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Author: Tinku Tara

f-R-R-f-3x-1-x-5-Find-f-x-

Question Number 198431 by hardmath last updated on 19/Oct/23 $$\mathrm{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R} \\ $$$$\mathrm{f}\:\left(\mathrm{3x}\:−\:\mathrm{1}\right)\:=\:\mathrm{x}\:+\:\mathrm{5} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$ Answered by AST last updated on 20/Oct/23 $${f}\left[\mathrm{3}\left(\frac{{x}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}}\right)−\mathrm{1}\right]=\frac{{x}+\mathrm{1}}{\mathrm{3}}+\mathrm{5}\Rightarrow{f}\left({x}\right)=\frac{{x}+\mathrm{16}}{\mathrm{3}} \\…

Question-198420

Question Number 198420 by Mingma last updated on 19/Oct/23 Answered by Frix last updated on 19/Oct/23 $$\int\frac{{x}^{\mathrm{2}} }{\left(\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx}\:\underset{{dx}=−\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} }}{\mathrm{4}{t}}} {\overset{{t}=\frac{\mathrm{2}+\sqrt{\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} }}{\mathrm{2}{x}−\mathrm{1}}} {=}}\: \\…

Question-198421

Question Number 198421 by mr W last updated on 19/Oct/23 Commented by mr W last updated on 19/Oct/23 $${given}\:{that}\:{the}\:{midpoints}\:{of}\:{the}\:{sides} \\ $$$${of}\:{a}\:{convex}\:{quadrilaterial}\:{are} \\ $$$${concyclic}.\:{if}\:{the}\:{lengthes}\:{of}\:{three}\:{of} \\ $$$${its}\:{sides}\:{are}\:{a},\:{b},\:{c}\:{respectively},\:{find}…