MAT102H5 Quiz: Quiz1A-sol.pdf

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2 Feb 2013
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MAT102H5 Full Course Notes
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Mat102f - introduction to mathematical proofs - fall 2012 - utm. Quiz 1 (version a) - september 21, 2012 - solutions: complete the following sentences: (2 marks) No explanation is need for this question. (a) the geometric mean of 4 and 9 is. 36 = 6 and their arithmetic mean is. 2 (4 + 9) = 6. 5 (b) a glass contains 5 ounces of wine and 3 ounces of water (mixed uniformly). 2 ounces of liquid from the glass and pour it into an empty cup, then the cup will contain. 4 = 1. 25 ounces of wine: given a positive number b , under what conditions does there exist a rectangular carpet with perimeter 2b and area b. Show your work and simplify your nal answer. (3 marks) Denote the dimensions of the carpet by x and y. The given information implies that xy = and. 2x + 2y = 2b . x2 b x + b.

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