Who did John Adams propose should be the commander in chief of the Continental army? What was the main reason he suggested this person?

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Ответ:

erikloza12pdidtx

11.06.2020

History

Explanation:

Given: $f(x, y) = \sin(x + 2y)$ P(-2, -3)

The unit vector in the direction of $\theta = 3\pi/4$ is given by

$\vec{\textbf{u}} = \left(-\dfrac{\sqrt{2}}{2}\right)\hat{\textbf{i}} + \left(\dfrac{\sqrt{2}}{2}\right)\hat{\textbf{j}}$

The gradient of f(x, y) $\nabla{f(x, y)}$ is defined as

$\nabla{f(x, y)} = \dfrac{\partial{f}}{\partial{x}}\hat{\textbf{i}} + \dfrac{\partial{f}}{\partial{y}}\hat{\textbf{j}}$

$= \cos(x + 2y)\hat{\textbf{i}} + 2\cos(x+ 2y)\hat{\textbf{j}}$

so the gradient of f(x, y) at (-2,-3) is

$\nabla{f(-2, -3)} = \cos(-8)\hat{\textbf{i}} + 2\cos(-8)\hat{\textbf{j}}$

Therefore, the directional derivative D_uf(x, y) is

$D_uf(x, y) = \nabla{f(x, y)}\cdot \vec{\textbf{u}}$

$\:\:\:\:\:\:\:=\cos(-8)\left(-\frac{\sqrt{2}}{2}\right) + 2\cos(-8)\left(\frac{\sqrt{2}}{2}\right)$

$\:\:\:\:\:\:\:\:=\cos(-8)\left(\frac{\sqrt{2}}{2}\right) = -0.103$

Note: the arguments of the cosines are in radian measure.

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