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.