Evaluate ∫ y2dx + x dy along the following paths. (a) C = C1 is the line segment from (-13, -7) to (0, 6) (b) C = C2 is the arc of the parabola x = 36 - y2 from (-13, -7) to (0, 6).

Answers

Answer 1

a. Parameterize C₁ by

[tex](x(t),y(t)) = (1-t)(-13,-7) + t(0,6) = (-13+13t,-7+13t)[/tex]

with 0 ≤ t ≤ 1. Then both dx = 13 dt and dy = 13 dt, so that the line integral along C₁ is

[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_0^1 (-7+13t)^2(13\, dt) + (-13+13t)(13\,dt)[/tex]

[tex]\displaystyle \int_C y^2\,dx + x\,dy = 13 \int_0^1 (169t^2 - 169t + 36) \, dt[/tex]

[tex]\displaystyle \int_C y^2\,dx + x\,dy = 13 \left(\frac{169}3-\frac{169}2+36\right) = \boxed{\frac{611}6}[/tex]

b. Parameterize C₂ by

[tex](x(t),y(t)) = (36-t^2,t)[/tex]

with -7 ≤ t ≤ 6. Then dx = -2t dt and dy = dt, so the line integral is

[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 t^2(-2t\,dt) + (36-t^2)\,dt[/tex]

[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 (36-t^2-2t^3) \, dt[/tex]

[tex]\displaystyle \int_C y^2\,dx + x\,dy = \left(36\cdot6-\frac{6^3}3-\frac{6^4}2\right) - \left(36\cdot(-7)-\frac{(-7)^3}3-\frac{(-7)^4}2\right) = \boxed{\frac{5005}6}[/tex]


Related Questions

how is 7 square root 2 is equal to 49?

Answers

Answer:

Square root is how many times your multiply the number by itself. So 7 square root 2 is 7x7 which is 49.

Write two numbers that multiply to −33 and add to 8

Answers

Answer:

-3 and 11

Step-by-step explanation:

A partnership begins its first year with the following capital balances:
Alexander, Capital . . . . . . . . . . . . . . . . . . . . . . . . $ 90,000
Bertrand, Capital . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Coloma, Capital . . . . . . . . . . . . . . . . . . . . . . . . . . 160,000
The articles of partnership stipulate that profits and losses be assigned in the following manner:
∙ Each partner is allocated an interest equal to 5 percent of the beginning capital balance.
∙ Bertrand is allocated compensation of $45,000 per year.
∙ Any remaining profits and losses are allocated on a 3:3:4 basis, respectively.
∙ Each partner is allowed to withdraw up to $25,000 cash per year.
Assuming that the net income is $115,000 and that each partner withdraws the maximum amount
allowed, what is the balance in Coloma’s capital account at the end of the year?
a. $143,000
b. $135,000
c. $168,000
d. $164,000

Answers

Based on the information given the balance in Coloma’s capital account at the end of the year is: d. $164,000.

First step is to calculate the interest on capital for each partner

Alexander=$90,000×5%=$4,500

Bertrand=$100,000×5%=$5,000

Coloma=$160,000×5%=$8,000

Second step is to calculate Coloma capital and drawing

Coloma capital =$160,000 + (5% x $160,000)

Coloma capital=$160,000+ $8,000

Coloma capital=$168,000

Coloma drawing=$168,000-$25,000

Coloma drawing=$143,000

Third step is to calculate Coloma share of profit

Share of profit=$115,000-$45,000-$4,500-$5,000-$8,000

Share of profit=$52,500

Coloma profit=4/(3+3+4)×$52,500

Coloma profit=4/10×$52,500

Coloma profit=4/(3+3+4)×$52,500

Coloma profit=$21,000

Fourth step is to calculate balance in Coloma’s capital account

Coloma’s capital account balance=$143,000+$21,000

Coloma’s capital account balance=$164,000

Inconclusion the balance in Coloma’s capital account at the end of the year is: d. $164,000.

Learn more here:https://brainly.com/question/21270829

A store has apples on sale for $3.00 for 2 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $12.00? Complete the explanation

Answers

Answer:

you can buy 6 pounds of apples

Step-by-step explanation:

help pls :))))))))))))

Answers

Answer:

yes, the triangle are congruent by SAS

Answer:
we know that it is 0.6 km
so we convert into meters
and then get 600 m

Hope that helps

Answers

Answer:

ok thank u ig

Step-by-step explanation:

Which value of x is a solution of the inequality?
​3x−3≥9

Answers

Answer:

It's probably X since X doesn't have a written number for it it equals 1.

Step-by-step explanation:

Jasmine wants to make more cleaning solution

Answers

Answer:

here

Step-by-step explanation:

Method 1 Method 1 of 3: Making Liquid Cleaners

Mix equal parts water and vinegar in a spray bottle. Use distilled white vinegar and, if possible, distilled or filtered water.

