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STALIN [3.7K]
3 years ago
15

The material conditions of the transition

Advanced Placement (AP)
1 answer:
Finger [1]3 years ago
8 0
Women capitalism and industrialization
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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
I love the show wordgirl and totally think you should watch it. Do not put any negative comments on this question for i do not c
Alex Ar [27]

Answer:

I'll try to watch it (if I have time) thanks for the recomendation

Explanation:

8 0
3 years ago
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4. In the figure below, the measure of angle A is 35°. If the
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WILL BRAINLIEST! psychology...
a description of the three topics, concepts, or theories you learned about in the module that you consider most important; choose topics, concepts or theories from at least three lessons in the module
an explanation of how what you have learned about these three topics, concepts, or theories can be applied in your own life or in the lives of others close to you
at least one paragraph for each topic, concept, or theory, for a total of at least three paragraphs; use this organizer to help you format your work
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What are capital gains on an investment? A. Interest income that investors earn B. Income that investors earn from buying and se
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The Answer is B. Capital gains are talking only about investments or real estate. You only realize the gains when a property is sold. Since it is more money than what it is bought for.

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3. If someone had a split corpus callosum and saw an apple in their left eye would they be able to
mafiozo [28]

Answer:

They will not be able to explain that it is an apple, however, they will be able to draw it with their left hand.

Explanation: This is because of the main functions of both hemispheres of the brain. The left hemisphere of the brain recognizes and analyzes speech, while the right side is more responsible for verbal acuity.

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