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Category: Vector

Help-me-The-rate-of-change-of-w-x-3-y-2-z-y-3-z-2-xz-4-at-the-point-Q-0-1-2-in-the-direction-V-2i-j-2k-is-a-2-b-3-c-4-d-No-alternati

Question Number 182438 by neinhaltsieger369 last updated on 09/Dec/22 $$\: \\ $$$$\:\left[\boldsymbol{\mathrm{Help}}\:\:\boldsymbol{\mathrm{me}}!\right] \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{The}}\:\:\boldsymbol{\mathrm{rate}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{change}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{w}}\:\:=\:\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} \boldsymbol{\mathrm{y}}^{\mathrm{2}} \boldsymbol{\mathrm{z}}\:\:+\:\boldsymbol{\mathrm{y}}^{\mathrm{3}} \boldsymbol{\mathrm{z}}^{\mathrm{2}} \:−\:\boldsymbol{\mathrm{xz}}^{\mathrm{4}} \:\:\boldsymbol{\mathrm{at}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{point}}\:\:\boldsymbol{\mathrm{Q}}\left(\mathrm{0},\:\mathrm{1},\:\mathrm{2}\right) \\ $$$$\:\boldsymbol{\mathrm{in}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{direction}}\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{V}}}\:\:=\:\:\mathrm{2}\boldsymbol{\mathrm{i}}\:\:+\:\:\boldsymbol{\mathrm{j}}\:\:+\:\:\mathrm{2}\boldsymbol{\mathrm{k}}\:\:\boldsymbol{\mathrm{is}}: \\…

If-P-2-j3-and-Q-2-j3-and-R-j1-Show-that-angle-PRQ-is-right-angle-

Question Number 51263 by Tawa1 last updated on 25/Dec/18 $$\mathrm{If}\:\:\mathrm{P}\:=\:\mathrm{2}\:+\:\mathrm{j3}\:\mathrm{and}\:\mathrm{Q}\:=\:\mathrm{2}\:−\:\mathrm{j3}\:\mathrm{and}\:\mathrm{R}\:=\:\mathrm{j1} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\:\mathrm{angle}\:\:\mathrm{PRQ}\:\mathrm{is}\:\mathrm{right}\:\mathrm{angle} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18 $${P}\left(\mathrm{2},\mathrm{3}\right)\:\:\:{Q}\left(\mathrm{2},−\mathrm{3}\right)\:\:\:{R}\left(\mathrm{0},\mathrm{1}\right) \\ $$$${PQ}=\mathrm{6}\:\:\:\:{QR}=\sqrt{\mathrm{2}^{\mathrm{2}} +\left(−\mathrm{4}\right)^{\mathrm{2}}…

if-2x-1-x-1-2-find-the-value-8x-1-x-

Question Number 181707 by amin96 last updated on 28/Nov/22 $$\boldsymbol{{if}}\:\:\:\:\:\mathrm{2}\boldsymbol{{x}}+\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\:\:\mathrm{8}\boldsymbol{{x}}+\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}}=? \\ $$ Answered by mr W last updated on 29/Nov/22 $${t}=\sqrt{{x}}>\mathrm{0} \\ $$$${f}\left({t}\right)=\mathrm{2}{t}^{\mathrm{2}}…