Find the line integral along the curve C from the origin along the x-axis to the point (6, 0) and then counterclockwise around the circumference of the circle x2 y2

Answers

Answer 1

Parameterize C by the two vector functions,

r(t) = (1 - t) (0, 0) + t (6, 0) = (6t, 0)

with 0 ≤ t ≤ 1, and

s(t) = (6 cos(t), 6 sin(t))

with 0 ≤ t ≤ π/2.

Then the line integral over C is equal to the sum of the line integrals over each path:

[tex]\displaystyle \int_C dS = \int_0^1 \|r'(t)\| \, dt + \int_0^{\frac{\pi}2} \|s'(t)\| \, dt[/tex]

[tex]\displaystyle \int_C dS = \int_0^1 \sqrt{6^2 + 0^2} \, dt + \int_0^{\frac{\pi}2} \sqrt{(-6\sin(t))^2 + (6\cos(t))^2} \, dt[/tex]

[tex]\displaystyle \int_C dS = 6 \int_0^1 dt + 6 \int_0^{\frac{\pi}2} dt[/tex]

[tex]\displaystyle \int_C dS = 6 + \frac{6\pi}2 = \boxed{6+3\pi}[/tex]


Related Questions

Decide where the first digit of the quotient should be placed without performing division The first digit of the quotient for 2,370 = 24 should be in the Choose... ones tens hundreds thousands​

Answers

Answer:

tens place

Step-by-step explanation:

24 can't be into the thousands place or the hundreds place. hope this helps

Answer

 hundredths place

Step-by-step explanation:

When performing long division, the first digit of the quotient appears over the least significant digit of the first portion of the dividend that is greater than or equal to the divisor.

Here, when performing long division we compare ...

 64 vs 1 . . . no quotient digit

 64 vs 15 . . . no quotient digit

 64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, 2 in the hundredths place.

if u get this right u get branist

Answers

5(2)^2-2(7) = 6

6(7+2)/2 = 27

Therefor the correct answer is the < symbol.

I hope this helps! :)

Please help me with these questions. I’m genuinely confused.

Answers

Answer:

16: 5

17: 6 4/9

Step-by-step explanation:

I only will give u the answer for a few questions

Explain the meaning of 5?
a. 1 + 2 + 3 + 4 + 5
b. 5-4-3-2-1-0
c. 0 x 1 x 2 x 3 x 4 x 5
d. 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1​

Answers

A. 5 is being added

B. 5 is being subtracted

C. 5 is being multiplied

D. 5 is being multiplied

I hope these answers are correct

Write an equation for the nth term of the arithmetic sequence 7,2,-3,-8,

Answers

Answer:

-5n+12

Step-by-step explanation:

find the difference which is -5

then find the difference from -5 to 7 which is 12

put it in the sequence

-5n+12

Answer:

-5n+12 that would be your equation                                        

Which point would not be on the graph of the function y=+5?​

Answers

Answer:

Any point that does NOT have a positive 5 in the y position

This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
Nick wants to purchase a pair of binoculars that is on sale for $155.75. The sales tax rate in his county is 6.5%.



Calculate the amount of sales tax Nick will pay on the purchase. Round to the nearest cent if necessary.



sales tax: $



Part B
Fill in the blank question.
How much will Nick pay in all for the pair of binoculars after sales tax is included? Round to the nearest cent if necessary.



total cost: $

Answers

Answer:

Step-by-step explanation:

A) $155.75(0.065) = 10.12375 = $10.12

B) $155.75 + $10.12 = $165.87

Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 34-5=-2N+ 10? Select two options Ox= 5 0 -15 = -5x 0 5x = 15 0 -15 = 5x Ox = -5

Answers

Answer:

-15 = -5x

5x = 15

Step-by-step explanation:

What is 3/4+1 2/3+1/2=

Answers

35/12 is the correct answer

Answer:

Exact Form:

35/12

Decimal Form:

2.916- (6 goes on)

Mixed Number Form:

2 11/12

need some help with these!!

Answers

The answer is 24

Explanation: just divide by 2
It is C. 24

Because triangle A is double the size of triangle D

32/2 =16
40/2 = 20

48/2 = 24

Please help me with these questions. I’m genuinely confused.

Answers

Answer:

16. 1 4/5

17. 2 2/3

18. 4/11

19. 4 1/2

20. 4/7

21. 1/2

22. 1 2/5

23. 2 1/2

24. 4 2/3

Step-by-step explanation:

1. subtract whole numbers first

2. subtract fractions next (simplify if you can)

3. subtract fractions and whole numbers

For questions 3 - 6, find F'(x), the inverse of F(x).

