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M17 LE2 Sem1 09-10 Solns

# M17 LE2 Sem1 09-10 Solns - Math 17 Second Long Exam...

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Math 17 Second Long Exam Solutions V7, W3, Y3 I. 1. The first line has slope 11/2 while the second line has slope 2/11. The slopes are not negative reciprocal of each other, so the lines are not perpendicular. 2. The statement does not hold when x is negative. 3. Take f ( x ) = 2 x + 1 and g ( x ) = x + 2. Then ( f g )(1) = 7 6 = 5 = ( g f )(1) . 4. TRUE 5. The distance of the point (7 , - 3) to the center (5 , - 7) of the circle is 20, which is greater than 19, the radius of the circle. Hence, the point is outside the circle. II. 1. 9( x 2 / 3 - 1) - 5 = 4( x 2 / 3 - 1) 2 Let u = x 2 / 3 - 1 4 u 2 - 9 u + 5 = 0 (4 u - 5)( u - 1) = 0 u = 5 / 4 or u = 1 x 2 / 3 - 1 = 5 / 4 or x 2 / 3 - 1 = 1 x 2 / 3 = 9 / 4 or x 2 / 3 = 2 x = ± 27 / 4 or x 2 / 3 = ± 2 2 SS= { 27 / 4 , - 27 / 4 , 2 2 , - 2 2 } 2. 5 x + 7 - 2 x + 3 = 3 x + 4 ( 5 x + 7 - 2 x + 3) 2 = ( 3 x + 4) 2 5 x + 7 - 2 p (5 x + 7)(2 x + 3) + 2 x + 3 = 3 x + 4 - 2 10 x 2 + 29 x + 21 = - 4 x - 6 ( 10 x 2 + 29 x + 21) 2 = (2 x + 3) 2 10 x 2 + 29 x + 21 = 4 x 2 + 12 x + 9 6 x 2 + 17 x + 12 = 0 (3 x + 4)(2 x + 3) = 0 x = - 4 / 3 or u = - 3 / 2 It can be checked that - 4 / 3 satisfies the original equation while - 3 / 2 is an extraneous solution.

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