Category: Algebra

Question Number 9471 by tawakalitu last updated on 09/Dec/16 $$\mathrm{prove}\mathrm{by}\mathrm{mathematical}\mathrm{induction}$$$$\mathrm{a}+(\mathrm{a}+\mathrm{d})+(\mathrm{a}+2\mathrm{d})+\dots +[\mathrm{a}+(\mathrm{n}-1)\mathrm{d}]=\frac{1}{2}\mathrm{n}[2\mathrm{a}+(\mathrm{n}-1)\mathrm{d}]$$ Answered by mrW last updated on 10/Dec/16 $$\mathrm{for}\mathrm{n}=1:$$$$\mathrm{a}\overset{!} {=}\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{1}×\left[\mathrm{2a}+\left(\mathrm{1}−\mathrm{1}\right)\mathrm{d}\right]=\mathrm{a}…

Question Number 9455 by RasheedSoomro last updated on 09/Dec/16 $$\mathrm{Solve}\mathrm{the}\mathrm{following}\mathrm{system}\mathrm{of}\mathrm{equations}$$$$3\mathrm{x}-8\mathrm{z}=-11$$$$2\mathrm{y}-3\mathrm{x}=-3$$$$\mathrm{y}-4\mathrm{z}=-7$$$$\text{You can't use 'macro parameter character \#' in math mode}$$ Answered by geovane10math last updated…

Question Number 9449 by tawakalitu last updated on 08/Dec/16 $$2\mathrm{xy}=\mathrm{x}+\mathrm{y}\dots \dots \left(\mathrm{i}\right)$$$$6\mathrm{xz}=6\mathrm{z}-2\mathrm{x}\dots ..\left(\mathrm{ii}\right)$$$$3\mathrm{yz}=3\mathrm{y}+4\mathrm{z}\dots \dots .\left(\mathrm{iii}\right)$$$$$$$$\mathrm{Solve}\mathrm{for}\mathrm{x},\mathrm{y}\mathrm{and}\mathrm{z}$$ Answered by mrW last updated…

Question Number 74947 by chess1 last updated on 04/Dec/19 Answered by MJS last updated on 05/Dec/19 $$(x-1)(8x^3+4x^2-4x-1)\sqrt{1-x^2}=0$$$$\Rightarrow x=\pm 1\vee x=-\frac{1}{6}-\frac{\sqrt{7}}{3}\sin \left(\frac{1}{3}\arcsin \frac{\sqrt{7}}{14}\right)\vee x=-\frac{1}{6}+\frac{\sqrt{7}}{3}\sin (\frac{\pi }{3}+\frac{1}{3}\arcsin \frac{\sqrt{7}}{14})\vee x=-\frac{1}{6}-\frac{\sqrt{7}}{3}\cos (\frac{\pi }{6}+\frac{1}{3}\arcsin \frac{\sqrt{7}}{14})$$ Commented…

Question Number 140477 by ajfour last updated on 08/May/21 $$If\sin \theta +\sin {}^2\theta +\sin {}^3\theta +\dots .$$$$=\cos \theta and0<\theta <\frac{\pi }{2}then$$$$find\theta .$$ Answered by benjo_mathlover last updated on 08/May/21…