37. Verify Green's theorem in the plane for f (3x2- 8y2) dx + (4y - 6xy) dy, where C is the boundary of the
C
region defined by: (a) y = fx , y = x2 ; (b) x = 0, y = 0, x +y = 1 .
Ans. (a) common value = 3/2 (b) common value = 5/3
38. Evaluate f (3x +4y)dx + (2x --3y)dy where C, a circle of radius two with center at the origin of the xy
C plane, is traversed in the positive sense. Ans. - 87T
39. Work the previous problem for the line integral f (x2+y2)dx + 3xy2 dy. Ans. 127T
C 40. Evaluate f (x2-2xy)dx +(x2y+3)dy around the boundary of the region defined by y2 = 8x and x = 2
(a) directly, (b) by using Green's theorem. Ans. 128/5
(TT.2) 41. Evaluate f (6xy - y2) dx + (3x2 --- 2xy) dy along the cycloid x = 6 - sin 6, y = 1 - cos 6.

Answers

Answer 1

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

[tex]\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy[/tex]

and I assume C has a positive orientation in both cases

(a) It looks like the region has the curves y = x and y = x ² as its boundary***, so that the interior of C is the set D given by

[tex]D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}[/tex]

• Compute the line integral directly by splitting up C into two component curves,

C₁ : x = t and y = t ² with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = 1 - t with 0 ≤ t ≤ 1

Then

[tex]\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}[/tex]

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

[tex]\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}[/tex]

(b) C is the boundary of the region

[tex]D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}[/tex]

• Compute the line integral directly, splitting up C into 3 components,

C₁ : x = t and y = 0 with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = t with 0 ≤ t ≤ 1

C₃ : x = 0 and y = 1 - t with 0 ≤ t ≤ 1

Then

[tex]\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}[/tex]

• Using Green's theorem:

[tex]\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}[/tex]


Related Questions

2. What is the distance between points A and B?

A. -6 units
B. -1 unit
C. 5 units
D. 6 units

Answers

Answer:

5 units

Subtract -6 and -1, and you get -5. -5 can't be the answer since we are asked to find the distance, so it is the absolute value of -5, 5.

Answer:

D) 6 units

Explanation:

Point A is 5 units away from 0 (the middle)

Point B is 1 unit away from 0

5 + 1 = 6

Distance between two points cannot be negative

56-x=728+2x what's the answer?

Answers

56 - x = 728 + 2x

-x - 2x = 728 - 56

-3x = 672

x = 672/-3

x = -224

Hope that helps. If you have any doubts plz let me know.

Answer:

56-x=728+2x

1.) rearrange

[tex]56x = 728 + 2x \\ \ - x + 56 = 728 + 2x[/tex]

[tex] - x + 56 = 728 + 2 x \\ \\ - x + 56 = 2x + 728[/tex]

2.)subtract 56 on both side

[tex] - x + 56 = 2x + 728 \\ \ - x + 56 - 56 = 2x + 728 - 56[/tex]

3.) simplify

[tex] - x = 2x + 672[/tex]

4.)Subtract 2 on both sides

[tex] - x = 2x + 672 \\ \\ - x - 2x = 2x + 672 - 2x[/tex]

5.) simplify

[tex] - x - 2x = 2x + 672 - 2x \\ \\ - 3x = 2x + 672 - 2x \\ \\ - 3x = 672[/tex]

6.)divide both sides on the same equation

[tex] - 3x = 672 \\ \\ \frac{ - 3x}{ - 3} = \frac{672}{ - 3} [/tex]

7.) simplify

[tex]x = - 224[/tex]

8.) answer

[tex]x = - 224[/tex]

if u need any help, just let me know

1/8 times square root of eight =

Answers

Answer:

0.35355339059

Step-by-step explanation:

Please answer the question above!

Answers

Answer:

B) [tex]A=4x+8[/tex]

Step-by-step explanation:

Hi there!

Area of a trapezoid: [tex]A=\displaystyle\frac{1}{2}h(b_1+b_2)[/tex]

⇒ b₁ = x-3

⇒ b₂ = x+7

⇒ h = 4

Plug the given information into the equation:

[tex]A=\displaystyle\frac{1}{2}(4)[(x-3)+(x+7)]\\\\A=\displaystyle\frac{1}{2}(4)(x-3+x+7)\\\\A=2(2x+4)\\\\A=4x+8[/tex]

Therefore, the area of the trapezoid is [tex]4x+8[/tex].

