Question Number 212464 by liuxinnan last updated on 14/Oct/24 Commented by liuxinnan last updated on 14/Oct/24 $${is}\:{it}\:{right} \\ $$ Answered by MrGaster last updated on…
Question Number 212467 by Hanuda354 last updated on 14/Oct/24 $$\mathrm{Use}\:\:\mathrm{the}\:\:\mathrm{integration}\:\:\mathrm{by}\:\:\mathrm{parts}. \\ $$$$ \\ $$$$\int\:\frac{\mathrm{2}}{\:\sqrt{{r}^{\mathrm{2}} −\mathrm{4}}}\:{dr}\: \\ $$ Answered by mehdee7396 last updated on 14/Oct/24 $${r}=\mathrm{2}{coshx}\Rightarrow{dr}=\mathrm{2}{sinhxdx}…
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Question Number 212461 by MrGaster last updated on 14/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{prove}: \\ $$$$\:\:\int_{\mathrm{0}} ^{+\infty} \frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} +\mathrm{25}{x}^{\mathrm{2}} +\mathrm{160}}}=\int_{\mathrm{0}} ^{+\infty} \frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{95}{x}^{\mathrm{2}} +\mathrm{2560}}} \\ $$ Commented by Ghisom…
Question Number 212462 by MrGaster last updated on 14/Oct/24 $$\mathrm{1}.\:\mathrm{In}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{there}\:\mathrm{are}\:\mathrm{nt} \\ $$$$\mathrm{poins}\:\mathrm{arranged}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{nostraight}\:\mathrm{line}\:\mathrm{passesg} \\ $$$$\mathrm{throuh}\:\mathrm{more}\:\mathrm{than}\:\mathrm{3}\:\mathrm{points}.\mathrm{h} \\ $$$$\mathrm{Wat}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximume} \\ $$$$\mathrm{numbr}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\: \\ $$$$\mathrm{thatcan}\:\mathrm{pass}\:\mathrm{throughy} \\ $$$$\mathrm{exactl}\:\mathrm{3}\:\mathrm{points2}.\:\mathrm{If}\:\mathrm{thee} \\…
Question Number 212456 by Hanuda354 last updated on 14/Oct/24 $$\int\:\:\frac{\sqrt{\mathrm{9}{x}^{\mathrm{2}} −\mathrm{49}}}{{x}^{\mathrm{3}} }\:\:{dx}\:=\:? \\ $$ Answered by Sutrisno last updated on 14/Oct/24 $$\int\frac{\sqrt{\left(\mathrm{3}{x}\right)^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }}{{x}^{\mathrm{3}} }{dx}…
Question Number 212457 by 281981 last updated on 14/Oct/24 Answered by som(math1967) last updated on 14/Oct/24 $$\:\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{b}}&{{c}}&{{a}}\\{{c}}&{{a}}&{{b}}\end{vmatrix}=\mathrm{0} \\ $$$$\Rightarrow{a}\left({bc}−{a}^{\mathrm{2}} \right)−{b}\left({b}^{\mathrm{2}} −{ca}\right)+{c}\left({ab}−{c}^{\mathrm{2}} \right)=\mathrm{0} \\ $$$$\Rightarrow{a}^{\mathrm{3}} +{b}^{\mathrm{3}}…
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Question Number 212445 by ChantalYah last updated on 13/Oct/24 Commented by Frix last updated on 13/Oct/24 $$\mathrm{80cos}\:{A}\:?\:\mathrm{150sin}\:{A}\:=\mathrm{13} \\ $$$$ \\ $$$$\mathrm{80cos}\:{A}\:−\mathrm{150sin}\:{A}\:=\mathrm{13} \\ $$$$−\mathrm{170sin}\:\left({A}−\mathrm{tan}^{−\mathrm{1}} \:\frac{\mathrm{8}}{\mathrm{15}}\right)\:=\mathrm{13} \\…
Question Number 212415 by MrGaster last updated on 13/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{2}^{\frac{{k}}{{n}}} }{{n}+\frac{\mathrm{1}}{{k}}} \\ $$$$ \\ $$ Answered by Frix last updated on 13/Oct/24…