Question Number 82821 by VBash last updated on 24/Feb/20 $${Log}_{{y}} \:{x}+{Log}_{{x}} \:{y}\:=\mathrm{64} \\ $$$${find}\:{x}\:{and}\:{y} \\ $$ Commented by MJS last updated on 24/Feb/20 $$\mathrm{one}\:\mathrm{equation}\:\mathrm{in}\:\mathrm{two}\:\mathrm{unknown}\:\mathrm{gives}\:\mathrm{a} \\…
Question Number 148350 by Fikret last updated on 27/Jul/21 $$\frac{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+….+\frac{\mathrm{1}}{\mathrm{9}}}{\frac{\mathrm{9}}{\mathrm{1}}+\frac{\mathrm{8}}{\mathrm{2}}+…+\frac{\mathrm{1}}{\mathrm{9}}}=? \\ $$ Commented by liberty last updated on 27/Jul/21 $$=\:\frac{\mathrm{4609}}{\mathrm{48610}} \\ $$ Terms of Service…
Question Number 17270 by VEGAMIND last updated on 03/Jul/17 $$\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{x}}=\frac{\mathrm{1}+\sqrt{\mathrm{17}}}{\mathrm{2}}.\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}} \\ $$$$\frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{7}\boldsymbol{\mathrm{x}}−\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}+\mathrm{1}}\:\:\boldsymbol{\mathrm{decimal}}\:\boldsymbol{\mathrm{point}}. \\ $$ Commented by 18±1 last updated on 03/Jul/17 $$.\mathrm{2}\boldsymbol{{x}}=\mathrm{1}+\sqrt{\mathrm{17}}…
Question Number 17271 by VEGAMIND last updated on 03/Jul/17 $$\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{equation}}. \\ $$$$\sqrt{\frac{\mathrm{15}}{\mathrm{4}^{\mathrm{1}−\boldsymbol{\mathrm{x}}} }+\mathrm{4}^{\mathrm{1}−\boldsymbol{\mathrm{x}}} }=\mathrm{32}. \\ $$ Answered by RasheedSoomro last updated on 03/Jul/17 $$\sqrt{\frac{\mathrm{15}}{\mathrm{4}^{\mathrm{1}−\boldsymbol{\mathrm{x}}} }+\mathrm{4}^{\mathrm{1}−\boldsymbol{\mathrm{x}}}…
Question Number 148330 by 0731619 last updated on 27/Jul/21 Answered by qaz last updated on 27/Jul/21 $$\mathrm{y}_{\left(\mathrm{n}\right)} =\mathrm{2}^{\frac{\mathrm{n}+\mathrm{1}}{\mathrm{n}^{\mathrm{2}} −\mathrm{4n}}} \\ $$$$\mathrm{y}_{\left(\mathrm{n}\right)} '=\mathrm{2}^{\frac{\mathrm{n}+\mathrm{1}}{\mathrm{n}^{\mathrm{2}} −\mathrm{4n}}} \centerdot\left(\frac{\mathrm{n}+\mathrm{1}}{\mathrm{n}^{\mathrm{2}} −\mathrm{4n}}\right)\left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}−\frac{\mathrm{2n}−\mathrm{4}}{\mathrm{n}^{\mathrm{2}}…
Question Number 82782 by dorje last updated on 24/Feb/20 $$\:\: \\ $$$$\:\:\:\left(\mathrm{1}\right).\:\mathrm{9}\left(\mathrm{9}\boldsymbol{\div}\mathrm{3}\right)−\mathrm{6}\left(\mathrm{8}\boldsymbol{\div}\mathrm{3}\right)×\mathrm{2} \\ $$$$\:\:\:\:\left(\mathrm{2}\right).\:\mathrm{2}\frac{\mathrm{5}}{\mathrm{3}}+\mathrm{3}\frac{\mathrm{2}}{\mathrm{4}} \\ $$ Commented by mr W last updated on 24/Feb/20 $${i}\:{don}'{t}\:{think}\:{this}\:{forum}\:{is}\:{a}\:{right}…
Question Number 148285 by Khalmohmmad last updated on 26/Jul/21 $$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{x}^{\mathrm{2}} \mathrm{ln}{x}}{dx}=? \\ $$ Commented by ahmedNasser last updated on 26/Jul/21 $${let}\:{u}\:=\:{lnx}\:\:\:\:\therefore\:{du}\:=\:\frac{\mathrm{1}}{{x}}\:{dx}\:\:\:\:{x}\:=\:{e}^{{u}} \\ $$$$\int_{\mathrm{0}}…
Question Number 148284 by 0731619 last updated on 26/Jul/21 Answered by Olaf_Thorendsen last updated on 26/Jul/21 $$\mathrm{6}!!\:=\:\mathrm{6}×\mathrm{4}×\mathrm{2}\:=\:\mathrm{48} \\ $$$$\mathrm{8}!!!!!\:=\:\mathrm{8}×\mathrm{3}\:=\:\mathrm{24} \\ $$$$\mathrm{9}!!!!\:=\:\mathrm{9}×\mathrm{5}×\mathrm{1}\:=\:\mathrm{45} \\ $$$$!\mathrm{4}\:=\:\mathrm{4}!\left(\frac{\mathrm{1}}{\mathrm{0}!}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}\right)\:=\:\mathrm{9} \\ $$$$!\mathrm{5}\:=\:\mathrm{5}!\left(\frac{\mathrm{1}}{\mathrm{0}!}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}−+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}\right)\:=\:\mathrm{44}…
Question Number 17209 by sushmitak last updated on 02/Jul/17 $$\mathrm{Spin}\:\mathrm{only}\:\mathrm{magnetic}\:\mathrm{moment} \\ $$$$\mathrm{of}\:_{\mathrm{25}} \mathrm{Mn}^{\mathrm{x}+} \:\mathrm{is}\:\sqrt{\mathrm{15}}\mathrm{B}.\mathrm{M}.\:\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{is}? \\ $$$$\mathrm{i}\:\mathrm{did}\:\mathrm{following} \\ $$$$\mathrm{1s}^{\mathrm{2}} \mathrm{2s}^{\mathrm{2}} \mathrm{2p}^{\mathrm{6}} \mathrm{3s}^{\mathrm{2}} \mathrm{3p}^{\mathrm{6}} \mathrm{4s}^{\mathrm{2}}…
Question Number 148276 by 0731619 last updated on 26/Jul/21 Answered by mathmax by abdo last updated on 26/Jul/21 $$\mathrm{y}\left(\mathrm{n}\right)=\mathrm{e}^{\frac{\mathrm{n}^{\mathrm{2}} +\mathrm{n}}{\mathrm{n}^{\mathrm{3}} −\mathrm{4n}^{\mathrm{2}} }\mathrm{log2}} \:\Rightarrow\frac{\mathrm{dy}}{\mathrm{dn}}=\frac{\mathrm{d}}{\mathrm{dn}}\left(\mathrm{log2}×\frac{\mathrm{n}^{\mathrm{2}} \:+\mathrm{n}}{\mathrm{n}^{\mathrm{3}} −\mathrm{4n}^{\mathrm{2}}…