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MA102 ? Mathematics for Science
Semester II, 2015
Total Marks: [20 marks] Question 1
Based on data from the U.S. Census Bureau, the chief economist of Manpower, Inc.,
constructed the following formula giving the percent of the total female population in the
civilian labor force, P (t ), at the beginning of the tth decade ( t 0 corresponds to the year
1990): P (t ) 74
1 2.6 e 0.166t 0.04536t 2 0.0066 t 3 (0 t 11) Assume that this trend continued for the rest of the twentieth century.
a) What was the percent of the total female population in the civilian labor force at
the beginning of 2000?
b) What was the growth rate of the percent of the total female population in the
civilian labor forces at the beginning of 2000?
[10 marks] Question 2
A cylindrical container for storing cylindrical waste is to be constructed from lead and
have a thickness of 6 inches (see the accompanying figure). If the volume of the outside
cylinder is to be 16 ft 3 , find the radius and the height of the inside cylinder that will
result in a container of maximum storage capacity. 6 in r h 6 in Hint: Show that the storage capacity (inside volume) is given by 16 V (r ) r 2 r 1 2
2 1 7 0 r 2 [5 marks] Question 3
During daylight hours, some birds fly more slowly over water than over land because
some of their energy is expended in overcoming the downdrafts of air over open bodies
of water. Suppose that a bird that flies at a constant speed of 4 km/h over water and 6
km/h over land starts its journey at the point E on and island and ends at its nest N on
the shore of the mainland, as shown in the accompanying figure. Find the location of the
point P that allows the bird to complete its journey in the minimum time (solve for x ).
E 3 km
P Land x N 12 x
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