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Category: Coordinate Geometry

Trouver-toutes-les-fonctions-f-N-R-telque-a-b-N-f-a-2-b-2-f-a-2-f-b-2-et-f-1-1-

Question Number 149634 by puissant last updated on 06/Aug/21 $$\mathrm{Trouver}\:\mathrm{toutes}\:\mathrm{les}\:\mathrm{fonctions}\:\mathrm{f}:\mathbb{N}\rightarrow\mathbb{R}^{+} \\ $$$$\mathrm{telque}\:\forall\left(\mathrm{a},\mathrm{b}\right)\in\mathbb{N}, \\ $$$$\mathrm{f}\left(\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \right)=\mathrm{f}\left(\mathrm{a}^{\mathrm{2}} \right)+\mathrm{f}\left(\mathrm{b}^{\mathrm{2}} \right)\:\mathrm{et}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$ Answered by Ar Brandon last…

Question-149462

Question Number 149462 by liberty last updated on 05/Aug/21 Answered by Olaf_Thorendsen last updated on 05/Aug/21 $$\mathrm{A}\left(−\mathrm{3},\mathrm{0}\right)\:\mathrm{B}\left(\mathrm{1},−\mathrm{1}\right)\:\mathrm{C}\left(\mathrm{0},\mathrm{3}\right)\:\mathrm{D}\left(−\mathrm{1},\mathrm{3}\right) \\ $$$$\left(\mathrm{AC}\right)\::\:{y}\:=\:{x}+\mathrm{3} \\ $$$$\left(\mathrm{BD}\right)\::\:{y}\:=\:−\mathrm{2}{x}+\mathrm{1} \\ $$$$\mathrm{P}\:=\:\left(\mathrm{AC}\right)\cap\left(\mathrm{BD}\right)\:=\:\left(−\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{7}}{\mathrm{3}}\right) \\ $$$$\mathrm{P}\:=\:\left(\mid\mathrm{PA}\mid+\mid\mathrm{PB}\mid+\mid\mathrm{PC}\mid+\mid\mathrm{PD}\mid\right)_{{min}}…

Question-16789

Question Number 16789 by ajfour last updated on 26/Jun/17 Commented by ajfour last updated on 26/Jun/17 $$\:\mathrm{solution}\:\mathrm{to}\:\mathrm{Q}.\mathrm{16065} \\ $$$$\mathrm{find}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{M}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{Area}\left(\bigtriangleup\mathrm{MAB}\right)=\mathrm{2Area}\left(\bigtriangleup\mathrm{MCD}\right). \\ $$ Answered by…

show-that-1-2-1-2-1-x-5-dx-1-2-1-x-4-1-dx-1-2-1-x-4-

Question Number 147539 by alcohol last updated on 21/Jul/21 $${show}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{1}} ^{\:\mathrm{2}} \frac{\mathrm{1}}{{x}^{\mathrm{5}} }{dx}\:\leqslant\:\int_{\mathrm{1}} ^{\:\mathrm{2}} \frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx}\:\leqslant\int_{\mathrm{1}} ^{\:\mathrm{2}} \frac{\mathrm{1}}{{x}^{\mathrm{4}} } \\ $$ Answered by…