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elena-14-01-66 [18.8K]

2 years 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

1 answer:

Greeley [361]2 years 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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Fill in missing information to make the equality true: <br> (... +2a)2 = … +12ab2+4a2.

BigorU [14]

Answer:

I suppose it should be

6b² and (6b²)²

or

6b² and 36 $b^{4}$

Step-by-step explanation:

(a+b)² = a² + 2ab + b²

therefore

(6b²+2a)² = (6b²)² + 12ab² + 4a²

3 0

2 years ago

Read 2 more answers

Automobile repair costs continue to rise with the average cost now at $367 per repair (U.S. News & World Report website, Jan

tino4ka555 [31]

Answer:

$\mu = 367$

$\sigma = 88$

a. What is the probability that the cost will be more than $450?

We are supposed to find P(x > 450)

Formula : $z=\frac{x-\mu}{\sigma}$

$z=\frac{450-367}{88}$

$z=0.9431$

Refer the z table :

P(z<0.9431)=0.8264

P(z> 0.9431)=1-P(z<0.9431)=1- 0.8264= 0.1736

Hence the probability that the cost will be more than $450 is 0.1736

b)What is the probability that the cost will be less than $250?

We are supposed to find P(x<250)

Formula : $z=\frac{x-\mu}{\sigma}$

$z=\frac{250-367}{88}$

$z=-1.3295$

Refer the z table :

P(z<-1.3295)=0.0934

Hence the probability that the cost will be less than $250 is 0.0934

c)What is the probability that the cost will be between $250 and $450?

P(250<z<450)=P(z<450)-P(z<250) = 0.8264 - 0.0934 =0.733

Hence the probability that the cost will be between $250 and $450 is 0.733

d) If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost?

p = 0.05

refer the z table

z = -1.65

Formula : $z=\frac{x-\mu}{\sigma}$

$-1.65=\frac{x-367}{88}$

$-1.65 \times 88=x-367$

$-145.2+367=x$

$221.8=x$

Hence If the cost for your car repair is in the lower 5% of automobile repair charges, so, cost is $221.8

4 0

2 years ago

One fourth of all telephones at the office have built in speaker phones. One -half the phones with the built-in speaker phones h

Helga [31]

Answer:

$\frac{1}{8}$ of the phones in office has both a speaker phone and a conference-call capability

Step-by-step explanation:

Since total number of phones in the office is not given, the answer will be "in that terms".

let it be x

So built in speaker phones is (1/4)x

Hence conference call phones would be (1/2)(1/4x) = (1/8)x

Hence "1/8th of the phones in office has both a speaker phone and a conference-call capability"

7 0

2 years ago

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The automatic car wash at a service station can wash 96 cars over a 4-hour period. What is the average number of cars that can b

Evgen [1.6K]

Answer:

Divide 96/4 to get how many cars can be washed within a single hour. Cut that in half to get 12.

Step-by-step explanation:

96÷4=24 cars/hr

24÷2=12 Cars for every 30 minutes.

7 0

2 years ago

Write the first five terms of the geometric sequence in which a1=64 and the common ratio is 5/4

natita [175]

Remember that finding terms in a geometric sequence is done by multiplying the previous term by a common ratio $r$ . For example, we can say:

$a_2 = a_1 r$

$a_3 = a_2 r = (a_1 r)r = a_1 r^2$

We have $a_1 = 64$ . To find $a_2$ , let's multiply this term by $\frac{5}{4}$ :

$a_2 = 64 \cdot \frac{5}{4} = 80$

Now, let's use this to find all of our other terms:

$a_3 = 80 \cdot \frac{5}{4} = 100$

$a_4 = 100 \cdot \frac{5}{4} = 125$

$a_5 = 125 \cdot \frac{5}{4} = \frac{625}{4}$

Thus, our terms are 64, 80, 100, 125, and (625/4).

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2 years ago