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Nikitich [7]
3 years ago
15

The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x^2. Cross sections of the solid perpendi

cular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid?
My teacher isn't helpful at all and I'm starting to fail tests, please help
Mathematics
1 answer:
olga55 [171]3 years ago
7 0
He area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is 

<span>(x - x^2)^2 * sqrt(3)/4. </span>
<span>Integrating from x = 0 to x = 1, we have </span>
<span>[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4 </span>
<span>= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144. </span>

<span>Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...


</span>
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Andrews [41]

Answer:

-8 and 9

Step-by-step explanation:

-8 x 9  = -72

and  -8 + 9 = 1

7 0
2 years ago
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TEA [102]

Answer:

See explanation below

Step-by-step explanation:

Find the value of x in each of the following

1) x-1+5√x-1+3=0

5√x-1 = -x -2

Square both sides

25(x-1) = (-x-2)^2

25(x-1) = x^2+4x + 4

25x-25 = x^2+4x + 4

x^2 +4x + 4 - 25x + 25 = 0

x^2 - 21x + 29 = 0

x = 21±√21²-4(29)/2

x = 21±√441-116/2

x = 21±√325/2

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x = 21+18.03/2 and 21-18.03/2

x = 19.515 and 1.485

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6 0
2 years ago
Given the equations x + y = 20 and x - y = 8, which values of x and y
hammer [34]

Answer:

x = 14 and y = 6

Step-by-step explanation:

To find the solution to this problem, we plug in the values of x and y from each answer choice and simplify.

1.

  • (11) + (9) = 20. 20 = 20.
  • (11) - (9) = 20. 2 ≠ 8.

2.

  • (9) + (11) = 20. 20 = 20
  • (9) - (11) = 20. -2 ≠ 8.

3.

  • (14) + (6) = 20. 20 = 20.
  • (14) - (6) = 8. 8 = 8.

4.

  • (6) + (14) = 20. 20 = 20
  • (6) - (14) = 8. -8 ≠ 8.

Therefore, the correct answer is x = 14 and y = 6.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

6 0
2 years ago
Joelle is working on a school report in a word processor. She wants to place a figure which is 13.09 \text{ cm}13.09 cm13, point
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3 0
3 years ago
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3 years ago
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