Question Number 210574 by ChantalYah last updated on 13/Aug/24 $${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$${x}^{\mathrm{2}} +\left({k}+\mathrm{1}\right){x}+{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta, \\ $$$$\:{find}\:{the}\:{value}\:{of}\:{the} \\ $$$$\:{real}\:{constant}\:{k}\:{for} \\ $$$${which}\:\alpha=\mathrm{2}\beta \\ $$ Answered by…
Question Number 210606 by peter frank last updated on 13/Aug/24 Answered by A5T last updated on 14/Aug/24 $$\mathrm{3}\left({y}^{{log}_{\mathrm{5}} \mathrm{2}} \right)+\left({y}^{{log}_{{y}} \mathrm{2}×{log}_{\mathrm{5}} {y}} \right)=\mathrm{3}\left({y}^{{log}_{\mathrm{5}} \mathrm{2}} \right)+{y}^{{log}_{\mathrm{5}}…
Question Number 210559 by mathlove last updated on 12/Aug/24 $${deg}\:\left[{p}\left({x}^{\mathrm{2}} \right)\centerdot{q}\left({x}\right)\right]=\mathrm{20} \\ $$$${deg}\left[\frac{{p}\left({x}\right)^{\mathrm{3}} }{{q}\left({x}\right)^{\mathrm{2}} }\right]=\mathrm{2} \\ $$$${then}\:{deg}\:\:{q}\left({x}\right)=? \\ $$ Answered by mr W last updated…
Question Number 210573 by Spillover last updated on 12/Aug/24 Answered by mathmax last updated on 13/Aug/24 $$\mathrm{2}{I}=\int_{−\infty} ^{+\infty} \frac{{dx}}{{x}^{\mathrm{4}} +{ix}^{\mathrm{2}} +\mathrm{2}}\:\left({fonction}\:{paire}\right) \\ $$$${roots}\:\:\:\:\:\:{x}^{\mathrm{2}} ={t}\rightarrow{t}^{\mathrm{2}} +{it}+\mathrm{2}…
Question Number 210572 by Spillover last updated on 12/Aug/24 Answered by mathmax last updated on 13/Aug/24 $${I}=\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}\:\:{changement}\:{x}={t}^{\frac{\mathrm{1}}{\mathrm{4}}} {give} \\ $$$${I}=\frac{\mathrm{1}}{\mathrm{16}}\int_{\mathrm{0}} ^{\infty}…
Question Number 210565 by maths_plus last updated on 12/Aug/24 Answered by mr W last updated on 13/Aug/24 Commented by mr W last updated on 13/Aug/24…
Question Number 210571 by hardmath last updated on 12/Aug/24 $$\mathrm{If}\:\:\mathrm{x},\mathrm{y},\mathrm{z}\in\mathrm{R}^{+} \:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}−\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{y}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{z}}\:\:\leqslant\:\:\mathrm{1} \\ $$ Answered by A5T last updated…
Question Number 210492 by a.lgnaoui last updated on 11/Aug/24 $$\mathrm{un}\:\mathrm{objet}\:\boldsymbol{\mathrm{C}}\:\mathrm{situe}\:\mathrm{a}\:\mathrm{une}\:\mathrm{hsuteur}\:\boldsymbol{\mathrm{h}} \\ $$$$\mathrm{est}\:\mathrm{lache}\:\mathrm{sans}\:\mathrm{vitesse}\:\:\mathrm{initiale}\:\left(\boldsymbol{\mathrm{v}}_{\mathrm{0}} =\mathrm{0}\right) \\ $$$$\mathrm{par}\:\mathrm{un}\:\mathrm{un}\:\mathrm{petit}\:\mathrm{avion}\:\mathrm{volant}\:\mathrm{a}\:\mathrm{basse} \\ $$$$\mathrm{altitue}\:\mathrm{cet}\:\mathrm{objet}\:\mathrm{est}\:\mathrm{capte}\:\mathrm{par}\:\mathrm{une}\: \\ $$$$\mathrm{prrsonne}\:\:\mathrm{entraine}\:\mathrm{le}\:\mathrm{long}\:\mathrm{de}\:\mathrm{la}\:\:\mathrm{couronne}\: \\ $$$$\mathrm{a}\:\mathrm{vitesse}\:\mathrm{const}\boldsymbol{\mathrm{a}}\mathrm{nte}\left(\boldsymbol{\mathrm{v}}\right)\: \\ $$$$\left.−\mathrm{1}\right)\:\mathrm{Determiner}\:\mathrm{l}\:\mathrm{instant}\:\mathrm{de}\:\mathrm{recuperariion} \\ $$$$\mathrm{de}\:\mathrm{l}\:\mathrm{objet}\:…
Question Number 210524 by hardmath last updated on 11/Aug/24 Commented by hardmath last updated on 11/Aug/24 $$\boldsymbol{\mathrm{r}}\:=\:? \\ $$ Answered by mr W last updated…
Question Number 210516 by hardmath last updated on 11/Aug/24 $$\mathrm{Find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\mathrm{1}\:+\:\mathrm{3x}\:+\:\mathrm{5x}^{\mathrm{2}} \:+\:\mathrm{7x}^{\mathrm{3}} \:+\:\mathrm{9x}^{\mathrm{4}} \:+\:\mathrm{11x}^{\mathrm{5}} \:+\:…\:=\:\mathrm{15} \\ $$ Answered by mm1342 last updated on 12/Aug/24…