Answer d because the y intercept is 3 and its a positive slope
15,19,26,51,18,21,22,33,31,20,28,19,18
40 + 2x - 30 + x + 20 = 180
3x + 30 = 180
3x = 150
x = 50
m<B = 2x - 30
m<B = 2(50) - 30
m<B = 100 - 30
m<B = 70
3 feet is equal to 1 yard and 3 feet is 36 inches. 288 inches divided by 36 is 8 so 8 yards is equal to 288 inches.
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[x^4/4-2x^3/3-x^2/2+2x]_{-1}^{1}](https://tex.z-dn.net/?f=%3D2%5Cpi%5Bx%5E4%2F4-2x%5E3%2F3-x%5E2%2F2%2B2x%5D_%7B-1%7D%5E%7B1%7D)
![=2\pi([1/4-2/3-1/2+2]-[1/4+2/3-1/2-2])](https://tex.z-dn.net/?f=%3D2%5Cpi%28%5B1%2F4-2%2F3-1%2F2%2B2%5D-%5B1%2F4%2B2%2F3-1%2F2-2%5D%29)

= 16 π /3 as before