Question Number 17446 by Tinkutara last updated on 05/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{closest}\:\mathrm{to} \\ $$$$\mathrm{100}\left(\mathrm{12}\:−\:\sqrt{\mathrm{143}}\right). \\ $$ Commented by ajfour last updated on 06/Jul/17 $$\mathrm{100}\left(\mathrm{12}−\sqrt{\mathrm{143}}\right)=\frac{\mathrm{100}}{\mathrm{12}+\sqrt{\mathrm{143}}} \\ $$$$\:\:\approx\frac{\mathrm{100}}{\mathrm{24}}\:\approx\:\mathrm{4}.\mathrm{2}\: \\…
Question Number 148519 by learner001 last updated on 28/Jul/21 $$ \\ $$$$\mathrm{a}_{\mathrm{n}} =\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}} \\ $$$$\mathrm{let}\:\epsilon>\mathrm{0}\:\mathrm{be}\:\mathrm{given},\:\mid\mathrm{a}_{\mathrm{m}} −\mathrm{a}_{\mathrm{n}} \mid=\mid\frac{\mathrm{m}}{\mathrm{m}+\mathrm{1}}−\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}}\mid=\mid\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}\mid=\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}\:\mathrm{provided} \\ $$$$\mathrm{m}>\mathrm{n},\:\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}<\frac{\mathrm{m}+\mathrm{1}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}<\epsilon.\:\mathrm{if}\:\mathrm{N}>\frac{\mathrm{1}−\epsilon}{\epsilon}\:\mathrm{then}\:\mid\mathrm{a}_{\mathrm{m}} −\mathrm{a}_{\mathrm{n}} \mid<\epsilon\:\forall\:\mathrm{n},\mathrm{m}\geqslant\mathrm{N} \\ $$ Commented by…
Question Number 17444 by Tinkutara last updated on 06/Jul/17 $$\mathrm{Evaluate}:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\frac{{dx}}{\mathrm{cos}^{\mathrm{3}} \:{x}\:\sqrt{\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{x}}} \\ $$ Answered by Arnab Maiti last updated on 10/Jul/17 $$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 148513 by mathdanisur last updated on 28/Jul/21 $$\mathrm{6}\:+\:{log}_{\mathrm{2}} \:{sin}\mathrm{15}°\:-\:{log}_{\frac{\mathrm{1}}{\mathrm{2}}} {sin}\mathrm{75}°\:=\:? \\ $$ Answered by liberty last updated on 29/Jul/21 $$\chi\:=\:\mathrm{6}\:+\mathrm{log}\:_{\mathrm{2}} \mathrm{sin}\:\mathrm{15}°+\mathrm{log}\:_{\mathrm{2}} \mathrm{sin}\:\mathrm{75}° \\…
Question Number 148515 by mathdanisur last updated on 28/Jul/21 $${Find}\:{the}\:{sum}\:{of}\:{the}\:{roots}\:{of}\:{the}\:{equation}: \\ $$$${x}^{\mathrm{2}} \:-\:\mathrm{2}{x}\:-\:\mathrm{3}\:\mid{x}\:-\:\mathrm{1}\mid\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$ Answered by dumitrel last updated on 28/Jul/21 $$\mid{x}−\mathrm{1}\mid^{\mathrm{2}} −\mathrm{3}\mid{x}−\mathrm{1}\mid+\mathrm{2}=\mathrm{0}\Rightarrow\mid{x}−\mathrm{1}\mid\in\left\{\mathrm{1},\mathrm{2}\right\} \\…
Question Number 17440 by virus last updated on 05/Jul/17 $$\mathrm{3}{x}−\mathrm{4}{y}=\mathrm{0},\mathrm{4}{y}−\mathrm{5}{z}=\mathrm{0},\mathrm{5}{z}−\mathrm{3}{x}=\mathrm{0} \\ $$$${then}\:{x},{y},{z}\:{is}\:{AP},{GP},{HP},{AGP}?????? \\ $$ Answered by sushmitak last updated on 06/Jul/17 $$\frac{{x}}{{y}}=\frac{\mathrm{4}}{\mathrm{3}}={k},\frac{{y}}{{z}}=\frac{\mathrm{5}}{\mathrm{4}} \\ $$$${x}=\mathrm{4}{k} \\…
Question Number 82974 by Power last updated on 26/Feb/20 Commented by Power last updated on 27/Feb/20 $$\mathrm{sir}\:\mathrm{mind}\:\mathrm{is}\:\mathrm{power}\:\:\mathrm{pls} \\ $$ Answered by mind is power last…
Question Number 82975 by jagoll last updated on 26/Feb/20 $$\mathrm{To}\:\mathrm{the}\:\mathrm{member}\:\mathrm{in}\:\mathrm{forum}.\:\mathrm{please}\: \\ $$$$\mathrm{give}\:\mathrm{an}\:\mathrm{opinion}\:\mathrm{on}\:\mathrm{this}\:\mathrm{matter}. \\ $$$$\mathrm{George}\:,\:\mathrm{Lucia}\:\mathrm{and}\:\mathrm{12}\:\mathrm{of}\:\mathrm{their} \\ $$$$\mathrm{friends}\:\mathrm{will}\:\mathrm{sit}\:\mathrm{around}\:\mathrm{a}\:\mathrm{round}\:\mathrm{table}. \\ $$$$\mathrm{Many}\:\mathrm{of}\:\mathrm{their}\:\mathrm{arrangements}\:\mathrm{sit}\: \\ $$$$\mathrm{if}\:\mathrm{George}\:\mathrm{and}\:\mathrm{Lucia}\:\mathrm{always}\:\mathrm{flank} \\ $$$$\mathrm{5}\:\mathrm{of}\:\mathrm{their}\:\mathrm{friends}? \\ $$ Commented…
Question Number 17438 by Ruth1 last updated on 05/Jul/17 $$\mathrm{find}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{value}\:\mathrm{and}\:\mathrm{root}\:\mathrm{mean}\:\mathrm{square}\:\mathrm{of}\: \\ $$$$\mathrm{i}=\mathrm{25sin100}\Pi\mathrm{t}\:\:\:\:\:\mathrm{ranging}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 82972 by mathmax by abdo last updated on 26/Feb/20 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}\right){ln}\left(\mathrm{1}+{x}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com