Question Number 215350 by hardmath last updated on 03/Jan/25 $$\mathrm{Find}:\:\:\:\mathrm{x}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{2}^{\sqrt{\mathrm{200}}} \:\:\Rightarrow\:\:\mathrm{x}\:=\:? \\ $$ Answered by zetamaths last updated on 03/Jan/25 $$.{is}\:{just}\:{the}\:{lambert}\:{function} \\ $$$${x}^{{x}} =\mathrm{2}^{\sqrt{\mathrm{200}}}…
Question Number 215344 by universe last updated on 03/Jan/25 Answered by MrGaster last updated on 04/Jan/25 $$\:\mathrm{Let}\:\Sigma\:\mathrm{be}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{of}\:{D}. \\ $$$$\Sigma=\sum_{\mathrm{1}} \cup\sum_{\mathrm{2}} \cup\sum_{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{where} \\ $$$$\sum_{\mathrm{1}}…
Question Number 215331 by JasonHidd last updated on 03/Jan/25 Answered by mr W last updated on 03/Jan/25 $${f}\left({x}\right)\:{must}\:{be}\:{an}\:{odd}\:{integrable}\: \\ $$$${function},\:{i}.{e}. \\ $$$${f}\left(−{x}\right)=−{f}\left({x}\right) \\ $$$${e}.{g}.\: \\…
Question Number 215312 by ajfour last updated on 02/Jan/25 Commented by mr W last updated on 06/Jan/25 $${please}\:{try}\:{Q}\mathrm{215395} \\ $$ Answered by mr W last…
Question Number 215280 by universe last updated on 02/Jan/25 $${volume}\:{of}\:{solids}\:{generated}\:{by}\:{revolving} \\ $$$${the}\:{region}\:{bounded}\:{by}\:{the}\:{curve}\:{and}\:{line} \\ $$$$\:{the}\:{y}-{axis} \\ $$$$\:{y}={x}\:,{y}\:=\:{x}/\mathrm{2}\:,{x}\:=\:\mathrm{2} \\ $$ Commented by mr W last updated on…
Question Number 215313 by AlagaIbile last updated on 02/Jan/25 Answered by mr W last updated on 02/Jan/25 $$\angle{ABD}=\mathrm{135}° \\ $$$$\Rightarrow\angle{CBD}=\mathrm{45}° \\ $$$$\Rightarrow{CD}={CB}=\mathrm{2} \\ $$$$\Rightarrow{AD}=\sqrt{\left(\mathrm{12}+\mathrm{2}\right)^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}}…
Question Number 215282 by arkanmathematics63 last updated on 02/Jan/25 $${Show}\:{that}\:{x}=\mathrm{64}\:{and}\:{y}=\mathrm{729}\: \\ $$$$\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{y}}=\mathrm{13} \\ $$$$\sqrt{{x}}+\sqrt{{y}}=\mathrm{35} \\ $$ Commented by Ghisom last updated on 02/Jan/25 $$\mathrm{to}\:“\mathrm{show}\:\mathrm{that}\:{x}=\mathrm{64}\:\mathrm{and}\:{y}=\mathrm{729}''\:\mathrm{it}'\mathrm{s}\:\mathrm{enough} \\…
Question Number 215315 by depressiveshrek last updated on 02/Jan/25 $$\mathrm{Evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{2}}+…+\frac{\mathrm{1}}{\mathrm{4}{n}}\right) \\ $$ Answered by mr W last updated on 02/Jan/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}{n}+{k}}…
Question Number 215276 by ppch145 last updated on 02/Jan/25 $$\mathrm{I}\:\mathrm{produced}\:\mathrm{the}\:\mathrm{drawing}\: \\ $$$$\mathrm{shown}\:\mathrm{below}\:\left(\mathrm{Q}.\:\mathrm{215275}\right)\: \\ $$$$\mathrm{using}\:\mathrm{this}\:\mathrm{great}\:\mathrm{app},\:\mathrm{but}\: \\ $$$$\mathrm{unfortunately}\:\mathrm{it}\:\mathrm{refused}\:\mathrm{to}\: \\ $$$$\mathrm{get}\:\mathrm{saved}\:\mathrm{after}\:\mathrm{clicking}\: \\ $$$$“\mathrm{Save}''\:\mathrm{button}\:\mathrm{several}\:\mathrm{times}.\: \\ $$$$\mathrm{Also},\:\mathrm{the}\:“\mathrm{Export}\:\mathrm{As}\:\mathrm{Image}''\: \\ $$$$\mathrm{button}\:\mathrm{is}\:\mathrm{not}\:\mathrm{working}.\:\mathrm{Does}\: \\…
Question Number 215277 by efronzo1 last updated on 02/Jan/25 $$\:\:\:\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)\:=\:\frac{\mathrm{5}}{\mathrm{4}} \\ $$$$\:\:\:\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}−\mathrm{sin}\:\mathrm{x}\right)\:=\:? \\ $$ Answered by MrGaster last updated on 02/Jan/25 $$\underset{\mathrm{Commutative}\:\mathrm{law}\:\mathrm{of}\:\mathrm{multiplication}} {\underbrace{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\centerdot\left(\mathrm{1}−\mathrm{cos}\:{x}\right)\left(\mathrm{1}−\mathrm{sin}\:{x}\right)}}=\left(\frac{\mathrm{5}}{\mathrm{4}}\right)\left(\mathrm{1}−\mathrm{cos}\:{x}\right)\left(\mathrm{1}−\mathrm{sin}\:{x}\right) \\ $$$$\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}}…