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Category: Algebra

arcsin-sin-10-

Question Number 146589 by mathdanisur last updated on 14/Jul/21 $${arcsin}\:\left({sin}\:\mathrm{10}\right)\:=\:? \\ $$ Answered by SLVR last updated on 14/Jul/21 $${it}\:{is}\:\mathrm{3}\pi−\mathrm{10}.\:{Since}\:\mathrm{10}^{{c}} \cong\mathrm{3}\pi+\alpha\:{where} \\ $$$$\alpha\epsilon\left(−\pi/\mathrm{2}\:{to}\:\pi/\mathrm{2}\right) \\ $$$${So}\:{arcsin}\left({sin}\mathrm{10}\right)=\mathrm{3}\pi−\mathrm{10}…

Solve-x-2-x-2-2x-

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} \\…

P-n-P-n-Q-n-P-n-P-2-3-5-7-Q-1-4-6-8-Is-P-gt-Q-Is-Q-gt-P-

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…

arcsin-x-2-3-arcsin-x-2-3x-4-find-x-

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}}…

15-x-2-xy-3-y-2-xy-5-5-12-x-2-xy-6-y-2-xy-3-x-y-

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}}…

2-x-5-3-y-9-and-25-z-8-find-x-y-z-

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}}…

i-1-100-

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}}}…