Category: Arithmetic

Question Number 177000 by Ar Brandon last updated on 29/Sep/22 $$\mathrm{Let}a\mathrm{and}b\mathrm{be}\mathrm{positive}\mathrm{integers}.$$$$\mathrm{If}118!+119!=5^{a}b\mathrm{then}\mathrm{what}\mathrm{is}{a}_{\max }?$$ Answered by BaliramKumar last updated on 29/Sep/22 $$\mathrm{118}!\:+\:\mathrm{119}!\:=\:\mathrm{118}!\left(\mathrm{1}+\mathrm{119}\right)\:=\:\mathrm{120}×\mathrm{118}!…

Question Number 176950 by cortano1 last updated on 28/Sep/22 Answered by mr W last updated on 28/Sep/22 $$say\mathrm{\angle }AEC=\theta$$$$CB=4\sin \theta$$$$BE=4\cos \theta$$$$\frac{{AE}}{\mathrm{sin}\:\mathrm{45}°}=\frac{\mathrm{3}}{\mathrm{sin}\:\left(\theta−\mathrm{45}°\right)} \…

Question Number 176925 by Ar Brandon last updated on 28/Sep/22 Answered by mindispower last updated on 28/Sep/22 $$=x^2+y^2-2xy+x^2-4x+4$$$$\left({x}−{y}\right)^{\mathrm{2}} +\left({x}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{0}…

Question Number 111342 by pete last updated on 03/Sep/20 $$\mathrm{When}\mathrm{the}\mathrm{terms}\mathrm{of}\mathrm{a}\mathrm{Geometric}\mathrm{Progression}\left(\mathrm{GP}\right)$$$$\mathrm{with}\mathrm{common}\mathrm{ratio}\mathrm{r}=2\mathrm{is}\mathrm{added}\mathrm{to}\mathrm{the}\mathrm{corresponding}\mathrm{terms}$$$$\mathrm{of}\mathrm{an}\mathrm{Arithmetic}\mathrm{Provression}\left(\mathrm{AP}\right),$$$$\mathrm{a}\mathrm{new}\mathrm{sequence}\mathrm{is}\mathrm{formed}.\mathrm{If}\mathrm{the}\mathrm{first}\mathrm{terms}$$$$\mathrm{of}\mathrm{the}\mathrm{GP}\mathrm{and}\mathrm{AP}\mathrm{are}\mathrm{the}\mathrm{same}\mathrm{and}\mathrm{the}\mathrm{first}$$$$\mathrm{three}\mathrm{terms}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{sequence}\mathrm{are}$$$$3,7\mathrm{and}11\mathrm{respectively},\mathrm{find}\mathrm{the}{\mathrm{n}}^{\mathrm{th}}\mathrm{term}$$$$\mathrm{of}\:\mathrm{the}\:\mathrm{seauence}.…

Question Number 176850 by Ar Brandon last updated on 27/Sep/22 $$f\left(x\right)=2(x-1)$$$$\underset{50\mathrm{times}}{\underbrace{(fofo\dots of)}}\left(x\right)=?$$ Answered by mr W last updated on 27/Sep/22 $${f}\left({x}\right)=\mathrm{2}{x}−\mathrm{2}…