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Andre45 [30]
3 years ago
6

Your roommate is constantly cleaning your apartment and picking up after you, even though you're not really very messy.

Advanced Placement (AP)
1 answer:
sergejj [24]3 years ago
4 0
I wouldn't really mind their assistance.

Anyway, are there any selections? 


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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
What are 4 modifications of the physical environment?
masha68 [24]

Answer:

4

Explanation:

In this way you can learn how to answer even paragraphs questions using your note because they will be easier to remember

7 0
3 years ago
If Gary always requests his superior’s advice when solving a problem or making a decision, which type of decision maker is he?
iogann1982 [59]
<span>If Gary always requests his superior’s advice when solving a problem or making a decision, the type of decision maker he is is C. submissive.
He shies away from making the decision on his own, and instead asks for an authority figure to do it for him. 
Plungers make rash decisions, evaders avoid making the decision, and fatalists feel that they have absolutely no control over their own decisions. 
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3 years ago
What are 5 questions of trust in the lifespan development
nasty-shy [4]

Answer:

Im sorry so very hard

Thank you bye

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3 years ago
Would You Rather......Only use Microsoft Teams...or......Only use Discord....?
disa [49]

Answer:

microsoft teams

Explanation:

4 0
3 years ago
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