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Category: Algebra

arccos-cos-9-

Question Number 148339 by mathdanisur last updated on 27/Jul/21 $${arccos}\:\left({cos}\:\mathrm{9}\right)\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 27/Jul/21 $$\left.{x}\:=\:\mathrm{arccos}\left(\mathrm{cos9}\right)\right) \\ $$$$\left.{x}\:=\:\mathrm{arccos}\left(\mathrm{cos}\left(\mathrm{9}−\mathrm{2}\pi\right)\right)\right),\:\mathrm{9}−\mathrm{2}\pi\:\in\left[\mathrm{0},\pi\right] \\ $$$${x}\:=\:\mathrm{9}−\mathrm{2}\pi \\…

x-1-3-1-x-15-Find-the-limit-that-does-not-inclued-the-variable-x-in-the-opening-of-the-binomial-

Question Number 148333 by mathdanisur last updated on 27/Jul/21 $$\left(\sqrt[{\mathrm{3}}]{{x}}\:+\:\frac{\mathrm{1}}{\:\sqrt{{x}}}\right)^{\mathrm{15}} \\ $$$${Find}\:{the}\:{limit}\:{that}\:{does}\:{not}\:{inclued} \\ $$$${the}\:{variable}\:\boldsymbol{{x}}\:{in}\:{the}\:{opening}\:{of}\:{the} \\ $$$${binomial}. \\ $$ Answered by qaz last updated on 27/Jul/21…

Question-148321

Question Number 148321 by mathdanisur last updated on 27/Jul/21 Answered by dumitrel last updated on 27/Jul/21 $${p}\left({x}\right)={x}^{\mathrm{2021}} −{x}−\mathrm{1},{x}>\mathrm{0} \\ $$$${p}\left({a}\right)=\mathrm{0};{p}\left({x}\right)\:\nearrow\:{for}\:{x}\in\left({a},\infty\right);{a}>\mathrm{1} \\ $$$${if}\:{b}\geqslant{a}\Rightarrow{f}\left({b}\right)\geqslant{f}\left({a}\right)=\mathrm{0}\Rightarrow{b}^{\mathrm{2021}} \geqslant{b}+\mathrm{1}\Rightarrow \\ $$$${b}^{\mathrm{4042}}…

solve-x-x-1-4-How-can-we-get-the-complex-solution-

Question Number 148314 by Tawa11 last updated on 27/Jul/21 $$\mathrm{solve}:\:\:\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:\:=\:\:\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{How}\:\mathrm{can}\:\mathrm{we}\:\mathrm{get}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{solution} \\ $$ Commented by Tawa11 last updated on 27/Jul/21 $$\mathrm{what}\:\mathrm{is}\:\:\:\:\:\:\mathrm{W}_{\mathrm{n}} \left(−\:\mathrm{ln}\:\mathrm{4}\right) \\…

lg-2-10x-lg-10x-6-lg-x-x-

Question Number 148300 by mathdanisur last updated on 26/Jul/21 $${lg}^{\mathrm{2}} \left(\mathrm{10}{x}\right)\:+\:{lg}\left(\mathrm{10}{x}\right)\:=\:\mathrm{6}\:-\:{lg}\left({x}\right) \\ $$$${x}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 26/Jul/21 $$\mathrm{lg}^{\mathrm{2}} \left(\mathrm{10}{x}\right)+\mathrm{lg}\left(\mathrm{10}{x}\right)\:=\:\mathrm{6}−\mathrm{lg}\left({x}\right) \\…