Question Number 226538 by mr W last updated on 02/Dec/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 226533 by mr W last updated on 02/Dec/25 Answered by mr W last updated on 03/Dec/25 $${cube}\:{roots}\:{of}\:{unit}:\:\mathrm{1},\:\omega,\:\omega^{\mathrm{2}} \\ $$$$\mathrm{1}+\omega+\omega^{\mathrm{2}} =\mathrm{0} \\ $$$${e}^{{x}} =\underset{{n}=\mathrm{0}}…
Question Number 226534 by ajfour last updated on 02/Dec/25 Commented by ajfour last updated on 02/Dec/25 $${If}\:{AB}=\mathrm{2}\theta,\:{find}\:{everything}! \\ $$ Commented by mr W last updated…
Question Number 226509 by hardmath last updated on 01/Dec/25 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}\centerdot\left(\mathrm{2n}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:=\:? \\ $$ Answered by mr W last updated on 01/Dec/25 $$\frac{\mathrm{1}}{{n}\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{{A}}{{n}}+\frac{{B}}{\mathrm{2}{n}+\mathrm{1}}+\frac{{C}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 226507 by Lara2440 last updated on 01/Dec/25 Answered by Lara2440 last updated on 01/Dec/25 $$\mathrm{Smooth}\:\mathrm{manifold}\:{M},{N}\:\mathrm{and} \\ $$$$\mathrm{Differentiable}\:\mathrm{smooth}\:\mathrm{function}\:\:\phi;{M}\rightarrow{N} \\ $$$$\: \\ $$$$\phi\left({u},{v}\right)=\begin{cases}{−\mathrm{sin}\left({u}\right)−\mathrm{3sin}\left({v}\right)}\\{\:\:\:\:\mathrm{cos}\left({u}\right)+\mathrm{3cos}\left({v}\right)\:\:\:\:\:\:,\:{u}\in\left[−\pi,\pi\right]\:,\:{v}\in\left[−\mathrm{2}\pi,\mathrm{2}\pi\right]}\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}{v}}\end{cases} \\ $$$$\:…
Question Number 226513 by aba_math last updated on 01/Dec/25 $${Find}\:{gcd}\left({a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} ,{ab}\right)\:{if}\:{gcd}\left({a},{b}\right)=\mathrm{1} \\ $$ Answered by peace2 last updated on 02/Dec/25 $${a}={dx};{b}={dy};{gcd}\left({x},{y}\right)=\mathrm{1} \\ $$$${gcd}\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 226514 by Tawa11 last updated on 01/Dec/25 Answered by fantastic2 last updated on 02/Dec/25 $${E}_{{p}_{{box}} } ={mgh} \\ $$$${when}\:{box}\:{hits}\:{ground}\: \\ $$$${E}_{{k}} ={E}_{{p}} ={mgh}…
Question Number 226515 by mr W last updated on 01/Dec/25 Commented by Ghisom_ last updated on 02/Dec/25 $${S}_{{k}} =\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}\:\frac{{n}}{{n}^{\mathrm{4}} +{n}^{\mathrm{2}} +\mathrm{1}}\:=\frac{{k}\left({k}+\mathrm{1}\right)}{\mathrm{2}\left({k}^{\mathrm{2}} +{k}+\mathrm{1}\right)} \\…
Question Number 226485 by mr W last updated on 30/Nov/25 Answered by mr W last updated on 30/Nov/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 226469 by ajfour last updated on 30/Nov/25 Commented by ajfour last updated on 30/Nov/25 $${Find}\:{the}\:{common}\:{area}\:{of}\:{the} \\ $$$${smaller}\:{circles}.\:{Outer}\:{square} \\ $$$${has}\:{side}\:{length}\:{s}=\mathrm{2}\:{units}. \\ $$ Answered by…