Question Number 199385 by hardmath last updated on 02/Nov/23 $$\mathrm{Find}: \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}^{\mathrm{15}} \:\sqrt{\mathrm{1}\:+\:\mathrm{3x}^{\mathrm{8}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by witcher3 last updated on 02/Nov/23…
Question Number 199381 by Mingma last updated on 02/Nov/23 Answered by witcher3 last updated on 02/Nov/23 $$\left(\mathrm{202}\right)=\mathrm{2}.\mathrm{101} \\ $$$$\frac{\left(\mathrm{201}\right)!}{\mathrm{k}}\equiv\mathrm{0}\left[\mathrm{202}\right]\mathrm{0},\forall\mathrm{k}\in\left\{\mathrm{1},……\mathrm{201}\right)−\left\{\mathrm{2},\mathrm{101}\right) \\ $$$$\mathrm{J}\equiv\frac{\mathrm{201}!}{\mathrm{101}}+\frac{\mathrm{201}!}{\mathrm{2}}\left[\mathrm{202}\right] \\ $$$$\frac{\mathrm{201}!}{\mathrm{2}}=\mathrm{202}.\mathrm{3}.\mathrm{2}.\underset{\mathrm{k}=\mathrm{5},\mathrm{k}\neq\mathrm{101}} {\overset{\mathrm{201}} {\prod}}\mathrm{k}\equiv\mathrm{0}\left[\mathrm{202}\right]…
Question Number 199355 by hardmath last updated on 01/Nov/23 Answered by MathematicalUser2357 last updated on 04/Nov/23 $$\Omega\approx\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}!}{{n}^{{n}} }\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}{n}} }??? \\ $$ Terms…
Question Number 199308 by AR19 last updated on 01/Nov/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 199309 by universe last updated on 01/Nov/23 $$\:\:\:\:{a}_{{n}+\mathrm{1}\:} =\:{a}_{{n}} \:+\:\sqrt{{a}_{{n}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:\:,\:{a}_{\mathrm{0}} \:=\:\mathrm{0} \\ $$$$\:\:\:\:\mathrm{find}\:\mathrm{a}_{\mathrm{n}\:} \:=\:\:?? \\ $$ Answered by TheHoneyCat last updated…
Question Number 199290 by ajfour last updated on 31/Oct/23 $${If}\:{x}=\sqrt{{p}+{iq}}+\sqrt{{h}+{ik}} \\ $$$${and}\:\:\frac{{p}}{{q}}\neq\frac{{k}}{{h}}\:\:{then}\:{relate}\:{p},{q},{h},{k}\:\in\mathbb{R} \\ $$$${such}\:{that}\:{x}\in\mathbb{R}. \\ $$ Commented by Frix last updated on 31/Oct/23 $$\sqrt{{x}+{y}\mathrm{i}}={r}\mathrm{e}^{\mathrm{i}\theta} \:\mathrm{with}\:{r}>\mathrm{0}\wedge−\frac{\pi}{\mathrm{2}}<\theta\leqslant\frac{\pi}{\mathrm{2}}…
Question Number 199259 by hardmath last updated on 30/Oct/23 Commented by Frix last updated on 30/Oct/23 $$\sqrt{\sqrt{\mathrm{12345689654321233}\pm\mathrm{5333334096}\sqrt{\mathrm{12345679}}}}= \\ $$$$=\sqrt{\mathrm{111111127}\pm\mathrm{24}\sqrt{\mathrm{12345679}}}= \\ $$$$=\pm\mathrm{4}+\mathrm{3}\sqrt{\mathrm{12345679}} \\ $$$$\sqrt[{\mathrm{3}}]{{x}−{y}}=\sqrt[{\mathrm{4}}]{\mathrm{8}}=\mathrm{2} \\ $$…
Question Number 199226 by mr W last updated on 30/Oct/23 $${find} \\ $$$$\frac{\mathrm{2}\:\mathrm{sin}\:\mathrm{2}°+\mathrm{4}\:\mathrm{sin}\:\mathrm{4}°+…+\mathrm{180}\:\mathrm{sin}\:\mathrm{180}°}{\mathrm{90}}=? \\ $$$$ \\ $$$$\left[{an}\:{unsolved}\:{old}\:{question}\:#\mathrm{198900}\right] \\ $$ Answered by mr W last updated…
Question Number 199230 by hardmath last updated on 29/Oct/23 $$\mathrm{x}\:,\:\mathrm{y}\::\:\:\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{If}\::\:\:\:\mathrm{15}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{9}^{\boldsymbol{\mathrm{y}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{5}^{\frac{\mathrm{3}\boldsymbol{\mathrm{x}}}{\mathrm{2}\boldsymbol{\mathrm{y}}\:−\:\boldsymbol{\mathrm{x}}}} \:\:=\:\:? \\ $$ Answered by AST last updated on 29/Oct/23…
Question Number 199194 by hardmath last updated on 29/Oct/23 $$\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,… \\ $$$$\mathrm{a}_{\mathrm{1}} =\mathrm{1} \\ $$$$\mathrm{a}_{\mathrm{2n}} =\mathrm{n}\centerdot\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{a}_{\mathrm{2}^{\mathrm{100}} } \:=\:? \\ $$ Answered…