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]
4 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]4 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
Gary and his friends go to see a movie. Gary buys 5 movie tickets and a tub of popcorn for $5.50. If Gary wants to spend more th
Ugo [173]

Silently he crept through jagged thornbushes. Bare feet moved swiftly over hot, arid soil to the edge of a waterhole where the kudu was drinking. The great animal suddenly looked up, spiral horns curving sharply into the endless African sky. Nsue1 did not reach for his pouch of poisoned arrows. He had no heart for killing. This would not be the day he would change his childish boyhood name.

How does paragraph 1 contribute to Nsue’s development?

A.  

It establishes Nsue’s disappointment at not finding a suitable animal to bring to the feast.

B.  

It establishes Nsue’s apprehension of participating in the Festival of the New Moon.

C.  

It establishes Nsue’s desire to become a great storyteller like Gao, the Old One.

D.  

It establishes Nsue’s motivation to find something to take to the feast.

4 0
2 years ago
What is 3.4- -6 -2.5 ?
Arturiano [62]

Answer:

6.9 I think.

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
mai and priya were on scooters. mai traveled 15 meters in 6 seconds priya traveled 22 meters in 10 seconds. who was moving faste
Eduardwww [97]

Answer:

Its Mai

Step-by-step explanation:

I promise I know why

7 0
3 years ago
If 3/4 = x/8 then x is equal to what
pickupchik [31]

Answer:

x is 6

Step-by-step explanation:

3/4 * x/8

3*8=24 then,

divide by 4 which gives you 6.

Also if you simplify 6/8, it will give you 3/4.

3 0
3 years ago
Read 2 more answers
(n + 12) x 5 + 7n Need equivalent expression
astraxan [27]

Answer:

12n + 60

General Formulas and Concepts:

<u>Pre-Algebra</u>

Distributive Property

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

(n + 12) × 5 + 7n

<u>Step 2: Simplify</u>

  1. Distribute 5:                     5(n) + 5(12) + 7n
  2. Multiply:                            5n + 60 + 7n
  3. Combine like terms:        12n + 60
6 0
3 years ago
Other questions:
  • Helpppppp meeeee plzzzzz
    10·1 answer
  • The local store where Tim shops charges a 7% sales tax for clothing. Complete the table by figuring the cost of the jeans after
    5·1 answer
  • 50 Pts
    8·2 answers
  • How do you right 0.4 (repeating decimal) as a fraction in simplest form? Also could you do 0.21 (repeating decimal)
    10·1 answer
  • An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown
    11·1 answer
  • Please help I NEED THE ANSWER IN THE NEXT 2 MINUTES
    10·1 answer
  • If m varies directly as n and m = -4 when n = 32, find m when n = 3
    15·1 answer
  • The cost of 5 scarves is 73.75. what is the unit price
    5·1 answer
  • PLEASE HELP ME 100 POINTS AND BRAINLY!!!
    7·1 answer
  • Find the surface area of this triangular prism:
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!