3. F(x) = x-10

4. F (x) = x/6 + 3

5. F(x) = 3x + 7

6. F(x) = 8x

Answers

Answer:

3)  f'(x) = x + 10

4)  f'(x) = 6x - 18

5)  [tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or  [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex]

6)  f'(x) = ⅛x  or  [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex]  

Step-by-step explanation:

3. f(x) = x - 10

Step 1: In order to find the inverse function of f(x) = x - 10, start by replacing f(x) with y.  

y = x - 10

Step 2:  Switch x and y:

x = y - 10

Step 3: Add 10 to both sides to isolate y:

x + 10 = y - 10 + 10

x + 10 = y

Step 4: Replace y with f'(x):

f'(x) = x + 10  ⇒ This is the inverse function of f(x).

4.  [tex]\displaystyle\mathsf{f(x)=\:\frac{x}{6}\:+\:3}[/tex]

Replace f(x) with y:

[tex]\displaystyle\mathsf{y=\:\frac{x}{6}\:+\:3}[/tex]

Switch x and y:

[tex]\displaystyle\mathsf{x=\:\frac{y}{6}\:+\:3}[/tex]

Subtract 3 from both sides:

[tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}\:+\:3-3}[/tex][tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}}[/tex]

Multiply both sides by 6 to isolate y:

[tex]\displaystyle\mathsf{6(x-3)=\:\frac{y}{6}(6)}[/tex]

6x - 18 = y

Replace y with f'(x):

f'(x) = 6x - 18  ⇒ This is the inverse function of f(x).

5. f(x) = 3x + 7

Replace f(x) with y:

y = 3x + 7

Switch x and y:

x = 3y + 7

Subtract 7 from both sides:

x - 7 = 3y + 7 - 7

x - 7 = 3y

Multiply both sides by :

⅓(x - 7) = 3y (⅓)

[tex]\displaystyle\mathsf{\frac{1}{3}x-\frac{7}{3}=y}[/tex]

Replace y with f'(x):

[tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex]  or  [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex]   ⇒ This is the inverse function of f(x).

6. f(x) = 8x

Replace f(x) with y:

y = 8x

Switch x and y:

x = 8y

Multiply both sides by :

⅛(x) = ⅛(8y)

⅛x = y or  [tex]\displaystyle\mathsf{\frac{x}{8}=y}[/tex]  

Replace y with f'(x):

f'(x) = ⅛x  or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex]   ⇒ This is the inverse function of f(x).

I 13.12.21 Mather asianmen I choose the best answert the next two numbers in the pattern 1, 4, 9, 16 are. (A) 26,36 (B) 25, 36 (C) 24,35 (D) 36,48​

Answers

Answer:

(B) 25, 36

Step-by-step explanation:

1 = 1²

4 = 2²

9 = 3²

16 = 4²

25 = 5²

35 = 6²

i need help on this math problem

Answers

Answer:

[tex]\sqrt{81}[/tex] = 9

[tex]\sqrt{169}[/tex] = 13

Step-by-step explanation:

ok. 4. 62 decreased by 2 7 co 8 anolo 5. 14 increased by 14​

Answers

Answer: Arachidonic acid (AA, sometimes ARA) is a polyunsaturated omega-6 fatty acid 20:4(ω-6), or 20:4(5,8,11,14).

Step-by-step explanation: It is structurally related to the saturated arachidic acid found in cupuaçu butter.[3] Its name derives from the New Latin word arachis (peanut), but it is important to note that peanut oil does not contain any arachidonic acid.[4]

Find the dimensions of a rectangle (in m) with area 1,000 m2 whose perimeter is as small as possible. (Enter the dimensions as a comma separated list.)

Answers

The perimeter of the rectangle is the sum of its dimensions

The dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]

The area is given as:

[tex]\mathbf{A = 1000}[/tex]

Let the dimension be x and y.

