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Author: Tinku Tara

Question-11020

Question Number 11020 by ridwan balatif last updated on 07/Mar/17 Answered by sandy_suhendra last updated on 08/Mar/17 Commented by sandy_suhendra last updated on 08/Mar/17 $$\left.\mathrm{1}\right)\:\mathrm{P}\left(−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{A}\:,\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{B}\right)\:=\:\mathrm{P}\left(\mathrm{5},\mathrm{7}\right)…

Question-11019

Question Number 11019 by ridwan balatif last updated on 07/Mar/17 Answered by bahmanfeshki last updated on 07/Mar/17 $${I}=\int_{\mathrm{2}} ^{{n}} {xe}^{−\mathrm{2}{x}+\mathrm{4}} \:{dx}=−\frac{\mathrm{1}}{\mathrm{2}}\left(\left[{xe}^{−\mathrm{2}{x}+\mathrm{4}} \right]_{\mathrm{2}} ^{{n}} −\int_{\mathrm{2}\:\:} ^{{n}}…

Question-76555

Question Number 76555 by aliesam last updated on 28/Dec/19 Answered by MJS last updated on 28/Dec/19 $$\mathrm{if}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{located}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same}\:\mathrm{lines} \\ $$$$\mathrm{blue}\:\mathrm{area}\:=\:\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}{a}^{\mathrm{2}} \\ $$$$\mathrm{red}\:\mathrm{area}\:=\:\frac{\pi}{\mathrm{6}}{b}^{\mathrm{2}} \\ $$$$\Rightarrow\:{b}=\frac{\sqrt[{\mathrm{4}}]{\mathrm{27}}}{\:\sqrt{\mathrm{2}\pi}}{a} \\ $$$$\mathrm{s}=\frac{\pi}{\mathrm{3}}{b}=\frac{\sqrt[{\mathrm{4}}]{\mathrm{27}}\sqrt{\mathrm{2}\pi}}{\mathrm{6}}{a}…

Proof-that-1-3n-lt-n-2-for-every-positive-integer-n-4-

Question Number 142085 by Rexzie last updated on 30/May/21 $${Proof}\:{that}\:\mathrm{1}+\mathrm{3}{n}<{n}^{\mathrm{2}} \:{for}\:{every}\:{positive}\:{integer}\:{n}\geqslant\mathrm{4} \\ $$ Answered by MJS_new last updated on 26/May/21 $$\mathrm{it}'\mathrm{s}\:\mathrm{wrong}\:\mathrm{for}\:\frac{\mathrm{3}−\sqrt{\mathrm{13}}}{\mathrm{2}}\leqslant{n}\leqslant\frac{\mathrm{3}+\sqrt{\mathrm{13}}}{\mathrm{2}} \\ $$ Answered by…