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
sp2606 [1]
3 years ago
11

Set up a double integral for calculating the flux of the vector field ????⃗ (????⃗ )=????⃗ , where ????⃗ =⟨x,y,z⟩, through the p

art of the upward oriented surface z=3(x2+y2) that lies above the disk x2+y2≤25.
Mathematics
1 answer:
Tema [17]3 years ago
4 0

Answer:

-937.5π

Step-by-step explanation:

F (r) = r = (x, y, z) the surface equation z = 3(x^2 + y^2) z_x = 6x, z_y = 6y the normal vector n = (- z_x, - z_y, 1) = (- 6x, - 6y, 1)

Thus, flux ∫∫s F · dS is given as;

∫∫ <x, y, z> · <-z_x, -z_y, 1> dA

=∫∫ <x, y, 3x² + 3y²> · <-6x, -6y, 1>dA , since z = 3x² + 3y²

Thus, flux is;

= ∫∫ -3(x² + y²) dA.

Since the region of integration is bounded by x² + y² = 25, let's convert to polar coordinates as follows:

∫(θ = 0 to 2π) ∫(r = 0 to 5) -3r² (r·dr·dθ)

= 2π ∫(r = 0 to 5) -3r³ dr

= -(6/4)πr^4 {for r = 0 to 5}

= -(6/4)5⁴π - (6/4)0⁴π

= -937.5π

You might be interested in
steve paid 10% tax on a purchase of 40$ . select the dollar amount of the tax ad the total dollar amont steve paid on the number
poizon [28]
$4 is the amount of tax Steve paid 
4 0
2 years ago
Read 2 more answers
I need to know how to determine the product of the fractions and simplify
FinnZ [79.3K]
1      3     1×3       3
--- × --- = ------ = ----
2      4      2×4      8

5       5       5×5         25
--- × ---- = --------- = -------
6       7       6×7         42

hope is understandably 

5 0
2 years ago
the graph below has A) no linear factors B) two dissimilar linear factors or C) one repeated linear factor
luda_lava [24]
The correct answer is NO LINEAR FACTORS (option A ).
8 0
3 years ago
Read 2 more answers
In a line of students. Jenna is number 8. The teacher says that a rule for a number patter is add 4. The first student in line s
tatyana61 [14]
She says 35 because number 7 in line says 31, so 31+4=35...

I hope this helped you!
7 0
2 years ago
I’m not sure how to do this please help
Nikolay [14]

Answer:

B :step 2   she didnt collect all the like terms and calculate

Step-by-step explanation:

first rewrite  remove all (  )Parentheses

2nd   collect all like terms and calculate

a^4 + 7a -16 -12^a^3 + 5a -3

a^4 + 12a - 19 - 12a^3     ( Like terms are 7a +5a  and -16 +-3)

so she skipped the second step

3 0
2 years ago
Other questions:
  • Ms. Huggins collected data from each of her four math classes to see if having an after-school job was independent or dependent
    10·1 answer
  • Has an x-intercept of (4,0) and a y- intercept of (0,-2)
    10·1 answer
  • The graph of an exponential function passes through the point (0,15) and (1,10). What is the equation of the exponential functio
    14·1 answer
  • Use Pascal's Triangle to expand (b - 3a)^4
    14·1 answer
  • A quality-control engineer samples 100 items manufactured by a certain process, and finds that 15 of them are defective. True or
    14·1 answer
  • I'm stuck... what is the answer to this equation? <br><br><br>3p + 2 ≥ -10
    12·1 answer
  • Slope:<br> what is the slope?
    8·1 answer
  • To find the average of a set of numbers, add up all the items and divide by.
    11·2 answers
  • HELP ME! I WILL GIVE BRAINLIEST
    8·1 answer
  • Two ramps are being built with the same slope. The first ramp is twice the height of the second ramp. Does the first ramp have t
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!