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Question-207935

Question Number 207935 by meo last updated on 31/May/24 Answered by Frix last updated on 01/Jun/24 $$\forall{x}\in\mathbb{R}:\:{F}\left({x}\right)>\mathrm{0} \\ $$$${F}'\left({x}\right)=\mathrm{0} \\ $$$$\mathrm{2}{x}−\mathrm{1}−\frac{\mathrm{4}{x}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }=\mathrm{0} \\ $$$$\mathrm{2}{x}^{\mathrm{5}}…

Find-the-value-of-0-2-dx-sin-6-x-cos-6-x-

Question Number 207949 by mnjuly1970 last updated on 31/May/24 $$ \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:{the}\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\boldsymbol{\Omega}\:=\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\:\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{6}} \boldsymbol{{x}}\:+\:\boldsymbol{{cos}}^{\mathrm{6}} \boldsymbol{{x}}}\:=\:?\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−− \\…

Anybody-with-knowledge-or-books-on-mathemtical-modeling-

Question Number 207951 by MWSuSon last updated on 31/May/24 $$\mathrm{Anybody}\:\mathrm{with}\:\mathrm{knowledge}\:\mathrm{or}\:\mathrm{books}\:\mathrm{on} \\ $$$$\mathrm{mathemtical}\:\mathrm{modeling}? \\ $$ Commented by TheHoneyCat last updated on 01/Jun/24 Modeling of what? shapes? physical phenomenon? dynamical system? statistical modeling? it is hard to find math that doesn't show up in any sort of modeling, so I think you'll get better results by being slightly more precise... Commented by MWSuSon…

Find-lim-x-2-x-2-x-1-x-2-

Question Number 207943 by hardmath last updated on 31/May/24 $$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:\frac{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{1}\right)}{\mid\mathrm{x}\:+\:\mathrm{2}\mid}\:\:=\:\:? \\ $$ Commented by mr W last updated on 31/May/24 $$=\frac{\left(\mathrm{2}+\mathrm{2}\right)\left(\mathrm{2}+\mathrm{1}\right)}{\mid\mathrm{2}+\mathrm{2}\mid}=\mathrm{3}…

An-ordered-data-consists-of-6-even-numbers-and-4-odd-numbers-The-average-of-the-odd-numbers-is-2022-The-3rd-5th-6th-and-8-th-numbers-are-odd-The-data-range-is-24-and-the-interquarti

Question Number 207937 by efronzo1 last updated on 31/May/24 $$\:\:\mathrm{An}\:\mathrm{ordered}\:\mathrm{data}\:\mathrm{consists}\:\mathrm{of}\: \\ $$$$\:\mathrm{6}\:\mathrm{even}\:\mathrm{numbers}\:\mathrm{and}\:\mathrm{4}\:\mathrm{odd}\:\mathrm{numbers}. \\ $$$$\:\mathrm{The}\:\mathrm{average}\:\mathrm{of}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{numbers}\: \\ $$$$\:\mathrm{is}\:\mathrm{2022}.\:\mathrm{The}\:\mathrm{3rd},\:\mathrm{5th},\:\mathrm{6th}\:\mathrm{and} \\ $$$$\:\mathrm{8}\:\mathrm{th}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{odd}.\: \\ $$$$\:\mathrm{The}\:\mathrm{data}\:\mathrm{range}\:\mathrm{is}\:\mathrm{24}\:,\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\:\mathrm{interquartile}\:\mathrm{range}\:\mathrm{is}\:\mathrm{14}.\: \\ $$$$\:\mathrm{The}\:\mathrm{largest}\:\mathrm{possible}\:\mathrm{average} \\…