Question Number 201599 by mr W last updated on 09/Dec/23 Commented by AST last updated on 09/Dec/23 $${Are}\:{those}\:{numbers}\:{areas}\:{or}\:{lengths}? \\ $$ Commented by mr W last…
Question Number 201561 by Mingma last updated on 09/Dec/23 Answered by ajfour last updated on 11/Dec/23 Commented by ajfour last updated on 11/Dec/23 $$\mathrm{2}\theta+\mathrm{2}\phi=\frac{\pi}{\mathrm{2}} \\…
Question Number 201562 by Mingma last updated on 09/Dec/23 Answered by mr W last updated on 09/Dec/23 $${r}={radius}\:{of}\:{quarter}\:{circle} \\ $$$${a}={side}\:{length}\:{of}\:{square} \\ $$ Commented by mr…
Question Number 201627 by professorleiciano last updated on 09/Dec/23 Answered by mr W last updated on 10/Dec/23 $${for}\:\mathrm{200}\:{meals}\:\mathrm{6}\:{cooks}\:{each}\:{working}\: \\ $$$$\mathrm{6}\:{hours}\:{are}\:{needed},\:{i}.{e}.\:{totally} \\ $$$$\mathrm{36}\:{working}\:{hours}\:{are}\:{needed}\:{for}\: \\ $$$$\mathrm{200}\:{meals}. \\…
Question Number 201595 by mokys last updated on 09/Dec/23 $$\left.\mathrm{1}\right)\:\:\mid\frac{\mathrm{3}+\mathrm{2}{x}}{\mathrm{3}{x}}\mid\:\leq\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\mathrm{1}\leq\:\mid\:\frac{{x}−\mathrm{3}}{\mathrm{1}−\mathrm{2}{x}}\mid\leq\:\mathrm{2} \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\:\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{35}}{{x}+\mathrm{2}}\:>\:\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{4}\right)\:−\mathrm{1}\:\leq\:\frac{{x}+\mathrm{1}}{{x}−\mathrm{2}}\:\leq\mathrm{2} \\ $$…
Question Number 201644 by Calculusboy last updated on 10/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201613 by hardmath last updated on 09/Dec/23 $$\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R} \\ $$$$\begin{cases}{\mathrm{xy}\:+\:\mathrm{yz}\:+\:\mathrm{zx}\:=\:\mathrm{3}}\\{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{5}}\end{cases}\:\:\:\:\:\rightarrow\:\:\:\:\mathrm{max}\left(\boldsymbol{\mathrm{z}}\right)\:=\:? \\ $$ Answered by aleks041103 last updated on 09/Dec/23 $${x}+{y}+{z}=\mathrm{5}\Rightarrow{z}=\mathrm{5}−{x}−{y} \\ $$$$\Rightarrow{xy}+\left({x}+{y}\right)\left(\mathrm{5}−\left({x}+{y}\right)\right)=\mathrm{3} \\…
Question Number 201581 by cortano12 last updated on 09/Dec/23 Answered by mr W last updated on 09/Dec/23 Commented by mr W last updated on 09/Dec/23…
Question Number 201582 by MathedUp last updated on 09/Dec/23 $$\mathrm{Solve}…. \\ $$$${y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)=\mathrm{0}\:,\: \\ $$$${y}^{\left(\mathrm{2}\right)} \left(\mathrm{0}\right)=\mathrm{0}\:,\:{y}^{\left(\mathrm{1}\right)} \left(\mathrm{0}\right)=−\mathrm{1}\:,\:{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\boldsymbol{\mathcal{L}}\left\{{y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)\right\}=\mathrm{0} \\ $$$${s}^{\mathrm{2}} \boldsymbol{\mathrm{F}}\left({s}\right)−{sy}\left(\mathrm{0}\right)−{y}'\left(\mathrm{0}\right)−\boldsymbol{\mathcal{L}}\left\{\mathrm{sin}\left({t}\right){y}\left({t}\right)\right\}=\mathrm{0} \\ $$$$\mathrm{Holy}…×\mathrm{uck}…
Question Number 201615 by hardmath last updated on 09/Dec/23 $$\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}}\:+\:\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{c}}\:\geqslant\:\frac{\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)^{\mathrm{2}} }{\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}} \\ $$ Answered by AST…