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Category: Algebra

Convert-i-2-2-1-2-into-polarform-

Question Number 19405 by $@ty@m last updated on 10/Aug/17 $${Convert}\:{i}\sqrt{\frac{\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{1}}{\mathrm{2}}}\:{into}\:{polarform}. \\ $$ Answered by Tinkutara last updated on 10/Aug/17 $$\sqrt{\frac{\mathrm{2}\sqrt{\mathrm{2}}\:−\:\mathrm{1}}{\mathrm{2}}}\left(\mathrm{cos}\:\frac{\pi}{\mathrm{2}}\:+\:{i}\:\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\right) \\ $$ Commented by $@ty@m…

If-f-x-4-x-4-x-2-find-f-1-17-f-16-17-

Question Number 150469 by mathdanisur last updated on 12/Aug/21 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4}^{\boldsymbol{\mathrm{x}}} }{\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{2}}\:\:\:\mathrm{find}\:\:\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{17}}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{16}}{\mathrm{17}}\right)\:\overset{?} {=} \\ $$ Answered by gsk2684 last updated on 12/Aug/21 $${f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right)\:=\frac{\mathrm{4}^{{x}} }{\mathrm{4}^{{x}} +\mathrm{2}}+\frac{\mathrm{4}^{\mathrm{1}−{z}}…

In-ABC-A-B-C-the-following-relationship-holds-R-2-R-F-8F-r-3-

Question Number 150453 by mathdanisur last updated on 12/Aug/21 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:,\:\bigtriangleup\mathrm{A}^{'} \mathrm{B}^{'} \mathrm{C}^{'} \:\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{relationship}\:\mathrm{holds}: \\ $$$$\mathrm{R}^{\mathrm{2}} \mathrm{R}^{'} \mathrm{F}^{'} \:\geqslant\:\mathrm{8F}\left(\mathrm{r}^{'} \right)^{\mathrm{3}} \\ $$ Terms of…

sin-pi-14-sin-3pi-14-sin-5pi-15-

Question Number 84913 by M±th+et£s last updated on 17/Mar/20 $$ \\ $$$${sin}\frac{\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{3}\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{5}\pi}{\mathrm{15}}=? \\ $$ Commented by jagoll last updated on 17/Mar/20 $$\mathrm{sin}\:\frac{\pi}{\mathrm{14}}\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{14}}\mathrm{sin}\:\frac{\mathrm{5}\pi}{\mathrm{14}}\:?\:\mathrm{or}\:\mathrm{not} \\ $$ Commented…

Solve-the-equation-x-3-x-2-8x-15-x-2-1-

Question Number 150435 by mathdanisur last updated on 12/Aug/21 $$\boldsymbol{\mathrm{S}}\mathrm{olve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mid\mathrm{x}\:-\:\mathrm{3}\mid^{\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:-\:\mathrm{8x}\:+\:\mathrm{15}}{\boldsymbol{\mathrm{x}}\:-\:\mathrm{2}}} \:=\:\mathrm{1} \\ $$ Answered by amin96 last updated on 12/Aug/21 $${x}\neq\mathrm{2}\:\:\:\Rightarrow\:\:{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{15}=\mathrm{0}\:\:\left({x}−\mathrm{5}\right)\left({x}−\mathrm{3}\right)=\mathrm{0}…