Answer:

Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have that
The line pass through the points
<em>Find the value of the constant of proportionality k</em>
For x=2/5, y=1/2
substitute


No because it is not within the shaded area
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:
Please see the attachments. For reasons I cannot fathom, the Brainly censor seems to think there are unapproved words contained in this text, so I cannot post it as text. Among other things, that means you probably will not be able to copy and paste the formulas into your spreadsheet—you will have to type them.
I apologize if you are offended by any of the words contained in this answer. I hope you will take them in the intended context—a math problem about the use of Excel.