Quest HW 1 - roberts (eer474) – Quest HW 1 – seckin –...

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Unformatted text preview: roberts (eer474) – Quest HW 1 – seckin – (56425) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the x-intercept of the straight line passing through the points P (3 , 6) and Q (7 , 4). 1. x-intercept = 16 2. x-intercept = 33 2 3. x-intercept = 31 2 4. x-intercept = 15 correct 5. x-intercept = 17 Explanation: The slope of the straight line passing through the points P (3 , 6) and Q (7 , 4) is given by slope = rise run = − 1 2 . By the point slope formula, therefore, this line has equation y − 4 = − 1 2 ( x − 7) . Now the x-intercept of the line is the solution of y = 0, i.e. , the solution of 2 x = 30. Consequently, x-intercept = 15. 002 10.0 points Rationalize the denominator of 9 √ 6 + √ 3 . 1. 9 √ 6 − √ 3 2. 3 parenleftBig √ 6 + √ 3 parenrightBig 3. √ 6 + √ 3 3 4. 3 parenleftBig √ 6 − √ 3 parenrightBig correct 5. 9 parenleftBig √ 6 − √ 3 parenrightBig Explanation: Multiplying the numerator and denomina- tor by the conjugate of the denominator, we see that 9 √ 6 + √ 3 = 9( √ 6 − √ 3) ( √ 6 + √ 3)( √ 6 − √ 3) = 9( √ 6 − √ 3) 6 − 3 . Consequently, 9 √ 6 + √ 3 = 3 parenleftBig √ 6 − √ 3 parenrightBig . 003 10.0 points Rationalize the denominator of 8 √ x + 4 − √ x − 3 . 1. 8 parenleftBig √ x + 4 + √ x − 3 parenrightBig 2. 8 7 parenleftBig √ x + 4 + √ x − 3 parenrightBig correct 3. 8 parenleftBig √ x + 4 − √ x − 3 parenrightBig 4. 8 7 parenleftBig √ x − 4 + √ x + 3 parenrightBig 5. 8 7 parenleftBig √ x − 4 − √ x + 3 parenrightBig Explanation: roberts (eer474) – Quest HW 1 – seckin – (56425) 2 By the difference of squares, ( √ x + 4 − √ x − 3)( √ x + 4 + √ x − 3) = ( √ x + 4) 2 − ( √ x − 3) 2 = 7 . Thus, after multiplying both the numerator and the denominator in the given expression by √ x + 4 + √ x − 3 , we obtain 8 7 parenleftBig √ x + 4 + √ x − 3 parenrightBig . 004 10.0 points Simplify the expression ( − 9 b 2 ) parenleftbigg 1 9 b 3 parenrightbigg ( − 9 b 3 ) as much as possible. 1. 9 b 8 correct 2. 3 b 8 3. 9 b 5 4. b 8 5. 9 b 2 Explanation: By the Laws of Exponents, ( − 9 b 2 ) parenleftbigg 1 9 b 3 parenrightbigg ( − 9 b 3 ) = 9 · 9 9 b 2+3+3 = 9 b 8 . 005 10.0 points Express the number x = parenleftbigg 2 3 parenrightbigg 4 − 3- 4 in the form a b , where a and b are integers. 1. x = 59 27 2. x = 5 27 correct 3. x = 32 27 4. x = 16 27 5. x = 5 54 Explanation: Notice first that parenleftbigg 2 3 parenrightbigg 4 = parenleftbigg 2 3 parenrightbigg 4 ....
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This note was uploaded on 11/08/2010 for the course MATH 408K taught by Professor Gualdani during the Spring '09 term at University of Texas.

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Quest HW 1 - roberts (eer474) – Quest HW 1 – seckin –...

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