Question Number 210079 by Spillover last updated on 30/Jul/24 $${Find}\:{directional}\:{derivatives}\left({D}_{{v}} \right){of}\:\: \\ $$$${f}\left({x},{y},{z}\right)=\mathrm{3}{xy}^{\mathrm{3}} −\mathrm{2}{xz}^{\mathrm{2}} \:\:{in}\:{the}\:{direction}\:{of}\:{the} \\ $$$${v}=\mathrm{2}{i}−\mathrm{3}{j}+\mathrm{6}{k}. \\ $$$${then}\:{Evaluate}\:{directional}\:{derivatives}\: \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{3},\mathrm{1},−\mathrm{2}\right) \\ $$ Terms of…
Question Number 210078 by Spillover last updated on 29/Jul/24 $${Find}\:{the}\:{directional}\:{derivative}\:{of} \\ $$$${f}\left({x},{y}\right)=\mathrm{4}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \:\:\:{in}\:{the}\:{direction}\:{given} \\ $$$${by}\:{the}\:{angle}\:\theta=\frac{\pi}{\mathrm{3}}\: \\ $$$${and}\:{also}\:{Evaluate}\:{directional}\:{derivatives} \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right) \\ $$ Answered by…
Question Number 210036 by peter frank last updated on 29/Jul/24 Answered by Prithwish last updated on 29/Jul/24 $${ab}=\left(\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \theta}{\mathrm{cos}\:\theta}\right)\left(\frac{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \theta}{\mathrm{sin}\:\theta}\right) \\ $$$${ab}=\mathrm{sin}\:\theta\mathrm{cos}\:\theta \\ $$$${a}^{\mathrm{2}} +\overset{\mathrm{2}}…
Question Number 210072 by peter frank last updated on 29/Jul/24 Answered by Frix last updated on 29/Jul/24 $$\mathrm{The}\:\mathrm{incircle}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangular}\:\mathrm{triangle}\:\mathrm{with} \\ $$$$\mathrm{sides}\:{a},\:{b},\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:\mathrm{is}\:\frac{{a}+{b}−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}{\mathrm{2}}\:\:\:\:\:\left(\ast\right) \\…
Question Number 210034 by peter frank last updated on 29/Jul/24 Commented by peter frank last updated on 29/Jul/24 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x} \\ $$ Commented by Frix last…
Question Number 210080 by Spillover last updated on 30/Jul/24 $${Given}\:{that}\:\:{det}\:\begin{bmatrix}{{a}}&{{b}}&{{c}}\\{{d}}&{{e}}&{{f}}\\{{g}}&{{h}}&{{i}}\end{bmatrix}={n} \\ $$$$ \\ $$$${find}\:{det}\begin{bmatrix}{{d}+\mathrm{2}{a}}&{{e}+\mathrm{2}{b}}&{{f}+\mathrm{2}{c}}\\{\mathrm{2}{a}}&{\mathrm{2}{b}}&{\mathrm{2}{c}}\\{\mathrm{4}{g}}&{\mathrm{4}{h}}&{\mathrm{4}{i}}\end{bmatrix} \\ $$$$ \\ $$ Commented by Frix last updated on 30/Jul/24…
Question Number 210081 by Spillover last updated on 29/Jul/24 $${Reduce}\:\: \\ $$$$ \\ $$$$\:\:\:\begin{bmatrix}{\mathrm{3}}&{−\mathrm{2}}&{\mathrm{4}}&{\mathrm{7}}\\{\mathrm{2}}&{\mathrm{1}}&{\mathrm{0}}&{−\mathrm{3}}\\{\mathrm{2}}&{\mathrm{8}}&{−\mathrm{8}}&{\mathrm{2}}\end{bmatrix}\:\:\:\:{into}\:{echelon}\:{form} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210011 by hardmath last updated on 28/Jul/24 $$\mathrm{Find}:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\:\frac{\mathrm{ln}\:\left(\mathrm{cos}\:\left(\frac{\pi\mathrm{x}}{\mathrm{2}}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}}\:\mathrm{dx}\:\:=\:\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 209986 by a.lgnaoui last updated on 28/Jul/24 $$\mathrm{Solve}\: \\ $$$$\:\boldsymbol{\mathrm{ax}}^{\mathrm{3}} −\boldsymbol{\mathrm{bx}}\sqrt{\boldsymbol{\mathrm{x}}}\:+\boldsymbol{\mathrm{c}}=\mathrm{0}\:\:\:\:\: \\ $$$$\:\left(\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}},\:\boldsymbol{\mathrm{c}}\right)\in\mathbb{R}^{\mathrm{3}} \:\:\:\:\mathrm{and}\:\boldsymbol{\mathrm{x}}\in\mathbb{R} \\ $$$$\left(\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}\:\boldsymbol{{for}}\:\boldsymbol{{a}}=\mathrm{1},\:\:\boldsymbol{{b}}=\mathrm{9},\boldsymbol{{c}}=\mathrm{8}\right) \\ $$ Answered by mr W last…
Question Number 209980 by a.lgnaoui last updated on 27/Jul/24 $$\mathrm{determiner}\:\mathrm{h}\:? \\ $$$$\boldsymbol{\mathrm{CD}}=\mathrm{20}\:\:\:\:\boldsymbol{\mathrm{AB}}=\mathrm{30} \\ $$$$\boldsymbol{\mathrm{h}}\mathrm{1}=\mathrm{25} \\ $$$$ \\ $$ Commented by a.lgnaoui last updated on 27/Jul/24…