Question Number 42375 by Joel578 last updated on 24/Aug/18 $$\mathrm{Find}\:\mathrm{value}\:\mathrm{of}\:\:\alpha\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system} \\ $$$$\mathrm{has}\:\mathrm{infinite}\:\mathrm{many}\:\mathrm{solutions} \\ $$$$ \\ $$$${x}\:−\:\mathrm{3}{z}\:=\:−\mathrm{3} \\ $$$$−\mathrm{2}{x}\:−\:\alpha{y}\:+\:{z}\:=\:\mathrm{2} \\ $$$${x}\:+\:\mathrm{2}{y}\:+\:\alpha{z}\:=\:\mathrm{1} \\ $$ Commented by Joel578…
Question Number 173431 by mnjuly1970 last updated on 11/Jul/22 Commented by Rasheed.Sindhi last updated on 11/Jul/22 $$\left({a},{b}\right)=\left(\mathrm{10},\mathrm{13}\right),\left(\mathrm{13},\mathrm{10}\right); \\ $$$${n}=\mathrm{3197}=\mathrm{23}×\mathrm{139} \\ $$ Commented by mr W…
Question Number 173430 by dragan91 last updated on 11/Jul/22 Commented by Rasheed.Sindhi last updated on 11/Jul/22 $${a}=\mathrm{0},\:{b}={c}=\mathrm{2} \\ $$$${a}=−\mathrm{1},\left({b},{c}\right)=\left(\mathrm{0},\mathrm{1}\right),\left(\mathrm{1},\mathrm{0}\right),\left(\mathrm{1},\mathrm{1}\right) \\ $$ Commented by dragan91 last…
Question Number 173426 by Shrinava last updated on 11/Jul/22 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}: \\ $$$$\left(\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} \right)\left(\mathrm{h}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{3}} +\mathrm{h}_{\boldsymbol{\mathrm{b}}} ^{\mathrm{3}} +\mathrm{h}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{3}} \right)\:\geqslant\:\mathrm{5832}\:\sqrt{\mathrm{3}}\:\mathrm{r}^{\mathrm{6}} \\ $$…
Question Number 173420 by AgniMath last updated on 11/Jul/22 Answered by Rasheed.Sindhi last updated on 11/Jul/22 $${x}+{y}+{z}=\mathrm{0}; \\ $$$$\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{z}^{\mathrm{2}} }+\frac{\mathrm{1}}{{y}^{\mathrm{2}} +{z}^{\mathrm{2}} −{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{{z}^{\mathrm{2}}…
Question Number 173421 by Shrinava last updated on 11/Jul/22 $$\mathrm{In}\:\mathrm{triangle}\:\:\mathrm{ABC},\:\mathrm{AD}\:\mathrm{is}\:\mathrm{the}\:\mathrm{bisector} \\ $$$$\mathrm{of}\:\:\angle\mathrm{A}\:\:\mathrm{meets}\:\:\mathrm{BC}\:\mathrm{at}\:\mathrm{D},\:\mathrm{if}\:\:\mathrm{2}\angle\mathrm{C}=\angle\mathrm{B} \\ $$$$\mathrm{and}\:\mathrm{AB}=\mathrm{DC}.\:\mathrm{Find}\:\angle\mathrm{BAC} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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
Question Number 107867 by I want to learn more last updated on 13/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com