Question Number 205626 by mr W last updated on 25/Mar/24 $${if}\:{a}+{b}+{c}=\frac{\mathrm{1}}{{a}+\mathrm{1}}+\frac{\mathrm{1}}{{b}+\mathrm{2}}+\frac{\mathrm{1}}{{c}+\mathrm{3}}=\mathrm{0}, \\ $$$${find}\:\left({a}+\mathrm{1}\right)^{\mathrm{2}} +\left({b}+\mathrm{2}\right)^{\mathrm{2}} +\left({c}+\mathrm{3}\right)^{\mathrm{2}} =? \\ $$ Answered by A5T last updated on 25/Mar/24…
Question Number 205594 by cortano12 last updated on 25/Mar/24 Answered by Red1ight last updated on 25/Mar/24 $${y}^{\mathrm{2}} =\mathrm{4}{x} \\ $$$${y}=\mathrm{2}\sqrt{{x}} \\ $$$$\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{\:\sqrt{{x}}}=\frac{\mathrm{2}}{{y}} \\ $$$$\left({x}_{\mathrm{0}} ,{y}_{\mathrm{0}}…
Question Number 205588 by cortano12 last updated on 25/Mar/24 Answered by A5T last updated on 25/Mar/24 Commented by A5T last updated on 25/Mar/24 $${BC}={r}\sqrt{\mathrm{2}};{BD}^{\mathrm{2}} ={r}^{\mathrm{2}}…
Question Number 205551 by aba last updated on 24/Mar/24 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{into}\:\mathrm{cycles} \\ $$$$\mathrm{with}\:\mathrm{disjoints}\:\mathrm{support}\:\mathrm{of}\:\mathrm{c}^{\mathrm{k}} ,\:\mathrm{where}\:\mathrm{c}=\left(\mathrm{123}…\mathrm{n}\right)\:? \\ $$ Answered by TheHoneyCat last updated on 01/Apr/24 $$\mathrm{please}\:\mathrm{don}'\mathrm{t}\:\mathrm{re}−\mathrm{post}\:\mathrm{your}\:\mathrm{questions}. \\ $$$$\mathrm{especially}\:\mathrm{a}\:\mathrm{single}\:\mathrm{day}\:\mathrm{after}……
Question Number 205545 by Abdullahrussell last updated on 24/Mar/24 Commented by mr W last updated on 24/Mar/24 $$=\mathrm{768612}\:? \\ $$ Answered by A5T last updated…
Question Number 205559 by mnjuly1970 last updated on 24/Mar/24 $$ \\ $$$$\:\:\:{Question}.\:\left({math}\:{analysis}\right) \\ $$$$\:\:\left({X}\:,{d}\:\right)\:{is}\:{a}\:{metric}\:{space}\:{and} \\ $$$$\:\:\left({p}_{{n}} \right)_{{n}=\mathrm{1}} ^{\infty} \:{is}\:{a}\:{sequence}\:{in}\:{X}. \\ $$$$\:\:\:\left({p}_{{n}} \right)_{{n}=\mathrm{1}} ^{\:\infty} {is}\:{cauchy}\:{if}\:{and}\:\:{only}\:{if} \\…
Question Number 205534 by hardmath last updated on 23/Mar/24 $$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{n}\:\mathrm{x}^{\boldsymbol{\mathrm{n}}} \:\mathrm{e}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:=\:? \\ $$ Answered by Mathspace last updated…
Question Number 205528 by hardmath last updated on 23/Mar/24 $$\mathrm{Let}\:\:\:\forall\mathrm{x}\:\in\:\mathrm{A}\:\rightarrow\:\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{And}\:\:\:\mathrm{card}\left(\mathrm{A}\right)\:>\:\mathrm{card}\:\mathrm{N} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{card}\left(\mathrm{A}'\right)\:>\:\mathrm{card}\:\mathrm{N} \\ $$ Answered by Berbere last updated on 24/Mar/24…
Question Number 205527 by MATHEMATICSAM last updated on 23/Mar/24 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{are}\:\mathrm{one} \\ $$$$\mathrm{another}'\mathrm{s}\:\mathrm{cube}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\left({b}^{\mathrm{2}} \:−\:\mathrm{2}{ac}\right)^{\mathrm{2}} \:=\:{ac}\left({a}\:+\:{c}\right)^{\mathrm{2}} . \\ $$ Answered by A5T last updated…
Question Number 205514 by aba last updated on 23/Mar/24 $$\mathrm{Quelle}\:\mathrm{est}\:\mathrm{la}\:\mathrm{decomposition}\:\mathrm{en}\:\mathrm{cycles} \\ $$$$\mathrm{a}\:\mathrm{support}\:\mathrm{disjoints}\:\mathrm{de}\:\mathrm{c}^{\mathrm{k}} \:,\:\mathrm{ou}\:\mathrm{c}=\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:…\:\mathrm{n}\right)\:? \\ $$ Commented by TheHoneyCat last updated on 01/Apr/24 On parle de permutations? et si oui... Vous êtes sur que la permutation en question c'est (1,...n) (à savoir l'identité ?) Commented by…