\frac{\mathrm{2}}{\mathrm{1}−{x}}\right)}{\frac{\mathrm{1}}{\mathrm{1}−{x}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)}−{f}\left(\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−{x}}}\right)\right) \\ $$$$=\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{2}{x}\right)}{{x}\left(\mathrm{1}−{x}\right)}−\frac{\mathrm{2}\left(\mathrm{1}+{x}\right)\left(\mathrm{1}−{x}\right)}{{x}}+{f}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right) \\…
Question Number 199783 by majidghafari66 last updated on 09/Nov/23 $$\int{xdx}=? \\ $$ Answered by mathfreak01 last updated on 09/Nov/23 $$\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:+{C} \\ $$ Terms of…
Question Number 199708 by tri26112004 last updated on 08/Nov/23 $${n}^{\mathrm{20}} +\mathrm{11}^{{n}} =\mathrm{2023}\:\left({n}\in{N}\right) \\ $$$${n}=¿ \\ $$ Commented by Rasheed.Sindhi last updated on 08/Nov/23 $${f}\left({n}\right)={n}^{\mathrm{20}} +\mathrm{11}^{{n}}…
Question Number 199709 by tri26112004 last updated on 08/Nov/23 $${u}_{\mathrm{1}} \:=\:\mathrm{2}\: \\ $$$${u}_{{n}+\mathrm{1}} \:=\:\mathrm{3}{u}_{{n}} \:+\:\mathrm{2} \\ $$$${u}_{{n}} \:\rightarrow\:{n}\:¿ \\ $$ Answered by mr W last…
Question Number 199711 by Mingma last updated on 08/Nov/23 Answered by mr W last updated on 08/Nov/23 Commented by mr W last updated on 08/Nov/23…
Question Number 199736 by MathedUp last updated on 08/Nov/23 $$\int\int_{\:\boldsymbol{\mathcal{S}}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\mathrm{d}\hat {\boldsymbol{\mathrm{S}}} \\ $$$$\hat {\boldsymbol{\mathrm{F}}}=−{yz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −{xz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xy}\boldsymbol{\mathrm{e}}_{\mathrm{3}} \: \\ $$$$\hat {\boldsymbol{\mathrm{S}}};\:\begin{pmatrix}{\hat {{x}}}\\{\hat…