Question Number 228478 by Math1 last updated on 18/Apr/26 $$\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\in\:\mathbb{R} \\ $$$$\mathrm{a}\left(\mathrm{1}−\mathrm{a}\right)\:+\:\mathrm{b}\left(\mathrm{3}−\mathrm{b}\right)\:+\:\mathrm{c}\left(\mathrm{5}−\mathrm{c}\right)\:+\:\mathrm{d}\left(\mathrm{7}−\mathrm{d}\right) \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{max}}\left(\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\right)\:=\:? \\ $$ Commented by Ghisom_ last updated on 18/Apr/26 $$\mathrm{max}\:\left({a},\:{b},\:{c},\:{d}\right)\:\mathrm{means}\:\mathrm{what}\:\mathrm{exactly}? \\…
Question Number 228474 by ajfour last updated on 18/Apr/26 Commented by ajfour last updated on 18/Apr/26 $${Parabola}\:{is}\:\:{y}=\left({h}−{x}\right)^{\mathrm{2}} \\ $$$${Find}\:{circle}\:{radius}\:{in}\:{terms}\:{of}\:{h}. \\ $$$${How}\:{much}\:{is}\:{r}\:{for}\:{h}=\mathrm{1}? \\ $$ Commented by…
Question Number 228497 by ajfour last updated on 18/Apr/26 Answered by TonyCWX last updated on 18/Apr/26 $${OD}^{\mathrm{2}} \:=\:{x}^{\mathrm{4}} −{c}^{\mathrm{2}} \\ $$$$\frac{\mathrm{1}}{{x}^{\mathrm{4}} −{c}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:=\:\mathrm{1} \\…
Question Number 228499 by ajfour last updated on 18/Apr/26 Commented by ajfour last updated on 18/Apr/26 $${If}\:{point}\:{of}\:{contact}\:{is}\:{T}\left({h},{k}\right) \\ $$$${find}\:{h},\:{as}\:{well}\:{as}\:{p}. \\ $$ Answered by Ghisom_ last…
Question Number 228464 by fantastic2 last updated on 17/Apr/26 $$\int{x}\mathrm{sin}^{−\mathrm{1}} {xdx} \\ $$ Commented by fantastic2 last updated on 18/Apr/26 $$\int{udv}={uv}−\int{vdu} \\ $$$${here}\:{u}=\mathrm{sin}^{−\mathrm{1}} {x}\Rightarrow{du}=\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}…
Question Number 228455 by mr W last updated on 15/Apr/26 Answered by vnm last updated on 16/Apr/26 $$\mathrm{4}\left(\mathrm{4}×\mathrm{3}×\mathrm{2}+\mathrm{2}\left(\mathrm{3}×\mathrm{2}×\mathrm{1}\right)+\mathrm{6}\left(\mathrm{3}×\mathrm{3}×\mathrm{4}\right)\right)=\mathrm{1008} \\ $$ Answered by mr W last…
Question Number 228448 by Lara2440 last updated on 15/Apr/26 Answered by Lara2440 last updated on 15/Apr/26 $$\: \\ $$$$\mathrm{Please}\:\mathrm{check}\:\mathrm{the}\:\mathrm{logic}\:\mathrm{behind}\:\mathrm{my}\:\mathrm{proof}\:\mathrm{and}\:\mathrm{let}\:\mathrm{me}\: \\ $$$$\mathrm{know}\:\mathrm{if}\:\mathrm{any}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{derivation}\:\mathrm{is}\:\mathrm{incorrect}. \\ $$$$\mathrm{and}…… \\ $$$$\mathrm{The}\:\mathrm{description}\:\mathrm{for}\:{r}\:\mathrm{in}\:\mathrm{my}\:\mathrm{previous}\:\mathrm{image}\:\mathrm{was}…
Question Number 228451 by Math1 last updated on 15/Apr/26 Answered by fantastic2 last updated on 15/Apr/26 Commented by fantastic2 last updated on 15/Apr/26 $${O}_{\mathrm{2}} {Z}\bot{O}_{\mathrm{1}}…
Question Number 228440 by fantastic2 last updated on 14/Apr/26 $$\mathrm{3}^{{x}} +\mathrm{9}^{{x}} +\mathrm{27}^{{x}} =\mathrm{14} \\ $$ Answered by Lara2440 last updated on 15/Apr/26 $$\mathrm{3}^{{x}} \:\overset{\mathrm{Substitution}} {=}{u}\:,\:{u}>\mathrm{0}…
Question Number 228430 by Kassista last updated on 13/Apr/26 Answered by TonyCWX last updated on 16/Apr/26 $$\mathrm{det}\left({g}\left({x}\right)\right)\:=\:\mathrm{64sin}\left({x}\right)\mathrm{ln}\left({x}\right)−\:\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{5}\right)\right] \\ $$$${M}_{{g}} \left({x}\right)\:=\:\mathrm{64cos}\left({x}\right)\mathrm{ln}\left({x}\right)\:+\:\frac{\mathrm{64sin}\left({x}\right)}{{x}}\:−\:\mathrm{ln}\left(\mathrm{2}\right)\left[−\mathrm{sin}\left({x}\right)\right]\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{5}\right)\right]\:−\:\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left(\mathrm{2}{x}\:−\:\mathrm{3}\right)\right]…