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…
Question Number 201604 by ajfour last updated on 09/Dec/23 Commented by ajfour last updated on 09/Dec/23 $${Both}\:{circles}\:{in}\:{blue}\:{have}\:{equal} \\ $$$${radii}.\:{Find}. \\ $$ Answered by mr W…
Question Number 201573 by sonukgindia last updated on 09/Dec/23 Answered by witcher3 last updated on 09/Dec/23 $$=\int_{−\infty} ^{\infty} \frac{\mathrm{e}^{−\mathrm{2024x}} +\mathrm{e}^{−\mathrm{2020}} }{\left(\mathrm{e}^{−\mathrm{2025x}} +\mathrm{e}^{−\mathrm{2019x}} \right)\left(\left(−\mathrm{4x}^{\mathrm{3}} +\left(\mathrm{4x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}}…
Question Number 201533 by Rodier97 last updated on 08/Dec/23 $$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{Un}\:=\:{ln}\:\left({cos}\:\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\right) \\ $$$$\:\:\:\:{show}\:\:{that}\:{Un}\:\leqslant\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$…
Question Number 201534 by Mathspace last updated on 08/Dec/23 $${let}\:{f}\left({x}\right)={tanx} \\ $$$${find}\:{f}^{\left({n}\right)} \left({x}\right)\:{with}\:{n}\:{integr} \\ $$$${natural} \\ $$ Commented by Frix last updated on 09/Dec/23 $$\mathrm{There}'\mathrm{s}\:\mathrm{a}\:\mathrm{very}\:\mathrm{complicated}\:\mathrm{formula},\:\mathrm{you}\:\mathrm{must}…
Question Number 201557 by hardmath last updated on 08/Dec/23 $$\mathrm{5}\:\centerdot\:\underset{\:\mathrm{50}} {\underbrace{\mathrm{555}…\mathrm{5}}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{product}. \\ $$ Answered by aleks041103 last updated on 09/Dec/23 $$\mathrm{5}.\mathrm{5}=\mathrm{25}…