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
RSB [31]
3 years ago
13

Suppose that surface σ is parameterized by r(u,v)=⟨ucos(3v),usin(3v),v⟩, 0≤u≤7 and 0≤v≤2π3 and f(x,y,z)=x2+y2+z2. Set up the sur

face integral (you don't need to evaluate it). ∫σ∫f(x,y,z)dS=∫R∫f(x(u,v),y(u,v),z(u,v))∥∥∥∂r∂u×∂r∂v∥∥∥dA = 2pi/3 ∫ 0 7 ∫ 0 u^2+v^2 ∥∥∥ ∥∥∥dudv
Mathematics
1 answer:
Bad White [126]3 years ago
6 0

Looks like you have most of the details already, but you're missing one crucial piece.

\sigma is parameterized by

\vec r(u,v)=\langle u\cos3v,u\sin3v,v\rangle

for 0\le u\le7 and 0\le v\le\frac{2\pi}3, and a normal vector to this surface is

\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\left\langle\sin3v,-\cos3v,3u\right\rangle

with norm

\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=\sqrt{\sin^23v+(-\cos3v)^2+(3u)^2}=\sqrt{9u^2+1}

So the integral of f(x,y,z)=x^2+y^2+z^2 is

\displaystyle\iint_\sigma f(x,y,z)\,\mathrm dA=\boxed{\int_0^{2\pi/3}\int_0^7(u^2+v^2)\sqrt{9u^2+1}\,\mathrm du\,\mathrm dv}

You might be interested in
I need help ASAP !!!!!
s2008m [1.1K]

Answer:

the answer is -352..........

6 0
2 years ago
Maggie's brother is 4 years younger than four times her age. The sum of their ages is 26.
Gelneren [198K]

Answer:

Maggie is 6 years old

Step-by-step explanation:

M + B = 26

B = 26 - M

4M - 4 = B

4M - 4 = 26 - M

5M = 30

M = 6

Maggie is 6 years old

3 0
3 years ago
Slove algebraically<br><br>3x - 4y = -24<br>x +4y=8<br>​
Vanyuwa [196]

Solve algebrically 3x - 4y = -24 and x + 4y = 8 is x = -4 and y = 3

<u>Solution:</u>

We have been given two equations which are as follows:

3x - 4y = -24   ----- eqn 1

x + 4y = 8   -------- eqn 2              

We have been asked to solve the equations which means we have to find the value of ‘x’ and ‘y’.

We rearrange eqn 2 as follows:

x + 4y = 8

x = 8 - 4y  ------eqn 3

Now we substitute eqn 3 in eqn 1 as follows:

3(8 - 4y) -4y = -24

24 - 12y - 4y = -24

-16y = -48

y = 3

Substitute "y" value in eqn 3. Therefore the value of ‘x’ becomes:

x = 8 - 4(3)

x = 8 - 12  = -4

Hence on solving both the given equations we get the value of x and y as -4 and 3 respectively.

5 0
3 years ago
Use the following data set to answer question 8:
stira [4]

Answer:

15.1 to nearest tenth.

Step-by-step explanation:

The 7 is the lowest number so the mean would increase if taken away.

New mean = (8 + 12 + 13 + 15 +  18 + 19+21) / 7

= 106 / 7

= 15.14

6 0
2 years ago
Factorise: a^2 + 8a - 20
REY [17]
Which two numbers add up to <span>88</span><span> and multiply to </span><span>−20?
</span><span>−2</span><span> and </span><span>10
</span>
Rewrite the expression using the above:

Answer:
(a−2)(a+10)<span>
</span>
6 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following values is the solution to the equation -35x = -105 ? 3 -3
    12·2 answers
  • Mrs.Tong is baking brownies for a school party.The
    10·1 answer
  • How many 12-inch rulers will be about the same length as a sheet of paper
    6·2 answers
  • 3. Two numbers are in the ratio 3:5. If their difference is 12, what are the numbers?​
    13·1 answer
  • 6. An ice cream costs 15 more than a cold drink. If the cost of
    13·2 answers
  • What angle is this?
    15·1 answer
  • Simplify the expression:<br> (1 + 6g)(3) =
    11·1 answer
  • What's the circumference of a circle with radius of 12 inches . use 3.14 for pi
    10·1 answer
  • Charlie is thinking about buying a game for his Xbox that cost $60 and requires a subscription to basic Xbox live that cost $10
    11·2 answers
  • In the middle school band, there are 5 flutes for every 2 tubas. Write the ratio of flutes to tubas in three different ways.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!