Mathematics High School

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above.
F(x, y, z) = xyi + 5zj + 7yk, C is the curve of intersection of the plane x + z = 8 and the cylinder x2 + y2 = 9.

Answers

Answer 1
 ∫c F · dr 
= ∫∫s curl F · dS, by Stokes' Theorem 
= ∫∫ <2, 0, -x> · <-z_x, -z_y, 1> dA 
= ∫∫ <2, 0, -x> · <1, 0, 1> dA, since z = 2 - x 
= ∫∫ (2 - x) dA. 

Since the region of integration is inside x^2 + y^2 = 9, convert to polar coordinates: 
∫(r = 0 to 3) ∫(θ = 0 to 2π) (2 - r cos θ) * (r dθ dr) 
= ∫(r = 0 to 3) (2 * 2π - 0) * r dr 
= 2πr^2 {for r = 0 to 3} 
= 18π. 

Related Questions

4x^2+4y^2=64
what are the domain and range

Answers

Use a graphing tool and you'll see a circle form. This circle has a center of (0,0) and radius of 4. Side note: this equation is equivalent to x^2+y^2 = 16 after you divide everything by 4

Looking at the graph, the smallest x can be is -4. The largest x can be is 4. So the domain in interval notation is [tex][-4,4][/tex]

Similarly the range in interval notation is also [tex][-4,4][/tex] because the lowest you can go is y = -4. The highest you can go is y = 4

what is another name for plane Z?

Answers

Other names for "plane Z" include:
___________________________
1) The "z-plane"; 
___________________________
2) The "complex plane";
___________________________
3) the "domain of the z-transform"
_____________________________

Which answer describes the type of sequence?

1, 6, 7, 13, ...

A. geometric

B. neither arithmetic nor geometric

C. arithmetic

Answers

b: neither arithmetic nor geometric


The given sequence describes the type of sequence that is neither arithmetic nor geometric. which is the correct answer would be an option (B).

What is an arithmetic sequence?

An arithmetic sequence is defined as an arrangement of numbers that is a particular order.

The sequence is given in the question following as:

1, 6, 7, 13, ...

We have to identify the type of given sequence

As per the given question, we have

1, 6, 7, 13, ...

For checking as an arithmetic sequence :

Common difference between 1 and 6 is d = 6 - 1 = 5

Common difference between 6 and 7 is d = 7 - 6 = 1

Since the common difference between consecutive terms is not the same, this means it's not an arithmetic sequence.

For checking as a geometric sequence :

Common ratio between 1 and 6 is r = 6/1 = 6

Common ratio between 6 and 7 is r = 7/6

Since the common ratio between consecutive terms is not the same, this means it's not a geometric sequence

Thus, the given sequence describes the type of sequence that is neither arithmetic nor geometric.

Learn more about arithmetic sequence here:

brainly.com/question/21961097

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Perform the operations, multiply, and simplify.-a^3b (3a^2 b^5 - ab^4 - 7a ^2
b.

Answers

I hope this helps you



3a^5.b^6-a^4.b^5-7a^5.b

for the parallelogram, if m<2+5x-28 abd m<4=3x-10, find m< 3. ...?

Answers

Final answer:

After finding the value of x by equating m<2 and m<4, we calculate m<4 and then use the property of supplementary angles in a parallelogram to find that m<3 is 163 degrees.

Explanation:

To solve for m<3 in the parallelogram with m<2 = 5x - 28 and m<4 = 3x - 10, we first find the value of x. Given that opposite angles in a parallelogram are equal (m<2 = m<4), we set the two equations equal to each other and solve for x:

5x - 28 = 3x - 10

5x - 3x = 18

2x = 18

x = 9

Now that we have the value of x, we can substitute it into the equation for either angle to find the measure of that angle. Since m<4 = 3x - 10:

m<4 = 3(9) - 10 = 27 - 10 = 17

In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, to find m<3, we subtract m<4 from 180 degrees:

m<3 = 180 - m<4

m<3 = 180 - 17 = 163

Thus, m<3 in the parallelogram is 163 degrees.

