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Author: Tinku Tara

Question-210761

Question Number 210761 by mr W last updated on 18/Aug/24 Commented by mr W last updated on 18/Aug/24 $${find}\:{the}\:{radius}\:{R}\:{of}\:{the}\:{largest}\:{sphere} \\ $$$${which}\:{can}\:{be}\:{placed}\:{between}\:{the}\:{red} \\ $$$${and}\:{blue}\:{planes}\:{in}\:{the}\:{first}\:{octant}. \\ $$$${assume}\:\mathrm{0}<{p}\leqslant{a},\:\mathrm{0}<{q}\leqslant{b},\:\mathrm{0}<{r}\leqslant{c}.…

Question-210754

Question Number 210754 by mokys last updated on 18/Aug/24 Answered by Berbere last updated on 19/Aug/24 $$\mathrm{1}+{N}^{{r}} \sim{N}^{{r}} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\underset{{k}=\mathrm{1}} {\overset{{N}} {\sum}}{k}^{{s}} }{{N}^{{s}} }=\underset{{N}\rightarrow\infty}…

Question-210701

Question Number 210701 by noraell last updated on 17/Aug/24 Answered by Berbere last updated on 18/Aug/24 $${f}'\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\geqslant\mathrm{1}\:{Increase}\:{steictly}\: \\ $$$${f}\:{is}\:{bijection}\:\mathbb{R}\rightarrow\mathbb{R}\Rightarrow{f}^{−} \:{existe} \\ $$$$\mathrm{2}{f}\left({x}\right)+\mathrm{3}{f}^{−} \left({x}\right)=\mathrm{10} \\…

If-sin1-a-1-cos1-cos2-1-cos2-cos3-1-cos44-cos45-

Question Number 210718 by hardmath last updated on 17/Aug/24 $$\mathrm{If}\:\:\:\mathrm{sin1}°\:=\:\mathrm{a} \\ $$$$\frac{\mathrm{1}}{\mathrm{cos1}°\centerdot\mathrm{cos2}°}\:+\:\frac{\mathrm{1}}{\mathrm{cos2}°\centerdot\mathrm{cos3}°}\:+…+\:\frac{\mathrm{1}}{\mathrm{cos44}°\centerdot\mathrm{cos45}°}\:=\:? \\ $$ Commented by Spillover last updated on 18/Aug/24 $${i}\:{get}\:\mathrm{22}\:? \\ $$ Terms…