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lys-0071 [83]
3 years ago
15

Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise.

Mathematics
1 answer:
anzhelika [568]3 years ago
3 0

By Green's theorem, the circulation of \vec F(x,y)=\langle2xy^2,4x^3+y\rangle around C is equal to

\displaystyle\iint_D\frac{\partial(4x^3+y)}{\partial x}-\frac{\partial(2xy^2)}{\partial y}\,\mathrm dx\,\mathrm dy

where D is the region with C as its boundary. The integral is equivalent to

\displaystyle\int_0^\pi\int_0^{\sin x}(12x^2-4xy)\,\mathrm dy\,\mathrm dx=\boxed{\frac{23\pi^2}2-48}

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You buy tires for $150 per tire. You want to replace all four tires The dealership
a_sh-v [17]

$540

Step-by-step explanation:

$150 × 4 = $600

$600 ÷ 10 = $60

$600 - $60 = $540

7 0
3 years ago
Moby sold half his toy car collection, and then bought 12 more cars the next day. He now has 48 toy cars. How many cars did he h
castortr0y [4]

Answer: 72 cars.

Step-by-step explanation:

Let be "x" the number of toys that Moby had to start with.

According to the information given in the exercise, Moby sold half his toy car collection. This can be represented with the following expression:

\frac{1}{2}x

Then he bought 12 more cars, giving a total amount of 48 toy cars.

Therefore, the equation that represents this situation is the equation shown below:

x-\frac{1}{2}x+12=48

Now you must solve for "x" in order to find its value.

You get that this is:

\frac{1}{2}x+12=48\\\\\frac{1}{2}x=48-12\\\\\frac{1}{2}x=36\\\\x=(36)(2)\\\\x=72

7 0
3 years ago
Victor is measuring his bodily dimensions. his neck is 14.72 inches in circumference, and his forearm is 25.81 centimeters long.
Triss [41]

The length of his neck is longer than the length of his forearms by 44.86 %.

<h3>Calculations and Parameters:</h3>

Given:

Length of his neck = 14.72 inches

Length of his forearm = 25.81 cm

We know that:

1 inch = 2.54 cm

So, 14.72 inches = 14.72×2.54

=37.39 cm

So, the Length of his neck becomes 37.39 cm

So, the length of his neck is longer than the length of his forearms.

The difference between them is given by

37.39-25.81

=11.58 cm

so, the Percentage of change would be

11.58/25.81 * 100

=44.86%

Read more about percentages here:

brainly.com/question/7255460

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6 0
2 years ago
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harina [27]

Answer:

Exact Form:

x= -3/2

Decimal Form:

x= -1.5

Mixed Number Form

x= -1 1/2

Step-by-step explanation:

4 0
3 years ago
Find the value of x (5x+4)=(8x-71)
sesenic [268]

Answer:

5x +4 =8x - 71

-3x +4 = -71

-3x= -75

x= 25

3 0
3 years ago
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