Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's Theorem to evaluate the line integral
∫C 8y^2 x dx + 6x^2 y dy

Answers

Answer 1

Let D denote the region whose boundary is C. By Green's theorem,

[tex]\displaystyle \int_C 8y^2x\,\mathrm dx + 6x^2y\,\mathrm dy = \iint_D \frac{\partial(6x^2y)}{\partial x} - \frac{\partial(8y^2x)}{\partial y} \,\mathrm dx\,\mathrm dy \\\\ = \int_0^3 \int_0^3 (12xy-16yx)\,\mathrm dx\,\mathrm dy \\\\ = -4 \int_0^3 \int_0^3 xy\,\mathrm dx\,\mathrm dy = \boxed{-81}[/tex]


Related Questions

List the domain and range of the relation {(1, -9), (8,8), (0, -9), (8, 1), (1,9)}

Answers

Answer:

D={1, 8,0}

R={-9, 8,1,9}

Step-by-step explanation:

Here,

we, know, domain(D) =set of all first elements

thus, D={1,8,0}

again, range(R) =set of all second elements

thus R={-9,8,1,9}

Ken Ken 5x5 please help

Answers

Answer:

5x5= 25

Step-by-step explanation:

5+5+5+5+5= 25

In the number 6.253
(a) What is the place value of 2 ...................................................................
(b) What is the value represented by 5 ...................................................................

Answers

Answer:

place value of 2 is 100

Step-by-step explanation:

please brainleist my answer

Answer:

The place value of 2 in 6.253 is 200

Step-by-step explanation:

Place value of 2 is occurring in hundreds

a number is multipilied by 6, and that the sum is equal to the product of 2 and 19. find the number

Answers

Answer:

[tex]take \: the \: number = x \\ thenx \times 6 = 2 \times 19 \\ \\ 6x = 38 \\ x = \frac{38}{6} \\ x = 6.33 \\ thank \: you[/tex]

the numeral 16 is a _____ of 4 because it is the product of a given number sbd any whole number

Answers

Answer:

perfect square

Step-by-step explanation:

A perfect square is a number multiplied by itself:

16 = 4^2 = 4 * 4

how many inches is in 140 feet?​

Answers

Hey there!

The formula for feet to inches is to simply multiply the length value by 12.

So, multiply 140 by 12.

I believe your answer would be 1680 inches.

Hope this helps!

Have a great day!

Answer:

140 feet is 1680 inches. Don't forget to put your units in; your teacher may dock off points for forgetting to put in the unit.

Step-by-step explanation:

A foot is 12 inches, so you must multiply 140 by 12.

[tex]140\times12=1680[/tex]

Suppose Sofia is considering a 5-year loan for $6,000 at an interest rate of 7%. Use the table to complete the statements. Type the correct answer in each box. Round your answer to the nearest cent. Monthly Payment per $1,000 of Principal Rate 1 Year 2 Years 3 Years 4 Years 5 Years 6.5% $86.30 $44.55 $30.65 $23.71 $19.57 7.0% $86.53 $44.77 $30.88 $23.95 $19.80 7.5% $86.76 $45.00 $31.11 $24.18 $20.04 8.0% $86.99 $45.23 $31.34 $24.41 $20.28 8.5% $87.22 $45.46 $24.65 $24.65 $20.52 9.096 $87.45 $45.68 $31.80 $24.89 $20.76 Sofia's monthly payment would be $118.80 The total number of monthly payments that Sofia would make over the life of the loan is 60 finance charge on her loan would be $1,128.00​

Answers

a) The monthly payment for Sofia, who is considering the 5-year loan of $6,000 at an interest rate of 7%, would be $118.80.

b) The total number of monthly payments that Sofia would make for the 5-year loan of $6,000 at an interest rate of 7% is 60.

c) The total finance charge for Sofia, who is considering the 5-year loan of $6,000 at an interest rate of 7%, would be approximately $1,128.00.

How is monthly payment calculated?

The monthly payment to pay off a mortgage can be calculated using an online finance calculator as below.

Data and Calculations:

Loan amount = $6,000

Maturity period = 5 years

Interest rate = 7%

N (# of periods) = 60 months (5 years x 12)

Results:  

Monthly Payment = $118.81 ($34.02 + $84.79)

Mortgage Payment = $7,128.60 ($118.81 x 60)

Total of 60 Mortgage Payments $7,128.60

Total Interest = $1,128.60 ($7,128.60 - $6,000)

Monthly Amortization Schedule (for the first 3 months)

 Date Beginning Balance   Interest    Principal        Ending

                                                         Repayment    Balance

1 3/2022       $6,000.00             $35.00     $83.81       $5,916.19

2 4/2022         $5,916.19               $34.51     $84.30      $5,831.90

3 5/2022        $5,831.90              $34.02     $84.79      $5,747.11

Learn more about calculating monthly payments at https://brainly.com/question/24576997

Answer:

The table shows monthly payments for every $1,000 of principal borrowed. For a 5-year loan at 7%, the payment on a $1,000 loan would be $19.80.