So, we have:

[tex]\mathbf{A = xy = 1000}[/tex]

Make x the subject

[tex]\mathbf{x = \frac{1000}{y}}[/tex]

The perimeter is calculated as:

[tex]\mathbf{P = 2(x + y)}[/tex]

Substitute [tex]\mathbf{x = \frac{1000}{y}}[/tex]

[tex]\mathbf{P = 2(\frac{1000}{y} + y)}[/tex]

Expand

[tex]\mathbf{P = \frac{2000}{y} + 2y}[/tex]

Differentiate

[tex]\mathbf{P' = -\frac{2000}{y^2} + 2}[/tex]

Set to 0

[tex]\mathbf{ -\frac{2000}{y^2} + 2 = 0}[/tex]

Rewrite as:

[tex]\mathbf{ -\frac{2000}{y^2} = -2}[/tex]

Divide both sides by -1

[tex]\mathbf{\frac{2000}{y^2} = 2}[/tex]

Multiply y^2

[tex]\mathbf{2000 = 2y^2}[/tex]

Divide by 2

[tex]\mathbf{1000 = y^2}[/tex]

Take square roots of both sides

[tex]\mathbf{y = \sqrt{1000 }}[/tex]

[tex]\mathbf{y = 10\sqrt{10 }}[/tex]

Substitute [tex]\mathbf{y = \sqrt{1000 }}[/tex] in [tex]\mathbf{x = \frac{1000}{y}}[/tex]

[tex]\mathbf{x = \frac{1000}{\sqrt{1000}}}[/tex]

[tex]\mathbf{x = \sqrt{1000}}[/tex]

[tex]\mathbf{x = 10\sqrt{10 }}[/tex]

Hence, the dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]

Read more about perimeters at:

https://brainly.com/question/6465134

Solve the system. Estimate the solution first. Enter whole numbers for the estimated solution and
improper fractions in simplest form for the algebraic solution.

6x + y = 2
1 x - 4y = 2

The estimated solution is (__,__)

Answers

Answer:

using substitution method you'll be able to get the value of x then after finding x

Analyze the solution set of the following system by following the given steps. 2x + y = 5 3y = 9 − 6x Write each equation in slope-intercept form. y = -2 x + 5 y = -2 x + 3 What do the equations have in common? How are they different?

Answers

Step-by-step explanation:

Given the following systems of linear equations, 2x + y = 5, and 3y = 9 − 6x

Write each equation in slope-intercept form.

The slope-intercept form is: y = mx + b, where m = slope, and b = y-intercept.

2x + y = 5

Subtract 2x from both sides:

2x - 2x + y = - 2x + 5

y = -2x + 5 ⇒ This is the slope-intercept form, where the slope, m = -2, and the y-intercept, b = 5.

3y = 9 − 6x

Divide both sides by 3 to isolate y:

3y = − 6x + 3

[tex]\frac{3y}{3} = \frac{-6x + 9}{3}[/tex]

y = -2x + 3 ⇒ This is the slope-intercept form, where the slope, m = -2, and the y-intercept, b = 3.

What do the equations have in common?

y = -2x + 5

y = -2x + 3

These equations have the same slope, m = -2.

How are they different?

They have different y-intercepts.

y = -2x + 5  ⇒ The y-intercept is (0, 5), where b = 5.

y = -2x + 3  ⇒ The y-intercept is (0, 3), where b = 3.

The equations have the same slope but different y-intercepts, meaning they are parallel lines that run parallel to each other and are spaced vertically apart by a difference of 2 units.

Step 1: Write each equation in slope-intercept form.

Given system of equations:

1. 2x + y = 5

2. 3y = 9 - 6x

Slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.

Let's rewrite the equations in slope-intercept form:

1. 2x + y = 5

  Subtract 2x from both sides: y = -2x + 5

2. 3y = 9 - 6x

  Divide both sides by 3: y = -2x + 3

Step 2: The equations have the same slope (-2) but different y-intercepts 5 and 3.

The common slope (-2) indicates that the lines represented by these equations have the same steepness or inclination.

The difference in y-intercepts means that the lines are parallel and run parallel to each other.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ3

(28 ⋅ 5−5 ⋅ 190)−2 ⋅ 5 to the power of negative 2 over 2 to the power of 3, whole to the power of 4 ⋅ 228. Help.

Answers

Answer 5-5.190 =-945 -2=-947 2-2=0+3 =3+7=-935

Step-by-step explanation:

Express 24 minutes as a fraction of 2'/2 hours. ​

Answers

Step-by-step explanation:

1hr = 60

½ hr = 30

60 + 30 = 90

A small pizza at Little Italy pizzeria costs $9.50, and each topping is an additional $0.50. So the cost of ordering a pizza can be determined by the equation y=0.50x+9.50, where y represents the cost of the pizza and x represents the number of toppings.

Step 2 of 2 : Use the graph to estimate to the nearest quarter of a dollar ($0.25) the cost of a small pizza with 8 toppings.

Answers

Answer:

$13.50 for 8 toppings

Step-by-step explanation:

pls help me i will mark you brilliant​

Answers

2. a) 3 days.

b) 1 hour.

