Question Number 211563 by MrGaster last updated on 13/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}.\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{x}}−\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}.\boldsymbol{{e}}^{\boldsymbol{{x}}} +\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered by…
Question Number 211548 by MrGaster last updated on 12/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{y}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{{x}\mathrm{y}}=\mathrm{12}}\\{\boldsymbol{{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{4}}\end{cases} \\ $$$$ \\ $$ Answered by Frix last updated…
Question Number 211546 by MrGaster last updated on 12/Sep/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{13}}}=? \\ $$ Answered by Frix last updated on 12/Sep/24 $$\int\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{13}}}\:\overset{\left[{t}=\frac{{x}−\mathrm{2}+\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}}{\mathrm{3}}\right]}…
Question Number 211537 by cherokeesay last updated on 12/Sep/24 Answered by mr W last updated on 12/Sep/24 $$\sqrt{\left({R}−\mathrm{2}\right)^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }−\mathrm{2}=\sqrt{{R}^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} } \\ $$$$\sqrt{{R}^{\mathrm{2}} −\mathrm{4}{R}}=\mathrm{2}+\sqrt{{R}^{\mathrm{2}}…
Question Number 211535 by hardmath last updated on 12/Sep/24 Answered by BaliramKumar last updated on 12/Sep/24 $${x}\:=\:\mathrm{7}\:−\:\frac{\mathrm{6}}{{x}} \\ $$$${x}\:=\:\left(\mathrm{1},\:\mathrm{6}\right) \\ $$ Terms of Service Privacy…
Question Number 211528 by mnjuly1970 last updated on 12/Sep/24 $$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{−\mathrm{1}} \:\left({x}^{\mathrm{2}} \:\right)}{{x}^{\:\mathrm{2}} }\:{dx}=\:?\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$…
Question Number 211529 by MrGaster last updated on 12/Sep/24 $$\mathrm{known}:\boldsymbol{{x}}+\boldsymbol{\mathrm{y}}=\mathrm{3},\mathrm{ask}: \\ $$$$\boldsymbol{\mathrm{min}}\left(\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}+\sqrt{\boldsymbol{\mathrm{y}}\mathrm{2}−\mathrm{4}}\right)=? \\ $$ Answered by MrGaster last updated on 12/Sep/24 $$\mathrm{1}.\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}+\sqrt{\left(\mathrm{3}+\boldsymbol{{x}}\right)^{\mathrm{2}} −\mathrm{4}}…
Question Number 211531 by MrGaster last updated on 12/Sep/24 $$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{{x}}\right)^{\mathrm{2}} }\boldsymbol{{dx}}. \\ $$ Answered by Frix last updated on 13/Sep/24 $$\underset{\mathrm{0}} {\overset{\infty}…
Question Number 211524 by Tawa11 last updated on 12/Sep/24 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:=\:\:\mathrm{4x} \\ $$ Answered by Frix last updated on 12/Sep/24 $$\mathrm{We}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate}. \\ $$$${x}\approx.\mathrm{183193} \\ $$$${x}\approx\mathrm{2}.\mathrm{50781}…
Question Number 211558 by mnjuly1970 last updated on 12/Sep/24 $$ \\ $$$$ \\ $$$$\:\:\:\:\:−−−−−−−−−−−− \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\Omega}=\:\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{n}}+\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{n}}+\mathrm{1}}\:\right)=\:\boldsymbol{{a}\pi} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\boldsymbol{{a}}^{\mathrm{2}} =\:? \\ $$$$\:\:\:\:\:\:\:−−−−−−−−−−−− \\ $$…