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elena-14-01-66 [18.8K]
1 year ago
5

Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (-2,1), (-2,-3), (1,-1) , (

1,5), and back to (-2,1), in that order. Use Green's theorem to evaluate the integral:
Integral(C) (2xy) dx +(xy^2) dy
Mathematics
1 answer:
Greeley [361]1 year ago
6 0

The given points are the vertices of the quadrilateral

Q=\left\{(x,y)\mid-2\le x\le1,\dfrac{2x-5}3\le y\le\dfrac{4x+11}3\right\}

By Green's theorem, the line integral is

\displaystyle\int_C2xy\,\mathrm dx+xy^2\,\mathrm dy=\iint_Q\frac{\partial(xy^2)}{\partial x}-\frac{\partial(2xy)}{\partial y}\,\mathrm dA

=\displaystyle\int_{-2}^1\int_{(2x-5)/3}^{(4x+11)/3}y^2-2x\,\mathrm dy\,\mathrm dx=\boxed{61}

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7) Let the random variable X represent the amount of money Dan makes doing lawn care in a randomly selected week in the summerAs
Sphinxa [80]

Answer:

Option A. 0.6 is the right answer.

Step-by-step explanation:

Given information is:

Mean = $240

SD = $60

The probability of Dan making less than $255 has to be found.

Let x = 255

First of all, we will find the z-score of the given value

z = \frac{x-mean}{SD}\\z = \frac{255-240}{60}\\z = \frac{15}{60}\\z = 0.25

Now the z-score table will be used to see the probability of less than 0.25

Using the z-score table, we get:

P(x<0.25) = 0.5987

As the answer choices are rounded off to one decimal place, we will round off our answer to one digit after the decimal point

0.5987 => 0.6

Hence,

Option A. 0.6 is the right answer.

6 0
1 year ago
Tyra is training for a bicycle race. Each week she rides a total distance greater than 10 km and less than or equal to 30 km. If
atroni [7]

Our distance is x
We know each week she rides a total distance greater than 10 km and less than or equal to 30 km
We can write this like the following:
x > 10
x <= 30

It also tells us the distance is always an even number and a multiple of 3. Ask your self, what are some numbers between 10 and 30 and is a multiple of 3.

12, 18, 24 and 30

So the possible distances are 12, 18, 24, 30 

Notice each number is an even number and you can divide the number by 3 evenly so they are numbers with 3 being a multiple. 




3 0
1 year ago
The cost for a company to manufacture x bracelets can be represented by the function C(x). Complete the sentence below using the
gizmo_the_mogwai [7]
The cost for a company to manufacture "x".... 
These statements tell you what X is. (The word cost refers to what the function will tell us. In other words C(x) = The Cost for the Company)) 

So as we keep going the problem goes onto: 
.... bracelets
So the number of bracelets is X. 

The function is: C(x) 

And how functions work are quite simple. You plug in a number (x) and get out a number (y).

So, C(256) = 1536

So, they made 256 bracelets at a cost of 1536 dollars. 

This is no different than if I said the function was: 
C(x) = 6x
And then asked, what would the function equal when x = 256. It's the same thing, so don't let it trip you up! 

Answer 1: 1536$
Answer 2: 256

3 0
2 years ago
Read 2 more answers
Shelby, Allen, and Denise printed their digital photos. Each requested the same size prints. Shelby paid $2.70 for 5 prints. All
tekilochka [14]
Person:    Number of prints      Total Cost
Shelby             5                               2.70
Allen               11                              3.24
Denise            20                             4.05

To solve for the variable cost:
11 - 5 = 6
3.24 - 2.70 = 0.54
0.54 / 6 = 0.09 per print

To solve for the fixed cost
0.09 x 5 = 0.45
2.70 - 0.45 = 2.25 

y = 2.25 + 0.09x

y = 2.25 + 0.09(5) = 2.25 + 0.45 = 2.70
y = 2.25 + 0.09(11) = 2.25 + 0.99 = 3.24
y = 2.25 + 0.09(20) = 2.25 + 1.8 = 4.05
4 0
1 year ago
Read 2 more answers
Jada wants to know how fast the water comes out of her faucet. What information would she need to know to be able to determine t
Mashutka [201]

Answer:

The distance the water is traveling and the time it took.

Step-by-step explanation:

The speed formula is s= d/t so I would guess that is what the question means.

(Sorry if I didn't take a lot of time to answer, it had caps so I would guess that you needed the answer fast. )

4 0
1 year ago
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