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
Viefleur [7K]
3 years ago
11

Surface integrals using a parametric description. evaluate the surface integral \int \int_{s} f(x,y,z)dS using a parametric desc

ription of the surface.
f(x,y,z)=x2+y2, where S is the hemisphere x2+y2+z2=36, for z>=0
Mathematics
1 answer:
DiKsa [7]3 years ago
7 0

You can parameterize S using spherical coordinates by

\vec s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle

with 0\le u\le2\pi and 0\le v\le\frac\pi2.

Take the normal vector to S to be

\dfrac{\partial\vec s}{\partial\vec v}\times\dfrac{\partial\vec s}{\partial\vec u}=36\langle\cos u\sin^2v,\sin u\sin^2v,\cos v\sin v\rangle

(I use \vec s_v\times\vec s_u to avoid negative signs. The orientation of the normal vector doesn't matter for a scalar surface integral; you could just as easily use \vec s_u\times\vec s_v=-(\vec s_v\times\vec s_u).)

Then

f(x,y,z)=f(6\cos u\sin v,6\sin u\sin v,6\cos v)=36\sin^2v

and the integral of f over S is

\displaystyle\iint_Sf(x,y,z)\,\mathrm dS=\int_0^{\pi/2}\int_0^{2\pi}36\sin^2v\left\|\frac{\partial\vec s}{\partial v}\times\frac{\partial\vec s}{\partial u}\right\|\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{\pi/2}\int_0^{2\pi}(36\sin^2v)(36\sin v)\,\mathrm du\,\mathrm dv

=\displaystyle2592\pi\int_0^{\pi/2}\sin^3v\,\mathrm dv=\boxed{1728\pi}

You might be interested in
Can y’all help me on Thai one
natima [27]

Answer:

20.

$18.40.

Step-by-step explanation:

The mean number of people = (12+19+17+26+26)/5

= 100/5

= 20.

Karmin's original hourly rate = 480/30

= $16 per hour.

With a 15% rise it is 16 * 1.15

= $18.40 / hour.

3 0
3 years ago
2. Find the distance between (-2,1) and (3,4).
Nina [5.8K]

Answer:

\sqrt{34} or 5.83095

Step-by-step explanation:

Use the distance formula \sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^2 }

Make sure to round the answer appropriately if not asked for in square root form!!

8 0
3 years ago
6
bezimeni [28]

Answer:

260 stickers

Step-by-step explanation:

Let Gareth's stickers be x.

Hence Cheryl sticker is 160+x;

If Cheryl gave 185 stickers

to Gareth, it means:

Cheryl has at the moment;

160 + x - 185 = x - 25

At this time when Gareth receives 185 he now has:

x+ 185

Also when he receives x +185, he has 3 times Cherry's meaning:

x+185 =3(x-25)

x + 185 = 3x -75

185 + 75 = 3x-2x

260= x

x = 260.

Hence Gareth has 260 stickers

5 0
3 years ago
Convert the function into intercept form. Show your work. y=-x^2+5x-36
Montano1993 [528]

{ - x}^{2} + 5x + 36 \\  { - x}^{2}  + 9x - 4x + 36 \\  - x \times (x - 9) - 4(x - 4) \\  \\ answer \:  \:  - ( x - 9) \times (x \times 4)
3 0
3 years ago
a car decreased in value from $980 to $720 in one year what was the per cent of decrease to the nearest whole per cent ?
kolezko [41]

The decrease was 27%.

Step-by-step explanation:

Old value = $980

New value = $720

Decrease = Old value - New value

Decrease=980-720=\$260

Percent decrease = \frac{Decreased/ amount}{Old value}*100

Percent\ decrease=\frac{260}{980}*100\\Percent\ decrease=0.265*100\\Percent\ decrease= 26.5\%

Rounding off to near whole percent

Percent decrease = 27%

The decrease was 27%.

Keywords: Percentage, subtraction

Learn more about subtraction at:

  • brainly.com/question/13035995
  • brainly.com/question/13062539

#LearnwithBrainly

6 0
3 years ago
Other questions:
  • Fred has saved 4300 cent over 2 days from selling lemonade. how many dollars dose fred have ?
    15·2 answers
  • Use the Leading Coefficient Test to determine the end behavior of the polynomial function . f(x) = 5x ^ 4 - 2x ^ 2
    13·1 answer
  • Lonnie is using the recipe to make fruit punch. He wants to use 4 and 1/2 cups of pineapple juice. How many cups of orange juice
    15·1 answer
  • Simplify by combining like terms: 5x + 3x + 10x
    11·2 answers
  • How many whole cans can the company make out of each sheet of metal?
    7·1 answer
  • Obtuse equilateral Which name correctly classifies this triangle?
    6·1 answer
  • At the end where it’s cut off it says figures thank you please help ASAP
    9·1 answer
  • How do you figure out proofs​
    10·1 answer
  • Two cards are drawn in succession from a standard 52-card deck.1. What is the probability that the first card is red and the sec
    13·1 answer
  • Find the measure on z.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!