112-unknown-09spex01-key

112-unknown-09spex01-key - MATH 112 SPRING 2009 EXAM ONE 90...

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MATH 112 SPRING 2009 EXAM ONE 90 Minutes ANSWERS 1. (15 Points) Vital Errors (a) Simplify x 1 / 4 (2 x ) 1 / 3 Solution: x 1 / 4 (2 x ) 1 / 3 = x 1 / 4 · 2 1 / 3 · x 1 / 3 =2 1 / 3 · x 1 / 4+1 / 3 =2 1 / 3 · x 7 / 12 . (b) Factor completely: 6 t 2 +17 t +5 Solution: You can factor this a myriad of ways, the result is (3 t + 1)(2 t +5) (c) Simplify completely: ° a 2 +3 ± 1 Solution: ° a 2 +3 ± 1 = ² 1 a 2 +3 ³ 1 = ² 1 a 2 +3 · ² a 2 a 2 ³³ 1 = ² 1 a 2 + 3 a 2 a 2 ³ 1 = ² 1+3 a 2 a 2 ³ 1 = a 2 1+3 a 2 .
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2 2. (10 Points) Solve for x : x [7 (2 x −{ 8 x } )] = 12 . Solution: x [7 (2 x −{ 8 x } )] = 12 x [7 (2 x 8+ x )] = 12 x [7 2 x +8 x ] = 12 x 7+2 x 8+ x =1 2 4 x 15 = 12 4 x =2 7 x = 27 4 . 3. (10 Points) The points P ( 1 , 2) and Q ( 5 , 4) are the endpoints of a diameter of a circle. Find the center and radius of the circle. Solution: The center of the circle will be the midpoint of P and Q ,so Center = ° 1+( 5) 2 , 2+( 4) 2 ± =( 3 , 1) . The radius is the distance from the center to either P or Q (or half the distance between P and Q , you can use either method): Radius = ² ( 3 ( 1)) 2 +( 1 2) 2 = ² ( 2) 2 +( 3) 2 = 4+9= 13 . 4. (15 Points) Find the equation for the line that is perpendicular to x 2 y + 4 = 0 and passes through the point (4 ,
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112-unknown-09spex01-key - MATH 112 SPRING 2009 EXAM ONE 90...

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