Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the specified axis. y = x3, y = 8, x = 0; about x = 9 v =

For each in the interval , the corresponding shell has radius (horizontal distance from to the rotation axis) and height (vertical distance between and ). A shell of radius and height has area , so the volume is

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

step-by-step explanation:

because 1/3 is a fraction. we can tell because there is a divisor symbol between the 1 and the 3. if we were to add 2 fractions together, we would add the numerators, which is the number on top, but not the denominators, which is the number on the bottom

1/3+1/3=2/3

hope this !