Add lemon juice to disinfect surfaces. Mix one part lemon juice, one part white vinegar and two parts water in a spray bottle.

Add dish soap for persistent stains on carpet. ...

Tackle tough stains and grime with undiluted vinegar. ...

I need help with this problem no where on Brainly

Answers

Answer:

blue graph

Step-by-step explanation:

that graph looks similar to e^x

so f(-x) will be similar to e^-x

so it will be a reflection over y axis

see the picture below

determine the slope and y intercept and write the equation in slope intercept form

Answers

Answer: slope is 2 and the y-intercept is 1  intercept form is y=2x+1

Step-by-step explanation:

f x and r are inversely proportional and x = 9 when r = 72, then what is x when r = 40?

Answers

Answer:

16.2

Step-by-step explanation:

r = k/x

when x = 9 and r = 72 ,

72 = k/9

k = 72*9

When r = 40 ,

x = k/r

x = 72*9/40 = 16.2

y-3=1/2(x-7)

PLS HELP ME OUT GUYS

Answers

Answer:

X = -1

Step-by-step explanation:

y - 3 = 1/2 (x - 7)

x would equal -1.

The graph of the linear function is shown on the coordinate grid. What is the equation of this line?​

Answers

y=-1/3-2

Hope this helps!! :)

Suppose that you take 1000 simple random samples from a population and that, for each sample, you obtain a 95% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will contain the value of the unknown parameter?

Answers

Using the interpretation of a confidence interval, it is found that approximately 950 of those confidence intervals will contain the value of the unknown parameter.

A x% confidence interval means that we are x% confident that the population mean is in the interval.

Out of a large number of intervals, approximately x% will contain the value of the unknown parameter.

In this problem:

95% confidence interval.1000 samples.

0.95 x 1000 = 950

Hence, approximately 950 of those confidence intervals will contain the value of the unknown parameter.

A similar problem is given at https://brainly.com/question/24303674

Let C1 and C2 be two smooth parameterized curves that start at P0 and end at Q0 ≠ P0, but do not otherwise intersect. If the line integral of the function f(x, y, z) along C1 is equal to 43.1 and the line integral of f(x, y, z) along C2 is −15.9, what is the line integral around the closed loop formed by first following C1 from P0 to Q0, followed by the curve from Q0 to P0 along C2, but moving in the opposite direction? Incorrect: Your answer is incorrect.

Answers

We're given that

[tex]\displaystyle \int_{C_1} f(x,y,z) \,ds = 43.1[/tex]

and

[tex]\displaystyle \int_{C_2} f(x,y,z) \,ds = -15.9[/tex]

The closed loop formed by joining C₁ and C₂ is then C₁ U (-C₂), which is to say we follow C₁ normally, then traverse C₂ in the opposite direction. Then

[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = \int_{C_1} f(x,y,z) \,ds + \int_{-C_2} f(x,y,z) \,ds[/tex]

[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = \int_{C_1} f(x,y,z) \,ds - \int_{C_2} f(x,y,z) \,ds[/tex]

[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = 43.1 - (-15.9) = \boxed{59}[/tex]

what is the change from 3 to -8?

Answers

Answer:

-11

Step-by-step explanation:

3 - 11 = -8

Can someone please answer this question? Someone answered and they deleted their answer, so I need someone else to help me!
Please do not delete your answer, steal the points, or send links, I really need some help!

Answers

Check the picture below.

now, notice the triangles made, 3 right triangles with legs of 5 and 4 each.

looking at quadrilateral (1), from the leg 5 units long, we have a line with a run of -1 and a rise of 3, from the leg 4 units long, we have a line with a run of 4 and a rise of -1.

Now, quadrilaterals (2) and (4) display the same lengths and rise and runs, which means they're all congruent, quadrilateral (3) has no equal.

so 1 ≅ 2 and 1 ≅ 4.

25Y^2/5y-4 + 16/4-5y​

Answers

Answer:

5Y2y-5y

Step-by-step explanation:

5

Y

2

y

5

y

Write an equation perpendicular to x-4y=20 that passes through the point (2,-5)

Answers

Answer:

x – 4y = 20

Step-by-step explanation:

Put the line above in Slope Intercept Form

You can do that by solving for y

y = (1/4)x - 5

The slope, m above is 1/4

The perpendicular will a negative inverse slope m = -4

In Slope Intercept Form your perpendicular line starts below

y = -4x + b

Use the coordinates of the given point on the line (2, -5) to insert and solve for b

-5 = -4(2) + b

-5 = - 8 + b

Add 8 to both sides of the equation

-5 + 8 = b

3 = b

Finally your perpendicular line

y = -4x + 3

I hope this helps

Check my arithmetic

Answer:

×4y=20

Step-by-step explanation:

mark me as brainlist please

Pre college need help

Answers

Answer:

C

Step-by-step explanation:

What is the slope of the line that passes through the points
(−5,−7) and (4,−1)? Write your answer in simplest form.

