JS 19. Evaluate the integral || curlĒ dĞ using Stoke’s Theorem, where F =-yi+xj+ryck and S is the part of the sphere r2 + y2 + 22 = 4 that lies above the cy-planes, oriented upward. A. 27 B. 0 C. 87 D. -87 E. 47

Answers

Answer 1

The integral || curl F || dĞ is equal to -2. The correct answer is therefore option D that is -87.

To evaluate the integral || curl F || dĞ using Stoke's Theorem, we need to find a vector field F and a surface S such that the boundary of S is a closed curve C and the integral is equal to the flux of the curl of F through S. Using the given information, we can find the components of F as:

F = (-y, x, r)

The curl of F is given by:

curl F = (0, 0, 1)

The surface S is the part of the sphere r2 + y2 + z2 = 4 that lies above the cy-planes, oriented upward. This surface can be parameterized by:

x = rcosφcosθ

y = rcosφsinθ

z = rsinφ

where 0 ≤ φ ≤ π and 0 ≤ θ ≤ 2π.

The boundary of S is the curve C, which is the intersection of the sphere and the cy-plane. This curve can be parameterized by:

x = rcosθ

y = rsinθ

z = 0

where 0 ≤ θ ≤ 2π.

Using Stoke's Theorem, the integral || curl F || dĞ is equal to the flux of curl F through S, which is given by:

∫|| curl F || dĞ = ∫curl F · ndC

where n is the unit normal vector to the surface S.

Substituting the expressions for curl F and the parameterizations of S and C, we get:

∫|| curl F || dĞ = ∫(0, 0, 1) · (cosφcosθ, cosφsinθ, sinφ)dC

= ∫(sinφ)dC

= ∫sinθdθ

= [-cosθ]θ=0θ=2π

= -2

Learn more about Stoke's theorem at:

brainly.com/question/13105453

#SPJ4


Related Questions

I need help with this question please

Answers

Answer:

D

Step-by-step explanation:

Hector took 1 hour and 25 mintues to finish the test. (D)!

The theoretical probability of spinning a 9 is_?

Answers

Answer:

The theoretical probability of spinning a sum of 9 is 4/36 or 1/9.

Step-by-step explanation:

Answer: 0%

Step-by-step explanation:

What is the measurement of angle 2?
A- 20 degrees
B- 30 degrees
C- 70 degrees
D- 110 degrees

Answers

Answer:

∠ 2 = 70°

Step-by-step explanation:

∠ 2 and 70° are vertical angles and are congruent, then

∠ 2 = 70°

70 degrees since it was reflected

someone pls help im struggling if you do tysm ! <333 :)

Answers

Answer:

everything except -1 will be the answer

Step-by-step explanation:

4n + 13 < 9

n < -1

if n is -1, the answer would be 9(INCORRECT)

if n is -2, the answer would be 5(CORRECT)

if n is -3, the answer would be 1(CORRECT)

if n is -4, the answer would be -3(CORRECT)

the answer should be the first one

In the 2017 national Youth Risk Behavior Survey, 16.5% of high school students had ridden with a driver who had been drinking alcohol within the previous month. This data came from an SRS of 14,500 students. Find the probability of selecting an SRS of 14,500 students in which less than 15% had ridden with a driver who had been drinking alcohol within the previous month.

Answers

Maybe bf of the 24 election it would be better to have the 15% and it was probably be the way it would be through alcohol

2.

For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.


A. yes; y = -1/3x

B. yes; y = x – 3.3

C. yes; y = –3.3x

D. no

Answers

C. Because every y/x =-3.3 with no y-intercept.

Answer:

D. no

Step-by-step explanation:

im pretty sure its d. no

At a movie theater, a large popcorn cost $8.00 and small drinks cost $3.75 each. If you
buy d drinks and a large popcorn, what expression would represent your bill?

Answers

Answer:

large popcorn: $8

small drink: $3.75

= $8 + $3.75

= $11.75

Answer:

$11.75d

Step-by-step explanation:

add 8.00 and 3.75

you get 11.75 since U don't know how much it is for the drink, then U put d 11.75 so when U find d, you'll know that U can add it with your sum.

38=-5t²+40t+25 how would I solve for "t"?​

Answers

Answer:

Step-by-step explanation:

Please only answer this if ur not just guessing.
sally and belvedere are collecting shirt with a ratio of 4:10. if they collected 462 shirts altogether, how many shirts did sally collect?

Answers

Hey how you doing hope you have a wonderful day

Answer:

132

Step-by-step explanation:

the ratio for saly is 4 out of 14. so 4/14 is 0.28571429. and if you multiply that by the total collected shirts which is 462, you get 132 :)))

What is 1.154701 as a rational denominator?

Answers

Answer:

Convert to a mixed number by placing the numbers to the right of the decimal over

1000000

. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

1154701/1000000

Step-by-step explanation:

which line has a constant proportionality of 4

Answers

Answer:

Line A

Step-by-step explanation:

Line A has a constant of proportionality (slope) of 4.

