Question Number 75669 by peter frank last updated on 15/Dec/19 Commented by mathmax by abdo last updated on 15/Dec/19 $${let}\:{A}\:=\int\:\frac{{d}\theta}{{sin}^{\mathrm{4}} \theta\:+{cos}^{\mathrm{4}} \theta}\:\Rightarrow\:{A}\:=\int\:\:\:\:\frac{{d}\theta}{\left({cos}^{\mathrm{2}} \theta+{sin}^{\mathrm{2}} \theta\right)^{\mathrm{2}} −\mathrm{2}{cos}^{\mathrm{2}}…
Question Number 10133 by konen last updated on 26/Jan/17 $$\frac{\mathrm{1}+\mathrm{2}^{\mathrm{x}−\mathrm{y}} }{\mathrm{1}+\mathrm{2}^{\mathrm{y}−\mathrm{x}} }=\mathrm{4}\Rightarrow\mathrm{x}−\mathrm{y}=? \\ $$ Answered by ridwan balatif last updated on 26/Jan/17 $$\frac{\mathrm{1}+\mathrm{2}^{\mathrm{x}−\mathrm{y}} }{\mathrm{1}+\mathrm{2}^{−\left(\mathrm{x}−\mathrm{y}\right)} }=\mathrm{4}…
Question Number 75660 by mr W last updated on 15/Dec/19 $${find}\:{all}\:{solutions}\:\left({if}\:{exist}\right)\:{of} \\ $$$${x}^{\mathrm{2}} +\mathrm{5}{y}^{\mathrm{2}} =\mathrm{2016} \\ $$$${with}\:{x},{y}\:\in\:\mathbb{N}. \\ $$ Commented by mathmax by abdo last…
Question Number 75661 by peter frank last updated on 15/Dec/19 Answered by Kunal12588 last updated on 15/Dec/19 $${U}_{{n}} =\int{x}^{{n}} \:{cos}\:{x}\:{dx} \\ $$$${u}\:=\:{x}^{{n}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\&\:\:\:\:{dv}\:=\:{cos}\:{x}\:{dx} \\ $$$$\Rightarrow{du}\:=\:{nx}^{{n}−\mathrm{1}}…
Question Number 10124 by konen last updated on 25/Jan/17 $$\mathrm{x}=\mathrm{4}^{\left(−\mathrm{2}\right)^{−\mathrm{1}} } \\ $$$$\mathrm{y}=\left(\mathrm{0}.\mathrm{4}\right)^{−\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{2x}+\mathrm{4y}=? \\ $$ Answered by FilupSmith last updated on 25/Jan/17 $${x}=\mathrm{4}^{\left(−\mathrm{2}\right)^{−\mathrm{1}}…
Question Number 75655 by mr W last updated on 15/Dec/19 $${if}\:{z}\:\in\:\mathbb{C} \\ $$$${is}\:\mathrm{sin}^{\mathrm{2}} \:{z}+\mathrm{cos}^{\mathrm{2}} \:{z}=\mathrm{1}\:{also}\:{valid}? \\ $$ Answered by MJS last updated on 15/Dec/19 $$\mathrm{yes}.…
Question Number 141186 by SLVR last updated on 16/May/21 Commented by SLVR last updated on 16/May/21 $${Good}\:{evening}\:{sir}..\:{Mr}.{Dwaipayan}.. \\ $$$${i}\:{forgotten}\:{to}\:{write}\:{your}\:{explanation} \\ $$ Commented by SLVR last…
Question Number 10104 by konen last updated on 23/Jan/17 $$\frac{\mathrm{a}}{\mathrm{2}}=\frac{\mathrm{b}}{\mathrm{5}}\:,\sqrt{\mathrm{5a}}\:+\sqrt{\mathrm{2b}}\:=\mathrm{16} \\ $$$$\Rightarrow\frac{\mathrm{5a}}{\mathrm{2}}+\mathrm{b}=\overset{} {?} \\ $$ Answered by arge last updated on 23/Jan/17 $$\mathrm{5}{a}=\mathrm{2}{b},\sqrt{\mathrm{2}{b}}\:+\sqrt{\mathrm{2}{b}}\:=\mathrm{16} \\ $$$$\mathrm{2}\sqrt{\mathrm{2}{b}}\:=\mathrm{16}…
Question Number 10102 by konen last updated on 23/Jan/17 $$\mathrm{a}−\mathrm{b}=\frac{\mathrm{a}+\mathrm{b}}{\mathrm{7}}=\frac{\mathrm{a}×\mathrm{b}}{\mathrm{24}}\:\Rightarrow\mathrm{a}−\mathrm{b}=? \\ $$ Answered by mrW1 last updated on 23/Jan/17 $$\mathrm{a}−\mathrm{b}=\frac{\mathrm{a}+\mathrm{b}}{\mathrm{7}}=\frac{\mathrm{a}×\mathrm{b}}{\mathrm{24}}={u} \\ $$$${a}−{b}={u} \\ $$$${a}+{b}=\mathrm{7}{u} \\…
Question Number 141164 by iloveisrael last updated on 16/May/21 $$\:\:\:\:{Find}\:{maximum}\:{value}\: \\ $$$$\:\:\:{of}\:{the}\:{product}\:{xy}\left(\mathrm{72}−\mathrm{3}{x}−\mathrm{4}{y}\right) \\ $$$$\:\:\:\:{for}\:{positive}\:{value}\:{of}\:{x}\:\&\:{y}. \\ $$ Commented by mitica last updated on 16/May/21 $${max}=\mathrm{1152}\:{for}\:{x}=\mathrm{8},{y}=\mathrm{6} \\…