3 years ago

Look at the image to answer.

Mathematics

1 answer:

Katen [24]3 years ago

8 0

The correct answer is D

since 3.2222... is a repeating number, it is rational

0.112123123412345 is not repeating and doesn't have a cosistent pattern, so it isn't rational

1.589 is rational because this decimal stops and doesn't continue- it can also be written as a fraction ( $\frac{1589}{1000}$ )

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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)
Distance of centroid from axis of rotation, R = (2-0) = 2
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