My fellow math brodas, help

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:

[tex]\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[/tex]

Area of B:

[tex]\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[/tex]

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.

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the development is too auto-centric

there are too few green spaces

houses are too close to one another

houses are close to transportation networks

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Question 2 of 15
Examine Item A in your test documents. Where in the diagram does the
supremacy clause of the U.S. Constitution most come into play?
A. In the two small circles at the bottom
B. Where the "Federal" and "State" circles overlap
"
C. In the three boxes under "Delegated powers"
D. Where the small circles connect to the large circles

Which of the following scenarios does NOT align to the principles of the National Sustainable Development Strategy?

Argentina wants to build sustainable development, so the government takes Brazil's sustainable development plan and follows it exactly.
Indonesia creates a sustainable development plan that balances economic and social policy.
Malaysia develops a sustainable development plan that involves improving the quality of roads and telephone lines.
South Africa develops a plan to cut down on carbon emissions to improve air quality.
Bangladesh encourages construction and use of an environmentally friendly bio-gas plant in the rural areas with necessary support.

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Joe is playing a game at the fair. To
win, he must throw a ball and knock
down a bottle. Kim doesn't think the
bottle will fall over when the ball hits it
because the action and reaction forces
will cancel each other out.
Is Kim's claim correct?

Yes, because the forces are equal and in
opposite directions.
Yes, because the forces are the same
strength.
No, because the forces are acting on
different objects.

Name the types of migration and give an example of each

36. Assume that the list of numbers nums has more than 10 elements. The program below is intended to compute
and display the sum of the first 10 elements of nums.
Line 1: it 1
Line 2:
Line 3: REPEAT UNTIL (i > 10)
Line 4: (
Line 5: it i + 1
Line 6: sum sum + nums (i)
Line 7: )
Line 8: DISPLAY (sum)
Which change, if any, is needed for the program to work as intended?
(A) Lines 1 and 2 should be interchanged.
(B) Line 3 should be changed to REPEAT UNTIL (i 2 10).
(C) Lines 5 and 6 should be interchanged.
(D) No change is needed; the program works correctly.

Short Answers- Answer the following questions in
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independent

dependent

confounding

experimental

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common work styles needed by Human Resources Managers? Select three options.
excitability
integrity
leadership
stress tolerance
aggression
vulnerability