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
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.
