The two parabolas intersect for

and so the base of each solid is the set

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas,
. But since -2 ≤ x ≤ 2, this reduces to
.
a. Square cross sections will contribute a volume of

where ∆x is the thickness of the section. Then the volume would be

where we take advantage of symmetry in the first line.
b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

We end up with the same integral as before except for the leading constant:

Using the result of part (a), the volume is

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

and using the result of part (a) again, the volume is

Answer:
<u>x = 5</u>
Step-by-step explanation:
See attached image.
just divide 17 by 6 and you'll get your mixed number:
2 5/6
Answer:
600 seconds
Step-by-step explanation:
In this case we have to calculate the speed;
Speed = Distance/Time
Speed = 100/20 = 5 mph
Next to get our answer we have to calculate the amount of time
Time = Distance/Speed
Time = 3000/5 = 600 seconds