Question Number 71518 by TawaTawa last updated on 16/Oct/19 $$\mathrm{Express}\:\:\sqrt{\mathrm{28}}\:\:\mathrm{as}\:\mathrm{continued}\:\mathrm{fraction} \\ $$ Commented by Prithwish sen last updated on 16/Oct/19 $$\sqrt{\mathrm{28}}\:=\:\mathrm{1}+\:\sqrt{\mathrm{28}}−\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:=\:\mathrm{1}+\:\:\frac{\mathrm{27}}{\:\sqrt{\mathrm{28}}+\mathrm{1}}\:=\:\mathrm{1}+\frac{\mathrm{27}}{\mathrm{2}+\sqrt{\mathrm{28}}−\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:=\:\mathrm{1}+\frac{\mathrm{27}}{\mathrm{2}+\frac{\mathrm{27}}{\:\sqrt{\mathrm{28}}+\mathrm{1}}}\:=\:\mathrm{1}+\frac{\mathrm{27}}{\mathrm{2}+\frac{\mathrm{27}}{\mathrm{2}+\frac{\mathrm{27}}{\mathrm{2}+\frac{\mathrm{27}}{\mathrm{2}+._{._{..}…
Question Number 5978 by FilupSmith last updated on 08/Jun/16 $${f}\left(\mathrm{1}\right){f}\left(−\mathrm{1}\right)\leqslant\mathrm{0} \\ $$$$\mathrm{Is}\:\mathrm{this}\:\mathrm{true}? \\ $$$$\mathrm{When}\:\mathrm{is}\:\mathrm{this}\:\mathrm{not}\:\mathrm{true}? \\ $$ Commented by Yozzii last updated on 09/Jun/16 $${If}\:{x}\in\mathbb{R},\:{f}\left({x}\right)\in\mathbb{R}\:{is}\:{odd}\:\Rightarrow{f}\left({x}\right){f}\left(−{x}\right)=−\left({f}\left({x}\right)\right)^{\mathrm{2}} \leqslant\mathrm{0}…
Question Number 137037 by JulioCesar last updated on 29/Mar/21 Answered by mathmax by abdo last updated on 29/Mar/21 $$\mathrm{I}=\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{3}} −\mathrm{8}\right)^{\mathrm{2}} }\:\left(\mathrm{compolex}\:\mathrm{method}\right)\:\Rightarrow\mathrm{I}=\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{4}\right)^{\mathrm{2}} } \\…
Question Number 5965 by love math last updated on 07/Jun/16 $${log}_{\frac{\mathrm{1}}{\mathrm{2}}} \left({x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{12}\right)>{log}_{{x}+\mathrm{5}} \left({x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{12}\right) \\ $$ Commented by Yozzii last updated on 07/Jun/16 $$\frac{{lnu}}{{ln}\mathrm{0}.\mathrm{5}}>\frac{{lnu}}{{ln}\left({x}+\mathrm{5}\right)}\:\:\:\:\left({change}\:{of}\:{base}/{u}={x}^{\mathrm{2}}…
Question Number 5943 by sanusihammed last updated on 06/Jun/16 $${P}\:=\:\mathrm{9}{x}\:+\:\mathrm{8}{y} \\ $$$${xy}\:=\:\mathrm{2} \\ $$$$ \\ $$$${find}\:\:{p}. \\ $$ Answered by FilupSmith last updated on 06/Jun/16…
Question Number 137007 by SLVR last updated on 28/Mar/21 Commented by SLVR last updated on 28/Mar/21 $${kindly}\:{send}\:{me}\:{the}\:{solution} \\ $$ Commented by mr W last updated…
Question Number 5926 by FilupSmith last updated on 05/Jun/16 $$\mathrm{I}'\mathrm{m}\:\mathrm{curious}\:\mathrm{about}\:\mathrm{your}\:\mathrm{response}\:\mathrm{to}\:\mathrm{this} \\ $$$$ \\ $$$$\mathrm{Where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mistake}: \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\mathrm{100}−\mathrm{100}}{\mathrm{100}−\mathrm{100}} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\mathrm{10}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} }{\mathrm{10}\left(\mathrm{10}−\mathrm{10}\right)} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\left(\mathrm{10}−\mathrm{10}\right)\left(\mathrm{10}+\mathrm{10}\right)}{\mathrm{10}\left(\mathrm{10}−\mathrm{10}\right)} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\left(\mathrm{10}+\mathrm{10}\right)}{\mathrm{10}} \\…
Question Number 5924 by sanusihammed last updated on 05/Jun/16 $${Solve}\:{for}\:{x}\:{and}\:{y} \\ $$$$ \\ $$$$\mathrm{2}^{{x}} \:+\:\mathrm{3}^{{y}} \:=\:\mathrm{31}\:\:\:…………….\:{equation}\:\left({i}\right) \\ $$$$\mathrm{3}^{{x}\:} +\:\mathrm{2}^{{y}} \:=\:\mathrm{17}\:\:…………….\:{equation}\:\left({ii}\right) \\ $$$$ \\ $$$${please}\:{help}. \\…
Question Number 5920 by sanusihammed last updated on 05/Jun/16 $${Solove}\:{for}\:{x}\:{and}\:{y} \\ $$$$ \\ $$$$\mathrm{2}^{{x}} \:+\:\mathrm{3}^{{y}} \:=\:\mathrm{31}\:\:\:…………\:{eauation}\:\left({i}\right) \\ $$$$\mathrm{3}^{{x}} \:+\:\mathrm{2}^{{y}\:} \:=\:\mathrm{17}\:\:…………\:{equation}\:\left({ii}\right) \\ $$$$ \\ $$$${please}\:{help}. \\…
Question Number 71448 by aliesam last updated on 15/Oct/19 $${find}\:{the}\:{domain} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{{sin}\left({sin}\left({x}\right)\right)} \\ $$ Commented by kaivan.ahmadi last updated on 15/Oct/19 $${sin}\left({sinx}\right)=\mathrm{0}\Rightarrow{sinx}={k}\pi\:\:;{k}\in\mathbb{Z} \\…