Category: Algebra

Question Number 184875 by universe last updated on 13/Jan/23 Answered by Mathspace last updated on 13/Jan/23 $${let}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} {t}^{{n}} \:{for}\:\mid{t}\mid<\mathrm{1} \\ $$$${we}\:{have}\:{f}\left({t}\right)=\frac{\mathrm{1}}{\mathrm{1}+{t}} \\ $$$${but}\:{f}^{'}…

Question Number 184856 by mnjuly1970 last updated on 12/Jan/23 $$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mid\:\underset{} {\overset{} {{x}}}\:\:\mid\:−\mid\:\:{x}\underset{} {\overset{} {−}}\lfloor{ax}\rfloor\:\mid} \\ $$$$\:\:\:\:\:\:;\:\:\:{a}\:\in\:\left[\:\mathrm{3}\:,\:\mathrm{4}\:\right) \\ $$$$\:\:\:\:\:{find}\::\:\:\:\begin{cases}{\:\:{D}_{\:{f}} \:=?\:\left({domain}\:\right)}\\{\:\:\mathcal{R}_{\:{f}} \:=?\:\left({range}\:\right)}\end{cases} \\ $$$$ \\…

Question Number 184845 by Shrinava last updated on 12/Jan/23 $$\mathrm{x}\:\in\:\left[−\mathrm{0},\mathrm{5}\:;\:\mathrm{0},\mathrm{5}\right] \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\:\boldsymbol{\mathrm{x}}'\mathrm{s} \\ $$$$\mathrm{1}.\:\mathrm{4sin}^{\mathrm{2}} \pi\mathrm{x}−\mathrm{4sin}\pi\mathrm{x}\:+\:\mathrm{2}\:=\:\mathrm{2sin}^{\mathrm{2}} \pi\mathrm{y}−\mathrm{1} \\ $$$$\mathrm{2}.\:\mathrm{4sin}\pi\mathrm{x}\:=\:\mathrm{4sin}\pi\mathrm{y}\:−\:\mathrm{7}\:−\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \pi\mathrm{x}} \\ $$ Terms of Service Privacy…

Question Number 53775 by maxmathsup by imad last updated on 25/Jan/19 $${let}\:\:{A}\:=\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:\:{P}\:{inversible}\:{and}\:{D}\:{diagoanal}\:{in}\:{ordre}\:{to}\:{have} \\ $$$${A}\:={PDP}^{−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \:\:{with}\:{n}\:{integr}\:{nstural} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{e}^{{t}\:{A}} \:\:\:{with}\:{t}\:\in\:{R}\:\: \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{e}^{−{A}} \:\:.…

Question Number 53770 by Tawa1 last updated on 25/Jan/19 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{he}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{she}\:\:,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\mathrm{h},\:\mathrm{e}\:\:\mathrm{and}\:\:\mathrm{s}\:\:\mathrm{are}\:\mathrm{integers}\:. \\ $$ Answered by mr W last updated on 26/Jan/19 $${let}\:{he}={t} \\…