Category: Arithmetic

Question Number 211105 by peter frank last updated on 28/Aug/24 Answered by mm1342 last updated on 28/Aug/24 $$z=z_1{z}_2=cos\frac{12\pi }{5}+isin\frac{12\pi }{5}$$$$={cos}\frac{\mathrm{2}\pi}{\mathrm{5}}+{isin}\frac{\mathrm{2}\pi}{\mathrm{5}}={e}^{\frac{\mathrm{2}\pi}{\mathrm{5}}{i}\:} \Rightarrow{z}^{\mathrm{5}} ={e}^{\mathrm{2}\pi{i}} =\mathrm{1}…

Question Number 211020 by peter frank last updated on 26/Aug/24 Answered by mahdipoor last updated on 26/Aug/24 $$dV=\left(\pi y^2\right)\left(dx\right)=\pi \frac{{(x-a)}^2{(x-b)}^2}{c^2}dx$$$${V}=\int{dV}=\frac{\pi}{{c}^{\mathrm{2}} }\int_{{a}}…

Question Number 210974 by bns970 last updated on 25/Aug/24 $$\sqrt{25}$$ Answered by TonyCWX08 last updated on 25/Aug/24 $$\sqrt{25}$$$$=\pm 5$$ Commented…

Question Number 210719 by lmcp1203 last updated on 17/Aug/24 $$find63{!}^{36!}mod97thanks$$ Answered by A5T last updated on 19/Aug/24 $$\varphi \left(97\right)=96$$$$36!\equiv 0\left(mod96\right)\Rightarrow 36!=96k$$$$\left(\mathrm{63}!,\mathrm{97}\right)=\mathrm{1}\Rightarrow\mathrm{63}!^{\mathrm{36}!}…

Question Number 210607 by peter frank last updated on 13/Aug/24 Answered by A5T last updated on 14/Aug/24 $$\mathrm{75}\left(\mathrm{5}^{\mathrm{3}{log}_{\mathrm{2}} {x}} \right)=\mathrm{75}\left(\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{5}} \right)^{{log}_{\mathrm{2}} {x}×\mathrm{3}} =\mathrm{75}\left(\mathrm{2}^{{log}_{\mathrm{2}} {x}}…