PLEASE HELP! THANK YOU! Hint: It’s not C.

Mathematics

1 answer:

Jlenok [28]3 years ago

6 0

The correct answer is A. Each of the y values are 4 times their respective x values

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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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3 years ago

How many years will it take for a person in the United States eat 1,120 pounds of turkey (14 pounds)

Liono4ka [1.6K]

If I understand you, a person eats about 14 pounds of turkey a year. So we will divide all that turkey (1120 pounds) by 14 to find out how many years.

1,120 ÷ 14 = 80 So it will take 80 years. (Since babies can't eat that much turkey a year it will actually take more than 80 years - or the person can eat more than 14 pounds in some years to make up for their early years when they ate less) I know it's a math question, but I also like to be realistic about it. Who measures the amount of turkey they eat yearly anyway? :-)

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4 years ago

What is the distance between points (2,2) and (8,7)

Ganezh [65]

Answer: 1

Step-by-step explanation:

Please see attached