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PSYCHO15rus [73]
2 years ago
11

Evaluate the surface integral. S xz ds, s is the part of the plane 2x 2y z = 4 that lies in the first octant

Mathematics
1 answer:
maksim [4K]2 years ago
6 0

The value of the given surface integral is 4.

The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.

S(u,v)=(1-u)((1-u)(2,0,0)+u(0,2,0)+u(4,0,0)\\S(u,v)=(2(1-u)(1-v),2u(1-v),4v)

<h3>What is the surface integral?</h3>

A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.

with 0≤u≤1 and  0≤v≤1. Then the surface element ds  is equivalent to

ds=\||\:\left(s_u\times \:\:S_v\right)||dudv=12\left(1-v\right)dudv

The surface integral is then

\int \:\int \:_Sxzds=12\int _0^1\:\int _0^1\:\left(2\left(1-u\right)\left(1-v\right),2u\left(1-v\right),4v\right)dvdu=4

Therefore the value of the given surface integral is 4.

To learn more about the integral visit:

brainly.com/question/14295614

#SPJ2

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Then, dividing by 0.03, we get

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The change in world production is the difference between the amounts for the two years, so is

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3 years ago
What is the answer you this question
8_murik_8 [283]
Hello!

First, you will need to subtract -2 from 4 (4-(-2)). You'll need to do this because to find the slope, you'll need to subtract y² w/ y1 or 4-(-2) and divide it by x² - x1 or -1-(-3). So once you set up the equation it'll look like this...

4-(-2)/-1-(-3)

Now after you've subtracted the numbers, your equation will look like this...

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I hope this helps!
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3 years ago
6 workers can build a wall in 30 days. If after 6 days 3 more workers join, find the number of days to build the same wall?
viktelen [127]

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<h3>How to use inverse proportionality to determine building time of a wall</h3>

In this question we must use the definition of <em>inverse</em> proportionality, in which the number of workers (n), no unit, is inversely proportional to the <em>building</em> time (t), in days.

According to the statement, 6 workers spent 6 days building a wall and there are 24 days left for completion, but 3 more workers entered to reduce building time, which can be represented by the following expression:

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To learn more on inverse proportionality, we kindly invite to check this verified question: brainly.com/question/4838941

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Answer:  D

Step-by-step explanation:

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