Question Number 150462 by Tawa11 last updated on 12/Aug/21 Answered by puissant last updated on 12/Aug/21 $$\mathrm{I}=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{ln}\left(\frac{\mathrm{2}+\mathrm{3n}}{\mathrm{1}+\mathrm{3n}}\right) \\ $$$$\mathrm{posons}\:\mathrm{U}_{\mathrm{n}} =\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{ln}\left(\frac{\mathrm{2}+\mathrm{3n}}{\mathrm{1}+\mathrm{3n}}\right) \\…
Question Number 19388 by mrW1 last updated on 10/Aug/17 $$\mathrm{related}\:\mathrm{to}\:\mathrm{Q}.\mathrm{19333} \\ $$$$\mathrm{the}\:\mathrm{side}\:\mathrm{lengthes}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\: \\ $$$$\mathrm{integer}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle} \\ $$$$\mathrm{is}\:\mathrm{100},\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}\:\mathrm{triangles} \\ $$$$\mathrm{exist}?\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{them}? \\ $$ Commented by mrW1…
Question Number 19385 by NEC last updated on 10/Aug/17 $${tan}^{\mathrm{2}} \beta=−\mathrm{1} \\ $$$$ \\ $$$${find}\:\beta….\:{lets}\:{solve}\:{for}\:{fun} \\ $$ Commented by NEC last updated on 10/Aug/17 $${please}\:{help}…
Question Number 150453 by mathdanisur last updated on 12/Aug/21 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:,\:\bigtriangleup\mathrm{A}^{'} \mathrm{B}^{'} \mathrm{C}^{'} \:\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{relationship}\:\mathrm{holds}: \\ $$$$\mathrm{R}^{\mathrm{2}} \mathrm{R}^{'} \mathrm{F}^{'} \:\geqslant\:\mathrm{8F}\left(\mathrm{r}^{'} \right)^{\mathrm{3}} \\ $$ Terms of…
Question Number 84915 by M±th+et£s last updated on 17/Mar/20 $${if}\: \\ $$$${x}>\mathrm{0},{y}>\mathrm{0},{z}>\mathrm{0} \\ $$$${show}\:{that} \\ $$$$\frac{{x}+{y}}{{z}}+\frac{{z}+{y}}{\:{x}}+\frac{{z}+{x}}{{y}}\geqslant\mathrm{6}\:\: \\ $$ Answered by TANMAY PANACEA last updated on…
Question Number 150451 by ajfour last updated on 12/Aug/21 Commented by Ar Brandon last updated on 12/Aug/21 $$\mathrm{I}\:\mathrm{admire}\:\mathrm{your}\:\mathrm{posts}\:\mathrm{sir}.\:\mathrm{Sadly}\:\mathrm{I}\:\mathrm{have}\:\mathrm{very}\:\mathrm{little}\:\mathrm{knowledge} \\ $$$$\mathrm{on}\:\mathrm{geometry}.\:\mathrm{You}'\mathrm{re}\:\mathrm{so}\:\mathrm{advanced}.\:\mathrm{Hahaha}\:!\:\mathrm{I}\:\mathrm{hope}\:\mathrm{I}\:\mathrm{will}\:\mathrm{get} \\ $$$$\mathrm{there}\:\mathrm{someday}. \\ $$ Commented…
Question Number 150450 by jlewis last updated on 12/Aug/21 $$\mathrm{show}\:\mathrm{the}?\mathrm{connection}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{beta}\:\mathrm{distribution}\left(\mathrm{n},\mathrm{p}\right)\:\mathrm{and}\:\mathrm{hypergeometric} \\ $$$$\mathrm{distribution}\left(\mathrm{N},\mathrm{k},\mathrm{n}\right)\mathrm{in}\:\mathrm{a}\:\mathrm{limiting}\:\mathrm{case} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84913 by M±th+et£s last updated on 17/Mar/20 $$ \\ $$$${sin}\frac{\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{3}\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{5}\pi}{\mathrm{15}}=? \\ $$ Commented by jagoll last updated on 17/Mar/20 $$\mathrm{sin}\:\frac{\pi}{\mathrm{14}}\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{14}}\mathrm{sin}\:\frac{\mathrm{5}\pi}{\mathrm{14}}\:?\:\mathrm{or}\:\mathrm{not} \\ $$ Commented…
Question Number 150446 by mathdanisur last updated on 12/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84909 by naka3546 last updated on 17/Mar/20 $${Find}\:\:\:{all}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y}\right)\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} \:−\:\mathrm{3}{xy}^{\mathrm{2}} \:\:=\:\:\mathrm{2010} \\ $$$$\:\:\:\:\:\:\:\:{y}^{\mathrm{3}} \:−\:\mathrm{3}{x}^{\mathrm{2}} {y}\:\:=\:\:\mathrm{2009} \\ $$$${x},\:{y}\:\:\in\:\:\mathbb{R} \\ $$ Commented by john…