PLZ HELP THIS IS TIMED

Answers

Answer:

150

Step-by-step explanation:

116

Step-by-step explanation:

area of triangle is b times h divide by 2then for square is b times h

Please help me with this one

Answers

Answer:

Step-by-step explanation:

B two pairs of sides have the same slope.

I've done this before.

In the data set below, what is the mode? 9, 4, 9, 2, 8, 2, 1

Answers

Answer:

9 and 2

Step-by-step explanation:

both come out 2 times

As a goalie , Brooke is practicing blocking goals . Out of 750 shots , she blocks 600 of them . What is the experimental probability that she will block the next shot?

Answers

Answer:

80%

Step-by-step explanation:

Divide 600 by 750 to find the probability

Help i dont know how to do it, pls explain also how did you get ur answer so i can gain information how to do it next time. Thank you​

Answers

You can found the coordinates along the sides MQ and NQ

The distance for MQ is 6, and for NQ is 8

Then you can just use the Pythagorean Thm since it is a right triangle

6^2+8^2=MN^2
36+64= MN^2
100= MN^2
MN=10

So it would be D

What is the area of a circle with a radius of 3 cm

Answers

Answer:

Hey mate......

Step-by-step explanation:

This is ur answer......

A ≈ 28.27cm²

Hope it helps!

Mark me brainliest pls......

Follow me! :)

Answer:

28.26

Step-by-step explanation:

Area of a circle:

A = πr²

A = 3.14(3²)

A = 3.14(9)

A = 28.26

Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of cars. Matthew can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Jordan wants to know how long it will take them to wash all the cars in the lot if they work together.

Write an equation and solve for the time it will take Matthew and Arianna to wash all the cars together. Explain each step.

Answers

Answer:

≈ 6 hours 10 minutes

Step-by-step explanation:

Matthew can wash all the cars in 14 hours ⇒ 1/14 of all cars in 1 hourArianna can wash all the cars in 11 hours ⇒ 1/11 of all cars in 1 hour

Together they can wash in 1 hour:

1/14 + 1/11 = 25/154

Time needed to wash all the cars:

154/25 = 6.16 hours ≈ 6 hours 10 minutes

Somebody help me pleaseee ???

Answers

Answer:

Step-by-step explanation:

NI -
16
2
Which of the following is equivalent to
O 6
08
O 12
O 64

Answers

Answer:B

Step-by-step explanation:

The equivalent expression is 8.

Option B is the correct answer.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

[tex](16^{3/2})^{1/2}[/tex]

This can be written as,

= [tex]16^{3/2 \times 1/2}[/tex]

= [tex]16^{3/4}[/tex] ______(1)


Now,

16 = [tex]2^4[/tex] ______(2)

Now,

From (1) and (2),

= [tex]2^{4 \times 3/4}[/tex]

= 2³

= 8

Thus,

The equivalent expression is 8.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ7

Please help, solve for x

Answers

Answer:

x = 7

Step-by-step explanation:

5(x + 5) = 10 x 6

5x + 25 = 60

5x = 35

x = 7

Simply by dividing 3/5 (-4/9) ???!!

Answers

Hopes this helps:

Answer: -27/20

PLZZ HELP!! ASAP

Two 3 digit numbers are formed using the same integers and when they are added the form another 3 digit number with the same integers, find the added number?

options
a) 954
b) 682
c) 488
d) 890​

Answers

as for my ans is C...

can you correct me if im wrongX

trent is filling up a 15 gallon pool.If 1 gallon is about 3.79 liters,how many liters will fill up this pool?​

Answers

Answer: 56.85

Step-by-step explanation:

So, what you have to do is multiply 15 x 3.79=56.85.

I’ll give Brainly est help

Answers

Answer:

B. 25

Step-by-step explanation:

It’s 20, to find the area you have to do L time W and 4 time 5 is 20

27 please I’ll try to give you brainliest

Answers

Answer:

Hexogen  

Step-by-step explanation:

I need help please i don’t understand

Answers

9514 1404 393

Answer:

  no

Step-by-step explanation:

The dimensions will be those of a rectangular mirror if the diagonal measure is the hypotenuse of the right triangle with the given side lengths.

The Pythagorean theorem would require for some width w ...

  w^2 +24^2 = 30^2

  w^2 = 900 -576 = 324

  w = √324 = 18

A rectangular mirror with a length of 24 inches and a diagonal of 30 inches will have a width of 18 inches, not 16.

__

The attachment shows that a width of 16 inches is not consistent with a right-angle corner.

_____

Additional comment

If you reduce the given numbers to lowest terms by dividing them by 2, they become 8, 12, 15. That is, the two shortest sides are even and the longest is odd. Any set of integer dimensions for a right triangle must have an even number of odd numbers (0 or 2). These numbers cannot be a Pythagorean triple, so cannot make a right triangle.

What are the roots of the quadratic?
a) -3 and 0
b) -3 and 1
c) -1 and 3
d) -1 and -3

Answers

The answer is b) -3 and 1. (don’t take my word and wait for another answer) :)
Answer would be B) -3 and 1

A cylindrical container of six rubber balls has a height of 18 centimeters and a diameter of 3 centimeters. Each ball in the container has a radius of 1.5 centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number. - Could you help me with this?

