MAΘ Problem Set 3

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MAΘ Problem Set 3
September 11, 2003
1. What positive number x satisfies ln( x1 ) − ln( x13 ) = ln(4)?
2. If sin α + cos β = 2, find sin β + cos α.
3. The origin and the two points of intersection of the graph of y = x2 and
a horizontal line containing the point (0, 4) are taken as the three vertices
of a triangle. Find the area of this triangle.
4. Solve for real x:
p
p
( x2 + 13 − 2)( x2 + 13 + 3) = x2 + 13
.
5. The whole number a2 + 3a + 44 is divisible by the whole number a + 1.
Find the number of possible natural number values that a may take on.
6. √
Given that the number N = 941480149401 is a perfect sixth power, find
6
N (without the aid of a calculator). Justify your answer.
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