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Question-129087

Question Number 129087 by Adel last updated on 12/Jan/21 Answered by MJS_new last updated on 12/Jan/21 $$\mathrm{2}^{\mathrm{10}} \mathrm{10}!\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}×\mathrm{9}×\mathrm{11}×\mathrm{13}×\mathrm{15}×\mathrm{17}×\mathrm{19}\right)= \\ $$$$=\mathrm{10}!×\mathrm{11}×\left(\mathrm{3}×\mathrm{2}^{\mathrm{2}} \right)×\mathrm{13}×\left(\mathrm{7}×\mathrm{2}\right)×\mathrm{15}×\left(\mathrm{2}^{\mathrm{4}} \right)×\mathrm{17}×\left(\mathrm{9}×\mathrm{2}\right)×\mathrm{19}×\left(\mathrm{5}×\mathrm{2}^{\mathrm{2}} \right)= \\ $$$$=\mathrm{20}!…

a-if-y-x-m-1-x-n-where-n-Z-the-set-of-positive-integers-show-that-when-dy-dx-0-x-m-m-n-b-if-y-2-x-5-x-4-show-that-dy-dx-3-x-1-x-4-c-solve-the-equation-si

Question Number 63536 by Rio Michael last updated on 05/Jul/19 $$\left.{a}\right)\:\:{if}\:{y}=\:{x}^{{m}} \left(\mathrm{1}−{x}\right)^{{n}} ,\:{where}\:{n}\in\:\mathbb{Z}^{+} ,\:{the}\:{set}\:{of}\:{positive}\:{integers}, \\ $$$${show}\:{that}\:{when}\:\frac{{dy}}{{dx}}=\mathrm{0},\:{x}=\frac{{m}}{{m}+{n}} \\ $$$$\left.{b}\right){if}\:{y}\:=\:\mathrm{2}\left({x}−\mathrm{5}\right)\sqrt{{x}+\mathrm{4}}\:,{show}\:{that}\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{3}\left({x}+\mathrm{1}\right)}{\:\sqrt{{x}+\mathrm{4}}\:} \\ $$$$\left.{c}\right)\:{solve}\:{the}\:{equation}\:\:{sinx}−{sin}\mathrm{5}{x}+{cos}\mathrm{3}{x}\:=\:\mathrm{0}\:{for}\:\:\mathrm{0}°\leqslant{x}\leqslant\mathrm{180}° \\ $$ Commented by Prithwish…

Question-129061

Question Number 129061 by behi83417@gmail.com last updated on 12/Jan/21 Commented by mr W last updated on 12/Jan/21 $${is}\:{it}\:{not}\:{obvious}\:{that}\:{the}\:{maximal} \\ $$$${equilateral}\:{has}\:{the}\:{side}\:{length}\: \\ $$$$\mathrm{1}/\mathrm{cos}\:\mathrm{15}°=\sqrt{\mathrm{6}}−\sqrt{\mathrm{2}}? \\ $$ Commented…

What-is-the-Laplace-transform-of-f-t-4t-2-5sin-3t-

Question Number 129048 by bramlexs22 last updated on 12/Jan/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{Laplace}\:\mathrm{transform} \\ $$$$\mathrm{of}\:\mathrm{f}\left(\mathrm{t}\right)\:=\:−\mathrm{4t}^{\mathrm{2}} −\mathrm{5sin}\:\mathrm{3t}\: \\ $$ Answered by Dwaipayan Shikari last updated on 12/Jan/21 $$\mathscr{L}\left({f}\left({t}\right)\right)=−\mathrm{4}\int_{\mathrm{0}} ^{\infty}…

Question-128910

Question Number 128910 by shaker last updated on 11/Jan/21 Answered by bramlexs22 last updated on 11/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{n}} −\mathrm{2}^{\mathrm{n}} −\mathrm{nx}.\mathrm{2}^{\mathrm{n}−\mathrm{1}} +\mathrm{n}.\mathrm{2}^{\mathrm{n}} }{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} }= \\ $$$$\:\underset{{x}\rightarrow\mathrm{2}}…

Prove-that-even-obtaining-the-zero-s-the-following-equation-has-only-one-zero-f-t-1-2-t-1-t-2-t-2-t-2-

Question Number 128896 by ZiYangLee last updated on 11/Jan/21 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{even}\:\mathrm{obtaining}\:\mathrm{the}\:\mathrm{zero}\left(\mathrm{s}\right), \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{only}\:\mathrm{one}\:\mathrm{zero}. \\ $$$${f}\left({t}\right)=\left(\mathrm{1}+\sqrt{\mathrm{2}}{t}\right)\left(\mathrm{1}−{t}^{\mathrm{2}} \right)+{t}^{\mathrm{2}} \left({t}+\sqrt{\mathrm{2}}\right) \\ $$ Answered by Olaf last updated on 11/Jan/21…