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Category: Vector

check-that-the-function-u-x-t-exp-n-2-2-pi-2-L-2-t-sin-npix-L-n-1-2-satisfy-the-heat-equation-heat-equation-2-2-u-x-2-u-t-0-lt-x-lt-L-

Question Number 168977 by MikeH last updated on 23/Apr/22 $$\mathrm{check}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function} \\ $$$${u}\left({x},{t}\right)\:=\:\mathrm{exp}\left\{−\frac{{n}^{\mathrm{2}} \alpha^{\mathrm{2}} \pi^{\mathrm{2}} }{{L}^{\mathrm{2}} }{t}\right\}\:\mathrm{sin}\frac{{n}\pi{x}}{{L}} \\ $$$${n}\:=\:\mathrm{1},\mathrm{2},…\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{heat}\:\mathrm{equation} \\ $$$$\boldsymbol{\mathrm{heat}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\alpha^{\mathrm{2}} \frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }\:=\:\frac{\partial{u}}{\partial{t}},\:\mathrm{0}\:<\:{x}\:<\:{L}…

pi-4-pi-2-ln-ln-tan-x-dx-

Question Number 103190 by bemath last updated on 13/Jul/20 $$\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tan}\:{x}\right)\right)\:{dx}\: \\ $$ Answered by abdomathmax last updated on 13/Jul/20 $$\mathrm{ln}\left(\mathrm{tanx}\right)\:=\mathrm{t}\:\Rightarrow\:\mathrm{I}\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tanx}\right)\right)\mathrm{dx} \\…

Question-168121

Question Number 168121 by rexford last updated on 03/Apr/22 Answered by FelipeLz last updated on 04/Apr/22 $$\overset{\rightarrow} {{r}}\:=\:\left({a},\:{b},\:{c}\right) \\ $$$$\left.\begin{matrix}{\overset{\rightarrow} {{r}}\centerdot\hat {\imath}\:=\:{a}}\\{\overset{\rightarrow} {{r}}\centerdot\hat {\jmath}\:=\:{b}}\\{\overset{\rightarrow} {{r}}\centerdot\hat…

Question-101766

Question Number 101766 by 175mohamed last updated on 04/Jul/20 Commented by mr W last updated on 04/Jul/20 $$\mathrm{1}\:{m}^{\mathrm{3}} =\mathrm{100}^{\mathrm{3}} \:{cm}^{\mathrm{3}} \\ $$$$\frac{\mathrm{100}^{\mathrm{3}} \:{cm}^{\mathrm{3}} }{\mathrm{5}×\mathrm{4}×\mathrm{1}\:{cm}^{\mathrm{3}} }=\mathrm{50}\:\mathrm{000}…

Question-35789

Question Number 35789 by ajfour last updated on 23/May/18 Commented by ajfour last updated on 23/May/18 $${How}\:{many}\:{skew}\:{pair}\:{of}\:{lines} \\ $$$${are}\:{there}\:\left({when}\:{a}\:{line}\:{is}\:{drawn}\right. \\ $$$${by}\:{joining}\:{any}\:{two}\:{vertices} \\ $$$$\left.{of}\:{the}\:{cube}\right)\:? \\ $$…