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Question-204978

Question Number 204978 by SANOGO last updated on 04/Mar/24 Answered by witcher3 last updated on 04/Mar/24 $$\mathrm{Soit}\:\mathrm{U}_{\mathrm{n}} ^{\mathrm{k}} \:\mathrm{une}\:\mathrm{suite}\:\mathrm{de}\:\mathrm{cauchy}\:\:\mathrm{Dans}\:\mathrm{C}_{\mathrm{0}} \\ $$$$\forall\mathrm{k}\:\:\mathrm{U}_{\mathrm{n}} ^{\mathrm{k}} \in\mathrm{C}_{} ^{\mathbb{N}} ;\underset{\mathrm{n}\rightarrow\infty}…

1-1-cot-3x-dx-

Question Number 204961 by naka3546 last updated on 04/Mar/24 $$\int\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cot}\:\mathrm{3}{x}}\:{dx}\:=\:\: \\ $$ Answered by TonyCWX08 last updated on 04/Mar/24 $${let}\:{t}\:=\:\mathrm{3}{x} \\ $$$${dt}\:=\:\mathrm{3}\:{dx} \\ $$$$ \\…

2-2-matrix-A-and-B-satisfy-that-AB-A-BA-B-Prove-that-A-B-2-O-

Question Number 204957 by CrispyXYZ last updated on 03/Mar/24 $$\mathrm{2}×\mathrm{2}\:\mathrm{matrix}\:\boldsymbol{\mathrm{A}}\:\mathrm{and}\:\boldsymbol{\mathrm{B}}\:\mathrm{satisfy}\:\mathrm{that} \\ $$$$\boldsymbol{\mathrm{AB}}+\boldsymbol{\mathrm{A}}=\boldsymbol{\mathrm{BA}}+\boldsymbol{\mathrm{B}}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\left(\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}\right)^{\mathrm{2}} =\boldsymbol{\mathrm{O}}. \\ $$ Answered by Rajpurohith last updated on 04/Mar/24 $${Need}\:{not}\:{hold}\:{true}!…

Question-204851

Question Number 204851 by ibrahimabdullayev last updated on 28/Feb/24 Answered by A5T last updated on 29/Feb/24 $$\mathrm{5}^{\mathrm{2}} =\mathrm{6}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{2}×\mathrm{6}×\mathrm{5}{cos}\angle{ACB}\Rightarrow{cos}\angle{ACB}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$\mathrm{6}^{\mathrm{2}} =\mathrm{5}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{2}×\mathrm{5}×\mathrm{5}{cos}\angle{ABC}\Rightarrow{cos}\angle{ABC}=\frac{\mathrm{7}}{\mathrm{25}}…