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Category: Geometry

Is-it-correct-floor-x-x-x-floor-x-n-n-Z-x-1-lt-n-x-e-g-floor-3-3-floor-3-4-3-floor-2-5-3-floor-pi-4-

Question Number 7326 by sou1618 last updated on 23/Aug/16 $${Is}\:{it}\:{correct}? \\ $$$$\:\:{floor}\left({x}\right)=\lfloor{x}\rfloor=\left[{x}\right] \\ $$$$ \\ $$$$ \\ $$$${floor}\left({x}\right)=\left\{{n}\:\mid\:{n}\in\mathbb{Z}\:,\:{x}−\mathrm{1}<{n}\leqslant{x}\right\} \\ $$$${e}.{g}…. \\ $$$${floor}\left(\mathrm{3}\right)=\mathrm{3} \\ $$$${floor}\left(\mathrm{3}.\mathrm{4}\right)=\mathrm{3} \\…

Question-7314

Question Number 7314 by Rasheed Soomro last updated on 23/Aug/16 Commented by Rasheed Soomro last updated on 23/Aug/16 $${Top}\:{and}\:{bottom}\:{of}\:{a}\:{solid}\:{are}\:{congruent}\:{circles}. \\ $$$${Above}\:{is}\:{the}\:{cross}-{section}\:{of}\:{the}\:{solid},\:{which}\: \\ $$$${is}\:{obtained}\:{by}\:{cutting}\:{the}\:{solid}\:{in}\:{two}\:{equal}\:{parts}. \\ $$$${Find}\:{out}\:{the}\:{volume}\:{of}\:{the}\:{solid}.…

lim-x-x-2-x-1-x-2-1-lt-

Question Number 7243 by Sh505146@gmail.com last updated on 18/Aug/16 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{\left.{x}^{\mathrm{2}} +{x}+\mathrm{1}\right)}−\left(\sqrt{\left.{x}^{\mathrm{2}} +\mathrm{1}\right)}\right.\right. \\ $$$$< \\ $$ Commented by Rasheed Soomro last updated on 18/Aug/16…

Question-72672

Question Number 72672 by mr W last updated on 31/Oct/19 Commented by mr W last updated on 31/Oct/19 $${find}\:{u}_{{min}} \:{for}\:{the}\:{stone}\:{to}\:{hit}\:{the} \\ $$$${ground}\:{behind}\:{the}\:{sphere}. \\ $$$$\left({see}\:{also}\:{Q}\mathrm{72563},\:{with}\:{thanks}\:{to}\:\right. \\…

prove-pi-5-3-2-4-2-1-2-pi-

Question Number 72639 by kennethalli last updated on 31/Oct/19 $${prove}:\frac{\pi}{\mathrm{5}}\left(\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\pi \\ $$ Answered by MJS last updated on 31/Oct/19 $$\mathrm{are}\:\mathrm{you}\:\mathrm{serious}? \\ $$$$\frac{\pi}{\mathrm{5}}\left(\mathrm{3}^{\mathrm{2}}…