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Author: Tinku Tara

Solve-the-equation-2-u-x-y-sin-x-cos-y-subjected-to-the-boundary-conditions-at-y-pi-2-u-x-2x-and-x-pi-u-2sin-y-

Question Number 23445 by tawa tawa last updated on 30/Oct/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}:\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{x}\partial\mathrm{y}}\:=\:\mathrm{sin}\left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{y}\right),\:\:\:\mathrm{subjected}\:\mathrm{to}\:\mathrm{the}\:\mathrm{boundary} \\ $$$$\mathrm{conditions}\:\mathrm{at}\:\:\:\mathrm{y}\:=\:\frac{\pi}{\mathrm{2}},\:\:\:\:\frac{\partial\mathrm{u}}{\partial\mathrm{x}}\:=\:\mathrm{2x}\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{x}\:=\:\pi,\:\:\:\:\mathrm{u}\:=\:\mathrm{2sin}\left(\mathrm{y}\right) \\ $$ Answered by mrW1 last updated on 31/Oct/17 $$\:\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{x}\partial\mathrm{y}}\:=\:\mathrm{sin}\left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{y}\right)…

Find-a-unit-vector-which-is-perpendicula-to-a-vector-A-3coma5coma1-Sorry-for-writing-coma-cuz-i-dnt-see-a-key-for-it-

Question Number 23442 by chernoaguero@gmail.com last updated on 30/Oct/17 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{unit}\:\mathrm{vector}\:\mathrm{which}\:\mathrm{is}\:\mathrm{perpendicula} \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{A}\left(\mathrm{3coma5coma1}\right) \\ $$$$ \\ $$$$\mathrm{Sorry}\:\mathrm{for}\:\mathrm{writing}\:\mathrm{coma}\:\mathrm{cuz}\:\mathrm{i}\:\mathrm{dnt}\:\mathrm{see}\:\mathrm{a}\:\mathrm{key}\:\mathrm{for}\:\mathrm{it} \\ $$ Commented by $@ty@m last updated on 31/Oct/17…

Question-154514

Question Number 154514 by 0731619 last updated on 19/Sep/21 Commented by mr W last updated on 19/Sep/21 $${there}\:{is}\:{not}\:{much}\:{to}\:{solve}!\:{it}'{s}\:{a}\: \\ $$$${matter}\:{of}\:{definition}. \\ $$$$\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}=\frac{\left(\mathrm{2}{n}\right)!}{\left({n}!\right)^{\mathrm{2}} } \\ $$…