<img src="https://tex.z-dn.net/?f=7xy%28x%20-%207%29%20%3D%20%20" id="TexFormula1" title="7xy(x - 7) = " alt="7xy(x

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OLga [1]

3 years ago

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Mathematics

1 answer:

jeka943 years ago

8 0

7x^2y-49xy

(7x squared)

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Let divf = 6(5 − x) and 0 ≤ a, b, c ≤ 12. (a) find the flux of f out of the rectangular solid 0 ≤ x ≤ a, 0 ≤ y ≤ b, and 0 ≤ z ≤

dusya [7]

Continuing from the setup in the question linked above (and using the same symbols/variables), we have

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}(\nabla\cdot f)\,\mathrm dV$
$=\displaystyle6\int_{z=0}^{z=c}\int_{y=0}^{y=b}\int_{x=0}^{x=a}(5-x)\,\mathrm dx\,\mathrm dy\,\mathrm dz$
$=\displaystyle6bc\int_0^a(5-x)\,\mathrm dx$
$=6bc\left(5a-\dfrac{a^2}2\right)=3abc(10-a)$

The next part of the question asks to maximize this result - our target function which we'll call $g(a,b,c)=3abc(10-a)$ - subject to $0\le a,b,c\le12$ .

We can see that $g$ is quadratic in $a$ , so let's complete the square.

$g(a,b,c)=-3bc(a^2-10a+25-25)=3bc(25-(a-5)^2)$

Since $b,c$ are non-negative, it stands to reason that the total product will be maximized if $a-5$ vanishes because $25-(a-5)^2$ is a parabola with its vertex (a maximum) at (5, 25). Setting $a=5$ , it's clear that the maximum of $g$ will then be attained when $b,c$ are largest, so the largest flux will be attained at $(a,b,c)=(5,12,12)$ , which gives a flux of 10,800.

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7 minutes I'm pretty sure I'm sorry if I'm not but if I'm right can I have brainliest answer?

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Figure ABCD is a parallelogram with point C (3, -2). What rule would rotate the figure 90 degrees clockwise, and what coordinate

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B ) ( x , y ) → ( y, -x ) ; C`( -2, - 3 )

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The coordinates of triangle ABC are A(−4, 3), B(2, 3), and C(4, −1). A line segment runs through the triangle with endpoints Y(0

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We can say that the length of line segment Y'Z' will increase by a scale factor of 2.

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Employee I has a higher productivity rating than employee II and a measure of the total productivity of the pair of employees is

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