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
blondinia [14]
3 years ago
6

Let F⃗ =2(x+y)i⃗ +8sin(y)j⃗ .

Mathematics
1 answer:
Alik [6]3 years ago
4 0

Answer:

-42

Step-by-step explanation:

The objective is to find the line integral of F around the perimeter of the rectangle with corners (4,0), (4,3), (−3,3), (−3,0), traversed in that order.

We will use <em>the Green's Theorem </em>to evaluate this integral. The rectangle is presented below.

We have that

           F(x,y) = 2(x+y)i + 8j \sin y = \langle 2(x+y), 8\sin y \rangle

Therefore,

                  P(x,y) = 2(x+y) \quad \wedge \quad Q(x,y) = 8\sin y

Let's calculate the needed partial derivatives.

                              P_y = \frac{\partial P}{\partial y} (x,y) = (2(x+y))'_y = 2\\Q_x =\frac{\partial Q}{\partial x} (x,y) = (8\sin y)'_x = 0

Thus,

                                    Q_x -P_y = 0 -2 = - 2

Now, by the Green's theorem, we have

\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA = \int \limits_{-3}^{4} \int \limits_{0}^{3} (-2)\,dy\, dx \\ \\\phantom{\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA}= \int \limits_{-3}^{4} (-2y) \Big|_{0}^{3} \; dx\\ \phantom{\oint_C F \,dr = \iint_D (Q_x-P_y)\,dA}= \int \limits_{-3}^{4} (-6)\; dx = -6x  \Big|_{-3}^{4} = -42

You might be interested in
You go to the store to buy icecream. The icecream comes in a cylindrical tub that has a diameter of 5 inches and is 4 inches tal
telo118 [61]

Answer:78.5

Step-by-step explanation:

First you find the volume of a cylinder then you plug in the answers don't forget that to find the radius you do diameter divided by 2

5 0
3 years ago
Plzzzzzzzzzzzzzzzzaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
erastovalidia [21]

Answer:

Option A

Step-by-step explanation:

Number of employees exceeded their sales quota = 17

Number of employees met their sales quota = 13

Number of employees didn't exceed their sales quota = 3

Now, we need to find the ratio of the number employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota,

17:13 + 3\\=17:16

So, Option 'A' is correct.

Please mark as Brainliest!!

3 0
3 years ago
Slove the following equation.<br>6n - 3(n + 2) + 3(7n + 1) = 0​
Otrada [13]

Answer:

here is my working out to find answer, if u feel that the answer is wrong then do the reverse calculation by putting n value to the equation. hope u understood and stay safe!

6 0
2 years ago
Community Gym charges a $60 membership fee and a $60 monthly fee. Workout Gym charges a $200 membership fee and a $50 monthly fe
Kitty [74]

Answer:

14 months

Step-by-step explanation:

60x+60=50x+200

10x+60=200

10x=140

x=14

60(14)+60=900

50(14)+200=900

8 0
3 years ago
Look at the figure shown below:
kow [346]

Answer:  b) two sides and the included angle are congruent

<u>Step-by-step explanation:</u>

  RS = QS                 SIDES are congruent

∠PSR ≡ ∠PSQ         ANGLES are congruent

 PS = PS                  SIDES are congruent

ΔPSR ≡ ΔPSQ by the Side-Angle-Side (SAS) Congruency Theorem

Since we know the triangles are congruent, we can state that their parts are congruent:

Congruent-Parts of-Congruent-Triangles are-Congruent (CPCTC)

8 0
3 years ago
Other questions:
  • Write an equation for the translation of y = |x|. 15.5 units down
    5·2 answers
  • Joanne has a cylindrical, above ground pool. the depth (height) of the pool is 1/2 of its radius, and the volume is 1570 cubic f
    11·1 answer
  • Bodytemperatures ofhealthy koalasarenormally distributed with a mean of 35.6°C and a standard deviation of 1.3°C. a.What is the
    15·1 answer
  • ,,,,,,,,,,,,,,,,,,,,,,,,
    7·1 answer
  • Micah deposited $4000 between two savings account. One account earns 4% simple interest each year. The other account earns 2% si
    5·1 answer
  • The drama club has sold 942 tickets to their play if their theater seats 57 in each row how many full rows were there be how man
    12·1 answer
  • Helppppppppppppppppppppppppp
    11·2 answers
  • At a carnival luke bought 33 tickets . if he used 3 tickets trying to win the ring toss game,what is the ratio of tickets he has
    10·2 answers
  • Find the nth term of the quadratic sequence
    10·2 answers
  • Find the surface area of the prism.<br> 7 mm<br> 4 mm<br> 5 mm
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!