1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sidana [21]
3 years ago
13

????⃗ (x,y)=(3x−4y)????⃗ +2x????⃗ F→(x,y)=(3x−4y)i→+2xj→ and ????C is the counter-clockwise oriented sector of a circle centered

at the origin with radius 44 and central angle ????/3π/3. Use Green's theorem to calculate the circulation of ????⃗ F→ around ????C.
Mathematics
1 answer:
Karolina [17]3 years ago
6 0

By Green's theorem, the integral of \vec F along C is

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_D\left(\frac{\partial(2x)}{\partial x}-\frac{\partial(3x-4y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=6\iint_D\mathrm dx\,\mathrm dy

which is 6 times the area of D, the region with C as its boundary.

We can compute the integral by converting to polar coordinates, or simply recalling the formula for a circular sector from geometry: Given a sector with central angle \theta and radius r, the area A of the sector is proportional to the circle's overall area according to

\dfrac A{\frac\pi3\,\rm rad}=\dfrac{16\pi}{2\pi\,\rm rad}\implies A=\dfrac{8\pi}3

so that the value of the integral is

\dfrac{6\times8\pi}3=\boxed{16\pi}

You might be interested in
17/20
Lena [83]

Answer:

2.39 cm

Step-by-step explanation:

6 0
3 years ago
HELP HELP HELP HELP PLEASEEE
Sphinxa [80]

The valid probability distributions are the ones in options C and D.

<h3>Which of the following are valid probability distributions?</h3>

For discrete random variables with probabilities p₁, p₂, ..., pₙ, there are two rules:

  • All of these probabilities are numbers between 0 and 1.
  • p₁ + p₂ + ... + pₙ = 1.

So, for the first rule we can discard the first option, where we have negative probabilities.

To check the other 4 options, just add the probabilities and see if the addition gives 1.

The options that add up to 1 are C and D, so these two are the correct options.

D: 1/5 + 1/10 + 1/10 + 1/10 + 1/5 + 1/10 + 1/10 + 1/10 = 1

C: 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1

If you want to learn more about probability:

brainly.com/question/25870256

#SPJ1

3 0
2 years ago
Maria makes a fruit salad. The table shows the amounts of different kinds of fruit that she uses. Kind of Fruit Amount Grapes 3
Lerok [7]

Answer:

1/4

Step-by-step explanation:

i think i might be wrong but im trying im not the best at this but there you go

5 0
3 years ago
Read 2 more answers
The Genetics &amp; IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceivi
Reika [66]

Answer: The test statistic needed to test this claim= 10.92

Step-by-step explanation:

We know that the probability of giving birth to a boy : p= 0.5

i..e The population proportion of giving birth to a boy =  0.5

As per given , we have

Null hypothesis : H_0: p\leq0.5

Alternative hypothesis :  H_a: p>0.5

Since H_a is right-tailed , so the hypothesis test is a right-tailed z-test.

Also, it is given that , the sample size : n= 291

Sample proportion: \hat{p}=\dfrac{239}{291}\approx0.82

Test statistic : z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}} , where n is sample size ,  \hat{p} is sample proportion and p is the population proportion.

\Rightarrow\ z=\dfrac{0.82-0.5}{\sqrt{\dfrac{0.5(1-0.5)}{291}}}\approx10.92

i.e. the test statistic needed to test this claim= 10.92

Critical value ( one-tailed) for  0.01 significance level = z_{0.01}=2.326

Decision : Since Test statistic value (10.92)> Critical value (2.326), so we reject the null hypothesis .

[When test statistic value is greater than the critical value , then we reject the null hypothesis.]

Thus , we concluded that we have enough evidence at 0.01 significance level to support the claim that the YSORT method is effective in increasing the likelihood that a baby will be a boy.

7 0
3 years ago
These figures are congruent.What is the measurement of E?
Tcecarenko [31]

Answer:

they are congruent so e=44°

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • 9+7r&gt;r–3≥7r+3
    10·1 answer
  • Find the total amount of interest earned on this savings account. Time: 7 years Interest Rate: 2.5% Principal: $4,556 Interest:
    10·2 answers
  • Write the 2 digit number that matches the clue
    15·1 answer
  • Use the elimination method to solve the system of equations.
    5·1 answer
  • What is the sales tax of a $249 cell phone if the tax rate is 8%​
    11·2 answers
  • What is the volume of a cylinder with a radius of 7.5 cm and a height of 20 cm
    5·1 answer
  • What does the expression l∙w represent
    8·1 answer
  • What Will You nota miss about remote learning​
    15·2 answers
  • Charles and his brother are sharing the cost of a video game. The video game costs $30.70. If Charles saved $20 to buy the game
    14·1 answer
  • if the formula for number of people in bus is p=50b, where k= 50 people per bus show me the formula for number of buses per pers
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!