So, for a loan of $6,000, the payment would be $19.80 × 6 = $118.80.

A 5-year loan will have 60 monthly payments since 5 × 12 = 60.

Multiply the monthly payment by 60 months to get the total amount paid on the loan:

$118.80 × 60 = $7,128.

To calculate the total finance charge, subtract the principal amount from the total amount paid on the loan:

$7,128 − $6,000 = $1,128.

Step-by-step explanation:

What is 1^2 + 0.1^2?

Answers

Answer:

1.01

Step-by-step explanation:

1^2= 1

0.1^2= 0.01

1+0.01=1.01

The answer of 1^2+0.1^2 is 1.01

I need help on this problem

36-12x/6

Answers

Hope it helps! If it is, Brainliest please!

Gabby recorded the number of points she scored in her first 7 Basketball games. Which box and wiskers is correct?

Answers

Answer:

There is no Image

So Instead

There should be the lowest extreme aka 0, and hights extreme (Whatever number is last) Then you've got average (The Middle) and n the middle of it is the median.

Combine Like Terms
1. What is the simplest expression equivalent to 2 - 11 + 18 - 20.x ?
-7-21x
7-19x
7+21x
-7+19x

Answers

Answer:

-9x+20

Step-by-step explanation:

simplify each of the following.
[tex](2 \sqrt{3 + \sqrt{2)}{2} [/tex]

Answers

Answer:

[tex] \sqrt{2} + 2 \sqrt{3} [/tex]

Step-by-step explanation:

Simplify

[tex]2 \sqrt{3 } + \sqrt[2]{2} [/tex]

➡️ [tex] = \sqrt{2} + 2 \sqrt{3} [/tex] ✅

There is one third of a cake shared equally between 5 children. How much of the cake does each child receive? Use the number line to help you.

Answers

Answer:

1/3÷5

=1/3×1/5

=1/15

each child receive 1/15 of cake

what is the smallest positive integer that can be doubled to get a perfect cube and tripled to get a perfect square

Answers

Its 1

Doubled:-

[tex]\\ \rm\longmapsto 1\times 1=1=1^3[/tex]

Tripled

[tex]\\ \rm\longmapsto 1\times 1\times 1=1=1^2[/tex]

Which of the following statements is false?
If a number is divisible by 8, it must be divisible by 4.
If a number is divisible by both 9 and 10, it is divisible by 90.
The sum of two consecutive odd numbers is always divisible by 4.
If a number is not divisible by both 3 and 4, it is divisible by 12.​

Answers

Answer:

The last one

Step-by-step explanation:

It doesn't make sense for that to be true

6. Solve for x: 23x+1 = 210
Please please give detailed steps!! thank you

Answers

Answer:

x = 3

Step-by-step explanation:

Given

[tex]2^{3x+1}[/tex] = [tex]2^{10}[/tex]

Since bases on both sides are equal, both 2, then equate the exponents

3x + 1 = 10 ( subtract 1 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

Choose a linear function for the line represented by the point-slope equation y - 5 = 3(x - 2).

Answers

f(x) = 3x - 1

Step-by-step explanation:

[tex]y - 5 = 3(x - 2) \\ y - 5 = 3x - 6 \\ y = 3x - 6 + 5 \\ y = 3x - 1[/tex]

Express the formula d = rt in terms of the time, t. Use your formula to find the time when the distance is 40 and the rate is 8.
A)t= 4; 1 = 5
B)t= ; t = 0.2
C)t = dr; t = 320
D)t = d-r; t = 32

Answers

Answer:

t = d/r; t = 5

Step-by-step explanation:

Hi there!

1) Isolate t

d = rt

Divide both sides by r

d/r = rt/r

d/r = t

t = d/r

2) Solve for t when distance is 40 and the rate is 8

t = d/r

Replace d with 40 and rate with 8

t = 40/8

t = 5

I hope this helps!

Maggie studied for 2/5 of an
hour. Julie studied for 1/4 of an
hour. How much longer did
Maggie study?

Answers

Answer: 3/20

Concept:

When encountering questions that ask for [how much longer A comparing to B], the basic operation would be the value of A subtracted by the value of B.

Solve:

Given information

Maggie study time = 2/5 hours

Julie study time = 1/4 hours

Given expression deducted from the concept

Maggie (study time) - Julie (study time)

Substitute values into the expression

2/5 - 1/4

Find the denominators' Least Common Multiple (LCM)

First five multiples of 5: 5, 10, 15, 20, 25

First five multiples of 4: 4, 8, 12, 16, 20

Since [20] is the first term that appears in both multiples, it would be the LCM of 4 and 5

Convert the fractions to common denominator

2/5 = (2 × 4) / (5 × 4) = 8 / 20

1/4 = (1 × 5) / (4 × 5) = 5 / 20

Simplify by subtraction

=8/20 - 5/20

=(8 - 5) / 20

=[tex]\boxed{\frac{3}{20} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

solve this equation 2(y + 2) = 3(y - 7)

Answers

Answer:

[tex]2(y + 2) = 3(y - 7) \\ 2y + 2 \times 2 = 3y - 3 \times 7 \\ 2y + 4 = 3y - 21 \\ y \: terms \: togther \\ 3y - 2y = 4 + 21 \\ y = 25[/tex]

[tex]thank \: you[/tex]

Which of the following is not a polynomial?
O A. 3x4
O B. x8+2x3 +7
O C. 5x10 - 4x8 + 2
O D. 5- x2 + 7x0

Answers

Answer:

C

Step-by-step explanation:

is not a polynomial because it has a negative exponent.

