Question Number 173418 by Shrinava last updated on 11/Jul/22 Answered by aleks041103 last updated on 12/Jul/22 $$\left.\mathrm{1}\right)\:{obvious}\:{soln}.\:{x}=\mathrm{0} \\ $$$${Observe}\:{that}: \\ $$$$\frac{{t}^{\mathrm{2}} }{\left({t}\:{sinh}\left({t}\right)\:−\:{cosh}\left({t}\right)\right)^{\mathrm{2}} }\geqslant\mathrm{0}\:\left({equality}\:{for}\:{t}\neq\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{x}>\mathrm{0}…
Question Number 173411 by mnjuly1970 last updated on 11/Jul/22 $$ \\ $$$$\:\:\:\:\:\:\:\mathrm{Q}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\mathrm{26}\:!\:\right)^{\:\mathrm{58}} \:+\:\mathrm{k}\:\overset{\:\mathrm{29}} {\equiv}\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{and}\:,\:\:\mathrm{k}\:\in\:\mathbb{N}\:,\:\:\mathrm{find}:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\:\left(\:\mathrm{k}\:\right)=? \\ $$$$ \\ $$ Answered…
Question Number 173406 by Shrinava last updated on 11/Jul/22 $$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\left(\mathrm{1}\:+\:\mathrm{n}!\right)^{\boldsymbol{\mathrm{n}}!} }}{\mathrm{n}\:\centerdot\:\left(\mathrm{n}!\right)!} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 173396 by pete last updated on 11/Jul/22 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{statements}: \\ $$$${x}:\:\mathrm{Birds}\:\mathrm{fly} \\ $$$${y}:\:\mathrm{The}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue} \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{statements}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{represented}\:\mathrm{aa}\:{x}\Leftrightarrow{y}? \\ $$$$\left({i}\right)\:\mathrm{When}\:\mathrm{the}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue},\:\mathrm{the}\:\mathrm{birds}\:\mathrm{fly}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Either}\:\mathrm{the}\:\mathrm{bird}\:\mathrm{is}\:\mathrm{flying}\:\mathrm{or}\:\mathrm{the}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue}. \\ $$$$\left({iii}\right)\:\mathrm{Birds}\:\mathrm{fly}\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sky}\:\mathrm{is}\:\mathrm{blue}. \\…
Question Number 173393 by Shrinava last updated on 10/Jul/22 $$\mathrm{If}\:\:\mathrm{a},\mathrm{b}\geqslant\mathrm{0}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\int_{\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \int_{\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\mid\mathrm{ay}−\mathrm{ab}\:+\:\mathrm{bx}\mid\:\mathrm{dydx}\:\leqslant\:\mathrm{a}^{\mathrm{2}} \mathrm{b}^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 173383 by AgniMath last updated on 10/Jul/22 Answered by som(math1967) last updated on 10/Jul/22 $$\frac{\mathrm{1}}{\mathrm{1}+{a}+\frac{\mathrm{2}}{{b}}}\:+\frac{{ac}}{{ac}+\frac{{abc}}{\mathrm{2}}+{ac}.{c}^{−\mathrm{1}} } \\ $$$$\:\:+\frac{{a}}{{a}+{a}.{a}^{−\mathrm{1}} +{ac}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{1}+{a}+{ac}}\:+\frac{{ac}}{{ac}+\mathrm{1}+{a}}\:+\frac{{a}}{{a}+\mathrm{1}+{ac}}\:\bigstar \\ $$$$=\frac{\mathrm{1}+{a}+{ac}}{\mathrm{1}+{a}+{ac}}=\mathrm{1}…
Question Number 173377 by Shrinava last updated on 10/Jul/22 $$\mathrm{If}\:\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}>\mathrm{0} \\ $$$$\mathrm{And}\:\:\frac{\mathrm{1}}{\mathrm{a}+\mathrm{1}}\:+\:\frac{\mathrm{2}}{\mathrm{b}+\mathrm{1}}\:+\:\frac{\mathrm{3}}{\mathrm{c}+\mathrm{1}}\:+\:\frac{\mathrm{4}}{\mathrm{d}+\mathrm{1}}\:=\:\mathrm{1} \\ $$$$\mathrm{Then}\:\mathrm{find}\:\:\frac{\mathrm{a}}{\mathrm{a}+\mathrm{1}}\:+\:\frac{\mathrm{2b}}{\mathrm{b}+\mathrm{1}}\:+\:\frac{\mathrm{3c}}{\mathrm{c}+\mathrm{1}}\:+\:\frac{\mathrm{4d}}{\mathrm{d}+\mathrm{1}} \\ $$ Answered by Rasheed.Sindhi last updated on 10/Jul/22 $$\begin{array}{|c|}{\underset{\underset{} {\mathrm{And}\:\:\frac{\mathrm{1}}{\mathrm{a}+\mathrm{1}}\:+\:\frac{\mathrm{2}}{\mathrm{b}+\mathrm{1}}\:+\:\frac{\mathrm{3}}{\mathrm{c}+\mathrm{1}}\:+\:\frac{\mathrm{4}}{\mathrm{d}+\mathrm{1}}\:=\:\mathrm{1}}}…
Question Number 42304 by maxmathsup by imad last updated on 22/Aug/18 $${solve}\:{in}\:{Z}^{\mathrm{3}} \:\:\:\:{x}+\mathrm{2}{y}\:+\mathrm{3}{z}\:=\mathrm{12}\:\:. \\ $$ Commented by maxmathsup by imad last updated on 24/Aug/18 $${let}\:{consider}\:{the}\:{congruence}\:{modulo}\:\mathrm{3}\:\left(\:{Z}/\mathrm{3}{Z}\right)\:…
Question Number 173372 by Shrinava last updated on 10/Jul/22 Answered by a.lgnaoui last updated on 11/Jul/22 $$\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}×\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{xlog}^{\mathrm{7}} \mathrm{x}\right)}=\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{xlog}^{\mathrm{7}} \mathrm{x}\right)}−\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{1}+\mathrm{xlog}^{\mathrm{7}} \mathrm{x}\right)} \\ $$$$=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{xlog}^{\mathrm{7}}…