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nadezda [96]
3 years ago
9

1

Mathematics
1 answer:
ANEK [815]3 years ago
6 0

9514 1404 393

Answer:

  x > -5

Step-by-step explanation:

  (2/5)(x -1) < (3/5)(x +1) . . . . . given

  2(x -1) < 3(x +1) . . . . . . . . . . .multiply by 5

  2x -2 < 3x +3 . . . . . . . . . . .  eliminate parentheses

  -5 < x . . . . . . . . . . . . . . . . . . add -2x-3 to both sides

This matches the second answer choice: x > -5.

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Read 2 more answers
find the volume of a solid that is generated by rotating around the indicated axis the plane region bounded by the giveb curves:
Fofino [41]
Assuming the area below the line y=0 (i.e. x>1) does NOT count, the area to be rotated is shown in the graph attached.

A. Again, using Pappus's theorem,
Area, A = (2/3)*1*(1-(-1))=4/3  (2/3 of the enclosing rectangle, or you can integrate)
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Volume = 2 π RA = 2 π 2 * 4/3 = 16 π / 3 (approximately = 16.76 units)

B. By integration, using the washer method
Volume = 2\pi\int_{-1}^1(1-x^2)(2-x)dx
=2\pi\int_{-1}^1(x^3-2x^2-x+2)dx
=2\pi[x^4/4-2x^3/3-x^2/2+2x]_{-1}^{1}
=2\pi([1/4-2/3-1/2+2]-[1/4+2/3-1/2-2])
=2\pi(8/3)
= 16 π /3   as before



3 0
3 years ago
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