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Question Number 150853 by mathdanisur last updated on 15/Aug/21 $$\mathrm{log}_{\mathrm{2021}} \:\sqrt{\mathrm{x}\::\:\sqrt{\mathrm{x}\::\:\sqrt{\mathrm{x}\::..}}}\:=\:\mathrm{674} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$ Commented by liberty last updated on 16/Aug/21 $$\sqrt{\frac{\mathrm{x}}{\:\sqrt{\frac{\mathrm{x}}{\:\sqrt{\frac{\mathrm{x}}{\:\sqrt{\frac{\mathrm{x}}{\vdots}}}}}}}}\:=\:\mathrm{2021}^{\mathrm{674}} \\ $$$$\Leftrightarrow\sqrt{\frac{\mathrm{x}}{\mathrm{2021}^{\mathrm{674}}…
Question Number 85318 by Power last updated on 20/Mar/20 Commented by Power last updated on 21/Mar/20 $$+\mathrm{R}\left(\mathrm{x}\right)\:\:\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 19783 by NECC last updated on 15/Aug/17 $${The}\:{sides}\:{of}\:{a}\:{triangle}\:{are}\:{of} \\ $$$${lengths}\:\sqrt{\left({m}^{\mathrm{2}} −{n}^{\mathrm{2}} \right)}\:,{m}^{\mathrm{2}} +{n}^{\mathrm{2}} ,\:\mathrm{2}{mn}. \\ $$$${Show}\:{that}\:{it}\:{is}\:{a}\:{right}\:{angle}\:\Delta. \\ $$ Commented by Tinkutara last updated…
Question Number 150852 by mathdanisur last updated on 15/Aug/21 $$\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{xyz}\:\leqslant\:\left(\frac{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:-\:\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \:\leqslant\:\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85319 by sahnaz last updated on 20/Mar/20 $$\int\frac{\mathrm{2}+\mathrm{u}}{−\mathrm{u}^{\mathrm{2}} −\mathrm{u}}\mathrm{du} \\ $$ Answered by MJS last updated on 20/Mar/20 $$\int\frac{\mathrm{2}+{u}}{−{u}^{\mathrm{2}} −{u}}{du}=−\int\frac{{u}+\mathrm{2}}{{u}\left({u}+\mathrm{1}\right)}{du}= \\ $$$$=\int\frac{{du}}{{u}+\mathrm{1}}−\mathrm{2}\int\frac{{du}}{{u}}=\mathrm{ln}\:\mid{u}+\mathrm{1}\mid\:−\mathrm{2ln}\:\mid{u}\mid\:+{C} \\…
Question Number 85313 by john santu last updated on 20/Mar/20 $$\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{20}^{\mathrm{o}} \right)\:+\:\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{40}^{\mathrm{o}} \right)+\:\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{80}^{\mathrm{o}} \right)\:= \\ $$ Answered by john santu last updated…
Question Number 19774 by Tinkutara last updated on 15/Aug/17 $$\mathrm{A}\:\mathrm{balloon}\:\mathrm{is}\:\mathrm{ascending}\:\mathrm{vertically}\:\mathrm{with} \\ $$$$\mathrm{an}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{0}.\mathrm{2}\:\mathrm{ms}^{−\mathrm{2}} .\:\mathrm{Two}\:\mathrm{stones} \\ $$$$\mathrm{are}\:\mathrm{dropped}\:\mathrm{from}\:\mathrm{it}\:\mathrm{at}\:\mathrm{an}\:\mathrm{interval}\:\mathrm{of}\:\mathrm{2}\:\mathrm{s}. \\ $$$$\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{them}\:\mathrm{when}\:\mathrm{the} \\ $$$$\mathrm{second}\:\mathrm{stone}\:\mathrm{dropped}\:\mathrm{is}\:\left(\mathrm{take}\:{g}\:=\:\mathrm{9}.\mathrm{8}\right. \\ $$$$\left.\mathrm{ms}^{−\mathrm{2}} \right) \\ $$ Answered…
Question Number 150841 by mathdanisur last updated on 15/Aug/21 $$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{b}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 15/Aug/21…
Question Number 150840 by mathdanisur last updated on 15/Aug/21 $$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{arctan}\left(\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)}\:\mathrm{dx}\:=\:? \\ $$ Answered by mathmax by abdo last updated on 17/Aug/21 $$\mathrm{f}\left(\mathrm{a}\right)=\int_{\mathrm{0}}…