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Question-199392

Question Number 199392 by Calculusboy last updated on 03/Nov/23 Answered by mr W last updated on 03/Nov/23 $$\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({y}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{53} \\ $$$$\left({x}+\mathrm{2}\right)^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{13} \\…

Question-199393

Question Number 199393 by Calculusboy last updated on 02/Nov/23 Answered by cortano12 last updated on 03/Nov/23 $$\:\mathrm{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\frac{\mathrm{x}}{\mathrm{2011}}\right)\left(\mathrm{1}+\frac{\mathrm{2x}}{\mathrm{2012}}\right)\left(\mathrm{1}+\frac{\mathrm{3x}}{\mathrm{2013}}\right)−\mathrm{1}}{\mathrm{x}} \\ $$$$\:\:\mathrm{A}=\:\frac{\mathrm{1}}{\mathrm{2011}}\:+\frac{\mathrm{2}}{\mathrm{2012}}\:+\:\frac{\mathrm{3}}{\mathrm{2013}}\: \\ $$ Commented by essaad…

What-is-the-probability-that-in-a-class-of-18-people-there-exists-exactly-a-group-of-exactly-3-people-born-on-the-same-day-of-the-week-

Question Number 199353 by mr W last updated on 01/Nov/23 $${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{exactly}\:{a}\: \\ $$$${group}\:{of}\:{exactly}\:\mathrm{3}\:{people}\:{born}\:{on}\:{the} \\ $$$${same}\:{day}\:{of}\:{the}\:{week}? \\ $$ Commented by AST last updated on…

Question-199355

Question Number 199355 by hardmath last updated on 01/Nov/23 Answered by MathematicalUser2357 last updated on 04/Nov/23 $$\Omega\approx\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}!}{{n}^{{n}} }\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}{n}} }??? \\ $$ Terms…

Determine-the-continuity-ortherwise-of-the-following-functions-a-7x-2-x-3-x-2-2-b-x-2-4x-1-c-f-x-1-x-1-4-x-2-3-x-2-5-

Question Number 199312 by Mastermind last updated on 01/Nov/23 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{continuity}\:\mathrm{ortherwise}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{following}\:\mathrm{functions} \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\:\frac{\mathrm{7x}^{\mathrm{2}} +\mathrm{x}−\mathrm{3}}{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{1} \\ $$$$…