Category: Arithmetic

Question Number 177000 by Ar Brandon last updated on 29/Sep/22 $$\mathrm{Let}\:{a}\:\mathrm{and}\:{b}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{integers}. \\ $$$$\mathrm{If}\:\mathrm{118}!+\mathrm{119}!=\mathrm{5}^{{a}} {b}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:{a}_{\mathrm{max}} \:?\: \\ $$ 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 $${say}\:\angle{AEC}=\theta \\ $$$${CB}=\mathrm{4}\:\mathrm{sin}\:\theta \\ $$$${BE}=\mathrm{4}\:\mathrm{cos}\:\theta \\ $$$$\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 $$={x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{xy}+{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4} \\ $$$$\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 $$\mathrm{When}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}\left(\mathrm{GP}\right) \\ $$$$\mathrm{with}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{r}=\mathrm{2}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{the}\:\mathrm{corresponding}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{an}\:\mathrm{Arithmetic}\:\mathrm{Provression}\:\left(\mathrm{AP}\right), \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{formed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{and}\:\mathrm{AP}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}\:\mathrm{and}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{are} \\ $$$$\mathrm{3},\:\mathrm{7}\:\mathrm{and}\:\mathrm{11}\:\mathrm{respectively},\:\mathrm{find}\:\mathrm{the}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{seauence}.…

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