Answers

Answer:

170 cm²

Step-by-step explanation:

Height of Cylindrical container = 18 cm ; diameter of cylindrical container = 6 cm.

Hence, radius of cylindrical container = 6/2 = 3 cm

Rubber balls = 3 each have a radius of 3 cm.

Volume of a cylinder = π r² h

V = 3.14 * (3cm)² * 18 cm

V = 508.68 cm³

Volume of rubber ball = 4/3 π r³

V = 4/3 * 3.14 * (3cm)³

V = 113.04 cm³

Volume of 3 rubber balls = 3 * 113.04 = 339.12³

Take the difference to obtain answer :

Volume of cylinder - Volume of rubber ball

508.68 cm³ - 339.12³

= 169.56 cm²

170 cm² (nearest whole number

In a survey at a local university, 43% of students say that they get less than the recommended eight hours of sleep per night. In a group of 3500 students, how many would you expect get eight or more hours of sleep per night?

Answers

Answer:

1995

Step-by-step explanation:

Percent of students that get more than 8 hours of sleep = 100 -43 = 57%

Number of students that get more than 8 hours of sleep = 57% x 3500

0.57 x 3500 = 1995 students

Other Questions
All other things being equal, by how much will nominal GDP expand if the central bank increases the money supply by $100 billion, and the velocity of money is 3? PS: PLEASE DO NOT PUT A LINK IN THE ANSWER SECTION! Why is the Korean War sometimes referred to as the Forgotten War even though many thousands lost their lives in that conflict?a. because it did not last for very long and the participants did not fight very hard to achieve victoryb. because it took place in Asia while most well-known wars take place in Europe or Americac. because it occurred between two other great wars, World War II and the Vietnam Ward. because there was no clear victory or successful completion of the mission--for either side What concerned Northerners about the way of life of Southern slave owners?A. They feared the South would force the North to accept slavery.B. They worried that the South would overturn the Compromise of1850 and create a slave state in California.C. They feared the South would try to extend federal power over allstates.D. They worried that the low labor costs of the South would hurt theNorth's economic power.SUBMIT In Sahara the term erg is used to describe a(n) Answers are: A: oasis B: sand sea C:Rocky Mountain D:river how to write a Alcaic Stanza 13) Storico Co. just paid a dividend of $3.15 per share. The company will increase its dividend by 20 percent next year and then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on the companys stock is 12 percent, what will a share of stock sell for today? (4 pts) Evaluate the expression 2y + 10 + y2 of y=8 what is the rule for (f - g) (x)? Choose the best Spanish equivalent to the phrase.I gave my dad a tie for Fathers Day.A. Le di una corbata a mi pap para el Da del PadreB. Le doy una corbata a mi pap para el Da del PadreC. Le dimos una corbata a mi pap para el Da del PadreD. Le damos una corbata a mi pap para el Da del Padrethanks :) Which statement is completely accurate? O Atoms of the same element always have different numbers of neutrons. O Atoms of the same element can have neutrons but exist without protons. O Atoms of the same element always have different atomic weights. O Atoms of the same element can have different numbers of neutrons. a solution is prepared by dissolving 55g of CaCl2 into 300g of water. if the Kf of water is -1.86 c/m, shat is the freezing point depression of the solution I need help with these question! Please do step by step- How do back-arc basins form? View Available Hint(s) How do back-arc basins form? Tensional stresses resulting from slab suction stretch this part of the crust, causing it to thin vertically. Compressional forces bend the sedimentary layers in the back-arc region downward, creating a bowl-like depression. Compressional forces make the back-arc region thicker and denser than the volcanic arc. This higher density causes the back-arc region to sink into a basin shape. The back-arc region subsides into a downwarped basin shape from the added weight of addition of sediment from mass wasting events. A mountain range also forms on the side of the back-arc basin opposite of the volcanic arc, creating a lowland in between the two ranges. The mass of this atom is:u. 3 mass unitsb. 4 mass unitsc. 6 mass unitsd. 7 mass unitse. 11 mass units PLEASE HELP!A piece of metal is heated to a temperature of 50.0C and then placed in a calorimeter containing 50.0 g of water at 27.0C. The water temperature increases to 35.0C. How many joules of heat were transferred from the metal to the water? (Cwater = 4.18J/gC) ] 1) Convert the number 2,371,875,908 to scientific notation. Kyle owned a small business that sold and repaired several styles of bicycles. Last month, Kyle had sales of $15,000 and the costs of operating his business were $12,300. Which of the following is true about Kyle's business?The business earned a profit.The business should focus on expansion.The business experienced a loss.The business is not capitalizing on a need What is the volume of the cube of 3.1 m? Can you guys help me with this problem Its in the picture Function f(x) has a jump discontinuity at x = 8. Which statement identifies possible one-sided limits at x = 8?lim flx) DNE and lim f(x) DNElim f(x) DNE and lim Flx) = 120lim flx) = 85 and lim f(x) = 85*-37lim Flx) = 85 and lim flx) = 120O