Answers

9514 1404 393

Answer:

  2/3

Step-by-step explanation:

The slope is found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -(-7))/(4 -(-5)) = 6/9 = 2/3

The slope of the line is 2/3.

_____

The attached graph shows the equation of the line in point-slope form.

30 liters in 2 minutes = liters per minute

Answers

Answer:

0.06 would be the answer.

Step-by-step explanation:

Answer:

15 liters per minute

Step-by-step explanation:

30/2=15

Latisha works x hours each day. Demetrius works 1 more hour each day than Latisha. Which expressions both calculate the number of hours Demetrius works in a 5-day work week? 5 x + 1 and 5 ( x + 1 ) 5 x plus 1 and 5 times open paren x plus 1 close paren ( x + 1 ) × 5 and 5 × x + 1 open paren x plus 1 close paren times 5 and 5 × x + 1 5 ( x + 1 ) and 5 x + 5 5 times open paren x plus 1 close paren and 5 x plus 5 ( x + 1 ) × 5 and 5 + ( x × 1 )

Answers

The number of hours worked by both Latisha and Demetrius is; 5x + 5(x+1)

According to the question:

We are required to generate an expression that can be used to calculate the number of hours used to work by Latisha and Demetrius.

Since Latisha works x hours per day; In 5 days she works 5x hours.

Demetrius works 1 more hour each day than Latisha; In 5 days; she must have worked; 5(x +1) hours.

The sum of both of them gives; 5x + 5(x +1).

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https://brainly.com/question/16989990

a toll box has 10 screw drivers and 6 wrenches Bella puts 8 more wrenches in the tool box how many more wrenches are in the toolbox

Answers

If you are asking how many more are in the box it would be 8 because you added 8 more but in total there are 14 wrenches

geomtry plz help 10 points

Answers

Answer:

22.3<x<27.6

Step-by-step explanation:

X=greater than a number but less than another

22.3<27.6

Knowing that we can place 27.6 to the right of x and 22.3 to the left.

Hope this helps :)

Answer:

[tex]4.3<x<50.9[/tex]

Step-by-step explanation:

To find our Inequality sentence we have to add the largest number with the smaller much

[tex]27.6+23.3=50.9[/tex]

To find the second part of our inequality sentence we have to subtract the larger number from the smaller number

[tex]27.6-23.3=4.3[/tex]

Our inequality sentence is               [tex]4.3<x<50.9[/tex]

Brainliest please

which expression represents the product of 3 and 1 1/4 n 1.8

Answers

•ω• Hewo fren!

☆☆●◉✿ Answer:✿◉●☆☆

3•1 1/4•1.8= 6 3/4

☆☆●◉✿Step-by-step explanation:✿◉●☆☆

Let’s start of with 3•1 1/4~

3 times 1 and 1/4 is 3 3/4

Now let’s multiply 3 3/4 • 1.8

1.8 is also 1 8/10, simplified: 1 4/5.

3 3/4 • 1 4/5 = 6 3/4

THERE IS YOUR ANSWER! >o<

HOPE I HELPED!  ∧∧

→⇒brainliest please? ∑(OΔO )♥♥︎

5.You are driving at a constant speed of 20 m/s when you suddenly hit a patch large oil slick. You slam on the brakes and eventually skid to a complete stop. The skid marks are 40 meters long. Calculate the coefficient of kinetic friction between the oil-covered road
and the car tires.

Answers

The coefficient of kinetic friction between the oil-covered road

and the car tires. is 0.51

To solve this question, we would consider one of the equations of motion.

v² = u² + 2as, where

v = final velocity, which is also equal to 0

u = initial velocity, which is 20m/s

s = skid marks, which is 40 meters long

a = acceleration, which is unknown

0² = 20² + 2*a*40

0 = 400 + 80a

80a = -400

a = -400/80

a = -5 m/s

Also, it is known that acceleration a = (mu)g, where mu is the coefficient of kinetic friction and g is the acceleration due to gravity.

-5 = mu * 9.8

mu = -5/9.8

mu = 0.51

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Hey help please math I need help good luck I’ll I’ve point

Answers

Answer:

180 degrees

Step-by-step explanation:

180 degrees would flip the triangle halfway through a full circle. B is A upside down rotated halfway through a full circle.


What is the position of B on the number line below?
Write your answer as a fraction or mixed number

Answers

Step-by-step explanation:

B = 1 4/5

because 1 is completely to the left, and from the distance between 1 and 2 B is at the end of the 4th of 5 sub-segments.

and 1 4/5 would be also 9/5, because B includes the 5 sub-segments (of 5) between 0 and 1. and then the 4 of 5 sub-segments between 1 and 2. so that are 9 sub-segments in total.

and each sub-segment represents 1 out of 5 (= 1/5) parts of each number interval.

therefore, we have 9×1/5 = 9/5.

evaluate 6^2 - (9 divided by x) when x = 3

Answers

Answer:

33

Step-by-step explanation:

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