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.

please i need real time help

Answers

Answer 1

It looks like the integral is

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

where C is the circle of radius 2 centered at the origin.

You can compute the line integral directly by parameterizing C. Let x = 2 cos(t ) and y = 2 sin(t ), with 0 ≤ t ≤ 2π. Then

[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \int_0^{2\pi} \left((3x(t)+4y(t))\dfrac{\mathrm dx}{\mathrm dt} + (2x(t)-3y(t))\frac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt \\\\ = \int_0^{2\pi} \big((6\cos(t)+8\sin(t))(-2\sin(t)) + (4\cos(t)-6\sin(t))(2\cos(t))\big)\,\mathrm dt \\\\ = \int_0^{2\pi} (12\cos^2(t)-12\sin^2(t)-24\cos(t)\sin(t)-4)\,\mathrm dt \\\\ = 4 \int_0^{2\pi} (3\cos(2t)-3\sin(2t)-1)\,\mathrm dt = \boxed{-8\pi}[/tex]

Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on C nor in the region bounded by C, so

[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \iint_D\frac{\partial(2x-3y)}{\partial x}-\frac{\partial(3x+4y)}{\partial y}\,\mathrm dx\,\mathrm dy = -2\iint_D\mathrm dx\,\mathrm dy[/tex]

where D is the interior of C, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: [tex]-2\times \pi\times2^2 = -8\pi[/tex].


Related Questions

19. When the members of a high school club are
arranged in rows of 2, 3, or 4, there is one
person always left over. But when the club
members are arranged in rows of 5, no one is
left over. What is the least number of people
who could be in the club?
À 15 people
C 45 people
B 25 people D 85 people

Answers

9514 1404 393

Answer:

 B.  25 people

Step-by-step explanation:

The remainders tell you the number will be 1 more than some multiple of the least common multiple (LCM) of 2, 3, and 4. The LCM is 3·4 = 12, so we want some multiple (n) of that such that 12n+1 is a multiple of 5. We know this is the case for n=2.

The least number of people who could be in the club is 2·12+1 = 25.

Select the correct answer.
Based on these segment lengths, which group of segments cannot form a triangle?
OA 12,7,8
OB. 8, 7, 13
OC. 1,2,3
OD. 80,140, 70
Reset
Next
2021 EdimentumAll rights

Answers

Answer:

C

Step-by-step explanation:

If you add up the length of two sides, the sum must be greater than the third side of the triangle.

If you add 1 and 2, it equals 3

But that means it will be equal to the length of the third side, 3

It will be impossible to make a triangle with those lengths of sides no matter how the sides or angles are set.

It's sort of difficult to explain this without any visual

You can look up "triangle inequality" to find out more about this

Name the two input device​

Answers

Answer:

keyboard and mouse are two examples of input device

Answer:

keyboard and mouse

Step-by-step explanation:

If you like my answer than please mark me brainliest

Anyone’s knows how do this and the answer?

Answers

Answer:

12 -16. 19

4. 8. 22

3. -9. -4

Step-by-step explanation:

13-1 = 12

-10-6= -16

12 - -7 = 12+7=19

6-2 = 4

Keep subtracting

log base 4 (x+3)²- log base 4 y² = 0​

Answers

Answer:

x = - |y| - 3

Step-by-step explanation:

The Earth scientist most likely to study volcanoes is a (n)

A. Meteorologist

B. Geologist

C. Oceanographer

D. Astronomer

Answers

The answer is B Geologist

Answer:

geologist

Step-by-step explanation:

they work with the earths surface and natural land that changes

4 adults consumed food costing $60 for 3days. For the same food cost ,what would be the cost of food consumed by 7 adults for 5days?

Answers

Answer:

$175

Step-by-step explanation:

$60÷3÷4 =5

$5 is the cost of one adult's food for one day.

$5×7×5

=$175

$175 is the cost of food consumed by 7 adults for 5 days.

divide write your answer in simplest form 2/3 divided by 1/4

Answers

Answer:

8/3 or 2.6667

Step-by-step explanation:

when you divide fractions you use a technique called KCF

K = keep

C = change

F = flip

You write the equation [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{4}[/tex]

you keep [tex]\frac{2}{3}[/tex]

you change the symbol, so from ÷ you change it to x

and flip the last fraction, so you would have  [tex]\frac{4}{1}[/tex]

then you solve it

[tex]\frac{2}{3}[/tex] x  [tex]\frac{4}{1}[/tex] = [tex]\frac{8}{3}[/tex]

The result of 2/3 divided by 1/4 in simplest form is 8/3 .

