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

Factor 2x² + 13x + 20​

Answers

Answer:

(2x+5)(x+4)

Step-by-step explanation:

9514 1404 393

Answer:

  (x +4)(2x +5)

Step-by-step explanation:

To factor this, you look for factors of 2·20 = 40 that have a sum of 13.

The factor pairs of 40 are ...

  40 = 1·40 = 2·20 = 4·10 = 5·8

The sums of these factor pairs are 41, 22, 14, 13. The last one is the one we want.

There are several ways to use this factor pair. One of the more straightforward methods is to rewrite the middle term as a sum using these numbers:

  2x² +5x +8x +20

  = x(2x +5) +4(2x +5) . . . . . factor pairs of terms

  = (x +4)(2x +5) . . . . . . . . . factor out the common factor


2
5

y=
\,\,-11
−11

Answers

gbaijwghwugaggaufgwhhsuhwkhsiw

How do I answer this?

Answers

Answer:

Step-by-step explanation:

43 + 39 + <1 = 180                    Three angles make up a triangle of 180 degrees.

82 + <1 = 180                            Subtract 82 from both sides

<1 = 98

<2 = <1                                      They are vertically opposite

<2 = 98

The solution to an inequality is represented by the number line

Answers

Yes inequality is represented in number line

The product of 2 more than 5 times a number and 4 less than three times a number

Answers

Sorry I'm not sure if I'm right just my thinking...

set the number to be x so that (5x+2)(3x-4)??

how many numbers of four different digits can be formed from the integers 0,2,4,5,6. ​

Answers

Answer:

420 even numbers

Step-by-step explanation:

Answer

Total 4 digit even numbers = (Total even numbers) - (Total 3 digit even numbers)

Total even numbers: 4⋅6⋅5⋅4=480

Total 3-digit even numbers: 3⋅5⋅4⋅1=60

Total 4-digit even numbers: 480−60=420 ??

Step-by-step explanation:

A circle has a diameter of 6, an area of b square units, and a circumference of c units. What is the value of b + c ?

Answers

Answer:

Step-by-step explanation:

Diameter = 6 units

Radius = Diameter/2 = 6/2 = 3 units

Taking π=3.14

Circumference = 2(π)(r) = 2(3.14)(3) = 6(3.14) = 18.84 = c

c = 18.84

Area = π(r)^2 = π(3)^2 = 9π =9(3.14) = 28.26 = b

b = 28.26

So,

b + c = 28.26 + 18.84 = 47.1

Answer:

b=6π the unit(cm)

c=18.84 the unit(cm)

b+c=

9+18.84=27.84

Step-by-step explanation:

circumference=c

diameter=d

radius=r

area=b

d=2r

6=2r

6=r

2

r=3

b=πr^2

b=3×3π

=9π

c=2πr

=2(3.14)3

= 3.14×6

=18.84

Find the HCF of the following by long divosiin method 102,68,136​

Answers

Answer:

102=2*3*17

68=2*2*17

136=2*2*2*2*17

The common prime factors are 2 and 17

Highest common factor (HCF)=2*17=34

Hope it helps you.
For 108 it’s factors are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108.
For 68: 1, 2, 4, 17, 34, and 68
For 136: 1, 2, 4 , 8, 17, 34, 68, and 136.

So my answer I think is: 68

1. View The Truth Behind the Golden Ratio video (https://youtu.be/92ZiDsOf2z0)

for additional examples of
the Golden Ratio. Select your favorite example from the video (or your own
research) and explain why this specific example is so interesting to you.
(Possible keywords: the golden ratio + in nature, + in art, + in the human
body, + in geometry).

2. Now that you know more about the Golden Ratio, do you believe its
common presence shows evidence of a grand design within the universe or
is it simply a coincidence? Explain why you feel that way.

3. How does this topic reinforce or change your belief about the application of
math to your daily life?

Answers

According to the the video, the Golden Ratio is a figure in mathematics theorized by mathematicians as a value that indicates natures beauty symmetry

[tex]\mathbf{The \ value\ of \ the \ Golden \ ratio \ is \ \phi} = \mathbf{\dfrac{1 + \sqrt{5} }{2} }[/tex]

Good examples of the Golden Ratio in art and architecture is the Great Pyramid of Giza, constructed in 2570 B.C. and the temple of Parthenon for which construction began in 447 BC and the decoration completed in 432 BC

The reason the temple of Parthenon is so interesting is that the temple just like the pyramid were meant to last indefinitely, such that they can only be made to last so long by the deities, as such by building using the Golden Ratio found in nature including the spiral galaxies, is in recognition of nature's beauty which is aesthetically pleasing to the eyes, harmonious, and maybe preservative

2. The common presence of the Golden Ratio in the universe can be seen as both a grand design and a coincidence, however, due to the higher prevalence than random occurrence, it can be taken as a design that can be observed in nature

3. The topic helps reinforce the belief in the application of math to daily life, because it is a good portrayal of how math can contribute to all aspect of human life

Learn more about the Golden Ratio here:

https://brainly.com/question/20730582

https://brainly.com/question/22904993

https://brainly.com/question/15895546

Answer:

Step-by-step explanation:

for additional examples of the Golden Ratio. Select your favorite example from the video (or your own research) and explain

why this specific example is so interesting to you. (Possible keywords: the golden ratio + in nature, + in art, + in the human body, + in geometry).

