Question Number 196084 by Mingma last updated on 17/Aug/23 Answered by mr W last updated on 17/Aug/23 Commented by mr W last updated on 17/Aug/23…
Question Number 195790 by justenspi last updated on 10/Aug/23 $${a},{b},{c}\:{are}\:{positive}\:{real}\:{numbers}\:{and}\:{abc}\:=\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$\left({a}−\mathrm{1}+\frac{\mathrm{1}}{{b}}\right)\left({b}−\mathrm{1}+\frac{\mathrm{1}}{{c}}\right)\left({c}−\mathrm{1}+\frac{\mathrm{1}}{{a}}\right)\leqslant\mathrm{1} \\ $$ Commented by justenspi last updated on 10/Aug/23 $${Case}\left({I}\right)\left({a}−\mathrm{1}+\frac{\mathrm{1}}{{b}}\right),\left({b}−\mathrm{1}+\frac{\mathrm{1}}{{c}}\right),\left({c}−\mathrm{1}+\frac{\mathrm{1}}{{a}}\right)>\mathrm{0} \\…
Question Number 195611 by Mingma last updated on 05/Aug/23 Answered by mr W last updated on 06/Aug/23 $${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