Category: Algebra

Question Number 122854 by Study last updated on 20/Nov/20 Answered by mathmax by abdo last updated on 20/Nov/20 $${(-2)}^{\sqrt{2}}={\mathrm{e}}^{\sqrt{2}\ln (-2)}={\mathrm{e}}^{\sqrt{2}(\ln (-1)+\ln \left(2\right))}={\mathrm{e}}^{\sqrt{2}(\mathrm{i}\pi +\ln 2)}$$$$=\:\mathrm{e}^{\sqrt{\mathrm{2}}\mathrm{ln}\left(\mathrm{2}\right)+\mathrm{i}\sqrt{\mathrm{2}}\pi} \:=\mathrm{e}^{\sqrt{\mathrm{2}}\mathrm{ln}\left(\mathrm{2}\right)}…

Question Number 188366 by a.lgnaoui last updated on 28/Feb/23 $$xlnx=7$$$$x?$$ Answered by mr W last updated on 28/Feb/23 $${e}^{\mathrm{ln}\:{x}} \mathrm{ln}\:{x}=\mathrm{7} \…

Question Number 188343 by Shrinava last updated on 28/Feb/23 $$\mathrm{Find}:\mathrm{\Omega }=\underset{\mathbf{n}=1}{\sum ^{\mathrm{\infty }}}\left(\underset{\mathbf{x}\to 0}{\lim }{(1-\frac{5-\sqrt{25-{\mathrm{x}}^2}}{\mathrm{x}})}^{\frac{5\mathbf{n}}{\mathbf{x}}}\right)$$ Answered by SEKRET last updated on 28/Feb/23 $$\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}}…

Question Number 57251 by ANTARES VY last updated on 01/Apr/19 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19 $$T_n=\frac{n(n-1)}{\frac{1}{(n-1)!}+\frac{1}{(n-2)!}}$$$$=\frac{n(n-1)}{\frac{1+n-1}{(n-1)!}}\to (n-1)(n-1)!$$$$\left[\underset{{n}=\mathrm{3}} {\overset{\mathrm{2019}} {\sum}}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{1}\right)!\right]+\mathrm{2}\rightarrow\boldsymbol{{S}}+\mathrm{2}…

Question Number 57244 by ANTARES VY last updated on 01/Apr/19 Commented by mr W last updated on 01/Apr/19 $$\frac{HC}{AH}=\frac{AH}{BH}$$$$\Rightarrow HC=\frac{3^2}{4}=\frac{9}{4}=2.25$$$$\Rightarrow{none}\:{of}\:{the}\:{answers}\:{is}\:{correct}. \…