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…
Question Number 210515 by hardmath last updated on 11/Aug/24 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{11}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{13}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{17}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{19}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{23}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{29}^{\mathrm{2}} }\:+\:…\:=\:? \\ $$ Commented by mr W…
Question Number 210508 by hardmath last updated on 11/Aug/24 Answered by mr W last updated on 11/Aug/24 Commented by mr W last updated on 11/Aug/24…
Question Number 210533 by hardmath last updated on 11/Aug/24 Commented by mr W last updated on 12/Aug/24 $${typo}\:{AD}\centerdot\frac{\cancel{{m}}\:{n}}{{m}+{n}}−{AB}\centerdot\frac{{q}}{{p}+{q}}\:? \\ $$ Answered by mr W last…
Question Number 210496 by lmcp1203 last updated on 11/Aug/24 Commented by mr W last updated on 11/Aug/24 $${has}\:{that}\:{bracket}\:{a}\:{special}\:{meaning}? \\ $$ Commented by lmcp1203 last updated…
Question Number 210457 by peter frank last updated on 09/Aug/24 Commented by peter frank last updated on 09/Aug/24 $$\left(\mathrm{b}\right)\:\mathrm{and}\:\left(\mathrm{c}\right)\:\mathrm{help} \\ $$ Commented by mr W…
Question Number 210439 by universe last updated on 09/Aug/24 Commented by universe last updated on 09/Aug/24 $${prove}\:{that}\:{the}\:{sequence}\:{is}\:{bounded}\:{and}\: \\ $$$${convergent} \\ $$ Answered by aleks041103 last…