MATH 230 Final: Final spring 2013 solutions
15 Feb 2019
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Instructions: show all of your work on the pages provided! Explain your reasoning using complete sentences and correct grammar, spelling, and punctuation. All numerical answers must be exact; e. g. , you should write instead of 3. 14, 2 instead of 1. 414, and 1. Make sure that your nal answer is clearly indicated. Check to make sure you have pages 1 - 15. Calculators, course notes, textbooks, etc. are not allowed. Do not write your name on this exam! Write your netid and your student id number in the spaces provided at the top of this page. Consider a sphere s with center ( 1, 2, 1) and passing through the point (6, 2, 3). (a) (3 points) find an equation of the sphere. Answer: the radius of the sphere is just the distance from the center to the point (6, 2, 3):