I hope this helps!

true/false: the vertical axis in a bar chart always shows relative frequencies

Answers

Answer:

true

Step-by-step explanation: true

52% of 1000 registered voters intend to vote for Steven Collins for mayor. What is the 95% confidence interval to describe the total percentage of registered voters who intend to vote for Steven Collins?


A. (50.1%, 53.9%)

B. (48%, 56%)

C. (49.9%, 54.1%)

D. (48.9%, 55.1%)

Answers

Using the z-distribution, the 95% confidence interval to describe the total percentage of registered voters who intend to vote for Steven Collins is:

D. (48.9%, 55.1%)

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The other parameters are given as follows:

[tex]\pi = 0.52, n = 1000[/tex]

Hence the bounds of the interval are given by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{1000}} = 0.489[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{1000}} = 0.551[/tex]

As a percentage, option D is correct.

More can be learned about the z-distribution at https://brainly.com/question/25890103

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CP is equal to 200 SP is equal to 100 find the profit or loss​

Answers

Answer:

100

Step-by-step explanation:

if SP>CP,

It is profit [SP - CP = Profit]

if CP>SP,

It is loss   [CP - SP = Loss]

Here in the question CP>SP so,

loss = CP - SP

       =200 - 100

       = 100

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.

The area of a rectangle is 44m^2, and the length of the rectangle is 3m less than twice the width. Find the dimensions of the rectangle.

Answers

Answer:

the length=8

the rectangle=5.5

Step-by-step explanation:

+)convention:

the lengt=a

the width = b => the area of the rectangle = a.b=44m^2 (1)

+) "the length of the rectangle is 3m less than twice the width"

=> 2b-a = 3 (m)

=> a=2b-3

substitute a for (1), we get

the area of the rectangle = a.b = (2b-3).b=44 m^2

=> 2b^2-3b-44=0

=> b=-4 (wrong)

=> b= 5.5 =the width

the lengt = the area of the rectangle/the width=44/5.5=8 m

Find three solutions for this linear function and choose the correct graph by clicking on it. F(x) = x + 3

Answers

Answer: The picture that shows 0,3 and 0,3.

They are points on the graph that show the function

Step-by-step explanation: I know because I just did this. I passed!!!

During a science lab, four-fifths of the class completed the lab and earned a grade of 100. What percent of the class didnt earn a grade of 100?
F. 60%
G. 80%
H. 20%
J.45%

Answers

Answer: H. 20%

Step-by-step explanation: if 4/5 got 100 then 80% got 100 so the other 20% did not get a 100

A blueprint has a scale of 1cm : 4 feet. On the blueprint, a room is drawn with dimensions 5cm x 2cm.
Find the area of the room (the units of the answer are square feet).
It is a great idea to use a sheet of graph paper to work this problem.
square feet

Answers

Answer:

On the blue print, the room will measure 20 by 8 feet

Step-by-step explanation:

write the decimal values of the digits given in bold : 0.437




please tell step by step explaination​

Answers

Answer:

na na na na na I don't know

the sum of 3 and a number

Answers

Answer:

the number will vary the answer

Step-by-step explanation:

3×1=3

3×2=6

The graph of the reciprocal parent function, f(x) = ), is shifted 9 units
down and 11 units to the right to create the graph of g(x). What function is
g(x)?

Answers

Answer:

g(x) = [tex]\frac{1}{x+11}-9[/tex] is my choice

Step-by-step explanation:

I. If move right is +x and move down is -y

               then f(x) = [tex]\frac{1}{x}[/tex]

               +x = 11, -y = -9

                so g(x) = [tex]\frac{1}{x+11}-9[/tex]

Hope that help :D

Mrs. Kaur brought identical gift for her 6 nieces and nephews. She spent a total of $94.20. what was the cost of each gift.​

Answers

Answer:

$15.7 for each

Step-by-step explanation:

here, peice of 6 gifts= $94.20

now price of each gift= $94.20/6

answer is 15.7 dollars

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!

At a birthday party, five people are sharing 3/4 of a pan of lasagna. What equal-sized portion of the whole pan will each of the five people receive?

a. Draw a visual model to represent the situation and the solution.

b. Write an equation to represent the situation. Explain your reasoning.

