Category: Algebra

Question Number 9498 by FilupSmith last updated on 11/Dec/16 $$\mathrm{For}y=x^2,\mathrm{show}\mathrm{how}\mathrm{to}\mathrm{find}\frac{dy}{d\theta }$$ Commented by FilupSmith last updated on 11/Dec/16 $$\mathrm{Note}:\theta \mathrm{is}\mathrm{the}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{tangent}\mathrm{line}$$ Answered by…

Question Number 140556 by mathsuji last updated on 09/May/21 $$if,m>0,thendetermineallreal$$$$numbers\mathit{z}whichsatisfy$$$${\mathit{z}}^2\cdot (m^{\sqrt{\mathit{z}}-\mathit{z}}-1)-\sqrt{\mathit{z}}+1=0$$ Commented by MJS_new last updated on 10/May/21…

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…