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
Vsevolod [243]
2 years ago
13

Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with

outward normal orientation away from the origin
Mathematics
1 answer:
skad [1K]2 years ago
8 0

Parameterize S by the vector function

\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle

The integral of the field over S is then

\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv

\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv

\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}

You might be interested in
Please don't put links:(​
GalinKa [24]

1/2 brainlest please

Step-by-step explanation:

It would be 0 then 1/2 then 2/2 then finally 1

7 0
3 years ago
What is two thirds equal to
Luden [163]

Answer:

2/3 = 0.6666666666666667 or just 67%.

Step-by-step explanation:

5 0
3 years ago
Expand the expression 2/7(2s+3)
xxTIMURxx [149]
48/7 + 6/7 if your having any other trouble let me no


8 0
3 years ago
Read 2 more answers
8x(x-2017)-2x+4034=0
mash [69]

Answer:

¼ và 2017

Step-by-step explanation:

8 0
3 years ago
The packaging lists a model airplane’s length as 10.5 in. It also gives the scale as 1:83. What is the length of the actual airp
Lana71 [14]
\bf \cfrac{\stackrel{model}{length}}{\stackrel{actual}{length}}\qquad 1:83\qquad \cfrac{1}{83}\implies \cfrac{1}{83}=\cfrac{10.5}{x}\implies x=\cfrac{83\cdot 10.5}{1}
\\\\\\
x=871.5~inches
\\\\\\
\textit{there are 12 inches in 1 foot, thus }
\\\\\\
871.5~\underline{in}\cdot \cfrac{ft}{12~\underline{in}}\implies 72.625~ft 
\qquad \approx 73~ft
6 0
3 years ago
Other questions:
  • Will give brainliest-This graph compares shoe sizes for a group of 80 two-year-old boys and a group of 60 three-year-old boys. A
    10·2 answers
  • Does subtraction exhibit the property of closure over the set of real numbers.
    6·1 answer
  • How can logical reasoning be applied to writing proofs?
    5·1 answer
  • Which ratios are proportional to 14:21? choose all the answers that are correct
    11·1 answer
  • Grant is a member of a book club. He pays a $10 yearly membership fee and can purchase books through the club for $2.75 each. Hi
    8·2 answers
  • Consider the given rectangle with heightequals4timeswidth. Let x be the width of the rectangle. Write an expression for the​ per
    6·1 answer
  • At your job, you work a lot of overtime hours. Every hour of overtime that you work, you get paid 1 1 half times your normal pay
    10·1 answer
  • Need help with the slope​
    8·1 answer
  • Students in the student council are selling candy bars. They earn $0.75 on each candy bar they sell. Their goal is to earn at le
    8·1 answer
  • Use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!