Category: Algebra

Question Number 53709 by pieroo last updated on 25/Jan/19 $$\mathrm{A}\mathrm{supermarket}\mathrm{pays}\mathrm{its}\mathrm{sales}\mathrm{personnel}$$$$\mathrm{on}\mathrm{a}\mathrm{weekly}\mathrm{basis}.\mathrm{At}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{each}\mathrm{week},$$$$\mathrm{each}\mathrm{sales}\mathrm{person}\mathrm{receives}\mathrm{a}\mathrm{basic}$$$$\mathrm{weekly}\mathrm{wage}\mathrm{plus}\mathrm{bonus},\mathrm{which}\mathrm{varies}$$$$\mathrm{directly}\mathrm{as}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{complete}$$$$\mathrm{weeks}\mathrm{that}\mathrm{particular}\mathrm{person}\mathrm{has}$$$$\mathrm{worked}\mathrm{in}\mathrm{the}\mathrm{shop}.\mathrm{At}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{her}$$$$\mathrm{fourth}\:\mathrm{week}\:\mathrm{a}\:\mathrm{sales}\:\mathrm{girl}\:\mathrm{received}\:\mathrm{a}\:\mathrm{pay} \…

Question Number 184753 by cortano1 last updated on 11/Jan/23 Answered by qaz last updated on 11/Jan/23 $$\underset{{r}\rightarrow\infty} {{lim}}\frac{{r}^{{c}} \int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}^{{r}} \mathrm{sin}\:{xdx}}{\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}^{{r}} \mathrm{cos}\:{xdx}}=\underset{{r}\rightarrow\infty}…

Question Number 184738 by mnjuly1970 last updated on 11/Jan/23 $$$$$$\alpha ,\beta arerootsof,x^2-x-1=0$$$$(\alpha >\beta )and,t_n=\frac{{\alpha }^n-{\beta }^n}{\alpha -\beta }$$$$(n\in \mathbb{N}),if,b_1=1,b_n=t_{n-1}+t_{n-2}$$$$\:\:\:\left(\:{n}\:\geqslant\mathrm{2}\:\right)\:{find}\:{the}\:{value}\:{of}…

Question Number 184728 by mnjuly1970 last updated on 11/Jan/23 $$$$$$x^2-3x+1=0$$$$\alpha ,\beta areroots:$$$${({\alpha }^3+\frac{1}{\beta })}^3+{({\beta }^{{}^3}+\frac{1}{\alpha })}^3=?$$$$ \…

Question Number 119160 by zakirullah last updated on 22/Oct/20 Commented by zakirullah last updated on 22/Oct/20 $$\mathbf{find}\mathbf{the}\mathbf{position}\mathbf{vecter}\mathbf{of}\mathbf{a}\mathit{p}\mathbf{oint}\mathbf{R}$$$$\mathit{w}\mathit{h}\mathit{i}\mathit{c}\mathit{h}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{s}\mathit{t}\mathit{h}\mathit{e}\mathit{l}\mathit{i}\mathit{n}\mathit{e}\mathit{j}\mathit{o}\mathit{i}\mathit{n}\mathit{i}\mathit{n}\mathit{g}$$$$\mathit{t}\mathit{h}\mathit{e}\mathit{p}\mathit{o}\mathit{i}\mathit{n}\mathit{t}\mathit{w}\mathit{h}\mathit{o}\mathit{s}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{p}\mathit{o}\mathit{s}\mathit{i}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$$$\mathit{v}\mathit{e}\mathit{c}\mathit{t}\mathit{e}\mathit{r}\mathit{s}\mathit{a}\mathit{r}\mathit{e}\mathit{P}(\mathit{i}+2\mathit{j}-\mathit{k}),\mathit{Q}(-\mathit{i}+\mathit{j}+\mathit{k})\mathit{i}\mathit{n}$$$$\boldsymbol{{the}}\:\boldsymbol{{ratio}}\:\mathrm{2}:\mathrm{1}\:\boldsymbol{{internaly}}\:\boldsymbol{{and}}\:\boldsymbol{{externaly}}…