X+1/X=26/5<br>plz help me fast plz i will be thankful to you.❤❤

Find the area of the region that is inside r=3cos(theta) and outside r=2-cos(theta). Sketch the curves.

raketka [301]

Answer:

3√3

Step-by-step explanation:

r = 3 cos θ

r = 2 - cos θ

First, find the intersections.

3 cos θ = 2 - cos θ

4 cos θ = 2

cos θ = 1/2

θ = -π/3, π/3

We want the area inside the first curve and outside the second curve. So R = 3 cos θ and r = 2 - cos θ, such that R > r.

Now that we have the limits, we can integrate.

A = ∫ ½ (R² - r²) dθ

A = ∫ ½ ((3 cos θ)² - (2 - cos θ)²) dθ

A = ∫ ½ (9 cos² θ - (4 - 4 cos θ + cos² θ)) dθ

A = ∫ ½ (9 cos² θ - 4 + 4 cos θ - cos² θ) dθ

A = ∫ ½ (8 cos² θ + 4 cos θ - 4) dθ

A = ∫ (4 cos² θ + 2 cos θ - 2) dθ

Using power reduction formula:

A = ∫ (2 + 2 cos(2θ) + 2 cos θ - 2) dθ

A = ∫ (2 cos(2θ) + 2 cos θ) dθ

Integrating:

A = (sin (2θ) + 2 sin θ) |-π/3 to π/3

A = (sin (2π/3) + 2 sin(π/3)) - (sin (-2π/3) + 2 sin(-π/3))

A = (½√3 + √3) - (-½√3 - √3)

A = 1.5√3 - (-1.5√3)

A = 3√3

The area inside of r = 3 cos θ and outside of r = 2 - cos θ is 3√3.

The graph of the curves is:

desmos.com/calculator/541zniwefe

5 0

3 years ago

Kylie went into a grocery store and bought 3 apples and 4 bananas, costing a total of $6.50. Lily went into the same grocery sto

Katyanochek1 [597]

The system of equations that could be used to determine the price of each apple and the price of each banana is:

3x + 4y = 6.50

10x + 5y = 17.50

Where x is the price of each apple and y is the price of each banana

Step-by-step explanation:

The given is:

Kylie went into a grocery store and bought 3 apples and 4 bananas, costing a total of $6.50
Lily went into the same grocery store and bought 10 apples and 5 bananas, costing a total of $17.50

We need to write a system of equations that could be used to determine the price of each apple and the price of each banana

Assume that x represents the price per apple, and y represents the price per banana

∵ The price of each apple is $x

∵ The price of each banana is $y

∵ Kylie bought 3 apples and 4 bananas for a total $6.50

- Multiply x by 3 and y by 4, then add the products and equate

the sum by 6.50

∴ 3x + 4y = 6.50 ⇒ (1)

∵ Lily bought 10 apples and 5 bananas for a total $17.50

- Multiply x by 10 and y by 5, then add the products and equate

the sum by 17.50

∴ 10x + 5y = 17.50 ⇒ (2)

The system of equations that could be used to determine the price of each apple and the price of each banana is:

3x + 4y = 6.50

10x + 5y = 17.50

Where x is the price of each apple and y is the price of each banana

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

3 0

4 years ago

Jake went to the park. He spent 30 minutes walking on a trail. The rest of the time he spent relaxing in the park field. He spen

Katena32 [7]

The answer would be D: r+30=86 ; r+56

5 0

3 years ago

Read 2 more answers

Do the scatter plot .........................

Nuetrik [128]

For this case we have the following table:
1 190
2 220
3 200
4 330
5 300
6 410
7 450
8 410
9 530
10 650
11 570
12 650
13 750
14 720
15 700
16 800
The scatter diagram shows that as the weeks increase, sales increase.
Answer:
See attached image.

4 0

4 years ago

Which graph BEST represents the line of best fit for the scatterplot?

Vika [28.1K]

I would go with D :)

4 0

3 years ago

Read 2 more answers

X+1/X=26/5plz help me fast plz i will be thankful to you.❤❤​

X+1/X=26/5plz help me fast plz i will be thankful to you.❤❤