Question Number 60426 by cesar.marval.larez@gmail.com last updated on 20/May/19 $${the}\:{function}\:{is}\:{considered}\: \\ $$$${f}\left({x},{y}\right)={e}^{{xy}} +\frac{{x}}{{y}}+{sen}\left(\left(\mathrm{2}{x}+\mathrm{3}{y}\right)\pi\right)\:{Calcule}: \\ $$$$\frac{\partial{f}}{\partial{x}},\frac{\partial{f}}{\partial{y}},\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} },\frac{\partial^{\mathrm{2}} {f}}{\partial{x}\partial{y}}.\:\:\:{f}_{{x}} \left(\mathrm{0},\mathrm{1}\right),{f}_{{y}} \left(\mathrm{2},−\mathrm{1}\right),\:{f}_{{xx}} \left(\mathrm{0},\mathrm{1}\right),{f}_{{xy}} \left(\mathrm{2},−\mathrm{1}\right) \\ $$ Commented…
Question Number 191499 by Mastermind last updated on 24/Apr/23 $$\mathrm{x}\:+\:\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\:=\:\mathrm{0}.\mathrm{1614},\:\mathrm{find}\:\mathrm{x}?\mathrm{1II} \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{use}\:\mathrm{Lambert} \\ $$$$ \\ $$$$\mathrm{BOSSES},\:\mathrm{help}\:\mathrm{your}\:\mathrm{boy}! \\ $$ Commented by mr W last updated on…
Question Number 125960 by AST last updated on 26/Sep/22 $$ \\ $$ Answered by mahdipoor last updated on 16/Dec/20 $$\begin{cases}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mid{a}\mid^{\mathrm{2}} +\mid{b}\mid^{\mathrm{2}} }\\{\mathrm{2}{ab}\leqslant\mathrm{2}\mid{a}\mid.\mid{b}\mid}\end{cases} \\…
Question Number 60425 by cesar.marval.larez@gmail.com last updated on 20/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 191498 by MATHEMATICSAM last updated on 24/Apr/23 $$\mathrm{If}\:\mathrm{A}\left(\frac{\mathrm{2}{c}}{{a}}\:,\:\frac{{c}}{{b}}\right),\:\mathrm{B}\left(\frac{{c}}{{a}}\:,\:\mathrm{0}\right)\:\mathrm{and}\:\mathrm{C}\left(\frac{\mathrm{1}\:+\:{c}}{{a}}\:,\:\frac{\mathrm{1}}{{b}}\right) \\ $$$$\mathrm{are}\:\mathrm{three}\:\mathrm{points},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that},\: \\ $$$$\mathrm{i}.\:\:\frac{\left(\mathrm{AB}\right)^{\mathrm{2}} \:+\:\left(\mathrm{BC}\right)^{\mathrm{2}} }{\left(\mathrm{CA}\right)^{\mathrm{2}} }\:=\:\frac{{c}^{\mathrm{2}} \:+\:\mathrm{1}}{\left({c}\:−\:\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{ii}.\:\left(\mathrm{AB}\right)^{\mathrm{2}} \:+\:\left(\mathrm{BC}\right)^{\mathrm{2}} \:−\:\left(\mathrm{AC}\right)^{\mathrm{2}} \:=\:\frac{\mathrm{2}{c}\left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}}…
Question Number 60424 by Mr X pcx last updated on 20/May/19 $${let}\:{z}\:\in{C}\:{and}\:\:\mid{z}\mid<\mathrm{1}\:\:{find} \\ $$$${f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{zx}\right){dx}. \\ $$ Commented by maxmathsup by imad last updated…
Question Number 125958 by bramlexs22 last updated on 15/Dec/20 $$\:\:\:\:{y}\:{dx}\:+{x}\left(\mathrm{ln}\:{x}\:−\mathrm{ln}\:{y}−\mathrm{1}\right){dy}=\mathrm{0} \\ $$$$\:\:\:\:{where}\:{y}\left(\mathrm{1}\right)=\mathrm{0} \\ $$ Answered by Olaf last updated on 16/Dec/20 $${ydx}+{x}\left(\mathrm{ln}{x}−\mathrm{ln}{y}−\mathrm{1}\right){dy}\:=\:\mathrm{0} \\ $$$$\mathrm{Let}\:{y}\:=\:{xu} \\…
Question Number 60423 by Tawa1 last updated on 20/May/19 Answered by MJS last updated on 20/May/19 $$\begin{pmatrix}{\mathrm{20}}\\{\angle\mathrm{30}°}\end{pmatrix}\:=\begin{pmatrix}{\mathrm{10}\sqrt{\mathrm{3}}}\\{\mathrm{10}}\end{pmatrix} \\ $$$$\begin{pmatrix}{\mathrm{8}}\\{\angle−\mathrm{50}°}\end{pmatrix}\:=\begin{pmatrix}{\mathrm{8sin}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\\{−\mathrm{8cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\end{pmatrix} \\ $$$$\begin{pmatrix}{\mathrm{10}\sqrt{\mathrm{3}}}\\{\mathrm{10}}\end{pmatrix}\:+\begin{pmatrix}{\mathrm{8sin}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\\{−\mathrm{8cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\end{pmatrix}\:\approx\begin{pmatrix}{\mathrm{22}.\mathrm{46}}\\{\mathrm{3}.\mathrm{87}}\end{pmatrix} \\ $$$$\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{this}\:\mathrm{vector}\:\mathrm{is}\:\mathrm{22}.\mathrm{79} \\ $$$$\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{this}\:\mathrm{vector}\:\mathrm{is}\:\mathrm{E}\:\mathrm{9}.\mathrm{78}°\:\mathrm{N}…
Question Number 125959 by bramlexs22 last updated on 15/Dec/20 Answered by liberty last updated on 15/Dec/20 $${Let}\:{q}\:{denote}\:{the}\:{numbers}\:{of}\:{eggs}\:{originally} \\ $$$${in}\:{the}\:{basket}.\:{We}\:{want}\:{to}\:{find}\:{the}\:{least}\:{number} \\ $$$${of}\:{eggs}\:{in}\:{the}\:{basket}.\: \\ $$$$\Leftrightarrow\:{q}\:\equiv\:\mathrm{1}\left({mod}\:\mathrm{2}\right)\:\equiv\:\mathrm{1}\left({mod}\:\mathrm{3}\right)\equiv\:\mathrm{1}\left({mod}\:\mathrm{5}\right)\:\equiv\:\mathrm{0}\:\left({mod}\:\mathrm{7}\right) \\ $$$${the}\:{first}\:{three}\:{congruences}\:{then}…
Question Number 60422 by Tawa1 last updated on 20/May/19 Commented by MJS last updated on 20/May/19 $$\mathrm{what}'\mathrm{s}\:\mathrm{a}\:“\mathrm{lidless}\:\mathrm{box}''? \\ $$$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:“\mathrm{ends}''\:\mathrm{of}\:\mathrm{a}\:\mathrm{box}? \\ $$ Commented by Tawa1 last…