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
Vesna [10]
3 years ago
8

Calculate the flux of the vector field f⃗ (x,y,z)=cos(x2+y2)k⃗ through the disk x2+y2≤9 oriented upward in the plane z=4.

Mathematics
1 answer:
garik1379 [7]3 years ago
3 0
Parameterize the disk S by

\mathbf r(s,t)=\begin{cases}x(s,t)=s\cos t\\y(s,t)=s\sin t\\z(s,t)=4\end{cases}

where 0\le s\le3 and 0\le t\le2\pi. Call this parameterized region T. Then

\mathbf r_s\times\mathbf r_t=(\cos t\,\mathbf i+\sin t\,\mathbf j)\times(-s\sin t\,\mathbf i+s\cos t\,\mathbf j)=s\,\mathbf k

The flux over the disk is given by the surface integral

\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iint_T\mathbf f(x(s,t),y(s,t),z(s,t))\cdot(\mathbf r_s(s,t)\times\mathbf r_t(s,t))\,\mathrm ds\,\mathrm dt
=\displaystyle\int_{t=0}^{t=2\pi}\int_{s=0}^{s=3}(\cos(s^2)\,\mathbf k)\cdot(s\,\mathbf k)\,\mathrm ds\,\mathrm dt
=\displaystyle2\pi\int_{s=0}^{s=3}s\cos(s^2)\,\mathrm ds
=\displaystyle\pi\int_{\sigma=0}^{\sigma=9}\cos\sigma\,\mathrm d\sigma

(where we take \sigma=s^2)

=\pi\sin 9
You might be interested in
Help (evaluate the function)​
AveGali [126]

Answer:

16

Step-by-step explanation:

Replace the variable in the expression

f (-2) = (-2)^2-10 x -2

f  ( − 2 ) = − 4 + 20

Add  − 4  and  20

f  ( − 2 ) = 16

6 0
3 years ago
Solve using elimination.<br> 6x + 8y = -4<br> -6x - 10y = 14
jok3333 [9.3K]

Answer:

x = 6, y = -5.

Step-by-step explanation:

6x + 8y = -4

-6x - 10y = 14    Adding will eliminate  the terms in x:

0 - 2y = 10

y = 10/-2 = -5,

Plug this into the second equation:

-6x - 10(-5) = 14

-6x = 14 - 50 = -36

x = -36/-6

x = 6.

3 0
3 years ago
Read 2 more answers
Please help me with this and please select only three answers
ivann1987 [24]
A, E and D are your three answers and
8 0
3 years ago
Read 2 more answers
Write an expression to find the difference in the maximum area and minimum area of a nys high school soccer field. Then evaluate
givi [52]
The maximum area of the school soccer field is given by the maximum length times the maximum width.

Thus maximum area = 120 x 80 = 9,600 square yards.

The minimum area of the school soccer field is given by the minimum length times the minimum width.

Thus maximum area = 100 x 55 = 5,500 square yards.

Therefore, the difference between the maximum area and the minimum area is 9,600 - 5,500 = 4,100 square yards.
5 0
3 years ago
Please help with this question. Please give a solid answer and a well explanation.
sergeinik [125]

Answer: no

Step-by-step explanation:

the average is 14.6 miles so statement is correct but its not qualitative

8 0
3 years ago
Read 2 more answers
Other questions:
  • Booker owns 85 vidoe games he has 3 shelves to put the games on.each shelf can hold 40 video games.how many more vidoe games doe
    5·1 answer
  • If an area in the form of a circle is to be roped off by a rope 10 m long, what will be the radius of this area? Round your answ
    12·1 answer
  • Help please! i need get answers to 3 and 4 :)
    10·1 answer
  • Kristen lives directly east of the park. the football field is directly south of the park. the library sits on the line formed b
    9·2 answers
  • You flip a coin and roll the 20-sided figure. Find the probability of flipping tails and rolling at least a 14. The probability
    14·1 answer
  • Solve for y <br><br> -9 = y + 8
    5·2 answers
  • 2g +11 &lt;45 what is G?
    7·2 answers
  • In a souvenir shop, Jodi purchased 2 small picture frames and 1 large one for $28. Mike bought 3 medium-size frames and 2 large
    9·1 answer
  • If I have the diameter of the circle ⭕️ what’s the equation if I’m finding the area of the circle?If the equation for radius is<
    14·1 answer
  • Evaluate 7|4x−5|+9 when x=−1/8.<br><br> Enter your answer as a decimal in the box.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!