Evaluate the surface integral


S
F · dS
for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = yj − zk,
S consists of the paraboloid
y = x2 + z2, 0 ≤ y ≤ 1,
and the disk
x2 + z2 ≤ 1, y = 1.

Answers

Answer 1

Since S is closed, you can use the divergence theorem, which says

[tex]\displaystyle\iint_S \vec F(x,y,z) \cdot \mathrm d\vec S=\iiint_R \mathrm{div}\vec F(x,y,z)\,\mathrm dV[/tex]

where R is the interior of the surface S.

We have

div F (x, y, z) = ∂/∂x (0) + ∂/∂y (y) + ∂/∂z (-z) = 1 - 1 = 0

so the flux would be 0.

Answer 2

In this exercise we have to calculate the flux by the divergent theorem:

The flux would be ZERO

Since S is closed, you can use the divergence theorem, which says:

[tex]\int\limits\int\limits_s {F(x,y,z} \, ds= \int\limits \int\limits\int\limits_R {divF(x, y, z)} \, dv[/tex]

where R is the interior of the surface S. We have:

[tex]\nabla F (x, y, z) = 1-1= 0[/tex]

so the flux would be ZERO.

See more about vectorial calculus at : brainly.com/question/6960786


Related Questions

Write each parabola in the form y−k=a(x−h)^2 and determine its vertex: y=−4x^2+16x−19

Answers

X = -b/2a
-16/2(-4) = 2
Substitute 2 into the equation
Y = -4(2)^2 + 16(2) - 19
Y = -16 + 32 - 19 = -3
Vertex = (2, -3)
Vertex form y+3=-4(x-2)^2

Find 3 consecutive odd integers such that 10 times the first is 59 more than the third?

Answers

Answer: The required three consecutive odd integers are 7, 9 , 11.

Step-by-step explanation:

Let x , x+2 , x+4 be the three consecutive odd integers.

As per given ,  

10(x) = 59+x+4

⇒10x= 59+x+4

⇒ 9x= 63

⇒ x= 7   [ divide both sides by 7]

Hence, the required three consecutive odd integers are 7, 9 , 11.

50% of trick or treaters dressed up as a ghosts.
You have seen 33 ghosts. How many trick or
treaters did you see in all?

Answers

Answer:

66

Step-by-step explanation:

50% = 1/2

33 x 2 = 66

The area of a square is 81 m ^ 2 what is the perimeter of the square? How do you know?

Answers

Answer:

The answer is 36m.

Step-by-step explanation:

So, first of all, you need to remember that the formula for the area of a square is x^2, or one side multiplied by another side. Also recall that in a square all sides are equal. This means that x^2=81. Now, the square root of 81 equals 9 (you should have this memorized by now). So, if each side of the square is 9, and  there are 4 sides, the perimeter would be 9*4, which is 36m.

The linear equation when b= 5 and m = -2 is O y = 5x – 2. Oy= 5x + 2. y = -2x - 5. O y = -2x + 5​

Answers

Answer:

y = -2x + 5

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define given

y-intercept b = 5

Slope m = -2

Step 2: Write function

y = -2x + 5

Math problem pls help I will give brainiest

Answers

Answer:

y=5

Step-by-step explanation:

125 +125+13y+9y=360

punch it into math-way.

250+22y=360

22y= 110

y=5

One day Clare runs 4 miles. The next day she
runs 50% of that. How far does she run in total?

Answers

Clare runs 2 miles. 6 miles total. 50% is also 1/2.

Answer:

She runs 6 miles in total.

the first six multiples of 6

Answers

6, 12, 18, 24, 30, 36

A taxi company charges $2.25 for the 1st mile and then $0.20 per mile for each additional mile, or F= $2.25+ $0.20 (m-1) where F is the fare and m is the number of miles. If Juan’s taxi fare is $7.65 ,how many miles did he travel in the taxi?

Answers

Answer:

28

Step-by-step explanation:

F=2.25+0.20(m-1)

7.65=2.25+0.20(m-1)

5.4=0.20(m-1)

5.4/0.20=0.20(m-1)/0.20

27=m-1

28=m

Earl runs 60 meters in 40 seconds. How many meters per second does Earl run?

Answers

Earl runs 1.5 meters per second.................

Find the area of the parallelogram.

