Question Number 15504 by rish@bh last updated on 11/Jun/17 $$\mathrm{Solve}\:\lceil{x}^{\mathrm{2}} \rceil=\left(\lfloor{x}\rfloor\right)^{\mathrm{2}} +\mathrm{2}{x} \\ $$ Commented by rish@bh last updated on 11/Jun/17 $$\mathrm{I}\:\mathrm{got}\:\mathrm{only}\:\mathrm{0}\:\mathrm{and}\:.\mathrm{5}\:\mathrm{but}\:\mathrm{my}\:\mathrm{book} \\ $$$$\mathrm{says}\:\frac{{n}+\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{0} \\…
Question Number 15497 by FilupS last updated on 11/Jun/17 $${P}=\underset{{n}\in\mathbb{P}} {\overset{\infty} {\sum}}{n}\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Q}=\underset{{n}\notin\mathbb{P}} {\overset{\infty} {\sum}}{n} \\ $$$${P}=\mathrm{2}+\mathrm{3}+\mathrm{5}+\mathrm{7}+… \\ $$$${Q}=\mathrm{1}+\mathrm{4}+\mathrm{6}+\mathrm{8}+… \\ $$$$\: \\ $$$$\mathrm{Is}\:{P}>{Q}?\:\:\:\mathrm{Is}\:{Q}>{P}? \\ $$ Commented…
Question Number 81010 by M±th+et£s last updated on 08/Feb/20 $${show}\:{that} \\ $$$$\left({cos}\theta−{i}\:{sin}\theta\right)^{{n}} =\left({cosn}\theta−{i}\:{sin}\theta\right) \\ $$ Commented by MJS last updated on 08/Feb/20 $$\mathrm{wrong} \\ $$…
Question Number 146545 by mathdanisur last updated on 13/Jul/21 $${arcsin}\left({x}^{\mathrm{2}} -\mathrm{3}\right)\:=\:{arcsin}\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{4}\right) \\ $$$${find}\:\:\boldsymbol{{x}}=? \\ $$ Answered by Olaf_Thorendsen last updated on 14/Jul/21 $$\mathrm{arcsin}\left({x}^{\mathrm{2}} −\mathrm{3}\right)\:=\:\mathrm{arcsin}\left({x}^{\mathrm{2}}…
Question Number 146535 by mathdanisur last updated on 13/Jul/21 $$\begin{cases}{\frac{\mathrm{15}}{{x}^{\mathrm{2}} +{xy}}\:+\:\frac{\mathrm{3}}{{y}^{\mathrm{2}} +{xy}}\:=\:\mathrm{5},\mathrm{5}}\\{\frac{\mathrm{12}}{{x}^{\mathrm{2}} +{xy}}\:-\:\frac{\mathrm{6}}{{y}^{\mathrm{2}} +{xy}}\:=\:\mathrm{3}}\end{cases}\:\:\:\Rightarrow\:\:\mid{x}+{y}\mid=? \\ $$ Answered by liberty last updated on 14/Jul/21 $$\:\begin{cases}{\frac{\mathrm{30}}{{x}^{\mathrm{2}} +{xy}}+\frac{\mathrm{6}}{{y}^{\mathrm{2}}…
Question Number 146532 by mathdanisur last updated on 13/Jul/21 $$\mathrm{2}^{\boldsymbol{{x}}} \:=\:\mathrm{5}\:\:,\:\:\mathrm{3}^{\boldsymbol{{y}}} \:=\:\mathrm{9}\:\:{and}\:\:\mathrm{25}^{\boldsymbol{{z}}} \:=\:\mathrm{8} \\ $$$${find}\:\:\:\left({x}\centerdot{y}\centerdot{z}\right)=? \\ $$ Answered by puissant last updated on 13/Jul/21 $$\mathrm{e}^{\mathrm{xln2}}…
Question Number 146521 by mathdanisur last updated on 13/Jul/21 $$\left(\boldsymbol{{i}}\:-\:\mathrm{1}\right)^{−\mathrm{100}} \:=\:? \\ $$ Answered by mathmax by abdo last updated on 13/Jul/21 $$\left(\mathrm{i}−\mathrm{1}\right)^{−\mathrm{100}} =\left(−\mathrm{1}+\mathrm{i}\right)^{−\mathrm{100}} \:=\left(\sqrt{\mathrm{2}}\mathrm{e}^{\frac{\mathrm{i3}\pi}{\mathrm{4}}}…
Question Number 80982 by Power last updated on 08/Feb/20 Commented by mr W last updated on 08/Feb/20 $$=\frac{\mathrm{2}}{\:\sqrt{{e}^{\pi} }}\beth\left(\zeta\left({n}\right)\right) \\ $$ Commented by mr W…
Question Number 146508 by mathdanisur last updated on 13/Jul/21 $${Find}\:{the}\:{sum}\:{of}\:{the}\:{roots}\:{of}\:{the} \\ $$$${equation}: \\ $$$$\mathrm{16}\:\centerdot\:\mathrm{2}^{\mid\boldsymbol{{x}}\mid} \:+\:\mathrm{5}\:\centerdot\:\mathrm{2}^{\boldsymbol{{x}}} \:=\:\mathrm{42} \\ $$ Answered by Olaf_Thorendsen last updated on 13/Jul/21…
Question Number 146505 by mathdanisur last updated on 13/Jul/21 $$\underset{{x}\rightarrow\mathrm{7}} {{lim}}\:\frac{\sqrt{{x}\:-\:{a}}\:-\:\mathrm{4}}{{x}\:-\:\mathrm{7}}\:=\:{b}\:\:{find}\:\:{a}\centerdot{b}=? \\ $$ Answered by ajfour last updated on 13/Jul/21 $${i}\:{just}\:{dunno}\:\:{but}\:{letsee}\:{whtits} \\ $$$${bout}.. \\ $$$${if}\:{limit}\:{has}\:{to}\:{exist},\:{i}.{e}.…