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
s2008m [1.1K]
3 years ago
10

Evaluate the surface integral ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper S f (x

comma y comma z )dS using a parametric description of the surface. f (x comma y comma z )equalsx squared plus y squared​, where S is the hemisphere x squared plus y squared plus z squared equals 36​, for zgreater than or equals0 The value of the surface integral is nothing. ​(Type an exact​ answers, using pi as​ needed.)
Mathematics
1 answer:
kykrilka [37]3 years ago
6 0

Parameterize S by

\vec s(u,v)=6\cos u\sin v\,\vec\imath+6\sin u\sin v\,\vec\jmath+6\cos v\,\vec k

with 0\le u\le2\pi and 0\le v\le\frac\pi2. Take a normal vector to S,

\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=36\cos u\sin^2v\,\vec\imath+36\sin u\sin^2v\,\vec\jmath+36\cos v\sin v\,\vec k

which has norm

\left\|\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}\right\|=36\sin v

Then the integral of f(x,y,z)=x^2+y^2 over S is

\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\iint_S\left((6\cos u\sin v)^2+(6\sin u\sin v)^2\right)\left\|\frac{\partial\vec s}{\partial v}\times\frac{\partial\vec s}{\partial u}\right\|\,\mathrm du\,\mathrm dv

=\displaystyle36^2\int_0^{\pi/2}\int_0^{2\pi}\sin^3v\,\mathrm du\,\mathrm dv=\boxed{1728\pi}

You might be interested in
You are baking a casserole. The recipe calls for of a cup of beans to make 5 servings. How many cups of beans would you need to
Tomtit [17]

Answer:

5 cups

Step-by-step explanation:

5 0
2 years ago
Spiral Review A chili cook-off has adult tickets a and child tickets C. A group of visitors buys 3 adult tickets and 2 child tic
dem82 [27]

Equation 1 would be: 3a+2C

Equation 2 would be: 5a+3C

3 0
3 years ago
Write the equation of a line in slope-intercept form that passes through the given points.
ruslelena [56]

Answer:

<h2>         y = 0.25x + 2</h2>

Step-by-step explanation:

\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}

(0, 2)    ⇒     x₁ = 0,  y₁ = 2

(-4, 1)     ⇒     x₂ = -4,  y₂ = 1

So the slope:

\bold{m=\dfrac{1-2}{-4-0}=\dfrac{-1}{-4}=0.25}

The point-slope form of the equation of the line passing through point (x₀,y₀) and with slope m is:  y - y₀ = m(x - x₀)

m = 0.25

(0, 2)    ⇒     x₀ = 0,  y₀ = 2

Therefore:

               y - 2 = 0.25(x - 0)

               y - 2 = 0.25x                  {add 2 to both sides}

               y = 0.5x + 2          ←  the slope-intercept form of the equation

5 0
3 years ago
angle, a and angle, b are complementary angles. angle a measures 22, degrees. What is the measure of angle b?
Natali [406]

Answer:

158 degrees is angle b I think so

7 0
3 years ago
I need help ,, i don't understand !<br>​
otez555 [7]

Answer: B

Step-by-step explanation: The question is asking for the point greatly different from all the rest, the outlier. Point B is far away from the grouping of all the other points, making it the outlier.

7 0
3 years ago
Other questions:
  • Which is greater 3/4 or 10/12
    5·2 answers
  • Which function has zeros -4 and 2
    5·1 answer
  • Genevieve bought ten bundles of ten tulips at the flower market.
    8·1 answer
  • What is the domain of validity for csc theta =
    14·1 answer
  • The line PQ has equation 3x – 2y = 12. P is a point with coordinates (6, 3) and Q is the point
    14·1 answer
  • The houses on a city block were thought to be valued at $169,000, $133,000, $171,000, $145,000, $180,000, $172,000, and $149,000
    12·1 answer
  • chris can be paid in one of two ways. plan a is a salary of $450 per month, plus a commission of 8% of sales. Plan B is a salary
    15·1 answer
  • Pls help number 1 - 4
    10·2 answers
  • What value of x makes this proportion true?<br> 3/x = 15/40<br> A. 5<br> B. 28<br> C. 8<br> D. 105
    9·2 answers
  • Pls help asap, whoever answers gets brainliest, 5 stars, and a thanks!
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!