MAC2313 T1Solutions

MAC2313 T1Solutions - MAS 2313-03 Test 1 Fall 2007 Name:...

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Unformatted text preview: MAS 2313-03 Test 1 Fall 2007 Name: Show all work (No credit given if work is not shown). 7 points each unless indicated otherwise. 1. Write an equation of the sphere that passes through the point (1 , 1 , 2) and whose center is (2 , 3 , 4). The radius is the distance between (1 , 1 , 2) and (2 , 3 , 4), i.e. r = √ 1 + 4 + 4 = 3 Hence an equation for the sphere is ( x − 2) 2 + ( y − 3) 2 + ( z − 4) 2 = 9. 2. Describe the set of all points ( x, y, z ) that satisfy x 2 + y 2 + z 2 − 6 x + 2 y − 4 z = 0. Completing the square we get ( x − 3) 2 + ( y + 1) 2 + ( z − 2) 2 = 14 which describes the set of all points on a sphere of radius √ 14 and center C (3 , − 1 , 2). 3. Write an equation for the set of all points ( x, y, z ) whose distance from (1 , 1 , 1) is the same as the distance from (2 , , 3). (Simplify your equation). ( x − 1) 2 + ( y − 1) 2 + ( z − 1) 2 = ( x − 2) 2 + ( y − 0) 2 + ( z − 3) 2 or x 2 − 2 x + 1 + y 2 − 2 y + 1 + z 2 − 2 z + 1 = x 2 − 4 x + 4 + y 2 + z 2 − 6 z + 9 or x − y + 2 z − 5 = 0 (the equation of a plane)....
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This test prep was uploaded on 04/17/2008 for the course MATH 2313 taught by Professor Heister during the Spring '08 term at FSU.

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MAC2313 T1Solutions - MAS 2313-03 Test 1 Fall 2007 Name:...

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