Question Number 205669 by hardmath last updated on 26/Mar/24 Answered by Berbere last updated on 27/Mar/24 $${A}={X}^{\mathrm{5}} \\ $$$$\chi_{{A}} =\left(\mathrm{3}−{x}\right)\left(\mathrm{5}−{x}\right)−\mathrm{8}={X}^{\mathrm{2}} −\mathrm{8}{X}+\mathrm{7} \\ $$$$\left({x}−\mathrm{1}\right)\left({X}−\mathrm{7}\right)\:\:{D}=\begin{pmatrix}{\mathrm{1}\:\:\mathrm{0}}\\{\mathrm{0}\:\:\mathrm{7}}\end{pmatrix} \\ $$$${U}_{\mathrm{1}}…
Question Number 205671 by hardmath last updated on 26/Mar/24 Answered by Berbere last updated on 27/Mar/24 $$\left(\mathrm{1}−{x}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} {x}^{{k}} \begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}\Rightarrow\int_{\mathrm{0}} ^{{t}} \underset{{k}=\mathrm{0}} {\overset{{n}}…
Question Number 205670 by hardmath last updated on 26/Mar/24 Answered by Berbere last updated on 27/Mar/24 $$\Omega=\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \left(\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{{x}−\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}\right)^{\mathrm{2}} {dx} \\ $$$$\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}}…
Question Number 205626 by mr W last updated on 25/Mar/24 $${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…