Question Number 15916 by tawa tawa last updated on 15/Jun/17 Commented by tawa tawa last updated on 15/Jun/17 $$\mathrm{6a}\:\mathrm{and}\:\mathrm{b} \\ $$ Commented by tawa tawa…
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Question Number 146964 by mathdanisur last updated on 16/Jul/21 $${Simplify}: \\ $$$$\frac{\sqrt{\mathrm{2}}\:\centerdot\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}}}\:\centerdot\:\sqrt{\mathrm{2}\:-\:\sqrt{\mathrm{2}}}}{\:\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 16/Jul/21 $${x}\:=\:\frac{\sqrt{\mathrm{2}}\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}.\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}}{\:\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}} \\ $$$${x}\:=\:\frac{\sqrt{\mathrm{2}}\sqrt{\left(\mathrm{2}+\sqrt{\mathrm{2}}\right)\left(\mathrm{2}−\sqrt{\mathrm{2}}\right)}}{\:\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}} \\…
Question Number 146961 by mathdanisur last updated on 16/Jul/21 $$\sqrt{{sin}\left({x}\right)}\:\centerdot\:{cos}\left({x}\right)\:<\:\mathrm{0} \\ $$ Answered by TheHoneyCat last updated on 16/Jul/21 $$\mathrm{this}\:\mathrm{expression}\:_{''\sqrt{}''} \:\mathrm{requires}\:\mathrm{that}\:{sin}\left({x}\right)>\mathrm{0} \\ $$$$\mathrm{thus}\:{cos}\left({x}\right)<\mathrm{0} \\ $$$$…
Question Number 146960 by mathdanisur last updated on 16/Jul/21 Answered by TheHoneyCat last updated on 16/Jul/21 $$\mathrm{let}\:\mathscr{A}\:\mathrm{be}\:\mathrm{the}\:\mathrm{fuction}\:\mathrm{that}\:\mathrm{gives}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{surface} \\ $$$$\mathrm{let}\:\Delta={ABO} \\ $$$$\mathrm{let}\:{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{hatched}\:\mathrm{area} \\ $$$$\mathrm{let}\:{D}\:\mathrm{be}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{between}\:\left[\mathrm{AO}\right]\:\mathrm{and}\:\mathrm{the}\:\mathrm{circle}\:\mathscr{C}\left({O},{OR}\right) \\ $$$$\mathrm{let}\:{y}\:\mathrm{be}\:\mathrm{the}\:\mathrm{portion}\:{AOD}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}…
Question Number 15869 by prakash jain last updated on 14/Jun/17 $$\mathrm{If}\:{ax}^{\mathrm{2}} +\frac{{b}}{{x}}\geqslant{c}\:\mathrm{for}\:\mathrm{all}\:{x},{a},{b}>\mathrm{0}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{27}{ab}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{4}{c}^{\mathrm{2}} . \\ $$ Commented by prakash jain last…
Question Number 146943 by mathdanisur last updated on 16/Jul/21 $${b}_{\boldsymbol{{n}}+\mathrm{2}} \:\centerdot\:{b}_{\boldsymbol{{n}}+\mathrm{3}} \:\centerdot\:{b}_{\boldsymbol{{n}}+\mathrm{4}} \:=\:\mathrm{3}^{\mathrm{3}\boldsymbol{{n}}+\mathrm{3}} \\ $$$${geometric}\:{series}\:\:\boldsymbol{{b}}_{\mathrm{8}} \:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 16/Jul/21…
Question Number 146936 by mathdanisur last updated on 16/Jul/21 $$\begin{cases}{{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} +{xy}=\mathrm{37}}\\{{y}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}=\mathrm{26}}\end{cases}\:\Rightarrow\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =? \\ $$ Answered by TheHoneyCat last updated on 16/Jul/21…
Question Number 15865 by prakash jain last updated on 14/Jun/17 $${a},{b},{c}\in\mathbb{R}^{+\:} \mathrm{andIf}\:{a}+{b}+{c}=\mathrm{18}\:\mathrm{then}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{of}\:{a}^{\mathrm{2}} {b}^{\mathrm{3}} {c}^{\mathrm{4}} \:\mathrm{is} \\ $$ Answered by Tinkutara last updated on…
Question Number 146923 by mathdanisur last updated on 16/Jul/21 $${if}\:\:\:\:{arg}\:\left(\frac{{i}\:-\:{z}}{{i}}\right)\:=\:\frac{\pi}{\mathrm{4}} \\ $$$${find}\:\:\:\:{RemZ}\:+\:{ImZ}\:=\:? \\ $$ Answered by gsk2684 last updated on 16/Jul/21 $${arg}\left(\mathrm{1}+{iz}\right)=\frac{\pi}{\mathrm{4}} \\ $$$${arg}\left(\mathrm{1}+{i}\left({x}+{iy}\right)\right)=\frac{\pi}{\mathrm{4}} \\…