Category: Arithmetic

Question Number 2777 by Filup last updated on 27/Nov/15 $$\mathrm{Prove}\mathrm{that}:$$$$\zeta (-2n)=0$$ Answered by prakash jain last updated on 27/Nov/15 $$\mathrm{Functional}\mathrm{Equation}\mathrm{for}\zeta \left(s\right)$$$$\zeta\left({s}\right)=\mathrm{2}^{{s}}…

Question Number 68272 by peter frank last updated on 08/Sep/19 Answered by Kunal12588 last updated on 08/Sep/19 $$H_{max}=maximumheight$$$$R=horizontalrange$$$${H}_{{max}} ={h}=\frac{{u}_{{y}} ^{\mathrm{2}}…

Question Number 133764 by liberty last updated on 24/Feb/21 Answered by EDWIN88 last updated on 24/Feb/21 $$\mathrm{let}\mathrm{x}\mathrm{be}\mathrm{a}\mathrm{page}\mathrm{number}\mathrm{was}\mathrm{counted}\mathrm{twice}$$$$\mathrm{Assuming}\mathrm{the}\mathrm{pages}\mathrm{start}\mathrm{counting}\mathrm{at}1\mathrm{and}$$$$\mathrm{count}\mathrm{continously}\mathrm{up}\mathrm{we}\mathrm{use}\mathrm{formula}$$$$(1+2+3+\dots +\mathrm{n})+\mathrm{x}=1999$$$$\Rightarrow\mathrm{x}\:+\frac{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)}{\mathrm{2}}\:=\:\mathrm{1999}\:;\:\mathrm{since}\:\mathrm{x}\:\mathrm{is}\:\mathrm{positive}\:…

Question Number 68210 by peter frank last updated on 07/Sep/19 Answered by $@ty@m123lastupdatedon08/Sep/19$$Let\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}=R$$$\$\Rightarrow \sin A=aR,\sin B=bR,\sin C=cR\dots \left(1\right)$$$$\left(2\right)\frac{\sin (A-B)\sin C}{1+\cos (A-B)\cos C}$$$$=\:\frac{\mathrm{sin}\:\left({A}−{B}\right)\mathrm{sin}\:\left({A}+{B}\right)}{\mathrm{1}−\mathrm{cos}\:\left({A}−{B}\right)\mathrm{cos}\:\left({A}+{B}\right)} \…

Question Number 68203 by peter frank last updated on 07/Sep/19 Commented by Cmr 237 last updated on 07/Sep/19 $$\mathrm{ð}\mathrm{f}=\frac{\mathrm{ð}\mathrm{f}}{\mathrm{ð}\mathrm{x}}+\frac{\mathrm{ð}\mathrm{f}}{\mathrm{ð}\mathrm{y}}+\frac{\mathrm{ð}\mathrm{f}}{\mathrm{ð}\mathrm{z}}$$$$=2\mathrm{xy}+\cosh \left(\mathrm{yz}\right)+{\mathrm{x}}^2+\mathrm{xzsinh}\left(\mathrm{yz}\right)+\mathrm{xysinh}\left(\mathrm{yz}\right)$$ Commented…