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3 years ago

PLEASE HELP ME!!!

Mathematics

1 answer:

denpristay [2]3 years ago

8 0

Answer:

Step-by-step explanation:

Because when your born you don’t know where and how to find food.

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use green's theorem to evaluate the line integral along the given positively oriented curve. c 9y3 dx − 9x3 dy, c is the circle

Rina8888 [55]

The line integral along the given positively oriented curve is -216π. Using green's theorem, the required value is calculated.

<h3>What is green's theorem?</h3>

The theorem states that,

$\int_CPdx+Qdy = \int\int_D(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y})dx dy$

Where C is the curve.

<h3>Calculation:</h3>

The given line integral is

$\int_C9y^3dx-9x^3dy$

Where curve C is a circle x² + y² = 4;

Applying green's theorem,

P = 9y³; Q = -9x³

Then,

$\frac{\partial P}{\partial y} = \frac{\partial 9y^3}{\partial y} = 27y^2$

$\frac{\partial Q}{\partial x} = \frac{\partial -9x^3}{\partial x} = 27x^2$

$\int_C9y^3dx-9x^3dy = \int\int_D(-27x^2 - 27y^2)dx dy$

⇒ $-27\int\int_D(x^2 + y^2)dx dy$

Since it is given that the curve is a circle i.e., x² + y² = 2², then changing the limits as

0 ≤ r ≤ 2; and 0 ≤ θ ≤ 2π

Then the integral becomes

$-27\int\limits^{2\pi}_0\int\limits^2_0r^2. r dr d\theta$

⇒ $-27\int\limits^{2\pi}_0\int\limits^2_0 r^3dr d\theta$

⇒ $-27\int\limits^{2\pi}_0 (r^4/4)|_0^2 d\theta$

⇒ $-27\int\limits^{2\pi}_0 (16/4) d\theta$

⇒ $-108\int\limits^{2\pi}_0 d\theta$

⇒ $-108[2\pi - 0]$

⇒ -216π

Therefore, the required value is -216π.

Learn more about green's theorem here:

brainly.com/question/23265902

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3 0

2 years ago

Two angles of a triangle measure 22 and 53 what is the measure of the third angle

Musya8 [376]

The third angle is 105.
How do I know this?
Add 22 and 53:
22 + 53 = 75
All interior angles on a triangle should add up to 180.
Subtract 75 from 180:
180 - 75 = 105
105 is our answer.
Hope this helps! =)

3 0

3 years ago

I GIVEEEEE BRAINLILSTE

charle [14.2K]

Answer:

20.4cm²

Step-by-step explanation:

base= 10.2

height= 2

10.2×2=20.4cm²

3 0

3 years ago

Read 2 more answers

What is 1788.10643 rounded to the nearest hundredth??

wariber [46]

1788.11. Because the 0 will go to 1 because of the 6

3 0

3 years ago

Jack and Julio each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store.

o-na [289]

Cost of one daylily is $2 and cost of one geranium is $4.

Step-by-step explanation:

Let,

Cost of one daylily = x

Cost of one geranium = y

According to given statement;

x+5y=22 Eqn 1

13x+y=30 Eqn 2

From Eqn 1;

x=22 - 5y

Putting this value of x in Eqn 2;

$13(22-5y)+y=30\\286-65y+y=30\\-64y=30-286\\-64y=-256$

Dividing both sides by -64

$\frac{-64y}{-64}=\frac{-256}{-64}\\y=4$

Putting y=4 in Eqn 1

$x+5(4)=22\\x+20=22\\x=22-20\\x=2$

Cost of one daylily is $2 and cost of one geranium is $4.

Keywords: linear equation, substitution method

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4 0

3 years ago