Menu Close

Category: Algebra

How-many-real-numbers-x-satisfy-the-equation-3-2x-2-3-x-3-3-x-3-0-

Question Number 111724 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{x}\:\mathrm{satisfy}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{3}^{\mathrm{2x}+\mathrm{2}} −\mathrm{3}^{\mathrm{x}+\mathrm{3}} −\mathrm{3}^{\mathrm{x}} +\mathrm{3}=\mathrm{0}\:? \\ $$ Commented by mohammad17 last updated on…

A-park-has-the-shape-of-a-regular-hexagon-of-sides-2km-each-A-boy-walks-a-distance-of-5km-along-the-sides-of-the-park-What-is-the-direct-distance-between-the-start-point-and-the-end-point-

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

x-2021-x-2022-x-4043-dx-

Question Number 177193 by peter frank last updated on 02/Oct/22 $$\int\:\:\:\frac{\mathrm{x}^{\mathrm{2021}} }{\mathrm{x}^{\mathrm{2022}} +\mathrm{x}^{\mathrm{4043}} }\mathrm{dx} \\ $$ Answered by cortano1 last updated on 02/Oct/22 $$\frac{\mathrm{1}}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2021}} +\mathrm{1}\right)}\:=\frac{\mathrm{1}}{\mathrm{x}}\:−\frac{\mathrm{x}^{\mathrm{2020}}…

Question-46110

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

Question-177173

Question Number 177173 by Shrinava last updated on 01/Oct/22 Answered by Peace last updated on 02/Oct/22 $${let}\:{f}\left({x}\right)={e}^{−\frac{\mathrm{1}}{{x}+\mathrm{1}}} ,{applie}\:{Taylors}\:{lagrange}\:{formul}\:\Rightarrow\exists{c}\in\left[\mathrm{0},\mathrm{1}\right]\:{such}\:{that} \\ $$$${f}\left({x}\right)={f}\left(\mathrm{0}\right)+{xf}'\left({c}\right)={e}^{−\mathrm{1}} +{x}.\frac{{e}^{−\frac{\mathrm{1}}{\mathrm{1}+{c}}} }{\left(\mathrm{1}+{c}\right)^{\mathrm{2}} } \\ $$$${We}\:{have}\:\forall{c}\in\left[\mathrm{0},\mathrm{1}\right]\:\frac{{e}^{−\frac{\mathrm{1}}{\mathrm{1}+{c}}}…