Yes it should be C hope this helps

What is the probability of getting tails on two coins only (there are 3 coins by the way)

Answers

Answer:

1/2

please mark me brainliest

Benchmark of 6/10, how do I get this worked out

Answers

Answer:

0.60 or 60% is the answer!

Step-by-step explanation:

Hope I helped

g(x) = sqr root of x+3

What is the domain of g?

Answers

Answer:

[tex]all \: real \: numbers \: except \: \\ x + 3 < 0 \\ \: \: \: \: x < - 3[/tex]

Answer:

X is the domain and sqr root of X+3 is the range.

is a graph with asymptotes discontinious?

Answers

Answer:

In order for the function to be discontinuous at an asymptote, the curve needs to exist on both sides of the asymptote. If the curve only exists on one side of the asymptote, then there's no discontinuity at that point.

Step-by-step explanation:

If a curve only exists on one side the asymptotes, there is no discontinuity. If it exists on both sides of the asymptotes, there is discontinuity.
Hope this helps, please give me brainliest:)

A.38°

B.136°

C.112°

D.92°

Answers

Answer:

Step-by-step explanation:

( C ). 112°

Plsssssssssssssssss help fast

Answers

Answer:

yes tht right pls mark me branilest

Your answer is correct.

Area of a trapezium=1/2×(upper base+lower base)×height
Area=1/2×(20+25)×15=337.5

Hope my answer helped u :)

whats 40 euros to usd?

Answers

Answer:

47.06 United States Dollar

[tex]\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}[/tex]

47.6 US Dollars

Hope it helpsThanks.

Given: 40,905; 40,509; 40,095; and 40,059, the correct arrangement of these numbers from the least to the greatest value is:

40,905; 40,509; 40,095; and 40,059.
40,059; 40,095, 40,509; and 40,905.
40,059; 40,095; 40,905; and 40,509.
40,095; 40,059; 40,509; and 40,905.
40,509; 40,905; 40,095; and 40,059.

Answers

Answer:

Step-by-step explanation:

40905

40509

50095

40059

Is greatest to least. You want it to go the other way around.

40059

40095

40509

40905

The smallest number is determined by the number on the right. Then your keep going left to get to the largest. The answer is the second one down.

Find the equation (in terms of x) of the line through the points (-3,0) and (4,5)​

Answers

Step-by-step explanation:

steps are in the picture above.

Note:if you need to ask any question please let me know.
Other Questions
A(-2,3)Triangle ABC has vertices at A(-2,3), B(-3,6), andC(2,-1) Is triangle ABC a night triangle? If so, whichangle is the night angle?O No, the triangle has no right angles.O Yes, the right angle is angle AO Yes, the right angle is angle BO Yes, the right angle is angle CVAC (2-1)B (-3,-6) While Ana finishes her homework, Alex takes out the trash and feeds the cats. 6. Solve for x: 23x+1 = 210Please please give detailed steps!! thank you A.38B.136C.112D.92 Mr. Jones took a survey of college students and found that 60 out of 64 studentsare liberal arts majors. If a college has 7505 students, what is the expectednumber of students who are liberal arts majors? 16) Label each sentence with its sentence pattern; Noun-Verb (N-V), Noun-Verb-Noun (N-V-N), Noun-Linking Verb-Noun (N-LV-N) or Noun-Linking Verb-Adjective. (N-LV-Adj.). Which of the three physical regions in South America is Brazil in? how did farming negatively impact the lives of everyday people If (px + 5)(qx + 3) = 8x2 + rx + 15 for all values of x,and p + q = 6, what are the two possible values for r? help ---------------------------------------------- The reaction X - Y has a reaction enthalpy of - 64 kJ moJ-1 and an activation energy of 22 kJ moJ^-1. What is the activation energy for the y -> x reaction? 5) List two adverbs that describe another soldier's response when he hears this rumor. Look inthe fifth paragraph of the excerpt. Is this sentence correctly punctuated: "Can't we go into the house?" He asked. "I'm feeling very cold." If it's wrong write the correctly punctuated sentence. 2. To be safe while doing science, you should learn the meaning ofsymbols. Gabby recorded the number of points she scored in her first 7 Basketball games. Which box and wiskers is correct? Select all ratios equivalent to 6:3. Plz help me with this binary division whith full process/explanation 1001010 101 How goal succession takes place? Explain the conditions responsible for goal succession. Pringle's variety pack 18 cups for $6.48 cost per cup The country best known for the state approach in the 1980s, where the government played a central role in economic decision-making was: