Category: Algebra

Question Number 10872 by Saham last updated on 28/Feb/17 $$\mathrm{In}\mathrm{a}\mathrm{cultural}\mathrm{gathering}\mathrm{of}400\mathrm{people},\mathrm{there}\mathrm{are}270\mathrm{men}\mathrm{and}200$$$$\mathrm{musicians}.\mathrm{Of}\mathrm{the}\mathrm{latter},80\mathrm{are}\mathrm{singers}.60\mathrm{of}\mathrm{the}\mathrm{women}\mathrm{are}\mathrm{not}\mathrm{musicians}$$$$\mathrm{and}220\mathrm{of}\mathrm{the}\mathrm{men}\mathrm{are}\mathrm{not}\mathrm{singers}.\mathrm{How}\mathrm{many}\mathrm{of}\mathrm{the}\mathrm{women}\mathrm{are}$$$$\mathrm{musicians}\mathrm{but}\mathrm{not}\mathrm{singers}.\mathrm{if}\mathrm{there}\mathrm{are}150\mathrm{singers}\mathrm{altogether}\mathrm{and}$$$$40\mathrm{men}\mathrm{are}\mathrm{both}\mathrm{musicians}\mathrm{and}\mathrm{singers}.$$ Answered by Abdulhalim Ghadady last…

Question Number 10867 by Saham last updated on 28/Feb/17 $$\left(1\right)$$$$\mathrm{Show}\mathrm{that}:$$$$\frac{{\mathrm{x}}^{2\mathrm{n}+1}-{\mathrm{y}}^{2\mathrm{n}+1}}{\mathrm{x}-\mathrm{y}}={\mathrm{x}}^{2\mathrm{n}}+{\mathrm{x}}^{2\mathrm{n}-1}\mathrm{y}+\dots +{\mathrm{xy}}^{2\mathrm{n}-1}+{\mathrm{y}}^{2\mathrm{n}}$$$$\left(2\right)$$$$\mathrm{Show}\mathrm{that}:$$$$\frac{\mathrm{x}^{\mathrm{2n}}…

Question Number 10856 by Joel576 last updated on 27/Feb/17 $$\mathrm{Find}\mathrm{all}\mathrm{the}\mathrm{solution}\mathrm{that}\mathrm{fulfilled}\mathrm{the}\mathrm{equation}\mathrm{below}$$$${(1+\frac{1}{x})}^{x+1}={(1+\frac{1}{2013})}^{2013}$$ Answered by DrDaveR last updated on 12/Mar/17 $$Just-2014.Therecanbenopositvesolution.Thefunctionis$$$${monotinically}\:{decreasing}\:\:{so}\:{there}\:{could}\:{be}\:{one}\:{negative}\:…

Question Number 76340 by Master last updated on 26/Dec/19 Commented by behi83417@gmail.com last updated on 26/Dec/19 $$\mathrm{x}=-1,0$$ Answered by behi83417@gmail.com last updated on…

Question Number 10795 by j.masanja06@gmail.com last updated on 25/Feb/17 $$\mathrm{by}\mathrm{use}\mathrm{sketching}\mathrm{determine}\mathrm{the}\mathrm{range}$$$$\mathrm{or}\left(\mathrm{ranges}\right)\mathrm{of}\mathrm{the}\mathrm{value}\mathrm{x}\mathrm{can}\mathrm{take}\mathrm{for}$$$$\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{inqualities}$$$$\left(\mathrm{i}\right){3\mathrm{x}}^2-19\mathrm{x}-6⩽0$$$$\left(\mathrm{ii}\right){2\mathrm{x}}^2-5\mathrm{x}-3⩾0$$ Commented by sandy_suhendra…