a group of 54 randomly selected students from one school district for participated in a survey. Out of the 54 students in the su
rvey, 9 are enrolled in band camp. If there are a total of 1200 students in the school district which estimate is reasonable for the number of students in the whole school district who are enrolled in the bank camp.
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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
Point slope from would be 12x-y+26=0.
Black is the equation, 12x-y+26=0.
- Orange is <em>y-14=12(x+1)</em>
- Blue is <em>y-14=12(x-1)</em>
- Red is <em>y+14=12(x-1)</em>
- Green is <em>y-14=-12(x+1)</em>
