Question Number 190297 by Shrinava last updated on 31/Mar/23 Answered by Frix last updated on 31/Mar/23 $$\mathrm{Let}\:{u}=\mathrm{cos}\:{x}\:\wedge{v}=\mathrm{sin}\:{x} \\ $$$$\mathrm{Transforming}\:\mathrm{leads}\:\mathrm{to} \\ $$$${u}^{\mathrm{6}} +\mathrm{2}{u}^{\mathrm{3}} {v}^{\mathrm{3}} +\mathrm{2}{u}^{\mathrm{2}} {v}^{\mathrm{2}}…
Question Number 190284 by cortano12 last updated on 31/Mar/23 $$\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{if}\:\mathrm{4}^{\mathrm{2023}} \: \\ $$$$\mathrm{divides}\:\mathrm{by}\:\mathrm{7} \\ $$ Answered by alcohol last updated on 31/Mar/23 $$\mathrm{4}^{\mathrm{3}} \:\equiv\:\mathrm{1}\left({mod}\:\mathrm{7}\right) \\…
Question Number 124740 by ajfour last updated on 05/Dec/20 Commented by ajfour last updated on 05/Dec/20 $${Find}\:{eq}.\:{of}\:{circle}\:{passing}\:{through} \\ $$$${intersection}\:{points}\:{of}\:\:{curves} \\ $$$${y}={x}^{\mathrm{2}} −\mathrm{1}\:\:{and}\:\:{y}=\frac{{c}}{{x}}\:;\:\:\:\left({c}\:<\:\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\right) \\ $$ Answered…
Question Number 190275 by aye786naing last updated on 30/Mar/23 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{i}^{\mathrm{n}} \:\mathrm{for}\:\mathrm{every}\:\mathrm{positive} \\ $$$$\:\mathrm{integer}\:\mathrm{n},\:\mathrm{where}\:\mathrm{i}^{\mathrm{2}} \:=\:−\mathrm{1},\:\mathrm{i}^{\mathrm{3}} =\:\mathrm{i}^{\mathrm{2}} \mathrm{i},\:\mathrm{i}^{\mathrm{4}} \:=\:\mathrm{i}^{\mathrm{2}} \mathrm{i}^{\mathrm{2}} \:,\:{etc}. \\ $$ Answered by Frix last…
Question Number 190241 by astridmei last updated on 30/Mar/23 $${show}\:{that}\:{a}\circledast{b}={a}+{ab}+{b}\:{is}\:{a}\:{monoid}\:{when}\:{G}={Z} \\ $$ Answered by mehdee42 last updated on 30/Mar/23 $$\ast:\mathbb{Z}×\mathbb{Z}\rightarrow\mathbb{Z}\:\:;\:{a}\ast{b}={a}+{b}+{ab} \\ $$$$\left(\mathbb{Z},\ast\right)\:{is}\:{monoid}\:{whenever} \\ $$$$\left.\mathrm{1}\right)\forall{a},{b}\in\mathbb{Z}\:\rightarrow{a}\ast{b}\in\mathbb{Z} \\…
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Question Number 59164 by hovea cw last updated on 05/May/19 $$\mathrm{5}^{\mathrm{x}} =\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$ Answered by MJS last updated on 05/May/19 $$\mathrm{5}^{{x}} =\mathrm{0}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}\:\mathrm{for}\:{x}\in\mathbb{R}…