Question Number 124978 by rydasss last updated on 07/Dec/20 Answered by talminator2856791 last updated on 07/Dec/20 $$\:\:\mathrm{1000}{a}\:+\:\mathrm{100}{b}\:+\:\mathrm{10}{c}\:+\:{d}+\:{a}\:+\:{b}\:+\:{c}\:+\:{d}\:+\:{x}\:=\:\mathrm{2013},\:\: \\ $$$$\:{x}\:=\:{S}\left({S}\left(\mathrm{1000}{a}\:+\:\mathrm{100}{b}\:+\:\mathrm{10}{c}\:+\:{d}\right)\right) \\ $$$$\:\mathrm{1001}{a}\:+\:\mathrm{101}{b}\:+\:\mathrm{11}{c}\:+\:\mathrm{2}{d}\:+\:{x}\:=\:\mathrm{2013} \\ $$$$\:{a}\:=\:\mathrm{1} \\ $$$$\:\mathrm{101}{b}\:+\:\mathrm{11}{c}\:+\:\mathrm{2}{d}\:+\:{x}\:=\:\mathrm{1012}…
Question Number 190512 by 073 last updated on 04/Apr/23 Answered by som(math1967) last updated on 04/Apr/23 $$\:^{\mathrm{3}} \sqrt{\sqrt{\mathrm{15}}+\frac{\mathrm{196}}{\mathrm{54}}} \\ $$$$=\:^{\mathrm{3}} \sqrt{\sqrt{\mathrm{15}}+\frac{\mathrm{98}}{\mathrm{27}}} \\ $$$$=^{\mathrm{3}} \sqrt{\frac{\mathrm{27}\sqrt{\mathrm{15}}+\mathrm{98}}{\mathrm{27}}} \\…
Question Number 190508 by 073 last updated on 04/Apr/23 Answered by Frix last updated on 04/Apr/23 $${t}=\mathrm{tan}\:{x} \\ $$$$\frac{{t}+\mathrm{1}}{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{4}\left({t}+\mathrm{1}\right)^{\mathrm{2}} ={t}^{\mathrm{2}} +\mathrm{1} \\…
Question Number 124967 by mohammad17 last updated on 07/Dec/20 Commented by mohammad17 last updated on 07/Dec/20 $${please}\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 190501 by 073 last updated on 04/Apr/23 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{3}^{\mathrm{x}} }{\mathrm{x}!}=? \\ $$$$\mathrm{solution}? \\ $$ Answered by Frix last updated on 04/Apr/23 $$\mathrm{0} \\…
Question Number 190480 by aba last updated on 03/Apr/23 $$\mathrm{Proof}\:\mathrm{that}\:\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} \in\mathbb{R}\backslash\mathrm{Q} \\ $$ Answered by mehdee42 last updated on 04/Apr/23 $${lem}:\:{if}\:\:{p}\notin{Q}\Rightarrow\sqrt{{p}}\notin{Q} \\ $$$${clim}:\:\mathrm{2}^{\sqrt{\mathrm{2}}} \notin{Q} \\…
Question Number 59400 by hhghg last updated on 09/May/19 $$\left(\mathrm{4}^{\mathrm{6}} \right)^{\mathrm{2}} \\ $$ Answered by Pranay last updated on 09/May/19 $$\mathrm{4}^{\mathrm{12}\:=\:} \mathrm{16777216} \\ $$ Terms…
Question Number 124932 by aurpeyz last updated on 07/Dec/20 Answered by som(math1967) last updated on 07/Dec/20 $$\mathrm{Equivalent}\:\mathrm{capacitance} \\ $$$$\frac{\mathrm{1}}{\mathrm{C}}=\frac{\mathrm{1}}{\mathrm{4}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}=\frac{\mathrm{3}}{\mathrm{6}} \\ $$$$\mathrm{C}=\mathrm{2}\mu\mathrm{F} \\ $$$$\mathrm{charge}\:=\mathrm{12}×\mathrm{2}=\mathrm{24}×\mathrm{10}^{−\mathrm{6}} \mathrm{coulomb} \\…
Question Number 190464 by alcohol last updated on 03/Apr/23 $$\begin{cases}{{u}_{{n}+\mathrm{1}} \:=\:{u}_{{n}} −\mathrm{3}\:}\\{{v}_{{n}+\mathrm{1}} \:=\:\mathrm{4}{v}_{{n}} }\end{cases}\::\:{u}_{\mathrm{0}} \:=\:{v}_{\mathrm{0}} \:=\:\mathrm{1} \\ $$$${w}_{{n}} \:=\:\frac{\mathrm{1}−{u}_{{n}} }{{v}_{{n}} } \\ $$$$−\:{show}\:{that}\:{w}_{{n}} \:{is}\:{bounded} \\…
Question Number 124931 by ZiYangLee last updated on 07/Dec/20 $$\mathrm{If}\:\mathrm{3}^{\mathrm{2019}} +{k}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{11},\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer}\:{k}. \\ $$ Answered by MJS_new last updated on 07/Dec/20 $$\mathrm{3}^{\mathrm{0}} =\mathrm{11}{n}+\mathrm{1} \\…