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

3 gallons of acid = 100% concentration acid
? (water+acid) gallons = 15 concentration acid
Note: Every gallon of water added reduces the percentage concentration of acid. Therefore, the relationship is inverse proportionality.
Solution:
Total number of gallons (water+acid) = (3*100)/15 = 20 gallons
Therefore, gallons of water = 20-3 = 17 gallons
Do you want to solve for x and y?
What is the objective?
Hey, let's figure this out together. :)
The answer is 1 and 6. Now we can prove that is true.
1 x 6 = 6
1 + (6) = 7
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