3. a) 20 km

b) 1200 l

Can someone help me with this I have a headache and don't have the time or energy to use my brain

Answers

Answer:

Step-by-step explanation:

First subtract the 7 on each side [ 3 -7 ]
Then multiply both sides by 5 [-4 x 5 ]
Answer
X = -20

C D
Given: r is inversely proportional to s. If r = 16 when s = 3, then write the formula for the relation between r and s.
a. r=s/48
C. r=s/16
b. r= 48/s
d. r= 16/s
Please select the best answer from the choices provided
A
B
ОООО
Submit
Next
Save and Exit
Mark this and retum

Answers

Answer:

You choose but it looks like what you have labeled B

Step-by-step explanation:

R = K / S         INVERSE PROPORTION

16 = K / 3        VALUES GIVEN: MULTIPLY BY 3 ON BOTH SIDES

16*3 = k

K =  48

Answer: R = 48/S

Write 0.007 as a fraction.
Do not try to simplify your answer.
05

Х
5
?

Answers

Answer:

7/1000

Step-by-step explanation:

free 100 xp answer with fav movies pls for 100 free xp , 100 free xp always is given by algebros every day. Please do enjoy this plentiful amount of free xp I care about how you are feeling introduce yourself with telling me about your fav movie and why it is your fav. Enjoy! Please answer

Answers

Step-by-step explanation:

My favorite movie would have to be the Pirates of the Caribbean collection. Captain Jack sparrow aka Johnny Depp is is just great at his character.

Answer:

FREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XP

Step-by-step explanation:

A man walks 50km a day he gets R1 for every 1000 steps. How much money will he have at the end of his 50km walk if 1,6Km is = to 2000 steps.​

Answers

we have 1,6Km is = to 2000 steps => 1 km = 1250 steps

=>  50km = 1250 x 50 = 62500 steps

so he'll have: 62500/1000 = 62,5 R1

ok done. Thank to me :>

What is the slope of a line passing through the points (2, 5) and (0, −4)?

Answers

Answer:

9/2

Step-by-step explanation:

m=∆y/∆x

m= (5+4)/(2—0)

m=9/2

what number multiplied by 5 9 has a product of 1

Answers

I think the answer is five

$200 is shared between Bill and Ann. Ann’s share is $50 more than Bill’s share. Calculate the size of each of their shares.

Answers

First subtract the difference between the two:

200 - 50 = 150

Now divide that by 2:

150/2 = 75

Bills share is $75

Now add the $50 to 75 to get Ann's share:

75 + 50 = $125

Ann's share is $125

Bill's share is $75

Other Questions
How many minutes is 6:45 to 9:25 ? Define the term "failure." What historic African region is called the"Birthplace of Humanity?"A, Djene DjenoB. AxumC. NokD. Egypt No links!!!!!!!!!!! Wrong answer will be reported Work out the surface of the solid cuboid.8m6m2mThe diagram is not drawn to scale speech delivered by library prefect Eukaryotes that are not fungi, animals, or plants are classified in a "catch-all" category called ________. A. archaea B. protists C. bacteria D. seaweeds Properties of gases are dependent upon the pressure, temperature, and volume of the container they are in, as well as the number of gas particles. true or false una laptop agarra mas internet que una computadora de escritorio? which lobe of the brain is responsible for visual information? What is a symptom of too much stress over a long period of time?-insomnia-hallucinations-elevated antibodies-low-grade fever What is the porpuse of death? WILL MARK A BRAINLIEST!!! PLS HELP!!!Never gonna give you upNever gonna let you downNever gonna run around and desert youNever gonna make you cryNever gonna say goodbyeNever gonna tell a lie and hurt you Weather report, pls help me yall i dont wanna fail this class i beg you plss Need a persuasive essay on how JFK uses the 3 persuasive techniques in "The Immigrant Contribution" need a hook, thesis, and a citation for each body paragraph, also need a sayback for each body paragraph and a summarization of the main points in the conclusion, Please help?? :$):jfidifkvk place each of the labels in the proper position to denote whether they would pass through the filtration membrane or not. The school is 100 meters from Miguel's house.The following describes the most recent trip.He walked 75 meters towards school in 3min. Miguel realized that he left his iPad athome. He tumed around and walked home at thesame speed.He spent 5 min. looking for his iPad. Then he walked all the way to school at 50meters per minute.Use the graph tool to create a graph that accuratelyrepresents Miguel's walk.yeah sue decides that she will deal with her shyness by joining a poetry reading group instead of just sitting at home and daydreaming of meeting someone. her decision is based on the ______________ principle as mediated by her ego. Please answer all the questions!