Category: Algebra

Question Number 139577 by bemath last updated on 29/Apr/21 $$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{number}\frac{{(\mathrm{x}-1)}^2}{2}+\frac{{(\mathrm{y}-2)}^2}{4}+\frac{{(\mathrm{z}-3)}^2}{6}+3=\mid \mathrm{x}-1\mid +\mid \mathrm{y}-2\mid +\mid \mathrm{z}-3\mid$$ Answered by mr W last updated on 29/Apr/21 $${a}=\mid{x}−\mathrm{1}\mid\geqslant\mathrm{0},\:{b}=\mid{y}−\mathrm{2}\mid\geqslant\mathrm{0},\:{c}=\mid{z}−\mathrm{3}\mid\geqslant\mathrm{0} \…

Question Number 139544 by melanie last updated on 28/Apr/21 Answered by bemath last updated on 28/Apr/21 $$\mathrm{Tanzalin}\mathrm{formula}$$$$\begin{array}{|cc|}\hline \mathrm{u}\left(\mathrm{diff}\right)& \mathrm{dv}\left(\mathrm{integrate}\right)\\ 4\mathrm{x}& \cos (2-3\mathrm{x})\\ 4& -\frac{1}{3}\sin (2-3\mathrm{x})\\ 0& -\frac{1}{9}\cos (2-3\mathrm{x})\\ \hline\end{array}$$$$\mathrm{I}=-\frac{4\mathrm{x}\sin (2-3\mathrm{x})}{3}+\frac{4\cos (2-3\mathrm{x})}{9}+\mathrm{c}$$ Answered by…

Question Number 8468 by FilupSmith last updated on 12/Oct/16 $$\mathrm{Prove}\mathrm{or}\mathrm{disprove}\mathrm{that}:$$$${(2k+1)}^n\in \mathbb{O}\mathrm{\forall }k,n\in \mathbb{Z}$$ Answered by Rasheed Soomro last updated on 12/Oct/16 $$\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{n}} =$$\left(\begin{array}{c}\mathrm{n}\\ 0\end{array}\right)$$\left(\mathrm{2k}\right)^{\mathrm{n}}…

Question Number 139532 by mathdanisur last updated on 28/Apr/21 $$\frac{1}{3}-\frac{x-3}{9}+\frac{{(x-3)}^2}{27}+\dots =?$$ Commented by mr W last updated on 28/Apr/21 $$=\frac{1}{x}$$ Commented…

Question Number 139502 by bemath last updated on 28/Apr/21 $$\sqrt{{\mathrm{x}}^2+8\mathrm{x}}⩽24-(\mathrm{x}+2)(\mathrm{x}+6)$$$$$$ Answered by TheSupreme last updated on 28/Apr/21 $$domain:x<-8\vee x>0$$$$\begin{cases}{\mathrm{24}−\left({x}+\mathrm{2}\right)\left({x}+\mathrm{6}\right)>\mathrm{0}\rightarrow\mathrm{12}−{x}^{\mathrm{2}}…