Division: It is one of the four basic mathematical operation, the other three being addition, subtraction, multiplication.

Given, division of [tex]\frac{2}{3}[/tex] by [tex]\frac{1}{4}[/tex].

Division of fractional terms:

[tex]=\dfrac{\frac{a}{b}}{\frac{c}{d}}\\= (a)\times(d)/(b)\times(c)[/tex]

Apply, division process of fractional terms.

[tex]=\dfrac{\frac{2}{4}}{\frac{1}{3}}\\ = (2)\times(4)/(1)\times(3)[/tex]

[tex]= \frac{8}{3}[/tex]

Know more about division,

https://brainly.com/question/29775887

#SPJ6

Need answers in 2 minutes ASAP

Answers

Step-by-step explanation:

f(10)=10

f(-2)=-2

f(a)=a

f(a+b)=a+b

g(10)=5×10-12=3

g(-2)=5×(-2)-12=-10-12=-22

g(a)=5×a-12=5a-12

g(a+b)=5×(a+b)-12=5a+5b-12

h(10)=(10)^2 +4(10)-7=100+40-7=133

h(-2)=(-2)^2 +4(-2)-7=4-8-7=-11

h(a)=a^2 +4a -7

h(a+b)=(a+b)^2 +4a+4b-7=a^2+2ab+b^2+4b-7

The sum of twice a number and three

Answers

Answer:

i dont get what youre asking

Step-by-step explanation:

Answer:

2n + 3

Step-by-step explanation:

n = number

Sum of twice a number (2n) and (3)

-> 2n + 3

find the value of a and b in (a,2)=(2,b)​

Answers

Answer:

a=2 and b=2...............

Which graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then decreases its speed, as time increases?

A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins at 0, goes up at first, is steady for a while, and then goes down over time.
A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins in the middle of the vertical axis, goes down at first, is steady for a while, and then goes up over time.
A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins at 0, goes up at first, goes down for a while, and then is steady over time.

Answers

9514 1404 393

Answer:

  A

Step-by-step explanation:

If you read your own question, you find that it answers itself.

The problem statement tells you that speed ...

  ... increasing its speed, constant speed, then decreases

And it tells you the graphs show ...

  (a) begins at 0, goes up, is steady for a while, and then goes down

  (b) begins in the middle, goes down, is steady, and then goes up

  (c) begins at 0, goes up, goes down, and then is steady

___

The first graph has the increasing, steady, decreasing pattern you're looking for.

Problem 2
Find the area of each shaded region. Show or explain your reasoning.
A
2 cm
B
2 cm
2cm
6 cm
5 cm
3 cm
6 cm
8 cm
C С
D
15 cm
8 cm
8 cm
15 cm
9 cm
6 cm
10 cm

Answers

Step-by-step explanation:

A

this is the combination of a 4×6 rectangle and a 2×2 square. nothing is excluded.

so, the area is

(6-2)×6 + 2×2 = 4×6 + 4 = 24 + 4 = 28 cm²

B

this is the area of the large 8×5 rectangle minus the area of the small 2×3 rectangle.

so the area is

8×5 - 3×2 = 40 - 6 = 34 cm²

C

Basically the same thing as for B. large rectangle minus smaller rectangle.

so, the area is

15×10 - 9×6 = 150 - 54 = 96 cm²

D

the area of a triangle is

baseline × height / 2

or baseline here is 2×8, and the height is 5

so we get the area

2×8 × 5 / 2 = 8×5 = 40 cm²

Solve for x
ax+bx=10

Answers

Answer:

[tex]ax + bx = 10 \\ \\ x(a + b) = 10 \\ \\ x = \frac{10}{a + b} [/tex]

I hope I helped you^_^

Find the midpoint of the segment with the given endpoints. (-7,-4) and (3,7)?

Answers

9514 1404 393

Answer:

  (-2, 1.5)

Step-by-step explanation:

The coordinates of the midpoint are the average of the end point coordinates:

  ((-7, -4) +(3, 7))/2 = (-7+3, -4+7)/2 = (-4, 3)/2 = (-2, 1.5)

The coordinates of the midpoint are (-2, 1.5).

