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Category: Permutation and Combination

Verify-wether-f-is-invertible-f-x-1-2x-3-

Question Number 165376 by MikeH last updated on 31/Jan/22 $$\mathrm{Verify}\:\mathrm{wether}\:{f}\:\mathrm{is}\:\mathrm{invertible}\: \\ $$$${f}\:\left({x}\right)\:=\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\ $$ Answered by Rasheed.Sindhi last updated on 31/Jan/22 $${f}\:\left({x}\right)\:=\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\ $$$${y}=\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\…

Obtain-a-general-formula-for-the-sequence-2-3-4-5-8-9-16-17-32-33-assuming-the-sequence-continues-in-that-pattern-

Question Number 165361 by MikeH last updated on 31/Jan/22 $$\mathrm{Obtain}\:\mathrm{a}\:\mathrm{general}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{sequence} \\ $$$$\:\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{4}}{\mathrm{5}},\frac{\mathrm{8}}{\mathrm{9}},\frac{\mathrm{16}}{\mathrm{17}},\frac{\mathrm{32}}{\mathrm{33}},… \\ $$$$\mathrm{assuming}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{continues}\:\mathrm{in}\:\mathrm{that} \\ $$$$\mathrm{pattern}. \\ $$ Commented by MJS_new last updated…

Question-164996

Question Number 164996 by Mathematification last updated on 24/Jan/22 Answered by mr W last updated on 25/Jan/22 $${AB}={x}_{\mathrm{1}} +{x}_{\mathrm{2}} \\ $$$${AB}=\sqrt{\left(\mathrm{3}+\mathrm{2}\right)^{\mathrm{2}} −\left(\mathrm{3}−\mathrm{2}\right)^{\mathrm{2}} }+\sqrt{\left(\mathrm{2}+\mathrm{1}.\mathrm{5}\right)^{\mathrm{2}} −\left(\mathrm{4}.\mathrm{5}−\mathrm{2}\right)^{\mathrm{2}} }…

Question-99194

Question Number 99194 by bemath last updated on 19/Jun/20 Answered by bramlex last updated on 19/Jun/20 $${suppose}\:{probability}\:{win}\:{or}\:{draw}\:{or}\:{lose}\:{are} \\ $$$${same}\:{is}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${not}\:{to}\:{lose}\:{in}\:{those}\:{three}\:{matches}\: \\ $$$${case}\left(\mathrm{1}\right)\:\left(\mathrm{3}{w}\right)\Rightarrow\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{3}} =\:\frac{\mathrm{1}}{\mathrm{27}} \\…

soit-K-un-corps-pour-toute-permutation-de-S-n-on-note-P-sa-matrice-dans-la-base-canonique-de-K-n-montrer-que-deux-permutations-1-et-2-sont-conjugues-dans-S-n-si-et-seulement-si-P-1

Question Number 164588 by ArielVyny last updated on 19/Jan/22 $${soit}\:{K}\:{un}\:{corps};\:{pour}\:{toute}\:{permutation} \\ $$$$\sigma\:{de}\:{S}_{{n}} ,\:{on}\:{note}\:{P}\left(\sigma\right)\:{sa}\:{matrice}\:{dans}\:{la}\:{base} \\ $$$${canonique}\:{de}\:{K}^{{n}} . \\ $$$${montrer}\:{que}\:{deux}\:{permutations}\:\sigma_{\mathrm{1}} \:{et}\:\sigma_{\mathrm{2}} \:{sont} \\ $$$${conjugues}\:{dans}\:{S}_{{n}} \:{si}\:{et}\:{seulement}\:{si}\: \\ $$$${P}\left(\sigma_{\mathrm{1}}…