Question Number 174649 by Shrinava last updated on 06/Aug/22 Commented by MJS_new last updated on 07/Aug/22 $$\mathrm{questions}\:\mathrm{like}\:\mathrm{this}\:\mathrm{one}\:\mathrm{make}\:\mathrm{no}\:\mathrm{sense}… \\ $$$$\int\frac{{dx}}{\mathrm{3}+\mathrm{cos}\:{x}}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\mathrm{arctan}\:\frac{\sqrt{\mathrm{2}}\mathrm{tan}\:\frac{{x}}{\mathrm{2}}}{\:\mathrm{2}}\:+{C} \\ $$$${a}_{{n}} \:\mathrm{is}\:\mathrm{not}\:\mathrm{unique}. \\ $$$$\mathrm{if}\:\mathrm{it}'\mathrm{s}\:\mathrm{polynomial}: \\…
Question Number 43569 by LYCON TRIX last updated on 12/Sep/18 $$\mathrm{Please}\:\mathrm{solve}\:\mathrm{these}\:\mathrm{questions}\:−\: \\ $$$$\mathrm{43496}\:,\:\mathrm{42473}\:,\:\mathrm{42474}\:,\:\mathrm{42472}\:,\:\mathrm{42471}\:, \\ $$$$\mathrm{42470}\:,\:\mathrm{42469}\:,\:\mathrm{42468}\:,\:\mathrm{42408}\: \\ $$ Commented by MJS last updated on 12/Sep/18 $$\mathrm{I}\:\mathrm{solved}\:\mathrm{one}\:\mathrm{of}\:\mathrm{these},\:\mathrm{where}\:\mathrm{and}\:\mathrm{how}\:\mathrm{do}\:\mathrm{I}\:\mathrm{get}…
Question Number 174635 by mnjuly1970 last updated on 06/Aug/22 Answered by aleks041103 last updated on 06/Aug/22 $${tanh}^{−\mathrm{1}} \left(−{x}\right)=−{tanh}^{−\mathrm{1}} \left({x}\right) \\ $$$$\Rightarrow{tanh}^{−\mathrm{1}} \:\:{is}\:{odd}. \\ $$$$\left(−{x}\right)=−\left({x}\right) \\…
Question Number 109090 by ajfour last updated on 21/Aug/20 $${Find}\:{all}\:{those}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\:\boldsymbol{{z}}^{\mathrm{12}} −\mathrm{56}\boldsymbol{{z}}^{\mathrm{6}} −\mathrm{512}=\mathrm{0}\:\:{whose}\:{imaginary} \\ $$$${part}\:{is}\:{positive}. \\ $$ Answered by floor(10²Eta[1]) last updated on 21/Aug/20…
Question Number 43549 by peter frank last updated on 11/Sep/18 $${solve}\:{x}\::\:\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)^{{x}^{\mathrm{2}} −\mathrm{3}} +\left(\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}}\right)^{{x}^{\mathrm{2}} −\mathrm{3}} =\mathrm{10} \\ $$ Commented by Cheyboy last updated on 12/Sep/18 $$\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)\left(\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}}\right)\:=\:\mathrm{1}…
Question Number 43544 by behi83417@gmail.com last updated on 11/Sep/18 Answered by MJS last updated on 12/Sep/18 $${x}={z}−\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${z}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{3}}{z}+\frac{\mathrm{2}}{\mathrm{27}}−\frac{\sqrt{\mathrm{2}}}{\mathrm{10}}=\mathrm{0} \\ $$$$\mathrm{trigonometric}\:\mathrm{solution}\:\mathrm{method} \\ $$$${z}_{{k}} =\mathrm{2}\sqrt{−\frac{{p}}{\mathrm{3}}}\mathrm{sin}\left(\frac{\mathrm{2}\pi{k}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}}\mathrm{arcsin}\left(\frac{\mathrm{9}{q}}{\mathrm{2}{p}^{\mathrm{2}}…
Question Number 43540 by abdo.msup.com last updated on 11/Sep/18 $${prove}\:{that}\:\mathrm{111}\:{divide}\:\mathrm{10}^{\mathrm{6}{n}+\mathrm{2}} \:+\mathrm{10}^{\mathrm{3}{n}+\mathrm{1}} \:+\mathrm{1} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 12/Sep/18 $$\mathrm{10}^{\mathrm{6}{n}} ×\mathrm{100}+\mathrm{10}^{\mathrm{3}{n}} ×\mathrm{10}+\mathrm{1} \\…
Question Number 109063 by mr W last updated on 20/Aug/20 Commented by mr W last updated on 20/Aug/20 $${see}\:{Q}\mathrm{107696} \\ $$ Terms of Service Privacy…
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Question Number 174587 by bekzodjumayev last updated on 05/Aug/22 Commented by kaivan.ahmadi last updated on 05/Aug/22 $${f}\left(−{x}\right)=−{f}\left({x}\right) \\ $$$$\Rightarrow{f}\:{is}\:{an}\:{odd}\:{function} \\ $$$$\Rightarrow{f}'\left({x}\right)={f}'\left(−{x}\right)\Rightarrow{f}'\:{is}\:{an}\:{even}\:{function} \\ $$$$\Rightarrow{fof}\left(−{x}\right)={f}\left(−{f}\left({x}\right)\right)=−{fof}\left({x}\right) \\ $$$$\Rightarrow{fof}\:{is}\:{an}\:{odd}\:{function}…