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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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A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measure SL 42,000 ft
horsena [70]

Answer:

a= 200

b = 210

Step-by-step explanation:

My assumption is, we have to find the length of sides of rectangle

Given

perimeter = 2a + 2b = 820 ft (i) (here a is smaller side and b is larger side)

area = a*b = 42,000 ft^2 (ii)

from eq (1)

2a + 2b = 820

=> 2(a+b) = 820

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=> a + b = 410

=> a = 410-b   (iii)

putting the value of a in eq(ii), we get

(410-b) *b = 42,000

410b - b^2 = 42,000

0 = b^2 - 410b + 42000

b^2 - 410b + 42000 = 0

b^2- 200b- 210b + 42000 = 0

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(b-200)(b-210) = 0

or

b= 210 and b = 200

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By putting value of b in eq(iii),

a = 410 -210 = 200

 

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Answer:

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B) 10 f

Step-by-step explanation:

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