Question Number 204640 by liuxinnan last updated on 24/Feb/24 $${f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{a}}}+\sqrt{\frac{{ax}}{{ax}+\mathrm{8}}} \\ $$$${a}>\mathrm{0}\:{x}>\mathrm{0} \\ $$$${prove}\:\mathrm{1}<{f}\left({x}\right)<\mathrm{2} \\ $$ Answered by lepuissantcedricjunior last updated on 26/Feb/24 $$\boldsymbol{{x}}>\mathrm{0}\:\boldsymbol{{a}}>\mathrm{0} \\…
Question Number 204657 by es last updated on 24/Feb/24 $${Consider}\:{point}\:{A}\:{inside}\:{a}\:{triangle} \\ $$$${with}\:{sides}\:\mathrm{3},\mathrm{4}\:{and}\:\mathrm{5}.\:{if}\:{d}\:\:{is}\:{the}\:{sum} \\ $$$$\:{of}\:{the}\:{distances}\:\:{of}\:{this}\:{point}\:{from} \\ $$$${the}\:{sides}.{what}\:{is}\:{the}\:{smallest} \\ $$$${value}\:{of}\:{d}? \\ $$$$ \\ $$ Answered by mr…
Question Number 204603 by liuxinnan last updated on 23/Feb/24 Commented by TonyCWX08 last updated on 23/Feb/24 $${Please}\:{use}\:{the}\:{latex}\:{form}. \\ $$$${I}\:{don}'{t}\:{understand}\:{what}\:{you}'{re}\:{trying}\:{to}\:{express}… \\ $$ Commented by liuxinnan last…
Question Number 204618 by es last updated on 23/Feb/24 $${if}\:\:\mathrm{7}{x}=\frac{\pi}{\mathrm{2}}\rightarrow\frac{{cosxsin}\mathrm{2}{xtan}\mathrm{3}{x}}{{cot}\mathrm{4}{xcos}\mathrm{5}{xsin}\mathrm{6}{x}}=? \\ $$ Answered by A5T last updated on 23/Feb/24 $$\frac{\frac{{cos}\left({x}\right){sin}\left(\mathrm{2}{x}\right){sin}\left(\mathrm{3}{x}\right)}{{cos}\left(\mathrm{3}{x}\right)}}{\frac{{cos}\left(\mathrm{4}{x}\right){cos}\left(\mathrm{5}{x}\right){sin}\left(\mathrm{6}{x}\right)}{{sin}\left(\mathrm{4}{x}\right)}} \\ $$$$=\frac{{sin}\left(\mathrm{4}{x}\right){cos}\left({x}\right){sin}\left(\mathrm{2}{x}\right){sin}\left(\mathrm{3}{x}\right)}{{cos}\left(\mathrm{3}{x}\right){cos}\left(\mathrm{4}{x}\right){cos}\left(\mathrm{5}{x}\right){sin}\left(\mathrm{6}{x}\right)}=\mathrm{1} \\ $$$$\left[{since}\:{sin}\left(\mathrm{4}{x}\right)={cos}\left(\mathrm{3}{x}\right);{cos}\left({x}\right)={sin}\left(\mathrm{6}{x}\right);\right. \\…
Question Number 204615 by lepuissantcedricjunior last updated on 26/Feb/24 $$\:\:\:\:\:\:\:\:\frac{\boldsymbol{\mathrm{exercice}}\:}{} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{prouver}}\:\int_{\mathrm{0}} ^{\boldsymbol{\pi}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \boldsymbol{{sin}}\left(\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\pi}}\right)\boldsymbol{{d}\mathrm{x}{d}\mathrm{y}}=\boldsymbol{\pi} \\ $$$$\: \\ $$$$\:\:……………\boldsymbol{{prof}}\:\boldsymbol{{cedric}}\:\boldsymbol{{junior}}……….. \\ $$$$ \\ $$…
Question Number 204598 by SEKRET last updated on 22/Feb/24 $$\:\:\:\:\:\:\:\:\int\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{dx}} \\ $$$$ \\ $$ Commented by Frix last updated on 23/Feb/24 $${t}=\mathrm{sin}^{−\mathrm{1}} \:\sqrt{{x}}\:\Rightarrow \\…
Question Number 204595 by SEKRET last updated on 22/Feb/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\:=\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:−\:\mathrm{16}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{57}\boldsymbol{\mathrm{x}}\:+\mathrm{1}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{a}}\right)=\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{b}}\right)=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{c}}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{a}}}\:+\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{b}}\:}\:+\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{c}}\:}\:=\:? \\ $$ Answered by mr W last updated on…
Question Number 204518 by Abdullahrussell last updated on 20/Feb/24 Answered by TonyCWX08 last updated on 20/Feb/24 $$ \\ $$$${let}\:{us}\:{solve}\:{y}^{{y}} =\mathrm{2}\:{first} \\ $$$${y}^{{y}} =\mathrm{2} \\ $$$${y}=\mathrm{2}^{\frac{\mathrm{1}}{{y}}}…
Question Number 204468 by MathedUp last updated on 18/Feb/24 $$\mathrm{How}\:\mathrm{Can}\:\mathrm{we}\:\mathrm{prove}\:\underset{{h}=−\infty} {\overset{\infty} {\sum}}\:{J}_{{h}} \left({z}\right)=\mathrm{1} \\ $$ Answered by Peace last updated on 19/Feb/24 $${J}_{{n}−\mathrm{1}} \left({x}\right)+{j}_{{n}+\mathrm{1}} \left({x}\right)=\frac{\mathrm{2}{n}}{{x}}{j}_{{n}}…
Question Number 204428 by sulaymonnorboyev140 last updated on 17/Feb/24 Commented by AST last updated on 17/Feb/24 $${Q}\mathrm{196938} \\ $$ Terms of Service Privacy Policy Contact:…