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

Area of triangle = 1/2 x base x height
Let the base be "b"
90 = 1/2 x 10 x b
90 = 5b
b = 18 ft
Base = 18 ft
3
------------
4(5z+16)
I'm assuming you want to include all of the numbers
Answer:
16 feet left
Step-by-step explanation:
one yard = 3 feet
so:
6 yards = 18 feet
24 inches = 2 feet
18 feet - 2 feet = 16 feet
Answer:
D
Step-by-step explanation:
We will use the order of operations to evaluate the expression.
From left to right , Multiplication/Division followed by Addition/Subtraction.
21 / 3 + 8 - 4
= 7 + 8 - 4
= 15 - 4
= 11
Therefore, the answer is D