Category: Algebra

Question Number 46139 by pieroo last updated on 21/Oct/18 $$\mathrm{A}\mathrm{park}\mathrm{has}\mathrm{the}\mathrm{shape}\mathrm{of}\mathrm{a}\mathrm{regular}\mathrm{hexagon}$$$$\mathrm{of}\mathrm{sides}2\mathrm{km}\mathrm{each}.\mathrm{A}\mathrm{boy}\mathrm{walks}\mathrm{a}\mathrm{distance}$$$$\mathrm{of}5\mathrm{km}\mathrm{along}\mathrm{the}\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{park}.$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{direct}\mathrm{distance}\mathrm{between}$$$$\mathrm{the}\mathrm{start}\mathrm{point}\mathrm{and}\mathrm{the}\mathrm{end}\mathrm{point}?$$ Commented by malwaan last updated…

Question Number 46110 by Tawa1 last updated on 21/Oct/18 Commented by math khazana by abdo last updated on 22/Oct/18 $$\mathrm{\Delta }=1-4=-3={\left(i\sqrt{3}\right)}^2\Rightarrow \alpha =\frac{1+i\sqrt{3}}{2}and\beta =\frac{1-i\sqrt{3}}{2}$$$$\Rightarrow\alpha={e}^{{i}\frac{\pi}{\mathrm{3}}} \:{and}\:\beta\:={e}^{−{i}\frac{\pi}{\mathrm{3}}} \:\Rightarrow\alpha^{\mathrm{101}}…

Question Number 177173 by Shrinava last updated on 01/Oct/22 Answered by Peace last updated on 02/Oct/22 $$letf\left(x\right)=e^{-\frac{1}{x+1}},applieTaylorslagrangeformul\Rightarrow \mathrm{\exists }c\in [0,1]suchthat$$$$f\left(x\right)=f\left(0\right)+{xf}^{\prime }\left(c\right)=e^{-1}+x.\frac{e^{-\frac{1}{1+c}}}{{(1+c)}^2}$$$${We}\:{have}\:\forall{c}\in\left[\mathrm{0},\mathrm{1}\right]\:\frac{{e}^{−\frac{\mathrm{1}}{\mathrm{1}+{c}}}…

Question Number 111623 by weltr last updated on 04/Sep/20 $$(x-2)(x+3){(x-1)}^2⩾0$$ Commented by ZiYangLee last updated on 04/Sep/20 $$x⩽-3\cup x⩾2?$$ Commented by…

Question Number 111601 by A8;15: last updated on 04/Sep/20 Answered by bemath last updated on 04/Sep/20 $$\frac{7.7^{2004}+7^{2004}+1}{7^{2004}+1}=\frac{8.7^{2004}+1}{7^{2004}+1}$$ Terms…