1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
What is the equivalent fraction of 9/15
kirill [66]

The equivalent fraction of 9/15 would be 3/5.


6 0
3 years ago
Read 2 more answers
I don’t understand this
MatroZZZ [7]

Answer:

your just finding area so

1.5×2.5=

1.5×1.5/2=

1.5×2.5=

I will put the answers in the comments I need to use a calculator

7 0
3 years ago
Read 2 more answers
***SOMEONE PLZ HELP ME***
Bingel [31]
If the perimeter is 16, the side length is 4 units.

To find the area of the shaded sections, you will use the fractional part that each section represents and multiply that fraction by the total area of the square.

Area of DEA is 1/4 of 16 square Units (4 x 4).

1/4 x 16 = 4 square units

Area of EFB is 1/8 of 16 square units.

1/8 x 16 = 2 square units

4 square units +2 square units equals 6 square units.

The area of the shaded region is 6 square units.

5 0
3 years ago
A rectangular prism is 12 inches long, 9 inches wide, and 6 inches high. What is the volume of the prism?
zmey [24]

Answer:

Volume = 12×9×6 = 648 inches^3

Step-by-step explanation:

Hope this helps! Have a nice day!

5 0
3 years ago
The perimeter of a rectangle is 22 inches. Find the dimensions if its length is 3 inches greater than its width.
MaRussiya [10]

Answer:

Length: 7

Width: 4

Step-by-step explanation:

We can create a system of equations for this problem, where w is the width and l is the length.

The perimeter of a rectangle is twice its length added to twice its width.

2l+2w=22

The length is 3 more than the width:

l = w+3

We can now substitute in w+3 as l in the equation 2l+2w=22.

2(w+3) + 2w = 22

Distribute the first terms:

2w+6+2w=22

Combine like terms:

4w+6=22

Subtract 6 from both sides:

4w=16

Divide both sides by 4:

w = 4

Now we know that w = 4. We can now substitute this inside an equation to find l.

l = w+3\\\\l = 4+3\\\\l=7

Hope this helped!

7 0
3 years ago
Other questions:
  • The probability that a fair coin tossed 10 times will land heads up on all ten tosses is 1 out of ____.
    5·2 answers
  • Which expression is equivalent to 10x2y+25x
    7·1 answer
  • Bruce traveled 15 kilometers in 60 minutes.Which ratio accurately shows how many minutes it took Bruce to travel one kilometer?
    9·1 answer
  • The pic is the question! Please help
    5·2 answers
  • Raymond takes a 28-inch by 21-inch rectangle of plywood and uses a table saw to cut from one corner of the piece of plywood to t
    14·1 answer
  • What is 40,0123 times 100,0345 ?????
    9·2 answers
  • Alguien sabe como resolver esto?
    6·2 answers
  • Help please, i need this answer asap!!!
    11·1 answer
  • Enter an inequality that represents the description, and then solve.
    11·1 answer
  • A recent survey at a local company showed that 300 employees, or 66⅔% of the company’s employees, carpool to work each day. How
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!