Question Number 128518 by shaker last updated on 08/Jan/21 Commented by bramlexs22 last updated on 08/Jan/21 $$\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{n}}} \:=\:\mathrm{u}\:\Rightarrow\:\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{n}}} \:+\:\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{n}}} \:=\:\frac{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}{\mathrm{u}} \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2u}}\:\Rightarrow\:\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{u}^{\mathrm{2}}…
Question Number 62982 by ANTARES VY last updated on 27/Jun/19 $$\frac{\boldsymbol{\mathrm{tg}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)−\mathrm{1}}{\boldsymbol{\mathrm{ctg}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}=\mathrm{2}\boldsymbol{\mathrm{sin}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)\:\:\boldsymbol{\mathrm{x}}\in\left(\mathrm{180}°;\mathrm{540}°\right) \\ $$$$ \\ $$ Answered by MJS last updated on 27/Jun/19 $$\frac{\mathrm{1}}{\mathrm{cot}}=\mathrm{tan} \\ $$$$\mathrm{tan}^{\mathrm{2}}…
Question Number 62981 by hovea cw last updated on 27/Jun/19 Commented by mathmax by abdo last updated on 27/Jun/19 $$\left.\mathrm{2}\right)\:{let}\:{A}\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{x}\mid{sin}\left(\mathrm{2}{x}\right)\mid}{\mathrm{3}+{sin}^{\mathrm{2}} {x}}\:{dx}\:{changement}\:{x}\:=\pi\:+{t}\:{give} \\ $$$${A}\:=\int_{−\pi}…
Question Number 128511 by benjo_mathlover last updated on 08/Jan/21 $$\:\mathcal{H}=\int\:\frac{\mathrm{2017x}^{\mathrm{2016}} +\mathrm{2018x}^{\mathrm{2017}} }{\mathrm{1}+\mathrm{x}^{\mathrm{4034}} +\mathrm{2x}^{\mathrm{4035}} +\mathrm{x}^{\mathrm{4036}} }\:\mathrm{dx}\: \\ $$ Answered by liberty last updated on 08/Jan/21 $$\mathcal{H}=\int\:\frac{\mathrm{2017x}^{\mathrm{2016}}…
Question Number 128508 by Lian last updated on 08/Jan/21 $${if}\:\:{x}^{{x}^{\mathrm{3}} } =\mathrm{3} \\ $$$${find}\:{x} \\ $$ Answered by mr W last updated on 08/Jan/21 $${if}\:{x}^{\mathrm{3}}…
Question Number 128509 by benjo_mathlover last updated on 08/Jan/21 Answered by liberty last updated on 08/Jan/21 $$\left(\Leftrightarrow\right)\:\frac{\mathrm{W}}{\mathrm{y}+\mathrm{x}}\:=\:\mathrm{6}\:\mathrm{days}\:\mathrm{where}\:\frac{\mathrm{W}}{\mathrm{y}}=\mathrm{10}\:\mathrm{days}\: \\ $$$$\mathrm{so}\:\mathrm{we}\:\mathrm{find}\:\frac{\mathrm{W}}{\frac{\mathrm{W}}{\mathrm{10}}+\mathrm{x}}=\mathrm{6}\:\Rightarrow\mathrm{W}=\frac{\mathrm{6W}}{\mathrm{10}}+\mathrm{6x} \\ $$$$\Rightarrow\mathrm{x}\:=\:\frac{\mathrm{4W}}{\mathrm{60}}\:=\:\frac{\mathrm{W}}{\mathrm{15}}\:,\:\mathrm{it}\:\mathrm{follows}\:\mathrm{that}\:\mathrm{Mrs}\:\mathrm{x}\:\mathrm{can} \\ $$$$\mathrm{finish}\:\mathrm{the}\:\mathrm{job}\:\mathrm{by}\:\mathrm{herself}\:\mathrm{in}\:\mathrm{15}\:\mathrm{days} \\ $$…
Question Number 62970 by ajfour last updated on 27/Jun/19 Commented by ajfour last updated on 28/Jun/19 $${Hope}\:{its}\:\:{correct}\:{and}\:{unique}.. \\ $$ Answered by ajfour last updated on…
Question Number 128505 by Lian last updated on 08/Jan/21 $${simplify}:\:\:\:\frac{\mathrm{5}^{{log}_{\frac{\mathrm{4}}{\mathrm{5}}} \mathrm{5}} }{\mathrm{4}^{{log}_{\frac{\mathrm{4}}{\mathrm{5}}} \mathrm{4}} } \\ $$ Commented by liberty last updated on 08/Jan/21 $$=\:\mathrm{0}.\mathrm{05}\:=\:\frac{\mathrm{5}}{\mathrm{100}}=\frac{\mathrm{1}}{\mathrm{20}} \\…
Question Number 128498 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{simplify}\:\mathrm{A}_{\mathrm{n}} =\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{i}\right)^{\mathrm{n}} }+\frac{\mathrm{1}}{\left(\mathrm{1}−\sqrt{\mathrm{3}}\mathrm{i}\right)^{\mathrm{n}} } \\ $$ Answered by TheSupreme last updated on 08/Jan/21 $$\mathrm{1}+{i}\sqrt{\mathrm{3}}=\mathrm{2}{e}^{{i}\frac{\pi}{\mathrm{3}}}…
Question Number 128499 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{find}\:\:\mathrm{u}_{\mathrm{n}} =\int_{\mathrm{1}} ^{\infty} \:\:\frac{\left[\mathrm{ne}^{−\mathrm{x}} \right]}{\mathrm{n}^{\mathrm{3}} }\mathrm{dx} \\ $$ Answered by TheSupreme last updated on…