Question Number 195611 by Mingma last updated on 05/Aug/23 Answered by mr W last updated on 06/Aug/23 $${a}={side}\:{length}\:{of}\:{small}\:{pentagon} \\ $$$${b}={side}\:{length}\:{of}\:{big}\:{pentagon} \\ $$$${b}=\mathrm{2}{a}\:\mathrm{sin}\:\mathrm{54}° \\ $$$${a}=\mathrm{2}{r}\:\mathrm{sin}\:\mathrm{36}°\:\Rightarrow{r}=\frac{{a}}{\mathrm{2}\:\mathrm{sin}\:\mathrm{36}°} \\…
Question Number 195570 by York12 last updated on 05/Aug/23 $$\mathrm{Given}\:\mathrm{three}\:\mathrm{Real}\:\mathrm{numbers}\:\left({x},{y},{z}\right),{such}\:{that} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{1} \\ $$$${maximize} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} −\mathrm{2}{z}^{\mathrm{4}} −\mathrm{3}\sqrt{\mathrm{2}}{xyz} \\ $$ Commented…
Question Number 195590 by Mingma last updated on 05/Aug/23 Answered by mr W last updated on 05/Aug/23 Commented by mr W last updated on 05/Aug/23…
Question Number 195484 by Shlock last updated on 03/Aug/23 Answered by mr W last updated on 03/Aug/23 Commented by mr W last updated on 03/Aug/23…
Question Number 195470 by Shlock last updated on 03/Aug/23 Answered by mr W last updated on 03/Aug/23 Commented by mr W last updated on 03/Aug/23…
Question Number 195322 by Rupesh123 last updated on 30/Jul/23 Answered by HeferH last updated on 31/Jul/23 $${say}\:{k}\:{is}\:{the}\:{incenter}\:{length} \\ $$$$\:{k}\:=\:\frac{{A}}{{s}} \\ $$$$\:{s}\:=\:\frac{{AB}+{AC}+{BC}}{\mathrm{2}} \\ $$$$\:{A}\:=\:\frac{\mathrm{3}{k}\centerdot{BC}}{\mathrm{2}} \\ $$$$\:\mathrm{1}\:=\:\frac{\mathrm{3}{BC}}{{AB}+{AC}+{BC}}…
Question Number 195178 by Shlock last updated on 26/Jul/23 Answered by mr W last updated on 26/Jul/23 $${DC}={BC}=\mathrm{2},\:{say} \\ $$$${KD}=\mathrm{1} \\ $$$$\angle{KCD}=\alpha,\:{say} \\ $$$$\left(\mathrm{1}+\mathrm{2}\:\mathrm{cos}\:\mathrm{60}°\right)\:\mathrm{tan}\:\left(\mathrm{60}°−\alpha\right)=\mathrm{2}\:\mathrm{sin}\:\mathrm{60}° \\…
Question Number 194985 by Erico last updated on 21/Jul/23 $$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\left[\left(\frac{\mathrm{1}}{\mathrm{n}}\right)^{\mathrm{n}} +\left(\frac{\mathrm{2}}{\mathrm{n}}\right)^{\mathrm{n}} +…\left(\frac{\mathrm{n}−\mathrm{1}}{\mathrm{n}}\right)^{\mathrm{n}} \right]=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 194967 by Rupesh123 last updated on 21/Jul/23 Answered by a.lgnaoui last updated on 23/Jul/23 $$\mathrm{4}\:\mathrm{cercles}\:\mathrm{disposes}\:\mathrm{comme}\:\mathrm{suit} \\ $$$$\left.\bullet\mathrm{1}\right)\:\:\mathrm{cercle}\:\boldsymbol{\mathrm{R}}\mathrm{ouge}\:\boldsymbol{\mathrm{C}}\mathrm{1}\left(\mathrm{Rayon}\:\boldsymbol{\mathrm{R}}\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\mathrm{2}\boldsymbol{\mathrm{R}}\mathrm{1}=\boldsymbol{\mathrm{AB}}=\mathrm{12}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{R}}\mathrm{1}=\mathrm{6} \\ $$$$\left.\bullet\mathrm{2}\right)\:\mathrm{cercle}\:\boldsymbol{\mathrm{V}}\mathrm{ert}\:\boldsymbol{\mathrm{C}}\mathrm{2}\left(\boldsymbol{\mathrm{R}}\mathrm{ayon}\:\boldsymbol{\mathrm{R}}\mathrm{2}\right)\:/ \\ $$$$\:\:\:\:\:\mathrm{demi}−\mathrm{cercle}\:\:\boldsymbol{\mathrm{C}}\left(\boldsymbol{\mathrm{A}},\boldsymbol{\mathrm{B}},\boldsymbol{\mathrm{C}}\right)…
Question Number 194796 by sniper237 last updated on 15/Jul/23 $${A}\:\mathrm{1}{m}^{\mathrm{2}} \:{rectangle}\:{which}\:{length}\:{is}\: \\ $$$${less}\:{than}\:\mathrm{1}\:{is}\:\:{a}\:{square}.\:{Why}? \\ $$ Answered by Frix last updated on 15/Jul/23 $$\mathrm{It}'\mathrm{s}\:\mathrm{obviously}\:\mathrm{false} \\ $$$${l}×{w}=\mathrm{1}…