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

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Unformatted text preview: 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 = (4 u- 5)( u- 1) = 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 ( √...
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This note was uploaded on 08/05/2011 for the course MATH 17 taught by Professor Aaronjamesporlante during the Spring '11 term at University of the Philippines Diliman.

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

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