Final Answer:

The measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 2x - 18 \).[/tex]

Explanation:

In a parallelogram, opposite angles are equal. Therefore, we can set up an equation based on the given angle measures:

[tex]\[ m\angle 2 + m\angle 3 = 180^\circ \][/tex]

Substitute the given expressions for[tex]\( m\angle 2 \) and \( m\angle 4 \):[/tex]

[tex]\[ (2 + 5x - 28) + (3x - 10) = 180 \][/tex]

Combine like terms:

[tex]\[ 5x + 3x - 28 - 10 + 2 = 180 \][/tex]

[tex]\[ 8x - 36 = 180 \][/tex]

Add 36 to both sides:

[tex]\[ 8x = 216 \][/tex]

Divide by 8:

[tex]\[ x = 27 \][/tex]

Now that we have the value for x, substitute it into the expression for \( [tex]m\angle 3 \):[/tex]

[tex]\[ m\angle 3 = 2(27) - 18 \][/tex]

[tex]\[ m\angle 3 = 54 - 18 \][/tex]

[tex]\[ m\angle 3 = 36 \][/tex]

Therefore, the measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 36^\circ \).[/tex]

When you multiply or divide an inequality by a ______ number, you must flip the inequality symbol.

Answers

When you multiply or divide an inequality by a negative number, you must flip the inequality symbol.

Write a proportion that can be used to find the cost of 10 notebooks if 3 notebooks cost $1.98.

Answers

The solution to the problem is as follows:


For 3 notebooks you pay $1.98 so the ratio is 1:0.66.
For 10 notebooks, then we could scale the ratio and it will become 10:6.60. So they will cost you $6.60.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

In ELECTRONICS, the total resistance to the flow of electricity in a circuit is called the impedance, Z. Impedance is represented by a complex number. The total impedance in a series circuit is the sum of individual imepedances. The impedance in one part of a circuit is Z1 = 3 + 4i. In another part of a circuit, the impedance is Z1 = 5 - 2i. What is the total impedance of the circuit?

Answers

Total impedance of circuit is Z1 + Z2

Here it is important that real numbers we sum with real numbers and complex numbers with complex numbers

Let Zs represent total impedance.

Zs = Z1 + Z2 = 3 + 4i + 5 - 2i = 3 + 5 + 4i - 2i = 8 + 2i

Answer is :

8+2i
Final answer:

The total impedance of the circuit is 8 + 2i.

Explanation:

The total impedance in a series circuit is the sum of the individual impedances. To find the total impedance of the circuit, add the real parts and imaginary parts separately. In this case, Z1 = 3 + 4i and Z2 = 5 - 2i. So, the total impedance Zt = (3 + 5) + (4 - 2)i. Simplifying this, Zt = 8 + 2i.

Solve the inequality.

p – 9 < –9

Answers

I hope this helps you




p-9 < -9


p-9+9 < -9+9


p <0

Crafty Grandma Edith sat her family down during Thanksgiving and told them they couldn’t have any pumpkin pie until they worked out this puzzle. Her 6-year-old granddaughter was the first to solve it! Can you work out what 9183 equals?

8809=6
7111=0
9881=5
6660=4
5531=0
2516=1
3590=2
6855=3
1012=1
5731=0
9191=2
9183=?

Answers

Here is the answer of the given question above. According to the puzzle given by Crafty grandma Edith, which was answered by her 6-year-old granddaughter during their thanksgiving gathering, the correct answer of 9183 would be number 3. Hope this is the answer that you are looking for. Thanks for posting!

A movie store sells DVDs for $11 each. What is the cost of n DVDs? Identify the situation as discrete or continuous.
A) C= 11n; continuous
B) C= 11+n; discrete
C) C= 11+n; continuous
D) 11n; discrete

Answers

d is the answer discreate

Answer:

Complete Quick Check of...

Lesson 4: Graphing a Function Rule

Algebra 1 A: Unit 5

Step-by-step explanation:

1.C) x,0,1,2,3, y,3,-1,-5,-9

2.A) True

3.D) $698.75

4.C) cant write it out.

5.D) C = 11n; discrete

:) hope this helps!

Transform the formula for the given variable: I=Prt solve for t

Answers

It would be I/Pr=t. All you must do is divide both sides by Pr.

An increase in total assets can be financed by an increase in which of the following capital components:


a. debt

b. preferred stock

c. common equity

d. All of the above ...?

Answers

An increase in total assets can be financed by an increase debt, preferred stock and common equity. So the answer is d. All of the above.

Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .

