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
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NI -
16
2
Which of the following is equivalent to
O 6
08
O 12
O 64
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.
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The theoretical probability of spinning a 9 is_?
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:
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
Answer:
D. no
Step-by-step explanation:
im pretty sure its d. no
I need help please i don’t understand
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.
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?
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
What is 1.154701 as a rational denominator?
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:
Please help, solve for x
Answer:
x = 7
Step-by-step explanation:
5(x + 5) = 10 x 6
5x + 25 = 60
5x = 35
x = 7
which line has a constant proportionality of 4
Answer:
Line A
Step-by-step explanation:
Line A has a constant of proportionality (slope) of 4.
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
as for my ans is C...
can you correct me if im wrongX
someone pls help im struggling if you do tysm ! <333 :)
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)
Somebody help me pleaseee ???
Answer:
Step-by-step explanation:
Please help me with this one
Answer:
Step-by-step explanation:
B two pairs of sides have the same slope.
I've done this before.
PLZ HELP THIS IS TIMED
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
What is the measurement of angle 2?
A- 20 degrees
B- 30 degrees
C- 70 degrees
D- 110 degrees
Answer:
∠ 2 = 70°
Step-by-step explanation:
∠ 2 and 70° are vertical angles and are congruent, then
∠ 2 = 70°
27 please I’ll try to give you brainliest
Answer:
Hexogen
Step-by-step explanation:
I need help with this question please
Answer:
D
Step-by-step explanation:
Hector took 1 hour and 25 mintues to finish the test. (D)!
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?
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.
In the data set below, what is the mode? 9, 4, 9, 2, 8, 2, 1
Answer:
9 and 2
Step-by-step explanation:
both come out 2 times
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?
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
38=-5t²+40t+25 how would I solve for "t"?
Answer:
Step-by-step explanation:
trent is filling up a 15 gallon pool.If 1 gallon is about 3.79 liters,how many liters will fill up this pool?
Answer: 56.85
Step-by-step explanation:
So, what you have to do is multiply 15 x 3.79=56.85.
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?
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 the area of a circle with a radius of 3 cm
Answer:
Hey mate......
Step-by-step explanation:
This is ur answer......
A ≈ 28.27cm²Hope 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.
Answer:
≈ 6 hours 10 minutesStep-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 hourTogether they can wash in 1 hour:
1/14 + 1/11 = 25/154Time needed to wash all the cars:
154/25 = 6.16 hours ≈ 6 hours 10 minutesAs 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?
Answer:
80%
Step-by-step explanation:
Divide 600 by 750 to find the probability
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.
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
What are the roots of the quadratic?
a) -3 and 0
b) -3 and 1
c) -1 and 3
d) -1 and -3
Simply by dividing 3/5 (-4/9) ???!!
I’ll give Brainly est help
Answer:
B. 25
Step-by-step explanation: