Category: Algebra

Question Number 145525 by mathdanisur last updated on 05/Jul/21 Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$f(x+2)+10f\left(x\right)=7f(x+1)$$$$f(x+2)-7f(x+1)+10f\left(x\right)=0$$$$r^2-7r+10=0$$$$\left({r}−\mathrm{2}\right)\left({r}−\mathrm{5}\right)\:=\:\mathrm{0} \…

Question Number 145522 by ArielVyny last updated on 05/Jul/21 $$montrerque{l}^{\prime }ensembledessuitesreellequi$$$$verifielarelation\mathrm{\forall }n\in \mathbb{N}$$$${aU}_{n+2}+{bU}_{n+1}+{cU}_n=0\left(1\right)estunespace$$$$vectorieldedimension2$$$$etdeterminerunebase$$$$$$…

Question Number 79974 by TawaTawa last updated on 29/Jan/20 Answered by Rio Michael last updated on 30/Jan/20 $$\mathbf{solution}$$$$[(p\vee q)\wedge (\sim p\vee r)]\Rightarrow (q\vee r)$$$$\mathrm{we}\mathrm{know}\mathrm{from}\mathrm{known}\mathrm{facts}\mathrm{that}$$$$\:−\left({p}\:\vee{q}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{contingency}\:\left(\mathrm{neither}\:\mathrm{a}\:\mathrm{tautology}\:\mathrm{nor}\:\mathrm{contradiction}\right) \…

Question Number 145499 by mathdanisur last updated on 05/Jul/21 $$\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\dots -\frac{1}{256}=\frac{\mathit{z}+1}{256}$$$$find\mathit{z}=?$$ Answered by gsk2684 last updated on 05/Jul/21 $$\mathrm{sum}\mathrm{of}8\mathrm{terms}\mathrm{in}\mathrm{G}.\mathrm{P}.$$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}−\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{8}} }{\mathrm{1}−\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)}\right)=\frac{\mathrm{84}+\mathrm{1}}{\mathrm{256}}\:…

Question Number 79946 by mr W last updated on 29/Jan/20 $$Find$$$${\int }_0^n\left[\sqrt[3]{x}\right]dx=?$$$$intermsofn.(n\in \mathbb{N})$$ Answered by key of knowledge last…