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Anika [276]
3 years ago
8

Nation state definition and examples​

Advanced Placement (AP)
1 answer:
AleksandrR [38]3 years ago
7 0
Nation state: a sovereign state whose citizens or subjects are relatively homogeneous in factors such as language or common descent. For example: England
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My fellow math brodas, help
DiKsa [7]

A. Depending on which variable you choose to integrate with, you can capture the total bounded region with either -2 ≤ x ≤ (-1 + √5)/2 or 1 ≤ y ≤ (5 + √5)/2, where the upper endpoints correspond to the coordinates of the appropriate intersections:

y = x² + 1

⇒   x = (x² - 2)² - 2

⇒   x⁴ - 4x² - x + 2 = 0

⇒   (x - 2) (x + 1) (x² + x - 1) = 0

⇒   x = 2, x = -1, x = -1/2 ± √5/2

⇒   y = 5, y = 2, y = (5 ± √5)/2

On the other hand, we can compute the areas of A and B separately, then sum those integrals. Area A is easier to compute by integrating with respect to y over 2 ≤ y ≤ (5 + √5)/2, while area B is easier to find by integrating x over -1 ≤ x ≤ (-1 + √5)/2.

B. I'll stick to the split-region approach.

First, we find equations for the appropriates halves of either parabola:

• y = x² + 1   ⇒   x = ± √(y - 1)

and x = -√(y - 1) describes the left half of the blue parabola;

• x = (y - 3)² - 2   ⇒   y = 3 ± √(x + 2)

and y = 3 - √(x + 2) describe the bottom half of the red parabola.

Now we can set up the integrals.

Area of A:

\displaystyle \int_2^{(5+\sqrt5)/2} \left(\left(-\sqrt{y-1}\right) - \left((y-3)^2-2\right)\right) \, dy \\ ~~~~~~~~ = -\int_2^{(5+\sqrt5)/2} \left((y-3)^2 - 2 + \sqrt{y-1}\right) \, dy

Area of B:

\displaystyle \int_{-1}^{(-1+\sqrt5)/2} \left(\left(3-\sqrt{x+2}\right) - \left(x^2+1\right) \right) \, dx \\ ~~~~~~~~ = - \int_{-1}^{(-1+\sqrt5)/2} \left(x^2 - 2 + \sqrt{x+2}\right) \, dx

Alternatively, one can prove that the regions A and B are symmetric across the line y = x + 3, so we can simply pick one of these integrals and double it.

C. Computing the integrals, we find

area of A = 2/3

area of B = 2/3

and so the total area is 2/3 + 2/3 = 4/3.

6 0
2 years ago
Which process reduces the amount of carbon dioxide in the atmosphere?
maw [93]

Answer:

Carbon sequestration is the process of capturing and storing atmospheric carbon dioxide. It is one method of reducing the amount of carbon dioxide in the atmosphere with the goal of reducing global climate change

3 0
2 years ago
Please help ASAP!
kumpel [21]
The answers should be in the reading, that’s why it says, “read the..answer the following questions..answers are in the lesson.”
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3 years ago
If Congress passes a law that conflicts with the Constitution, which one are we required to follow: the law or the Constitution?
Ostrovityanka [42]

Answer:

The constitution

Explanation:

the constitution is the whole basis for our rights and freedoms as humans. Congress SHOULDN'T ever pass anything that goes against it, but if they were to, you always follow thee constitution unless they want to work on amending it.

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Which of the following is an attribute of a fulfilling career?
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the answer is b...........................................................


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