math6 - Math 2144, Exam I, Sept. 20, 2010 Name: Score:...

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Unformatted text preview: Math 2144, Exam I, Sept. 20, 2010 Name: Score: Please read the instructions on each problem carefully, and indicate answers as directed. Show details in your work. If you simply give a solution without steps of how you derive this solution, you may not get credit for it. The total is 50 points 1. (5 points) A box with an open top has volume 2 m 3 . The box has a square base and the length of a side of the base is a . Express the surface area of the box S as a function of a . Solution The area of the base, which is a square, is a 2 . Assume the height of the box is h , the the total volume is V = a 2 h . We have a 2 h = 2 h = 2 a 2 The box has a bottom and four sides (no top lid). Therefore the surface area is A = (area of the bottom) + (area of four sides) = a 2 + 4 ah Since h = 2 a 2 , we have S = a 2 + 4 a 2 a 2 = a 2 + 8 a 1 2. (6 points) Find the domain of the function f ( x ) = log 4 x 2 + log 4 ( x + 5)- log 4 8- x Then express the function in a single logarithm....
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math6 - Math 2144, Exam I, Sept. 20, 2010 Name: Score:...

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