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Author: Tinku Tara

find-the-equation-of-the-cirvle-3x-2-3y-2-12x-6x-45-gt-0-x-2-y-2-4x-2y-15-gt-0-x-2-4x-y-2-2y-gt-15-x-2-4x-1-2-4-2-y-2-2y-1-2-2-2-gt-15-4-1-x-2-4x-4-y-2-2y-1-gt-20-x-2-2-x-1-

Question Number 222084 by atara last updated on 17/Jun/25 $${find}\:{the}\:{equation}\:{of}\:{the}\:{cirvle}\:\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} −\mathrm{12}{x}−\mathrm{6}{x}−\mathrm{45}>\mathrm{0} \\ $$$$ \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{2}{y}−\mathrm{15}>\mathrm{0} \\ $$$${x}^{\mathrm{2}} −\mathrm{4}{x}+{y}^{\mathrm{2}} −\mathrm{2}{y}>\mathrm{15} \\ $$$${x}^{\mathrm{2}} −\mathrm{4}{x}+\left(\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{4}\right)^{\mathrm{2}}…

Question-222097

Question Number 222097 by MathematicalUser2357 last updated on 17/Jun/25 Commented by mr W last updated on 17/Jun/25 $${wrong}! \\ $$$$\left({a}+{b}+{c}\right)^{{n}} =\underset{\underset{\mathrm{0}\leqslant{i},{j},{k}\leqslant{n}} {{i}+{j}+{k}={n}}} {\sum}\left(\frac{{n}!}{{i}!{j}!{k}!}{a}^{{i}} {b}^{{j}} {c}^{{k}}…

Question-222076

Question Number 222076 by Tawa11 last updated on 16/Jun/25 Answered by Ghisom last updated on 17/Jun/25 $$\mathrm{different}\:\mathrm{methods},\:\mathrm{I}\:\mathrm{like}\:\mathrm{this}\:\mathrm{one}: \\ $$$${x}={I}+{f};\:{I}\in\mathbb{Z}\wedge{f}\in\mathbb{R}\wedge\mathrm{0}\leqslant{f}<\mathrm{1} \\ $$$$\mathrm{4}\left({I}+{f}\right)^{\mathrm{2}} −\mathrm{40}{I}+\mathrm{51}=\mathrm{0} \\ $$$$\mathrm{solving}\:\mathrm{for}\:{f}: \\…

lim-n-1-1-2-2-3-3-n-n-n-1-2-n-2-1-2-n-2-1-12-e-1-4-n-2-Help-i-can-t-Solve-that-lim-n-a-n-

Question Number 222057 by wewji12 last updated on 16/Jun/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}^{\mathrm{1}} ×\mathrm{2}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{3}} ……×{n}^{{n}} }{{n}^{\frac{\mathrm{1}}{\mathrm{2}}{n}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}{n}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{12}}} ×{e}^{−\frac{\mathrm{1}}{\mathrm{4}}{n}^{\mathrm{2}} } }=??? \\ $$$$\mathrm{Help}…. \\ $$$$\mathrm{i}\:\mathrm{can}'\mathrm{t}\:\mathrm{Solve}\:\mathrm{that}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}}…