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Category: Relation and Functions

let-A-1-2-1-1-1-calculste-A-n-2-determine-e-A-and-e-2A-3-find-cos-A-and-sinA-is-cos-2-A-sin-2-A-I-4-determine-sh-A-and-ch-A-is-ch-2-A-sh-2-A-I-

Question Number 91268 by mathmax by abdo last updated on 29/Apr/20 $${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{1}\:\:\:\:\:−\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:\:{e}^{{A}} \:\:{and}\:{e}^{−\mathrm{2}{A}} \\ $$$$\left.\mathrm{3}\right){find}\:{cos}\left({A}\right){and}\:{sinA}\:\:\:{is}\:{cos}^{\mathrm{2}} {A}\:+{sin}^{\mathrm{2}} {A}\:={I}? \\ $$$$\left.\mathrm{4}\right)\:{determine}\:{sh}\left({A}\right)\:{and}\:{ch}\left({A}\right)\:\:{is}\:{ch}^{\mathrm{2}} {A}−{sh}^{\mathrm{2}} {A}\:={I}\:\:?…

f-x-2x-1-f-3-f-4-

Question Number 91085 by jagoll last updated on 28/Apr/20 $${f}\left({x}\right)\:=\:\lceil\mathrm{2}{x}−\mathrm{1}\rceil\: \\ $$$${f}\left(\mathrm{3}\right)\:,\:{f}\left(\mathrm{4}\right)\:=\:? \\ $$ Commented by  M±th+et+s last updated on 28/Apr/20 $${if}\:\left[…\right]\:{is}\:{ceil} \\ $$$${f}\left(\mathrm{3}\right)=\lceil\mathrm{6}−\mathrm{1}\rceil=\lceil\mathrm{5}\rceil=\mathrm{5} \\…

solve-y-y-2-sin-2-t-

Question Number 90972 by abdomathmax last updated on 27/Apr/20 $${solve}\:{y}^{''} \:+{y}\:=\frac{\mathrm{2}}{{sin}^{\mathrm{2}} {t}} \\ $$ Answered by Joel578 last updated on 27/Apr/20 $$\bullet\:\mathrm{Homogeneous}\:\mathrm{solution} \\ $$$$\mathrm{with}\:\mathrm{char}.\:\mathrm{eq}.\:\lambda^{\mathrm{2}} \:+\:\mathrm{1}\:=\:\mathrm{0}\:\rightarrow\:\lambda_{\mathrm{1},\mathrm{2}}…