Question Number 19654 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Two}\:\mathrm{swimmers}\:\mathrm{leave}\:\mathrm{point}\:{A}\:\mathrm{on}\:\mathrm{one} \\ $$$$\mathrm{bank}\:\mathrm{of}\:\mathrm{the}\:\mathrm{river}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{point}\:{B}\:\mathrm{lying} \\ $$$$\mathrm{right}\:\mathrm{across}\:\mathrm{the}\:\mathrm{other}\:\mathrm{bank}.\:\mathrm{One}\:\mathrm{of} \\ $$$$\mathrm{them}\:\mathrm{crosses}\:\mathrm{the}\:\mathrm{river}\:\mathrm{along}\:\mathrm{the}\:\mathrm{straight} \\ $$$$\mathrm{line}\:{AB}\:\mathrm{while}\:\mathrm{the}\:\mathrm{other}\:\mathrm{swims}\:\mathrm{at}\:\mathrm{right} \\ $$$$\mathrm{angle}\:\mathrm{to}\:\mathrm{the}\:\mathrm{stream}\:\mathrm{and}\:\mathrm{then}\:\mathrm{walks}\:\mathrm{the} \\ $$$$\mathrm{distance}\:\mathrm{that}\:\mathrm{he}\:\mathrm{has}\:\mathrm{been}\:\mathrm{carried}\:\mathrm{away} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{stream}\:\mathrm{to}\:\mathrm{get}\:\mathrm{to}\:\mathrm{point}\:{B}.\:\mathrm{What} \\…
Question Number 150721 by cesarL last updated on 14/Aug/21 $${calculate}\:{the}\:{convergence}\:{interval}\:{of}\:{the} \\ $$$${serie} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}} }{{n}!} \\ $$ Answered by ArielVyny last updated…
Question Number 85187 by mathocean1 last updated on 19/Mar/20 $${Show}\:{that}\:\forall\:{n},\:{p}\:\in\:\mathbb{N}^{\ast\:} \\ $$$${C}_{{n}−\mathrm{1}} ^{\:{p}−\mathrm{1}} +{C}_{{n}−\mathrm{1}} ^{\:{p}} ={C}_{{n}} ^{\:{p}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 85184 by Serlea last updated on 19/Mar/20 $$\mathrm{Serlea} \\ $$$$\mathrm{Shows}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digit}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{100}^{\mathrm{25}} −\mathrm{25} \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{4}. \\ $$ Commented by mr W last updated…
Question Number 85183 by Serlea last updated on 19/Mar/20 $$\mathrm{Hi}\:\mathrm{veterans} \\ $$$$\mathrm{Serlea}\:\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{three}\:\mathrm{digits}\:\mathrm{of}: \\ $$$$\mathrm{3005}^{\mathrm{11}} +\mathrm{3005}^{\mathrm{12}} +\mathrm{3005}^{\mathrm{13}} +…+\mathrm{3005}^{\mathrm{3002}} \\ $$$$ \\ $$$$…
Find-the-sum-of-all-possible-digits-that-comes-at-ten-s-place-for-3-n-where-n-is-any-natural-number-
Question Number 19646 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{digits}\:\mathrm{that} \\ $$$$\mathrm{comes}\:\mathrm{at}\:\mathrm{ten}'\mathrm{s}\:\mathrm{place}\:\mathrm{for}\:\mathrm{3}^{{n}} \:\mathrm{where}\:{n}\:\mathrm{is} \\ $$$$\mathrm{any}\:\mathrm{natural}\:\mathrm{number}. \\ $$ Commented by Tinkutara last updated on 16/Aug/17 $$\mathrm{help}\:\mathrm{pls}…
Question Number 150719 by mathdanisur last updated on 14/Aug/21 Commented by MJS_new last updated on 15/Aug/21 $$\frac{\mathrm{1}+\sqrt{\mathrm{21}}}{\mathrm{2}}\leqslant{x}+{y}\leqslant\mathrm{1}+\sqrt{\mathrm{11}} \\ $$ Commented by mathdanisur last updated on…
Question Number 150718 by mathdanisur last updated on 14/Aug/21 $$\mathrm{Calculate}: \\ $$$$\mathrm{Li}_{\mathrm{2}} \left(\boldsymbol{\mathrm{z}}\right)\:+\:\mathrm{Li}_{\mathrm{2}} \left(\mathrm{1}\:-\:\boldsymbol{\mathrm{z}}\right)\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 14/Aug/21 $$\mathrm{Li}\left({z}\right)\:=\:−\int_{\mathrm{0}} ^{{z}}…
Question Number 19643 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\sqrt{\mathrm{17}\:+\:\mathrm{8}{x}\:−\:\mathrm{2}{x}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{4}\:+\:\mathrm{12}{x}\:−\:\mathrm{3}{x}^{\mathrm{2}} }\:=\:{x}^{\mathrm{2}} \\ $$$$−\:\mathrm{4}{x}\:+\:\mathrm{13}. \\ $$ Answered by ajfour last updated on 13/Aug/17…
Question Number 85176 by jagoll last updated on 19/Mar/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{range}\: \\ $$$$\mathrm{function}\:\mathrm{y}\:=\:\sqrt{\mathrm{x}−\mathrm{1}}\:+\:\sqrt{\mathrm{5}−\mathrm{x}} \\ $$ Answered by john santu last updated on 19/Mar/20 $$\mathrm{Domain}\::\:\mathrm{x}\:\geqslant\:\mathrm{1}\:\wedge\:\mathrm{x}\:\leqslant\:\mathrm{5}\:\Rightarrow\:\mathrm{1}\:\leqslant\mathrm{x}\leqslant\mathrm{5} \\ $$$$\mathrm{Range}\::\:\mathrm{y}\:'\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}−\mathrm{1}}}\:−\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{5}−\mathrm{x}}}\:=\:\mathrm{0}…