Question Number 146610 by mathdanisur last updated on 14/Jul/21 $${How}\:{many}\:{roots}\:{does}\:{the}\:{equation} \\ $$$${have}? \\ $$$$\mathrm{5}^{\mathrm{3}\boldsymbol{{x}}} \:+\:\mathrm{27}\centerdot\mathrm{5}^{−\mathrm{3}\boldsymbol{{x}}} \:+\:\mathrm{9}\centerdot\mathrm{5}^{\boldsymbol{{x}}} \:+\:\mathrm{27}\centerdot\mathrm{5}^{−\boldsymbol{{x}}} \:=\:\mathrm{64} \\ $$ Answered by iloveisrael last updated…
Question Number 146606 by iloveisrael last updated on 14/Jul/21 Answered by som(math1967) last updated on 14/Jul/21 $${x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}+\frac{\mathrm{1}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}=\mathrm{20} \\ $$$$\frac{{x}^{\mathrm{2}} −{x}^{\mathrm{2}} +\mathrm{1}+\mathrm{1}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}=\mathrm{20} \\…
Question Number 81054 by peter frank last updated on 09/Feb/20 $${solve}\:{the}\:{differential} \\ $$$${equation} \\ $$$$\left({a}\right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\mathrm{sin}\:^{\mathrm{2}} \left({x}+{y}\right) \\ $$$$\left({b}\right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\mathrm{cos}\:\left({x}+{y}\right) \\ $$ Commented…
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 $${it}\:{is}\:\mathrm{3}\pi−\mathrm{10}.\:{Since}\:\mathrm{10}^{{c}} \cong\mathrm{3}\pi+\alpha\:{where} \\ $$$$\alpha\epsilon\left(−\pi/\mathrm{2}\:{to}\:\pi/\mathrm{2}\right) \\ $$$${So}\:{arcsin}\left({sin}\mathrm{10}\right)=\mathrm{3}\pi−\mathrm{10}…
Question Number 146587 by mathdanisur last updated on 14/Jul/21 $${arccos}\left(\frac{\pi}{\mathrm{2}}\:-\:\frac{\mathrm{1}}{\mathrm{2}}\:{arccos}\:\frac{\mathrm{4}}{\mathrm{5}}\right)\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 15501 by rish@bh last updated on 11/Jun/17 $$\mathrm{Solve} \\ $$$${x}^{\mathrm{3}} −\lfloor{x}\rfloor=\mathrm{3} \\ $$ Answered by mrW1 last updated on 11/Jun/17 $$\mathrm{x}=\mathrm{n}+\mathrm{f} \\ $$$$\lfloor\mathrm{x}\rfloor=\mathrm{n}…
Question Number 15504 by rish@bh last updated on 11/Jun/17 $$\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}}…