A nurse sees 24 patients in 6hrs. At this rate, how many patients will the nurse be able to see in an 8-hour period?
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We have been given that in triangle ABC angle A=45 angle B =40 and a=7. We are asked to find the equation that we can use to solve for 'f'.
We have two angles and opposite sides to these angles.
We will use Law of Sines to solve our given problem.
, where a, b and c are opposite sides corresponding to angles A, B, and C respectively.
The angle opposite to side b is 40 degrees and angle opposite to side a is 45 degrees.
Upon substituting these values in Law of Sines, we will get:
Therefore, our required equation would be .
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