MATH 230 Midterm: Test 1 winter 2013 solutions

• School: Northwestern University
• Department: Mathematics
• Course: MATH 230
• Professor: All

Document Summary

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 - 11. 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. Let s be the sphere given by the equation x2 8x + y2 + 24y + z2 12z = 171 (a) (5 points) find the center and radius of the sphere s. Answer: we begin by completing the square: x2 8y + 16 + y2 + 24y + 144 + z2 12z + 36 = 171 + 16 + 144 + 36.