Category: Arithmetic

Question Number 53262 by Tawa1 last updated on 19/Jan/19 $$\mathrm{find}\mathrm{x}:\frac{1}{\sqrt{\mathrm{x}+1+\sqrt{\mathrm{x}}}}-\frac{2}{\sqrt{\mathrm{x}-2+\sqrt{\mathrm{x}}}}=\sqrt{\mathrm{x}-1}$$ Commented by mr W last updated on 20/Jan/19 $$thereisnorealsolution!$$$$LHS:$$$${say}\:{x}+\sqrt{{x}}={u}\:>\mathrm{2}…

Question Number 118513 by I want to learn more last updated on 18/Oct/20 $$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\frac{\mathrm{x}-1}{\mathrm{x}}\right)=1+\mathrm{x},\mathrm{find}\mathrm{f}\left(2\right).$$ Answered by Dwaipayan Shikari last updated on 18/Oct/20 $${f}\left(\mathrm{2}\right)+{f}\left(\frac{\mathrm{2}−\mathrm{1}}{\mathrm{2}}\right)=\mathrm{1}+\mathrm{2}\rightarrow\left({a}\right)\:\:\:\left({Takng}\:{x}=\mathrm{2}\right)…

Question Number 118485 by bramlexs22 last updated on 18/Oct/20 $$Ifpartialfraction$$$$\frac{10x^2+px+18}{2x^3+5x^2+x-2}canbewritten$$$$as\frac{q}{2x-1}+\frac{4}{x+2}+\frac{r}{x+1}.Thenfindthe$$$$valueofp-q+2r.$$ Answered by benjo_mathlover last…

Question Number 118448 by peter frank last updated on 17/Oct/20 Answered by Olaf last updated on 17/Oct/20 $$\mathrm{A}=\pi \times 7^2-2{\int }_{-7}^{+7}(7-\sqrt{49-x^2})dx$$$$\mathrm{A}\:=\:\mathrm{49}\pi−\mathrm{4}\int_{\mathrm{0}} ^{+\mathrm{7}}…

Question Number 183646 by Rasheed.Sindhi last updated on 28/Dec/22 $$\mathcal{H}owmanyartificiallymadeweightsare$$$$\mathit{r}\mathit{e}\mathit{q}\mathit{u}\mathit{i}\mathit{r}\mathit{e}\mathit{d}\left(minimally\right)toweigh$$$$1,3,5,\dots ,79kg$$$$andwhatshouldbethey?$$ Commented by Rasheed.Sindhi last updated on 28/Dec/22…