The area of a circle is 78.5 cm^2. What is the diameter of the circle?
-5 cm
-10 cm
-12.5 cm
-39.25 cm

Answers

Answer:

10cm

Step-by-step explanation:

78,5=pi.r^2

Answer5:

Step-by-step explanation:

Determine the sum by suitable re arrangement .
a) 6254 + 1297 + 446 + 103 Ans:
b) 1983 + 647 + 217 + 353 2.​

Answers

Answer:

a.8100

b.3200

Step-by-step explanation:

hope you're okay

What is the fraction or mixed number and write in its simplest form.
3.8416

3.8416=—- (type an integer,proper fraction, or mixed number.)

Answers

Answer:

38416/10000

plss mark me brainliestt

Step-by-step explanation:

3.8416=38416/10000

Which statement describes the graph?

Answers

Answer:

the graph crosses the y-axis at -5 and x-axis at -6

QUESTION 1 11 How does the term quartile relate to how data values are grouped when using a five- number summory?​

Answers

Data from the Bureau of Labor Statistics has been put into order by placing data in the lower and upper quartiles. If data are placed in order, then the lower quartile is central to the lower half of the data and the upper quartile becomes central to its upper half.

which graph represents the following system of inequalities?
a
b
c
d

Answers

Answer:

A

Step-by-step explanation:

Mark me brainliest.

Both graphs need dashed lines, since they’re < and > and not ≤ or ≥.

You need to shade above y > -x - 4 and you need to shade below y < 2x - 3.

You want to only include the purple section on the right.

derivative : y=[(1+x^2)arctgx-x]/2

Answers

Answer:

s,-8*2-`±_'682-¥´owhsi

3/6, 1/12, 3/6, 3/60 determine the lcd by division of prime number

Answers

Answer:

LCD = 60

BRAINLIEST, PLEASE!

Step-by-step explanation:

All of the denominator numbers are multiples of 60, and since 60 is also equal to the largest denominator number, it's the LCD.

[tex]\lim_{n \to \0}(x/(tan⁡(x))^(cot⁡(x)^2 )[/tex]

Answers

It looks like the limit you want to compute is

[tex]\displaystyle L = \lim_{x\to0}\left(\frac x{\tan(x)}\right)^{\cot^2(x)}[/tex]

Rewrite the limand with an exponential and logarithm:

[tex]\left(\dfrac{x}{\tan(x)}\right)^{\cot^2(x)} = \exp\left(\cot^2(x) \ln\left(\dfrac{x}{\tan(x)}\right)\right) = \exp\left(\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right)[/tex]

Now, since the exponential function is continuous at 0, we can write

[tex]\displaystyle L = \lim_{x\to0} \exp\left(\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right) = \exp\left(\lim_{x\to0}\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right)[/tex]

Let M denote the remaining limit.

We have [tex]\dfrac x{\tan(x)}\to1[/tex] as [tex]x\to0[/tex], so [tex]\ln\left(\dfrac x{\tan(x)}\right)\to0[/tex] and [tex]\tan^2(x)\to0[/tex]. Apply L'Hopital's rule:

[tex]\displaystyle M = \lim_{x\to0}\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)} \\\\ M = \lim_{x\to0}\dfrac{\dfrac{\tan(x)-x\sec^2(x)}{\tan^2(x)}\times\dfrac{\tan(x)}{x}}{2\tan(x)\sec^2(x)}[/tex]

Simplify and rewrite this in terms of sin and cos :

[tex]\displaystyle M = \lim_{x\to0} \dfrac{\dfrac{\tan(x)-x\sec^2(x)}{\tan^2(x)}\times\dfrac{\tan(x)}{x}}{2\tan(x)\sec^2(x)} \\\\ M= \lim_{x\to0}\dfrac{\sin(x)\cos^3(x) - x\cos^2(x)}{2x\sin^2(x)}[/tex]

As [tex]x\to0[/tex], we get another 0/0 indeterminate form. Apply L'Hopital's rule again:

