Question Number 76715 by peter frank last updated on 29/Dec/19 $${If}\:{u}={arc}\mathrm{sin}\:\frac{{x}}{{y}}+{arc}\mathrm{tan}\:\frac{{y}}{{x}} \\ $$$${show}\:{that}\: \\ $$$${x}\frac{\partial{u}}{{dx}}+{y}\frac{\partial{u}}{{dy}}=\mathrm{0} \\ $$ Commented by abdomathmax last updated on 30/Dec/19 $$\frac{\partial{u}}{\partial{x}}\:=\frac{\mathrm{1}}{{y}\sqrt{\mathrm{1}−\frac{{x}^{\mathrm{2}}…
Question Number 142150 by iloveisrael last updated on 27/May/21 $$\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\right)\:=?\: \\ $$ Commented by liberty last updated on 27/May/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}}…
Question Number 76580 by Rio Michael last updated on 28/Dec/19 $$\mathrm{how}\:\mathrm{many}\:\mathrm{divisors}\:\mathrm{does}\:\mathrm{180045}\:\mathrm{has}? \\ $$ Commented by mr W last updated on 28/Dec/19 $$\frac{\mathrm{180045}}{\mathrm{5}}=\mathrm{36009} \\ $$$$\frac{\mathrm{36009}}{\mathrm{3}}=\mathrm{12003} \\…
Question Number 76576 by Rio Michael last updated on 28/Dec/19 $${Compute}\:{the}\:{Gcd}\:\left({greatest}\:{common}\:{divisor}\right) \\ $$$${of}\:\:\mathrm{45}\:{and}\:\mathrm{1287}\: \\ $$ Answered by john santu last updated on 28/Dec/19 $$\mathrm{45}\:=\:\mathrm{3}^{\mathrm{2}} ×\mathrm{5}…
Question Number 11005 by ajfour last updated on 06/Mar/17 $${prove}\:{that}\:\frac{\mathrm{9}}{\mathrm{4}}\:<\:\left(\mathrm{log}\:_{\mathrm{2}} \mathrm{3}\right)^{\mathrm{2}} \:<\:\frac{\mathrm{25}}{\mathrm{9}}\:\:. \\ $$ Answered by mrW1 last updated on 06/Mar/17 $$\mathrm{2log}_{\mathrm{2}} \:\mathrm{3}=\mathrm{log}_{\mathrm{2}} \:\mathrm{3}^{\mathrm{2}} =\mathrm{log}_{\mathrm{2}}…
Question Number 76536 by byaw last updated on 28/Dec/19 Commented by benjo 1/2 santuyy last updated on 28/Dec/19 $${good}\:{luck}\:{to}\:{sir} \\ $$ Answered by john santu…
Question Number 141972 by iloveisrael last updated on 25/May/21 Commented by Dwaipayan Shikari last updated on 25/May/21 $${x}°+\mathrm{20}°+\left(\mathrm{360}°−\mathrm{140}°\right)+\mathrm{90}°=\mathrm{360}° \\ $$$$\Rightarrow{x}°=\mathrm{30}° \\ $$ Commented by I…
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Question Number 10855 by Joel576 last updated on 27/Feb/17 $$\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}\:+\:\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}\:+\:\frac{\mathrm{5}}{\mathrm{3}!+\mathrm{4}!+\mathrm{5}!}\:+\:…\:+\:\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!}\:=\:? \\ $$ Answered by nume1114 last updated on 28/Feb/17 $$\:\:\:\:\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}+\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}+…+\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!} \\ $$$$=\underset{{n}=\mathrm{1}} {\overset{\mathrm{2014}} {\sum}}\frac{{n}+\mathrm{2}}{{n}!+\left({n}+\mathrm{1}\right)!+\left({n}+\mathrm{2}\right)!} \\…
Question Number 141890 by bekzodjumayev last updated on 24/May/21 Commented by bekzodjumayev last updated on 24/May/21 $$\boldsymbol{{Please}}\:\boldsymbol{{help}} \\ $$ Terms of Service Privacy Policy Contact:…