Find the missing value.
Hint: Use the number line to find the missing value.
-4=
-9
-15
-10
-5
0
5
10
15
Stuck? Review related articles/videos or use a hint.

Answers

Answer:

-4 = 5 - 9

Step-by-step explanation:

-4 = ? - 9

Add 9 to -4

5

The result of -4 = ? - 9 is 5

-4 = 5 - 9

-4 = -4



(20 points) please help

Answers

Answer: The antonym of multiply is divide.

Answer:

Divide

Step-by-step explanation:

Antonym simply means the opposite of the given word.

So the opposite of multiplication is division thus division is the answer.

HOPE THIS HELPED

BRAINIEST TO WHOEVER RIGHT

Answers

Answer:

(-6,6)

Step-by-step explanation:

Find the value of x 3(4x+3)

Answers

3(4x+3)=12x+9

i don't know what do you need,

if roots, let 12x+9=0

the root is x=-3/4

what is the following sum in simplest form? /8+3/2+/32

Answers

Answer:

C

Step-by-step explanation:

4. If A. 35
B.180
C.125
D.55

Answers

Answer:

C

Step-by-step explanation:

z=x as they are alternate angles and x=o as they are alternate exterior angles

Which statement about the function is true?
The graph of the function f(x) = -(x + 3)(x - 1) is shown
below.
6
NA
O The function is positive for all real values of x where
x < -1.
The function is negative for all real values of x
where
x < -3 and where x > 1
The function is positive for all real values of x where
x>0
The function is negative for all real values of x
where
X<-3 or x>-11
+
6
4
2
4
6
x
-2
-2
4
-6-
-
Mark this and retum
Save and Exit
Next
Submit

Answers

9514 1404 393

Answer:

  (b) The function is negative for all real values of x where x < -3 and where x > 1

Step-by-step explanation:

It is pretty easy to tell from the graph that the function is negative for x < -3 and for x > 1.

The product of 9 and 4 is divided by 6 .Make mathematical expressions and simplify​

Answers

Answer:

The answer is 6

Step-by-step explanation:

9×4/6

=36/6

=6.

Is a measure of 24 inches "far away from a mean of 16 inches? As someone with knowledge of statistics, you answer it depends" and request the standard deviation of the underlying
data
(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 24 inches from 16 inches?
(b) Is 24 inches far away from a mean of 16 inches?
(c) Suppose the standard deviation of the underlying data is 5 inches. Is 24 inches far away from a mean of 16 inches?
(a) 24 inches is
standard deviation(s) away from 16 inches.
ne doimal olan
nondad)

Answers

Answer:

I really need points plsss

Step-by-step explanation:

The maxwell family goes out for dinner and the price of the meal is $60 the sales tax on the meal is 7% and they also want to leave a 15% tip what is the total cost of the meal

Answers

So we start with the $60 untouched.

Then we add the tax which is $60•0.07= 4.20 that is the tax

Then add the tax to the total $60 + $4.20= $64.20

Next we must add the tip so $60•0.15= 9.

Then $64.20 + $9.00 = $73.20

Total cost of meal $73.20

Any questions? :)

Answer: $ 73.20

Step-by-step explanation:

60+(60*0.07)+(60*0.15)=73.2

If a set S has a total of 6 subsets that consist of 2 members each, then S consists of how many members

Answers

A set S has four members if there are six subsets of it, each with two members.

The combination formula, which is given by: can be used to determine the total amount of subsets with two members each.

[tex]^nC_k= \dfrac{n!}{(k!(n-k)!)}[/tex]

There are 6 subsets in this situation, each with 2 members.

So, [tex]^nC_2[/tex] = 6

Simplifying the equation:

n! / (2!(n-2)!) = 6

n(n-1) / (2 x 1) = 6

n(n-1) / 2 = 6

n(n-1) = 12

Expanding the equation:

[tex]n^2 - n = 12[/tex]

[tex]n^2 - n - 12 = 0[/tex]

Factoring the quadratic equation:

(n - 4)(n + 3) = 0

When all factors are set to zero and n is calculated:

n - 4 = 0    or    n + 3 = 0

n = 4        or    n = -3

Since n must be a positive integer.

So, n = 4 is the valid solution.

Thus, set S consists of 4 members.

Learn more about Combination here:

https://brainly.com/question/28720645

#SPJ12

Devaughn is 6 years younger than Sydney. The sum of their ages is 46 . What is Sydney's age?