Answers

D. There are more variations in the scores for 4th hour because the mode(repeating) is 16

Tina lives in a state that charges her 4.5% state income tax on her federal taxable income. If her federal taxable income is $61,600, how much does Tina pay in state income tax?

a. $1,545

b. $227

c. $4,372

d. $2,772

Answers

4.5% of 61,600

0.045(61,600) = 2772
61600*(4.5/100)=2772........

At the bank brent exchanges $50 in bills for 50 one-dollars coins. the total mass of the coins is 405 grams. estimate the mass of 1 one - dollar coin.

Answers

8 as you round up 405 to 400 and divide by 50 and get 8
The mass of each coin will be 8.1

determine the differential equation giving the slope of the tangent line at point (x,y) for the given family of curves.
x^2+y^2=2cx ...?

Answers

From Mathematica:DSolve[y′[x]=(y[x]2−x2)2xy[x],y[x],x]{{y[x]→−−x2+xC[1]−−−−−−−−−−√},{y[x]→−x2+xC[1]−−−−−−−−−−√}}Take the second solution and square each side:y[x]2=−x2+xC[1]Move the -x^2 from the RHS to the LHS.y[x]2+x2=xC[1]If the same procedure is applied to my answer then the following is the result:y[x]2+x2= 2cx+2C[1]where C[1] is zero. I am not sure that their expression is totally correct.

A circle has an area of 98mm^2. Find the circumference of the circle

Answers

circumfrence of the circle is
35.1

Hope this helps =]

Solve 16 1/2 ÷ 2 1/4

A:7 1/3

B:5 3/7

C:133/8

Answers

(16 1/2) / (2 1/4) =
(33/2) / (9/4) =
33/2 * 4/9 =
132/18 =
7 1/3 <==

At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?

a. x + y < 12
b. x + y > 12
c. x + y ≤ 12
d. x + y ≥ 12

Answers

the answer is:
x + y > 12

The sign is greater (>) because it says "she bought more than. The sign isnt "equal and greater" because once again she says she bought more and it doesnt say she bought at least...

the answer is B hope it helps

your weekly wage is $400 what is your annual?

Answers

400 times 52 equals 20800
28000
$400 x 52 = $28000



A box has a width 9 inches less than its height and a length 7 inches more than its height.
a. If h is the height of the​ box, write a polynomial that represents the volume of the box.
b. Use this polynomial to calculate the volume for h​ = 17 inches.

Answers

So everything in this problem is in terms of height (h). We'll abbreviate width to w and length to l and volume to v

l=h+7
w=h-9

a.
volume is height x width x length

v=h*(h+7)*(h-9)

now we have to multiply these values

h*(h+7)=h^2+7h

(h^2+7h)*(h-9)=h^3-9h^2+7h^2-63h=h^3-2h^2-63h

b.
now we plug in h=17
v=17^3 -2(17)^2 -63(17) = which comes out to 2686

note: **i suggest going through these steps on your own mostly because it's late and i'm tired and that seems like an awfully large number so you may want to check it

If 6 is 24% of a number, what is 40% of the same number?

(A) 8
(B) 10
(C) 15
(D) 20

Answers

the answer is 10.the unknown number is 25.

To find 40% of the number where 6 is 24%, we first determine the whole number by dividing 6 by 0.24 to get 25. Then we calculate 40% of 25, which is 10.

If we know that 6 is 24% of a number, we can find the whole number by dividing 6 by 0.24. Once we have the full number, we can calculate 40% of it. Let's do the calculation step by step.

Calculate the whole number using the given percentage: Whole number = 6 / 0.24.

Perform the division to find the whole number: Whole number = 25.

Calculate 40% of the whole number: 40% of 25 = 0.40 * 25.

Perform the multiplication to find 40% of the number: 40% of 25 = 10.

Therefore, 40% of the same number is 10.

"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.)
f (x) = cos(πx/2)

Answers

Answer: The derivate is f'(x) = -sin(πx/2)*(π/2)

Step-by-step explanation:

We want the value of the derivate at each point marked:

As you may know, the derivate of cos(x) is equal to -sin(x)

And in our case:

f(x) = cos(πx/2)

f'(x) = -sin(πx/2)*(π/2)

Where the rule used is that the derivate of f(g(x)) is equal to f'(g(x))*g'(x)

Now, as you may see, in both the marked points the curve changes of direction, so the tangent line in that point must be zero, letsinput the values of x in the derivate and see if this is true:

f'(0) = -sin(π*0/2)*(π/2) = -sin(0)*(π/2) = 0

f'(2) = -sin(π*2/2)*(π/2) = -sin(π)*(π/2) = 0

So this makes sense.

