Question Number 220854 by fantastic last updated on 20/May/25 $${Solve}\:{for}\:{x}\:\:\:{and}\:\:\:\:{y} \\ $$$$\mathrm{3}^{{x}} +\mathrm{3}^{{y}} =\mathrm{4},\:\:\mathrm{3}^{−{x}} +\mathrm{3}^{−{y}\:} =\frac{\mathrm{4}}{\mathrm{3}} \\ $$ Answered by SdC355 last updated on 20/May/25…
Question Number 220855 by fantastic last updated on 20/May/25 $${If}\:\:{b}\:\mathrm{cos}\left(\theta+\mathrm{120}^{\mathrm{0}} \right)={c}\:\mathrm{cos}\:\left(\theta+\mathrm{240}^{\mathrm{0}} \right)\:{then}\:{prove}\:{that} \\ $$$${b}−{c}=−\left({b}+{c}\right)\sqrt{\mathrm{3}}\:\mathrm{tan}\:\theta \\ $$ Answered by golsendro last updated on 20/May/25 $$\:\mathrm{b}\:\mathrm{cos}\:\left(\mathrm{180}−\left(\mathrm{60}−\theta\right)\right)\:=\:\mathrm{c}\:\mathrm{cos}\:\left(\mathrm{360}−\left(\mathrm{120}−\theta\right)\right) \\…
Question Number 220848 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\mathrm{2}}\:\sqrt{\frac{\left(\mathrm{2}\:−\:\mathrm{6}{x}\:+\:\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{2}} +\:\mathrm{4}\left(\mathrm{2}{x}\:−\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{x}^{\mathrm{3}} \right)}{\mathrm{2}{x}\:−\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{x}^{\mathrm{3}} }}\:{dx}\:\:\:\:\:\:\: \\ $$$$ \\ $$ Commented…
Question Number 220913 by SdC355 last updated on 20/May/25 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{an}\:\mathrm{Manager}??? \\ $$$$\mathrm{pls}\:\mathrm{ban}\:\mathrm{Question}\:\mathrm{Spamming}\:\mathrm{and}… \\ $$$$\mathrm{pls}\:\mathrm{fix}\:\mathrm{invisible}\:\mathrm{line}\:\mathrm{matrix}\:\mathrm{bug} \\ $$ Commented by mr W last updated on 21/May/25 $${the}\:{developer}\:{Tinku}\:{Tara}\:{doesn}'{t}…
Question Number 220850 by fantastic last updated on 20/May/25 $$\int\sqrt{\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}}.\frac{\mathrm{1}}{{x}+\mathrm{3}}{dx} \\ $$ Commented by Frix last updated on 20/May/25 $$\mathrm{Question}\:\mathrm{219193} \\ $$$$\mathrm{Why}\:\mathrm{you}\:\mathrm{ask}\:\mathrm{again}? \\ $$ Answered…
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Question Number 220904 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \frac{{x}^{\mathrm{4}} {y}^{\mathrm{3}} {z}^{\mathrm{2}} }{\left({x}+{y}+{z}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)−\left({x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \right)}\:{dxdydz}\:\:\:\:\:\:\: \\ $$$$\:…
Question Number 220842 by mnjuly1970 last updated on 20/May/25 $$ \\ $$$$\:\:\:\:\:\:\mathrm{J}=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{t}} {u}_{\pi} \left({t}\right){cos}\left({t}\right){dt}=? \\ $$$$ \\ $$$$\:{note}:\:\:{u}_{{c}} \left({t}\right)=\:\begin{cases}{\:\mathrm{0}\:\:\:\:\:\:\:\:{t}<{c}}\\{\:\mathrm{1}\:\:\:\:\:\:\:\:\:{t}>{c}\:\:}\end{cases}\:\:;\:\:\:\:{c}\geqslant\mathrm{0} \\ $$ Commented by…
Question Number 220843 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\alpha\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\mathrm{lim}_{{x}\rightarrow\mathrm{1}} \:\frac{\left(\mathrm{1}\:−\:{x}\right)^{\alpha} }{\:^{\mathrm{3}} \sqrt{\mathrm{1}\:−\:{x}^{\mathrm{4}} }}\:\:\:\:\:\:\:\:\in\left(\mathrm{0},\infty\right) \\ $$$$ \\ $$ Commented by SdC355…
Question Number 220896 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\:\int\int\int_{\:\left[\mathrm{0},\infty\right]^{\:\mathrm{3}} } \frac{{x}^{\mathrm{2}} {y}^{\mathrm{2}} {z}^{\mathrm{2}} }{\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \right)^{\mathrm{5}} }\:{dxdydz}\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$…