Category: Algebra

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}}…

Question Number 139474 by mathdanisur last updated on 27/Apr/21 $$let:{\mathrm{\Omega }}_{\mathit{n}}=\underset{0}{\stackrel{2\pi }{\int }}cos\left(x\right)\cdot cos\left(2x\right)\cdot \dots \cdot cos\left(nx\right)dx$$$$forwhichintegersn,1⩽n⩽10,is{\mathrm{\Omega }}_{\mathit{n}}\ne 0?$$ Answered by mathmax by abdo last updated…

Question Number 8352 by tawakalitu last updated on 09/Oct/16 $$\mathrm{make}\mathrm{t}\mathrm{the}\mathrm{subject}\mathrm{of}\mathrm{the}\mathrm{formular}.$$$$\mathrm{s}=\mathrm{ut}+\frac{1}{2}{\mathrm{gt}}^2+{3\mathrm{t}}^3$$ Answered by fernandodantas1996 last updated on 13/Oct/16 $$\mathrm{s}\:=\:\mathrm{t}\left(\mathrm{u}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{gt}+\mathrm{3t}^{\mathrm{2}} \right)\:\Leftrightarrow\:\mathrm{t}\:=\:\frac{\mathrm{s}}{\mathrm{u}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{gt}\:+\:\mathrm{3t}^{\mathrm{2}} }…

Question Number 139399 by mathsuji last updated on 26/Apr/21 $$\underset{0}{\stackrel{\pi /2}{\int }}\frac{log\left(sin\left(x/2\right)\right)+log\left(cos\left(x/2\right)\right)}{\sqrt{2}\cdot cos(\pi /4-x/2)}dx$$ Answered by Ar Brandon last updated on 26/Apr/21 $$\mathrm{Let}u=\frac{\pi }{2}-x$$…

Question Number 8301 by Rasheed Soomro last updated on 06/Oct/16 $$\mathrm{Is}\{{(\omega +\mathrm{i})}^0,{(\omega +\mathrm{i})}^1,{(\omega +\mathrm{i})}^2,\dots .,{(\omega +\mathrm{i})}^{\mathrm{n}}\}$$$$\mathrm{cyclic}\mathrm{for}\mathrm{any}\mathrm{value}\mathrm{of}\mathrm{n}?$$$$\mathrm{Determine}\mathrm{the}\mathrm{smallest}\mathrm{such}\mathrm{n}\mathrm{if}\mathrm{it}\mathrm{exists}.$$$$\omega \mathrm{is}\mathrm{a}\mathrm{complex}\mathrm{cuberoot}\mathrm{of}\mathrm{unity}\mathrm{and}$$$$\mathrm{i}=\sqrt{-1}$$…