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Category: Algebra

a-b-c-d-R-a-1-a-b-3-b-c-5-c-d-7-d-Find-max-a-b-c-d-

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-228497

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-228417

Question Number 228417 by s12345 last updated on 12/Apr/26 Commented by TonyCWX last updated on 12/Apr/26 $$\boldsymbol{\mathrm{First}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{all}},\:\boldsymbol{\mathrm{could}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{translate}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{English}}\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{more}}\:\boldsymbol{\mathrm{users}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{attempt}}\:\boldsymbol{\mathrm{it}}? \\ $$$$ \\ $$$$\boldsymbol{\mathrm{Secondly}},\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{not}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{homework}}\:\boldsymbol{\mathrm{solving}}\:\boldsymbol{\mathrm{forum}}. \\ $$ Commented by…

Question-228414

Question Number 228414 by fantastic2 last updated on 11/Apr/26 Commented by fantastic2 last updated on 11/Apr/26 $${suppose}\:{the}\:{shape}\:{of}\:{the}\:{red}\:{jelly}\:{is} \\ $$$$\mathrm{3}{d}\:{version}\:{of}\:{eq}\:{y}={b}^{\mathrm{2}} −{x}^{\mathrm{2}} \:{and}\:{it}\:{is}\:{sliced} \\ $$$${like}\:{the}\:{blue}\:{line}\:{in}\:{the}\:{picture} \\ $$$${find}\:{the}\:{volume}\:{of}\:{the}\:{small}\:{part}…

Find-lim-x-2-x-pi-2-tanx-

Question Number 228358 by Math1 last updated on 09/Apr/26 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\mathrm{lim}}\:\left[\left(\mathrm{x}\:−\:\frac{\pi}{\mathrm{2}}\right)\:\mathrm{tanx}\right]\:=\:? \\ $$ Answered by cherokeesay last updated on 09/Apr/26 Answered by Lara2440 last updated…

Two-cars-travel-from-point-A-to-point-B-a-distance-of-200km-Car-X-travels-at-an-average-speed-of-60km-h-with-a-tyre-radius-of-20cm-while-Car-Y-travels-at-an-average-speed-of-50km-h-with-a-tyre-radi

Question Number 228274 by necx122 last updated on 05/Apr/26 $${Two}\:{cars}\:{travel}\:{from}\:{point}\:{A}\:{to}\:{point} \\ $$$${B},\:{a}\:{distance}\:{of}\:\mathrm{200}{km}.\:{Car}\:{X}\:{travels} \\ $$$${at}\:{an}\:{average}\:{speed}\:{of}\:\mathrm{60}{km}/{h}\:{with}\:{a} \\ $$$${tyre}\:{radius}\:{of}\:\mathrm{20}{cm},\:{while}\:{Car}\:{Y}\:{travels} \\ $$$${at}\:{an}\:{average}\:{speed}\:{of}\:\mathrm{50}{km}/{h}\:{with}\:{a}\:{tyre} \\ $$$${radius}\:{of}\:\mathrm{25}{cm}.\:{Assuming}\:{all}\:{other} \\ $$$${conditions}\:{are}\:{identical},\:{which}\:{car} \\ $$$${arrives}\:{at}\:{point}\:{B}\:{first}? \\…

Quartic-x-4-ax-3-bx-2-cx-d-0-x-2-px-h-x-2-qx-k-0-p-q-a-h-k-b-pq-b-m-pq-m-say-pk-qh-c-hk-d-q-h-k-q-b-m-p-h-k-p-b-m-ph-qk-c-k-p-q-p-b-m-c-h-p-q-c-q-b-m-multiplying-d-a-2-4m-

Question Number 228265 by ajfour last updated on 04/Apr/26 $$\:\:{Quartic}:\:\:{x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} +{px}+{h}\right)\left({x}^{\mathrm{2}} +{qx}+{k}\right)=\mathrm{0} \\ $$$${p}+{q}={a} \\ $$$${h}+{k}={b}−{pq}={b}−{m}\:\:\:\left({pq}={m}\:{say}\right) \\ $$$${pk}+{qh}={c} \\ $$$${hk}={d}…