Pre-Calc Homework Solutions 400

Pre-Calc Homework Solutions 400 - 400 67. (a) Section 10.1...

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67. (a) Expected payoff 5 0 1 } 1 2 } 2 1 1 1 } 1 2 } 2 2 1 2 1 } 1 2 } 2 3 1 3 1 } 1 2 } 2 4 1 (b) } (1 2 1 x ) 2 } 5 1 1 2 x 1 3 x 2 1 1 nx n 2 1 1 (c) } (1 2 x 2 x ) 2 }5 x 2 (1 1 2 x 1 3 x 2 1 1 nx n 2 1 1 ) 5 x 2 1 2 x 3 1 3 x 4 1 1 nx n 1 1 1 (d) If x 5 } 1 2 } , the formula in part (c) matches the nonzero terms of the series in part (a). Since } [1 2 (1/ ( 2 1 ) / 2 2)] 2 }5 1, the expected payoff is $1. 68. (a) The area of an equilateral triangle whose sides have length s is } 1 2 } ( s ) 1 } ˇ 2 3 w s } 2 5 } s 2 ˇ 4 3 w } . The sequence of areas removed from the original triangle is } b 2 ˇ 4 3 w } 1 3 1 } b 2 } 2 2 } ˇ 4 3 w } 1 9 1 } b 4 } 2 2 } ˇ 4 3 w } 1 1 3 n 1 } 2 b n } 2 2 } ˇ 4 3 w } 1 or } b 2 ˇ 4 3 w } 1 } 3 b 2 4 ˇ 2 3 w } 1 } 3 2 b 4 2 3 ˇ 3 w } 1 1 } 3 n 4 b n 2 1 ˇ 1 3 w } 1 . (b) This is a geometric series with initial term a 5 } b 2 ˇ 4 3 w } and common ratio r 5 } 3 4 } , so the sum is } 1 b 2 2 ˇ (3 3 w / / 4 4 ) b 2 ˇ 3 w , which is the same as the area of the original triangle.
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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