Question Number 111643 by Dwaipayan Shikari last updated on 04/Sep/20 $$\left(\frac{\mathrm{7}}{\mathrm{3}}\right)!\left({with}\:{out}\:{calculator}\right) \\ $$ Answered by mathdave last updated on 04/Sep/20 $${solution}\: \\ $$$${but}\:{x}!=\Gamma\left({x}+\mathrm{1}\right) \\ $$$${let}\left(\frac{\mathrm{7}}{\mathrm{3}}\right)!=\Gamma\left(\frac{\mathrm{10}}{\mathrm{3}}\right)=\mathrm{2}.\mathrm{8871}…
Question Number 46045 by Tawa1 last updated on 20/Oct/18 $$\mathrm{A}\:\mathrm{number}\:\mathrm{is}\:\mathrm{said}\:\mathrm{to}\:\mathrm{be}\:''\mathrm{right}\:\mathrm{prime}''\:\mathrm{if}\:\mathrm{despite}\:\mathrm{dropping}\:\mathrm{the}\:\mathrm{left}\:\mathrm{most} \\ $$$$\mathrm{digits}\:\mathrm{successively},\:\:\mathrm{Number}\:\mathrm{continues}\:\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}.\:\: \\ $$$$\mathrm{For}\:\mathrm{example}:\:\:\mathrm{223}\:\mathrm{is}\:\mathrm{a}\:\mathrm{right}\:\mathrm{prime}\:\mathrm{because}\:\mathrm{despite}\:\mathrm{dropping}\:\mathrm{2}\:\mathrm{from}\:\mathrm{left} \\ $$$$\mathrm{most}\:\mathrm{part},\:\mathrm{we}\:\mathrm{obtain}\:\:\mathrm{23}\:\mathrm{as}\:\mathrm{the}\:\mathrm{prime}\:\mathrm{number}.\:\mathrm{Next},\:\mathrm{even}\:\mathrm{after}\:\mathrm{dropping}\: \\ $$$$\mathrm{2}\:\mathrm{from}\:\mathrm{left},\:\:\mathrm{3}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}. \\ $$$$\:\:\:\:\:\mathrm{How}\:\mathrm{many}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{right}\:\mathrm{prime}\:? \\ $$ Answered by MJS…
Question Number 46003 by MrW3 last updated on 19/Oct/18 Commented by MrW3 last updated on 20/Oct/18 $${Find}\:{the}\:{angle}\:\theta\:{when}\:{the}\:{rope}\:{starts} \\ $$$${to}\:{slide}.\:\left(\mu={coefficient}\:{of}\:{friction}\right) \\ $$ Answered by MrW3 last…
Question Number 111536 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{Let}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{10},\mathrm{11},…\:\mathrm{be}\:\mathrm{increasing} \\ $$$$\mathrm{sequence}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{that}\:\mathrm{are} \\ $$$$\mathrm{neither}\:\mathrm{the}\:\mathrm{square}\:\mathrm{nor}\:\mathrm{cube}\:\mathrm{of}\:\mathrm{an} \\ $$$$\mathrm{integer}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{2016th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{this} \\ $$$$\mathrm{sequence}. \\ $$ Commented by Rasheed.Sindhi…
Question Number 177068 by LOSER last updated on 30/Sep/22 $${Let}\:{a},{b},{c}\:{be}\:{real}\:{numbers}\:{such}\:{that}: \\ $$$${a}+{b}+{c}=\mathrm{0}.\:{Prove}\:{that}: \\ $$$$\frac{{a}^{\mathrm{2}} {b}^{\mathrm{2}} {c}^{\mathrm{2}} }{\mathrm{4}}+\frac{\left({ab}+{bc}+{ca}\right)^{\mathrm{3}} }{\mathrm{27}}\leqslant\mathrm{0} \\ $$ Answered by Frix last updated…
Question Number 45992 by sandeepkeshari0797@gmail.com last updated on 19/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Oct/18 $$\mathrm{2}+\mathrm{3}×\mathrm{1}=\mathrm{5} \\ $$$$\mathrm{2}+\mathrm{5}×\mathrm{2}=\mathrm{12} \\ $$$$\mathrm{3}+\mathrm{6}×\mathrm{3}=\mathrm{21} \\ $$$$\mathrm{8}+\mathrm{11}×\mathrm{4}=\mathrm{52}\:\:\:{i}\:{think}\:{so}… \\ $$$$…
Question Number 45976 by maxmathsup by imad last updated on 19/Oct/18 $${find}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{n}\left[{x}\right]} {cos}\left({nx}\right){dx}\:{and}\:{v}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{{n}\left[{x}\right]} {sin}\left({nx}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} {v}_{{n}} \:\:{and}\:\Sigma\:\frac{{u}_{{n}} }{{v}_{{n}}…
Question Number 45974 by maxmathsup by imad last updated on 19/Oct/18 $${calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{{n}} \:\:\:{e}^{−{n}\left[{x}\right]} \:{sin}\:\left(\mathrm{2}{x}\right){dx} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{cnvergence}\:{of}\:\Sigma\:{A}_{{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 45941 by arcana last updated on 19/Oct/18 $$\mathrm{Find}\:\mathrm{0}<\theta<\mathrm{2}\pi\:\mathrm{with}\:{x},{y}\:\in\mathbb{R} \\ $$$$ \\ $$$${x}\centerdot{sin}\theta={y}\centerdot{cos}\theta \\ $$ Answered by MJS last updated on 19/Oct/18 $$\mathrm{for}\:{x}=\mathrm{0}\vee{y}=\mathrm{0}\:\mathrm{it}'\mathrm{s}\:\mathrm{trivial} \\…
Question Number 45932 by Tawa1 last updated on 18/Oct/18 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\frac{\mathrm{1}.\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{2}.\mathrm{3}^{\mathrm{2}} \:+\:…\:+\:\mathrm{n}\left(\mathrm{n}\:+\:\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}^{\mathrm{2}} .\mathrm{2}\:+\:\mathrm{2}^{\mathrm{2}} .\mathrm{3}\:+\:…\:+\:\mathrm{n}^{\mathrm{2}} \left(\mathrm{n}\:+\:\mathrm{1}\right)}\:\:=\:\:\frac{\mathrm{3n}\:+\:\mathrm{5}}{\mathrm{3n}\:+\:\mathrm{1}} \\ $$ Commented by math khazana by abdo last…