3^x : write in terms of base e and simplify! ...?

Answers

3^x : write in terms of base e would 

3x=e^ln3^x

 =e^xln3
The given function is exponential. Meanwhile [tex]<b>change of base</b>[/tex] has something to do with logarithms. So we convert the function to logarithm function, change to the required base and convert back to exponential function.

Let

[tex]y = {3}^{x} [/tex]

Writing the above exponential equation as a logarithmic equation, we obtain;

[tex] log_{3}(y) = x[/tex]

We can apply the change of base formula to obtain,

[tex] \frac{ log_{e}(y) }{ log_{e}(3) } = x[/tex]

Or

[tex] \frac{ ln(y) }{ln(3) } = x[/tex]

We can cross multiply to obtain;

[tex] ln(y) = x ln(3) [/tex]

Taking logarithm of both sides to base e, we obtain;

[tex] {e}^{ ln(y) } = {e}^{x ln(3) } [/tex]

This implies that,

[tex]y= {e}^{x ln(3) } [/tex]
But we know that,
[tex]y = {3}^{x} [/tex]
Hence
[tex] {3}^{x} = {e}^{x ln(3)} [/tex]

can u show work 39472/78 ...?

Answers

We will use long division:
78 x 5 = 390
Subtracting, then bringing down 7
47 is smaller than 78 so
78 x 0 = 0
Bringing down 2, we get 472
78 x 6 = 468
Subtracting, the remainder is 4

The answer is 506 with a remainder of 4.

what is the answer to n * $3.25 = 325.00 ?

Answers

N is going be 100.
let's solve your equation step-by-step

n(3.25)=325

Step 1: Simplify both sides of the equation

3.25n=325

Step 2: divide both side by 3.25

3.25n/3.25=325/3.25

n=100

Three water pipes are used to fill a swimming pool. The 1st pipe alone takes 8 hours to fill the pool, the 2nd pipe alone takes 12 hours to fill the pool, and the 3rd pipe takes 24 hours to fill the pool. If all 3 pipes are opened at the same time, how long will it take all 3 together to fill the pool?

Answers

For 4 h. The first pipe fills the whole pool for 8 hours so from here we see that it fills 1/8 each hour. The second pipe fills it for 12 hours so it fills 1/12 each hour. The third pipe fills it for 24 hours so it fills 1/24 each hour. Now the three of them together fill 1/8 + 1/12 + 1/24 of the pool each hour. That equals: 1st pipe 3/24 of the pool each hour, the 2nd pipe 2/24 of the pool each hour and the 3rd 1/24 each hour. So, the three pipes together fill 3/24 + 2/24 + 1/24 each hour. That's 6/24 of the pool each hour.
1st hour: 6/24
2nd hour: 12/24
3rd hour: 18/24
4th hour: 24/24


Simplify -3p3 + 5p + (-2p2) + (-4) - 12p + 5 - (-8p3). Select the answer in descending powers of p.


1 - 7p - 2p2 + 5p3
5p3 - 2p2 - 7p + 1
1 + 7p + 2p2 - 5p3
-5p3 + 2p2 + 7p + 1

Answers

The answer is 5p³ - 2p² - 7p + 1 

-3p³ + 5p + (-2p²) + (-4) - 12p + 5 - (-8p³)
= -3p³ + 5p - 2p² - 4 - 12p + 5 + 8p³ 
= 8p³ - 3p³ - 2p² + 5p - 12p - 4 + 5
= 5p³ - 2p² - 7p + 1 

Answer:

B. 5p³ - 2p² - 7p + 1

Step-by-step explanation:

Good luck! Hope it was found helpful to you!

The folding chair has different settings that change the angles formed by its parts. Suppose m2 is 34 and m3 is 76. Find m1The diagram is not to scale.
A. 130
B. 110
C. 100
D. 120

Answers

the answer is

first, the sum of angles in triangle is always  180°
so mx + m2 +m3 = 180°, so mx=1800-76-34=70°
but according to the figure m1 + mx=180°, so m1=180-mx=180-70=110°

the m1 = 110°


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