Question Number 194961 by SirMUTUKU last updated on 20/Jul/23 Answered by mahdipoor last updated on 20/Jul/23 $${log}\mathrm{225}={log}\left(\mathrm{25}×\mathrm{9}\right)={log}\frac{\mathrm{100}}{\mathrm{4}}+{log}\mathrm{9}= \\ $$$${log}\mathrm{100}−{log}\mathrm{4}+\mathrm{2}{log}\mathrm{3}=\mathrm{2}−.\mathrm{6021}+\mathrm{2}×.\mathrm{4771}= \\ $$$$\mathrm{2}.\mathrm{3521} \\ $$ Terms of…
Question Number 194960 by Erico last updated on 20/Jul/23 $$\mathrm{Soit}\:{x}>\mathrm{1}.\:\mathrm{On}\:\mathrm{d}\acute {\mathrm{e}finie}\:\mathrm{la}\:\mathrm{suite}\:\left(\mathrm{p}_{\mathrm{n}} \right)\:\mathrm{par}\: \\ $$$$\mathrm{p}_{\mathrm{1}} ={x}\:\:\mathrm{et}\:\forall\mathrm{n}\in\mathrm{IN}^{\ast} \:\:\:\:\:\mathrm{p}_{\mathrm{n}+\mathrm{1}} =\mathrm{2p}_{\mathrm{n}} ^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{Montrer}\:\mathrm{que}\:\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{p}_{\mathrm{k}} }\right)=\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}}…
Question Number 194963 by C2coder last updated on 20/Jul/23 Answered by witcher3 last updated on 21/Jul/23 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2asin}\left(\mathrm{x}\right)}{\mathrm{1}−\mathrm{a}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)}\right)\mathrm{dx}..? \\ $$$$ \\…
Question Number 194931 by sonukgindia last updated on 20/Jul/23 Answered by HeferH last updated on 20/Jul/23 Commented by HeferH last updated on 20/Jul/23 $$\mathrm{6}{x}\:=\:\mathrm{2}\left(\mathrm{180}°−\mathrm{7}{x}\right) \\…
Question Number 194930 by mathlove last updated on 20/Jul/23 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}} {dx}=? \\ $$ Commented by DwaipayanShikari last updated on 20/Jul/23 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}}…
Question Number 194953 by dimentri last updated on 20/Jul/23 $$\:{Let}\:{P}\left({x}\right)=\:{x}^{\mathrm{2}} +\frac{{x}}{\mathrm{2}}+{b}\:{and} \\ $$$$\:\:{Q}\left({x}\right)={x}^{\mathrm{2}} +{cx}+{d}\:{be}\:{two}\: \\ $$$$\:\:{polynomial}\:{with}\:{real}\:{coefficients} \\ $$$$\:\:{such}\:{that}\:{P}\left({x}\right){Q}\left({x}\right)=\:{Q}\left({P}\left({x}\right)\right) \\ $$$$\:{for}\:{all}\:{real}\:{x}\:. \\ $$$$\:\:{Find}\:{all}\:{the}\:{real}\:{roots}\:{of}\: \\ $$$$\:\:{P}\left({Q}\left({x}\right)\right)=\mathrm{0}\: \\…
Question Number 194952 by pascal889 last updated on 20/Jul/23 $$\boldsymbol{\mathrm{x}}\:+\:\sqrt{\mathrm{17}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\:+\:\boldsymbol{\mathrm{x}}\sqrt{\mathrm{17}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:}\:=\mathrm{9} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{X}} \\ $$ Answered by Frix last updated on 20/Jul/23 $$\mathrm{Obviously}\:{x}=\mathrm{1}\vee{x}=\mathrm{4} \\…
Question Number 194900 by cortano12 last updated on 19/Jul/23 $$\:\:\:\:\:\:{Given}\:\:\:{d}\:=\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}+\:\sqrt{\mathrm{5}}}}{\mathrm{1}+\sqrt{\mathrm{5}}}\:\: \\ $$$$\:\:\:\:\:\:{then}\:\:{d}^{\mathrm{3}} −\mathrm{4}{d}^{\mathrm{2}} \:+\mathrm{8}{d}\:−\mathrm{2}\:=?\: \\ $$$$\:\:\:\:\: \\ $$ Answered by Frix last updated on 19/Jul/23…
Question Number 194903 by cortano12 last updated on 19/Jul/23 Commented by cortano12 last updated on 19/Jul/23 $$\:\:\:{x}\:=\:\sqrt{\mathrm{39}}\:\:\left(×\right) \\ $$$$\:\:\:{x}\:=\:\sqrt{\mathrm{30}}\:\left(\checkmark\right) \\ $$ Answered by MM42 last…
Question Number 194913 by cortano12 last updated on 19/Jul/23 Answered by witcher3 last updated on 19/Jul/23 $$\left(\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}''\left(\mathrm{x}\right)\right)\mathrm{cos}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\left.\underset{\mathrm{0}} {\int}^{\frac{\pi}{\mathrm{2}}} \mathrm{f}''\mathrm{cos}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{f}'\mathrm{cos}\left(\mathrm{x}\right)\right]_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} +\int\mathrm{f}'\mathrm{sin}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\left.=\left.−\mathrm{f}'\left(\mathrm{0}\right)+\mathrm{fsin}\left(\mathrm{x}\right)\right]_{\mathrm{0}}…