Question Number 217423 by MrGaster last updated on 13/Mar/25 Answered by MathematicalUser2357 last updated on 14/Mar/25 $$\mathrm{Triple}\:\mathrm{contour}\:\mathrm{integral} \\ $$$$\mathrm{Volume}\:\mathrm{integral} \\ $$ Terms of Service Privacy…
Question Number 217416 by peter frank last updated on 13/Mar/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 217417 by peter frank last updated on 13/Mar/25 Commented by mr W last updated on 13/Mar/25 $${for}\:{f}\left({g}\left({x}\right)\right)=\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{50}} \:{there}\:{is}\:{no} \\ $$$${unique}\:{solution}\:{for}\:{f}\left({x}\right)\:{and}\:{f}\left({x}\right). \\ $$…
Question Number 217408 by Intesar last updated on 13/Mar/25 $${l}\int\mathrm{sin}\:\mathrm{7}{xdx} \\ $$ Answered by SdC355 last updated on 13/Mar/25 $$−\frac{\mathrm{1}}{\mathrm{7}}\mathrm{cos}\left(\mathrm{7}{x}\right)+{C} \\ $$$$\mathrm{because}. \\ $$$$\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}\:\mathrm{cos}\left({t}\right)=−\mathrm{sin}\left({t}\right) \\…
Question Number 217441 by mr W last updated on 13/Mar/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}^{\mathrm{3}} \:\left(\mathrm{1}−{x}\right)}{{x}^{\mathrm{3}} }\:{dx}=? \\ $$ Answered by MrGaster last updated on 14/Mar/25 $$\int_{\mathrm{0}}…
Question Number 217402 by mr W last updated on 12/Mar/25 Answered by vnm last updated on 13/Mar/25 $${C}_{\mathrm{5}} ^{\mathrm{2}} \centerdot\mathrm{4}!\centerdot\mathrm{4}=\mathrm{10}\centerdot\mathrm{24}\centerdot\mathrm{4}=\mathrm{960} \\ $$ Commented by mr…
Question Number 217389 by Simurdiera last updated on 12/Mar/25 $$\mathrm{Resolver} \\ $$$$\frac{\mid{x}\:−\:\mathrm{1}\mid\:+\:\mid{x}\:+\:\mathrm{2}\mid}{\mid{x}\mid\:−\:\mathrm{1}}\:\leq\:\mathrm{3} \\ $$ Answered by A5T last updated on 13/Mar/25 $$\mathrm{when}\:−\mathrm{2}\leqslant\mathrm{x}<−\mathrm{1};\:\mid\mathrm{x}−\mathrm{1}\mid=\mathrm{1}−\mathrm{x},\:\mid\mathrm{x}+\mathrm{2}\mid=\mathrm{x}+\mathrm{2}\wedge\:\mid\mathrm{x}\mid=−\mathrm{x} \\ $$$$\Rightarrow\frac{\mid\mathrm{x}−\mathrm{1}\mid+\mid\mathrm{x}+\mathrm{2}\mid}{\mid\mathrm{x}\mid−\mathrm{1}}\leqslant\mathrm{3}\Rightarrow\frac{\mathrm{1}−\mathrm{x}+\mathrm{x}+\mathrm{2}}{−\mathrm{x}−\mathrm{1}}\leqslant\mathrm{3} \\…
Question Number 217384 by MATHEMATICSAM last updated on 12/Mar/25 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin351}°\:=\:−\:\sqrt{\frac{\mathrm{4}\:−\:\sqrt{\mathrm{10}\:+\:\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{8}}\:.} \\ $$ Answered by Sutrisno last updated on 14/Mar/25 $${cos}\mathrm{18}°=\frac{\sqrt{\mathrm{10}+\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}} \\ $$$${sin}\mathrm{351}°=−{sin}\mathrm{9}° \\ $$$$=−\sqrt{\frac{\mathrm{1}−{cos}\mathrm{18}°}{\mathrm{2}}} \\…
Question Number 217385 by Rasheed.Sindhi last updated on 12/Mar/25 $${a},{b},{c}\in\mathbb{R} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{9} \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{21} \\ $$$${ab}+{bc}+{ca}=? \\ $$ Commented…
Question Number 217381 by Rasheed.Sindhi last updated on 12/Mar/25 $$\mathrm{Let}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{be}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{satisfying} \\ $$$$\:\mathrm{the}\:\mathrm{equations} \\ $$$$\left(\mathrm{1}\right)\:\:\mathrm{a}\:+\mathrm{b}\:+\:\mathrm{c}=\:\mathrm{4} \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{c}^{\mathrm{3}} =\:\mathrm{34} \\ $$$$\mathrm{Find}\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca} \\ $$ Commented by…