Answers

52

if im wrong, sorry

if im right, yay

6 tables or 8 chair cost Rs 2400.What will 24 tables and 12 chairs cost?​

Answers

Step-by-step explanation:

cost of 1 table=2400/6=rs.400

or ,cost of 1 chair=2400/8=rs.300

now,

cost of 24 tables=24×400=9600

or,cost of 12 chairs=12×300=3600

or,

may be the question is,

6tables + 8 chairs= 2400

24 tables + 12 chairs=?

solution,

cost of 1 tables=rs.200

cost of 1 chair=rs.150

now,

cost of 24 tables=200×24=4800

cost of 12 chairs=150×12=1800

so, ans= 4800+1800=6600

Answer:

Rs.13200

Step-by-step explanation:

cost of 6 tables=Rs.2400

or,

cost of 8 chair=Rs.2400

cost of 1 table=2400/6

                      =Rs.400

cost of 1 chair=2400/8

                      =Rs.300

cost of 24 tables=24*400

                            =Rs.9600

cost of 12 chairs=12*300

                         =Rs.3600

total cost of 24 tables and 12 chairs=9600+3600

                                                          =Rs.13200

If the statement if I'm hungry, then I am not happy is assumed to be true is it's inverse of I am not hungry then I must be happy also always true

Answers

Answer:

yes!

Step-by-step explanation:

"i am not happy when hungry" is the inverse of "i am not hungry, i am happy."

Answer:

No

Step-by-step explanation:

Will give brainliest answer

Answers

Answer:

a

Step-by-step explanation:

plz gimme brainliest

How can you rewrite simple rational expressions in different forms using long division?
(50 POINTS)PLEASE!!!!!

Answers

Step 1: Factor both the numerator and denominator of the fraction. Step 2: Reduce the fraction. Step 3: Rewrite any remaining expressions in the numerator and denominator. Step 1: Factor both the numerator and denominator of the fraction.

a trapezoid is shown in the grid

Answers

Answer:

To prove that it is a trapezoid, remember that the definition of a trapezoid is a quadrilateral with exactly one pair of parallel sides. Therefore, to prove it is a trapezoid you must verify that one pair of sides is parallel. From algebra, remember that two lines are parallel if they have the same slope.

Find the equation of the parabola that has a vertex at (2,0) and a y-intercept of (0,12).
Question 19 options:

A)

y = 3(x + 2)2

B)

y = (x – 2)2

C)

y = (x + 2)2

D)

y = 3(x – 2)2

Answers

Answer:

D

Step-by-step explanation:

standard form would be 3x^2-12x+12

vertex form y=3(x-2)^2

Answer:

y = 3(x + 2)2

Step-by-step explanation:

Critical Thinking Point M is the midpoint of AB. The coordinates of point A are
(-8, 3) and the coordinates of Mare (–2, 1). What are the coordinates of point B?

Answers

Answer:-1,4

Step-by-step explanation:

Referring to the figure, find the volume of the solid
shown. Round to the nearest whole number.

Answers

First find the area of the triangle using the formula 1/2 x base x height:

1/2 x 22 x 13 = 143 square cm

Now for volume multiply the area by the depth of the figure:

143 x 30 = 4,290 cubic cm

Answer:

780

Step-by-step explanation:

First use pythagorean theorem to find the triangle, then multiply by 30

Use the ÷10 pattern to fill in blanks 400 and 0.4

Answers

Answer:

400÷10=0.4

stay safe and healthy

I don’t understand your question perfectly
According to what I understand, this might be your answer.
Ans: 400,40,4 and 0.4
Please mark brainlest if I helped u a bit
Other Questions
I don't want the answer I just want to know how to do it Write a report on a talk given recently to the school by an outsider PLEASE HELP MARK BRAINLIESTS!!!! add 8+5think of a number path start at 8 add 2 to make 10 Here is a circle, centre O, and the tangent to the circle at the point (-3, 4) on the circle. P (-3, 4) X -5 O O Find an equation of the tangent at the point P. Give your answer in the form y = ax + b where a and b are both fractions with denominator 4. The more acidic a solution is, the higher the pH will be. True False Urgent need help 1.20 What a isProper noun The outer boundary of cells; controls the entry and exit of substances Ankit's father is five years older than three times of Ankit's age. 50 years old, then calculate the present age of Ankit When this 3-digit number is rounded to the nearest hundred it rounds down to 600. The digit in the ones place is the third odd number that you count beginning with 1. The sum of the digits is 13. What is the number? Read the passage carefully. Choose a connection toanother text a reader could make to the passage.O This reminds me of reading and analyzing theConstitution in civics class.O This reminds me of how mundane everyday lifesometimes feels to me.This reminds me of an article about how people arereluctant to analyze their own ideas.This reminds me of the decline of manners inAmerican Society over time. What is the basic unit of structure and function of all living organisms?O mitochondrionODNAnucleuscell Given f(x) = x ^ 2 + 2x and g(x) = x - 1 , find (fg)(x)A) x^3 + 2x^2B) x^3 + x^2 + 2xC) x^3 - x^2 - 2xD) x^3 + x^2 - 2x Lilly drove her car east for a total of 6 hours at a constant velocity. In one-third of that time, she drove 160 kilometers. What was her velocity?Write your answer as a whole number. write the pronoun wordwho are those students? what ______are doing? which part of a flower has pollen grain? Given function g(x)=-x + 2x, determine value of the function for g(-3). Help me solve this pleasee Jimmy's dog weighed 60 pounds 4 months ago. Since then his weight has increased by 6% How much does Jimmy's dog weigh now