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Author: Tinku Tara

calculate-D-x-2-x-y-dxdy-with-D-is-the-triangle-0-A-B-0-origin-A-1-0-B-0-1-

Question Number 89314 by abdomathmax last updated on 16/Apr/20 $${calculate}\:\int\int_{{D}} \:{x}^{\mathrm{2}} \sqrt{{x}+{y}}{dxdy}\:{with}\:{D}\:{is}\:{the}\:{triangle} \\ $$$$\mathrm{0}\:{A}\:{B}\:\:\:\left(\mathrm{0}\:{origin}\right)\:\:\:{A}\left(\mathrm{1},\mathrm{0}\right)\:\:\:{B}\left(\mathrm{0},\mathrm{1}\right) \\ $$ Commented by abdomathmax last updated on 18/Apr/20 $${the}\:{equation}\:{of}\:{line}\:\left({AB}\right)\:{is}\:{x}+{y}=\mathrm{1}\:\Rightarrow{y}=\mathrm{1}−{x}\:\Rightarrow \\…

Show-that-0-1-0-1-x-y-x-y-2-dy-dx-0-1-0-1-x-y-x-y-2-dx-dy-

Question Number 89311 by nimnim last updated on 16/Apr/20 $$\:\:{Show}\:{that} \\ $$$$\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\:\mathrm{0}} {\overset{\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dy}\right\}{dx}=\underset{\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dx}\right\}{dy} \\ $$$$ \\…

I-have-a-leaderboard-with-the-data-of-runners-Each-runner-has-a-place-1st-2nd-etc-and-a-time-in-seconds-Every-day-I-have-been-comparing-the-data-What-information-is-important-to-not

Question Number 23773 by FilupES last updated on 06/Nov/17 $$\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{leaderboard}\:\mathrm{with}\:\mathrm{the}\:\mathrm{data}\:\mathrm{of}\:'\mathrm{runners}'. \\ $$$$\mathrm{Each}\:\mathrm{runner}\:\mathrm{has}\:\mathrm{a}\:'\mathrm{place}'\:\left(\mathrm{1st},\:\mathrm{2nd},\:\mathrm{etc}.\right), \\ $$$$\mathrm{and}\:\mathrm{a}\:'\mathrm{time}'\:\left(\mathrm{in}\:\mathrm{seconds}\right). \\ $$$$\: \\ $$$$\mathrm{Every}\:\mathrm{day}\:\mathrm{I}\:\mathrm{have}\:\mathrm{been}\:\mathrm{comparing}\:\mathrm{the}\:\mathrm{data}. \\ $$$$\mathrm{What}\:\mathrm{information}\:\mathrm{is}\:\mathrm{important}\:\mathrm{to}\:\mathrm{note}\:\mathrm{when} \\ $$$$\mathrm{looking}\:\mathrm{at}\:\mathrm{data}\:\mathrm{such}\:\mathrm{as}\:\mathrm{this}? \\ $$$$\: \\…

y-y-cos-x-1-2y-2-trouve-la-solution-de-lequation-differentielle-

Question Number 154846 by SANOGO last updated on 22/Sep/21 $${y}'=\frac{{y}\:{cos}\left({x}\right)}{\mathrm{1}+\mathrm{2}{y}^{\mathrm{2}} } \\ $$$${trouve}\:{la}\:{solution}\:{de}\:{lequation}\:{differentielle} \\ $$ Commented by tabata last updated on 22/Sep/21 $$\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}\:=\:\frac{\boldsymbol{{y}}}{\mathrm{1}+\mathrm{2}\boldsymbol{{y}}^{\mathrm{2}} }\:\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\: \\…