[tex]\displaystyle M = \lim_{x\to0} \frac{\sin(x)\cos^3(x) - x\cos^2(x)}{2x\sin^2(x)} \\\\ M = \lim_{x\to0} \frac{\cos^4(x) - 3\sin^2(x)\cos^2(x) - \cos^2(x) + 2x\cos(x)\sin(x)}{2\sin^2(x)+4x\sin(x)\cos(x)}[/tex]

Recall the double angle identity for sin:

sin(2x) = 2 sin(x) cos(x)

Also, in the numerator we have

cos⁴(x) - cos²(x) = cos²(x) (cos²(x) - 1) = - cos²(x) sin²(x) = -1/4 sin²(2x)

So we can simplify M as

[tex]\displaystyle M = \lim_{x\to0} \frac{x\sin(2x) - \sin^2(2x)}{2\sin^2(x)+2x\sin(2x)}[/tex]

This again yields 0/0. Apply L'Hopital's rule again:

[tex]\displaystyle M = \lim_{x\to0} \frac{\sin(2x)+2x\cos(2x)-4\sin(2x)\cos(2x)}{2\sin(2x)+4x\cos(2x)+4\sin(x)\cos(x)} \\\\ M = \lim_{x\to0} \frac{\sin(2x) + 2x\cos(2x) - 2\sin(4x)}{4\sin(2x)+4x\cos(2x)}[/tex]

Once again, this gives 0/0. Apply L'Hopital's rule one last time:

[tex]\displaystyle M = \lim_{x\to0}\frac{2\cos(2x)+2\cos(2x)-4x\sin(2x)-8\cos(4x)}{8\cos(2x)+4\cos(2x)-8x\sin(2x)} \\\\ M = \lim_{x\to0} \frac{4\cos(2x)-4x\sin(2x)-8\cos(4x)}{12\cos(2x)-8x\sin(2x)}[/tex]

Now as [tex]x\to0[/tex], the terms containing x and sin(nx) all go to 0, and we're left with

[tex]M = \dfrac{4-8}{12} = -\dfrac13[/tex]

Then the original limit is

[tex]L = \exp(M) = e^{-1/3} = \boxed{\dfrac1{\sqrt[3]{e}}}[/tex]

On solving equation 3*1/5b+5=50, the value of b will be?

Answers

Answer:

Step-by-step explanation:

14 1⁄16

Write a two-step equation and solve.

Four more than six times a number is 22

Five less than eleven times a number is 50

Seven less than nine times a number is -16

Answers

Step-by-step explanation:

1) let number=a

six times a number=6a

Condition:

6a+4=22

2) eleven times a number=11a

Condition:

11a-5=50

3) 9 times a number=9a

Condition:

9a-7=-16

Note:if you need to ask any question please let me know.

Solve the below:
4x+3y=7 3x-2y=9

Answers

4x+3y=7
3x-2y=9

12x+9y=21
12x-8y=36
^^Multiply top equation by 3 and multiply bottom equation by 4

12x+9y=36
- 12x-8y=36

17y=-15
^^Then subtract those two new equations

17y/17= -15/17

Y= -0.88
^^Next divide both sides by 17

4x+3* -0.88=7

4x + (-2.64) =7
-(-2.64) -(-2.64)

4x = 9.64

4x/4=9.64/4
X=2.41

^^then choose on equation and put your new y in the y spot and solve.


X=2.41

Y=-0.88

Your point/coordinate is (2.41,-.88)

Do you guys know this because I was trying to submit but it don’t let me I put 7/6 but it say I need different Way

Answers

Answer:

is 5

Step-by-step explanation:

Hope it is helful...

Answer:

5

Step-by-step explanation:

So first when dividing fractions you need to invert and multiply. Thus the fraction becomes:

1/4 * 20/1.

When simplified it becomes 20/4 which is 5.

HOPE THIS HELPED

express 3x-x^2 as m-(x-n)^2. Ill give brainliest to correct answer!
(Also please see the picture since you might mistake x having a square as a 2x)

Answers

This is simply done by Method of Completing the Square.

3x - x²

Add and subtract half the coefficient of x and square it.

( This is done so there'd be no alterations to the quadractic Expression)

So To start

We'd like x² to be positive...(So factor out a negative).

( - 3x )

Now In this case

You see there's a Negative Outside the the bracket

Instead of adding and Subtracting squared values of half the coefficient of X... We'd Add Twice and do not subtract.