Answers

Answer:

see below

Step-by-step explanation:

Take the amount of lasagna and divide by the number of people

3/4 ÷ 5=x

Copy dot flip

3/4*  1/5=x

3/20 each

What comes next in this sequence? - [ 1, 45, 104, 1034 ] - Please state the pattern and why you chose that answer.



A. 34556


B. 4567


C. 401


D. 54

Answers

Answer:

The answer is A. 34556

Step-by-step explanation:

The 5th term of the sequence would be a{5} = 10334.

What is a mathematical function, equation and expression?  

Sequence : A sequence is defined as an arrangement of numbers in a particular order.        

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is the sequence -

1, 45, 104, 1034

We can write the next term as -

a{n} = 10a{n - 1} - 6

So, we can write -

a{5} = 10 x 1034 - 6

a{5} = 10340 - 6

a{5} = 10334

Therefore, the 5th term of the sequence would be a{5} = 10334.

To solve more questions on functions, expressions and polynomials, visit the link below -

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3. What type of angle will the clock show when it is 6:55 pm?

Answers

Obtuse angle.

Hope you could understand that. Plzz let me know if you have any doubts.

Have a nice day :)

If 5cm and 3cm are added to the length and width of a square, the perimeter of the resulting rectangle is between twice and three times the perimeter of the original square. Find the possible lengths of the sides of the original square.

Answers

Answer:

The answer is between 2 and 4. 2 and 4 can be included if you are including the twice or three times. If it doesn't include those then it would only be anything inbetween.

Step-by-step explanation:

So to start off I would always give placeholder for all the sides. Lets label it x.

2(x+5) + 2(x+3) < 3(4x)

In the equation above, we created a simple equation with 2 representing 2 sides each and the 3 and 5 plugged in. That all is going to be less than 3 times the original perimeter which is 4x for the 4 sides.

2x + 10 + 2x + 6 < 12x

4x + 16 < 12x

16 < 8x

2 < x

We learn that the original x is greater than 2. We don't say it is equal to since it says between. Which doesn't usually include the number stated.

Now we repeat, just instead of 3 its 2 and instead of less than its greater than.

2x + 10 + 2x + 6 > 8x

4x + 16 > 8x

16 > 4x

4 > x

So your answer is between 2 and 4.

The possible lengths of the sides of the original square (x) any value between 4 cm and 8 cm, inclusive.

Let's denote the side length of the original square as "x" centimeters. The perimeter of the square is 4x.

When 5 cm and 3 cm are added to the length and width of the square,  a rectangle with dimensions (x + 5) cm and (x + 3) cm. The perimeter of the rectangle is 2 × (x + 5) + 2 × (x + 3) = 2x + 10 + 2x + 6 = 4x + 16.

According to the given information, the perimeter of the rectangle is between twice and three times the perimeter of the original square:

2 × perimeter of square ≤ perimeter of rectangle ≤ 3 × perimeter of square

Substitute the values:

2 × 4x ≤ 4x + 16 ≤ 3 × 4x

Simplify:

8x ≤ 4x + 16 ≤ 12x

Subtract 4x from all parts:

4x ≤ 16 ≤ 8x

Now, divide all parts by 4:

x ≤ 4 ≤ 2x

To know more about square here

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If M Need help asap ...................

Answers

The measure of angle DAC must be 60 degrees. Since a right angle is 90 degrees, the sum of the degrees of both of the angles must be that amount. If angle BAD is 30 degrees, the measure of angle DAC must be 60 degrees.

Help I'll mark you as brainiest

Answers

Answer:

It is a function and 0to^2 shows your function dt.c and 4c-3 shows your function is wrong and the answer is 0 and 31/4 to the power of 25 and shows that the function is 8.

Step-by-step explanation:

40 Points Please help me

Answers

the slope is 1/2 for those two points. it can be found using the slope formula.

Pls Someone Help me Question:make the greatest and smallest 4 digit number by using any one digit twice
= 8,2,7

Answers

Answer:

Greatest digit: 8872.

Smallest digit:2278.

9514 1404 393

Answer:

greatest: 8872smallest: 2278

Step-by-step explanation:

Greatest

The greatest possible number is created by putting the greatest allowable digit in the space available that has the highest possible place value. Here, the greatest digit is 8, and the highest place value of a 4-digit number is the thousands place: 8000. Once you have filled that place, you can use the digit 8 one more time in the hundreds place: 8800.