Answers

Answer:

Step-by-step explanation:

Area of parallelogram = base * height

                                    = 3 * 3

                                    = 9 square units

Need help will mark Brainliest

Answers

I believe it is x=55. I could be wrong lol

Assuming the triangle adds up to 180°, x = 55 because 55 + 5 = 60. 60 x 3 = 180

0.3, 0.08, 0.003, 0.83
In order from smallest to largest

Answers

0.003, 0.08, 0.3, 0.83

Answer:

0.003, 0.08, 0.3, 0.83

-a^2b^2c^2(a+b-c) find the product

Answers

Answer:

-a^3b^2c^2-a^2b^3c^2+a^2b^2c^3

I hope it will be useful.

List all sets that -1/3 belongs to.

Answers

Answer:

dfffffffff

Step-by-step explanation:

xcdsw23456iu76

The triangles below are congruent and their corresponding parts are marked

Answers

∠A ≅ ∠Z

you can determine this by seeing that both angles have two curved lines, therefor showing they have the same measurement.

∠B ≅ ∠Y

you can also determine this by seeing that they both have one curved line showing that they share the same measurement.

∠C ≅ ∠X

once again, you can determine this by seeing that both angles are marked with three curved lines, meaning they share the same measurements.

line AB ≅ line ZY

just like before, you can determine that they are equivalent to each other by seeing that both lines have three dashes showing that they have the same measurement.

line AC ≅ line ZX

you can determine these lines are equivalent because they both have one dash showing they are the same length as each other.

line BC ≅ line YX

once again, both lines have two dashes, showing that they are equivalent in length.

ΔCAB ≅ XZY

you can determine this by seeing that all three angles and all three sides on both triangles share measurements with the other triangle

a pump can fill 2400 litres an hour and its replacement model can fill 2.5% more, how man litters an hour can the new model fill​

Answers

Answer:

2,460 liters per hour

Step-by-Step Explanation:

The problem above requires only two operations: multiplication and addition. First, you have to answer this question: How much is 2.5% of 2,400 liters?"

You may do this by multiplying 2,400 by 2.5%.

2,400 x 2.5% (0.025) = 60 liters (this is the amount that the new model can fill more than old model).

Then, you have to add 60 liters to 2,400 liters.

2,400 liters + 60 liters = 2,460 liters

This means that the new model can fill 2,460 liters per hour.

Find the equation of the tangent line to y=sinx at x=2pie

Answers

Answer:

y = x - 2π

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

x₁ - x coordinate y₁ - y coordinate m - slope

Pre-Calculus

Unit Circle

Calculus

The definition of a derivative is the slope of the tangent line.

Derivatives of Trig Functions

sin(x) = cos(x)cos(x) = -sin(x)tan(x) = sec²(x)sec(x) = sec(x)tan(x)csc(x) = -csc(x)cot(x)cot(x) = -csc²(x)

Step-by-step explanation:

Step 1: Define

y = sinx

x = 2π

Step 2: Find Derivative

Take derivative:                   y' = cosx

This is the function of the tangent line for y.

Step 3: Find slope

Substitute in x into y':                    y'(2π) = cos2πEvaluate:                                        y'(2π) = 1

This tells us that the slope of the tangent line is 1 at x = 2π.

Step 4: Write equation

Find a point.

Substitute x into y:                     y(2π) = sin2πEvaluate:                                    y(2π) = 0Write coordinate:                      (2π, 0)

Write tangent function.

Substitute:                    y - 0 = 1(x - 2π)Simplify:                        y = x - 2π

This is the equation of the tangent line at x = 2π.

Please help!
Thanks in advance.

Answers

Answer:

y = (1/4)x + 5/2

Step-by-step explanation:

The lines slope needs to be opposite of the equation's so its positive (1/4)

This is the only slope listed that is that number so no need to calculate for the y value!

Write the slope intercept form of the equation of the line through the given point with the given slope

Through: (-2,1), slope = -3

Answers

Slope form: y= mx + b
Plug it in: y = -3x + b
1 = -3(-2) + b
1 = 6 + b
b = -5
Final equation: y = -3x -5

What Is 55 > -7x + 6 ?

Answers

Answer:

x>−7

Step-by-step explanation:

55−6>−7x

49>−7x

​7

​49

​​ <x

−7<x

x>−7

PLEASEEEE HELPPP MEEE :(

Answers

Answer:

Question 5 is B

Because after I simplified I got B and its the only one that makes sense.

if a coin is flipped 3 times, how likely are you to get tails 3 times in a row​

Answers

Answer:

Suppose you have a fair coin: this means it has a 50% chance of landing heads up and a 50% chance of landing tails up. Suppose you flip it three times and these flips are independent. What is the probability that it lands heads up, then tails up, then heads up? So the answer is 1/8, or 12.5%.