Reason: If you add outside the bracket and subtract the other inside the bracket... This will be wrong because there's a negative patiently waiting outside the bracket to Interact with the negative you subtracted to make it Positive.

See what I mean.

Let's say you added 2² and subtracted 2² in this problem

( - 3x - 2²)

If you decide to open the bracket

You'll have

+ 3x + 2²

NOW THIS IS WRONG BECAUSE WE ALTERED THIS EXPRESSION. WHERE'D 2² + 2² COME FROM?

THIS IS WHY YOU'LL ADD THE SQUARED COEFFICIENT OF X TWICE IN CASES LIKE THESE.

SO GOING BACK TO THE ORIGINAL QUESTION.

(x² - 3x )

Adding the half the coefficient of x twice and squaring them...

Coefficient of x = 3

Half of 3 = 3/2

Squaring it gives (3/2)²

NOW PROCEEDING

(3/2)² [ - 3x + (3/2)²]

If you open this bracket... (3/2)² will cancel out with (3/2)²

Meaning that we haven't altered the expression in any way

Moving On...

Applying basic factorizing principle

9/4 ( x - 3/2)².

Answer = 9/4 ( x - 3/2)² Which is in the Form m ( x - n )²

Therefore m = 9/4 and n = 3/2.

Hope This Helps

y=3x+2y is it a function how do you do it

Answers

9514 1404 393

Answer:

  yes

Step-by-step explanation:

Solve for y. You can do this by subtracting 3x+y from both sides of the equation.

  y -(3x+y) = 3x +2y -(3x +y)

  -3x = y

Or ...

  y = -3x

Each value of x maps to a single value of y, so this relation is a function.

_____

This equation is a first-degree polynomial in x. Any polynomial relation y=p(x) is a function, so this is a function.

Other Questions
Help me plz1. What is the changes in castle design over the medieval period?2. Reasons for the changes Plz help me in this math Simplify { 36 divided by (9) } divided { (-24) divided 6}step by step needed que quiete comprar Micaela Write two adjectives or descriptive phrases that describe each term: House of BurgessesJonathan EdwardsFrench and Indian WarEnglish Bill of Rights Great Awakening bi 5: rt gn (x +1)^2 (2x + 1)^2 What test do you need to do before draw blood from the radial artery? Which point on the number line best represents v57 Informational texts often contain technical _______.A. meaningsB. jargonC. ideasD. words Anna would like to purchase a new bike that costs $205. She already has $31 saved. If she saves a maximum of $12 a week, the following inequality can be used to find the minimum number of weeks, w, it will take Anna to save the money to purchase the bike. 12w+31 205Please show all steps thank you Magnesium occurs naturally in only three isotopes. ^24 Mg has an isotopic mass of 23.9850 amu and an abundance of 78.99%. ^25 Mg has an isotopic mass of 24.9858 amu and an abundance of 10.00%. Find the mass number of the last isotope of magnesium. Can someone please explain how to solve this? *done mine the notes* Can I please have help on a Timer You are adding two rational numbers with different signs.How can you tell if the sum will be positive, Negative,or Zero -3(-3x^2 + 2x)How do I distribute? Cholesterol can also accumulate in the walls of the coronary arteries. Explain the effect this might have Write a short story that end as he never came again. newspaper and radio are most common means of communication in nepal give your opinion to justify this statement To pay for a 15,300 car, Tony made a down payment of $3900 and took out a loan for the rest. On the loan , he paid monthly payment payment of $252.34 for 4 years. READ FOR BOOST OF CONFIDENCE NOT JSUT FOR THE POINTS THANK YOU HAVE A GOOD DAY!!Everyone who gets teased,named called,picked on and anything else you are going through at school or at home ignore them you have to belive your more than what people call you.You have to believe that you are perfect and you have people that you can talk to, you have people who love you and care for you.You belong in this world even if you think you dont you do. You are beautiful inside and out, dont let words get to you they might hurt a lot but you have to tell your self it not true. You have to tell your self you are smart, you are amazing, you are beautiful, you have a reason to be on this earth. So dont listen to other people when they are bullying you stand up to them get help do what ever they can. Dont take anything they say to heart. in which type of setting are characters most likely to lose their innocence? A. forest B. island C. Inn D. Paradise