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math10b2sol

# math10b2sol - Math 10B Test 2 100 pts Professor Evans...

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Math 10B Test 2 100 pts November 23, 2009 Professor Evans Directions: Answers alone are not sufficient. Show all work. Each problem is worth 20 points. (1) On January 2, 2008, Jack was given a \$100 savings account and Jane was given a \$60 savings account. On January 2, 2009, Jane was given another \$60 savings account. The accounts pay an annual interest rate of 50%. True or False : If Jack and Jane withdraw their money on January 2, 2010, they will each have the same amount. Justify. Solution: Jack ends up with 100(1 . 50) 2 = 225 dollars. Jane ends up with 60(1 . 50) 2 + 60(1 . 50) = 225 dollars. Hence the answer is True. (2) The base of a loaf of bread is the region inside the circle x 2 + y 2 = 1. Each cross-section perpendicular to the x -axis has the shape of a square. (Think of paper-thin square-shaped slices of bread.) Find the volume of the loaf of bread. Hint : The answer is between 1 and 8. Solution: The cross section at any given x is a square of side length 2 1 - x 2 . The area of this square is 4(1 - x 2 ). Hence the volume of the loaf is R 1 - 1 4(1 - x 2 ) dx = 16 / 3.

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math10b2sol - Math 10B Test 2 100 pts Professor Evans...

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