Now, the greatest digit available is the digit 7, and the left-most place you can put it is the tens place: 8870. Finally, the only digit and place available are the digit 2 and the ones place.

Your greatest 4-digit number is 8872.

Smallest

To form the smallest number, you use a similar process, filling places in the number from left to right with the smallest allowable digit. The smallest digit, 2, is allowed twice, so the smallest number that can be formed is 2278.

Which inequality is the same 7 - 2/b ≤ 5/b

Answers

B is less than or equal to 1

Answer:

1. B

2. A

Step-by-step explanation:

Those are the correct answers

Divide $2604 into a ratio of 2:1.

Answers

Answer : 2604 can be divided into 1736 and 868 in the ratio of 2:1.

Step-by-step explanation:

2x + x = 2604

or, 3x = 2604

or, x = 2604/3 = 868

so

2x = 2*868 = 1736

now

x = 868

Find the distance between the points (3,4) and (6,0).
I

Answers

Answer:

first you use distance formula then urr answer will come out....first u try ok.......

Please Help! Evaluate the function at each specified value of the independent variable and simplify. (If an answer is undefined, enter UNDEFINED.)

g(t) = 5t^2 − 8t + 3

Answers

Answer:

Given:

g(t) = 5t² − 8t + 3

Find the following

g(2)

g(2) = 5(2²) - 8(2) + 3 = 20 - 16 + 3 = 7

g(t - 2)

g(t - 2) = 5(t - 2)² - 8(t - 2) + 3 = 5t² - 20t + 20 - 8t + 16 + 3 = 5t² - 28t + 39

g(t) - g(2)

g(t) - g(2) = 5t² − 8t + 3 - 7 = 5t² − 8t - 4

g(t)=5t^2-8t+3

[tex]\\ \sf\longmapsto g(2)=5(2)^2-8(2)+3[/tex]

[tex]\\ \sf\longmapsto g(2)=5(4)-16+3[/tex]

[tex]\\ \sf\longmapsto g(2)=20-13[/tex]

[tex]\\ \sf\longmapsto g(2)=7\checkmark[/tex]

And

[tex]\\ \sf\longmapsto g(t-2)=5(t-2)^2-8(t-2)+3[/tex]

[tex]\\ \sf\longmapsto g(t-2)=5(t^2-4t+4)-8t+16+3[/tex]

[tex]\\ \sf\longmapsto g(t-2)=5t^2-20t+20-8t+19[/tex]

[tex]\\ \sf\longmapsto g(t-2)=5t^2-28t+39\checkmark[/tex]

And

[tex]\\ \sf\longmapsto g(t)-g(2)[/tex]

[tex]\\ \sf\longmapsto 5t^2-8t+3-7[/tex]

[tex]\\ \sf\longmapsto 5t^2-8t-4[/tex]

A city currently has a population of 8200 people, and is expected to grow by 4%
every year. To the nearest whole person, what is the population expected to be 10
years from now?

Answers

The population expected to be 10 years from now is 12,138.

Given that,

The population is 8,200 people.It should be predicted to grow by 4%.

Based on the above information,

The  population expected to be 10 years from now is

[tex]= Number\ of\ people \times (1+ growth\ rate)^{number\ of\ years}\\\\= 8,200 \times (1 + 0.04)^{10}\\\\[/tex]

= 12,138

Therefore we can conclude that The population expected to be 10 years from now is 12,138.

Learn more about the population here: brainly.com/question/16138725

jim can solve 4 math problems in 7 minuts. At this rate, about how many math problems can he solve in 25 minuts?

Answers

Answer:

14.

JIm can solve 4/7 math problems in a minute. that is the unit rate. how did i get that? 7/7 = 1 and thats what we need for a unit rate, the number one. that means we have to divide 4 by 7 too. therefore, 4/7.

we aren't done. we multiply 4/7 * 25 to find out how many math problems jim can solve in 25 minutes.

about.. 14.29 and we need a whole number since you cant solve a decimal of a math problem so he can solve 14 math problems in 25 minutes.

Step-by-step explanation:

Answer:

43.57

Step-by-step explanation:

divide 4/4 and 7/4 to get the base amount of minutes per question then multiply 1.75 by 25 minutes

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