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# Prelim 1 Short Answers - Prelim 1 Math 2930 show work 5...

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Prelim 1 Math 2930 Spring 2011 show work, 5 problems, no calculators 1 a) (4 points) Write your name and section number on your exam booklet. b) (12 points) A glass of water at 28 degrees C is placed into a freezer at - 18 C . The water temperature T ( t ) obeys Newton’s law of cooling until it reaches 2 C . How long does that take, if we know that it gets to 20 C in 15 minutes? c) (4 points) Solve (3 - 5 i ) c = i + 1 for the complex number c in the form of c = (real) + i (real). 2 a) (10 points) A certain radioactive material decays with a half-life of less than 30 years. We start with a mass y (0) = 1 gram of the material, and y ( t ) is the remaining mass after t years. Explain whether y (300) is more, or less, than 0 . 001 gram. b) (10 points) Solve x 0 + ( 1 + 1 t ) x = 0 with x (2) = 3, and state the interval of t values in which your solution is deﬁned. 3) (4 points for each part) a) Find a solution to y 00 = - 2 y with y (0) = 0 and y 0 (0) = 5. b) Check your answer to part (a) by substitution.

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Prelim 1 Short Answers - Prelim 1 Math 2930 show work 5...

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