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3 years ago

Multiply and simplify.

Mathematics

1 answer:

Shkiper50 [21]3 years ago

3 0

1)
2•5(3)√9y2 (3)√3y

2) 3xy

3) 2√3
----------
3 ( like a fraction )
Decimal : 1.15

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Prove the following trigonometric identities

alexandr1967 [171]

Answer:

Greetings !

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2 years ago

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

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}(\nabla\cdot f)\,\mathrm dV$
$=\displaystyle6\int_{z=0}^{z=c}\int_{y=0}^{y=b}\int_{x=0}^{x=a}(5-x)\,\mathrm dx\,\mathrm dy\,\mathrm dz$
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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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Step-by-step explanation:

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Read 2 more answers

Solve for X:

saveliy_v [14]

$- \frac{6}{5} x - 4 = - 46 \\ - \frac{6}{5} x = - 42 \\ - 6x = - 210 \\ x = 35$
Translate the words into math and solve for x. Any questions let me know.

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3 years ago

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Nana76 [90]

331.3%
Convert 53/16 to simplest form, 3 5/16, convert 5/16 into numbers —> 0.3125
Take the whole number and add it into the ones place: 3.3125
Move the decimal into two places then round to the nearest tenth: 331.3

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2 years ago