Step-by-step explanation:

Let u = 2i + 3j, v=-i, and w = 5i – 6j. What is the magnitude of 2(u - V + w)?

•10.0
•13.4
•17.1
•21.6

Answers

Answer:

B. 17.1

Step-by-step explanation:

Edge 2020. Hope this helps.

The magnitude of 2(u-v +w) is √292.

The given vectors are u = 2i + 3j, v=-i, and w = 5i – 6j.

We need to find the value of 2(u-v+w).

How to find the magnitude of vector?

The formula to determine the magnitude of a vector (in two-dimensional space) v = (x, y) is: |v| =√(x²+ y²). This formula is derived from the Pythagorean theorem.

Now, 2(2i + 3j-(-i)+5i-6j)

=2(2i+3j+i+5i-6j)

=2(8i-3j)=16i-6j

The magnitude of 16i-6j=√16²+6²=√256+36=√292

Therefore, the magnitude of 2(u-v +w) is √292.

To learn more about the magnitude of vectors visit:

https://brainly.com/question/24256726.

#SPJ2

Please I need help and I give brainliest thank you!!

Answers

Answer:

i believe it is x=4

Step-by-step explanation:

10x+7=12x-1

7=12x−1−10x

8=2x

divide

x=4

if you had to express a typical NBA player's salary with a single number (round to the nearest 100000) you would use

Answers

Answer:

wat

Step-by-step explanation:

4. Verify that the functions fand g are inverses of each other by showing that
f(g(x)) = x and g(f(x)) = x.

F(x)=2x-3/x+4
g(x) = 3+4x/2-x

Answers

Answer and step-by-step explanation:

We just have to apply one function in the other one. See:

→ f(g(x)):

[tex]f(x) = \dfrac{2x-3}{x+4}\\\\f(g(x)) = \dfrac{2g(x)-3}{g(x)+4} = \dfrac{2\cdot\dfrac{3+4x}{2-x}-3}{\dfrac{3+4x}{2-x}+4}\\\\f(g(x)) = \dfrac{\dfrac{6+8x}{2-x}-3}{\dfrac{3+4x}{2-x}+4}\\\\f(g(x)) = \dfrac{\dfrac{(6+8x)-3(2-x)}{2-x}}{\,\,\,\dfrac{(3+4x)+4(2-x)}{2-x}\,\,\,}=\dfrac{(6+8x)-3(2-x)}{(3+4x)+4(2-x)}\\\\f(g(x)) =\dfrac{6+8x-6+3x}{3+4x+8-4x}=\dfrac{11x}{11}\\\\\\\boxed{f(g(x)) = x}[/tex]

→ g(f(x)):

[tex]g(x) = \dfrac{3+4x}{2-x}\\\\g(f(x)) = \dfrac{3+4f(x)}{2-f(x)} = \dfrac{3+4\dfrac{2x-3}{x+4}}{2-\dfrac{2x-3}{x+4}}\\\\g(f(x)) = \dfrac{3+\dfrac{8x-12}{x+4}}{2-\dfrac{2x-3}{x+4}}\\\\g(f(x)) = \dfrac{\dfrac{3(x+4)+(8x-12)}{x+4}}{\,\,\,\dfrac{2(x+4)-(2x-3)}{x+4}\,\,\,}=\dfrac{3(x+4)+(8x-12)}{2(x+4)-(2x-3)}\\\\g(f(x)) =\dfrac{3x+12+8x-12}{2x+8-2x+3}=\dfrac{11x}{11}\\\\\\\boxed{g(f(x)) = x}[/tex]

What verifies that f and g are inverses of each other.

Q.E.D.

Write the standard form of the line that has a slope of −3/4 and y-intercept of −2. Include your work in your final answer.

Answers

First let’s write it in slope intercept form
Y=Mx+b —-> Y=-3/4x-2

Then we can put it in standard form
Ax+By=C

We move the x to the other side
3/4x+y=-2

And that’ll be your answer :)

*if Ax it’s not positive you will have to multiply by -1*

Help Please I really need help!

Answers

400+60x

because the flat rate will stay the same, depending on how many hours or labor is how much more money you will pay. 60 dollars per hour of labor

QUESTION 4 of 10: Market researchers often report discretionary income. Discretionary income is your disposable income minus your fixed
expenses. Your disposable income is $2,920. After you pay fixed expenses of rent, utilities, groceries, and a car payment, you have $900.
What percentage of your disposable income is discretionary?
a) 18%
b) 31%
c) 45%
d) 69%

Answers

Answer:31

Step-by-step explanation:

Answer:

b) 31 %

Step-by-step explanation:

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