quiz1-solutions - ing your work. (a) (3 points) 3 5 · log...

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CS 173, Quiz 1 Solutions Name: Netid: Discussion: This quiz has 2 pages containing 5 questions, totalling 20 points. You have 20 minutes to fnish. Showing your work may increase partial credit in case oF mistakes. 1. (5 points) ±or each oF the Following equations or claims, indicate whether it is correct For all real numbers. ( x + 4) 2 = x 2 + 4 x + 16 Correct Incorrect The middle term should be 8 x . IF x n = 0, 1 x + 1 x 2 = x + x 2 x 3 . Correct Incorrect IF x 6 and y 2, then x y 4. Correct Incorrect What iF y was -8? IF xy 17 y , then x 17. Correct Incorrect What iF y was negative? IF | 2 x 5 | ≤ 11, then 20 2 x 5. Correct Incorrect 2. (2 points) ±actor 195 into primes. 195 = 5 × 3 × 13 1
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3. (3 points) Solve x 2 1 < 3 x + 9. x 2 1 < 3 x + 9 implies that x 2 < 6 x + 18. So 20 < 5 x . So 4 < x . 4. Compute the following values, simplifying as much as possible and show-
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Unformatted text preview: ing your work. (a) (3 points) 3 5 · log 2 (32 3 ) 5 = log 2 (32 3 ) = 3 log 2 (32) = 3 · 5. So log 2 (32 3 ) 5 = 3. So the whole thing is equal to 9 5 . (b) (2 points) log 3 (81) log 3 1 27 = log 3 (81) − log 3 (27) = 4 − 3 = − 4 3 (c) (2 points) Suppose log k x = 8. Then log k ( x √ x ) = 12. This is because log k ( x √ x ) = log k ( x 1 . 5 ) = 1 . 5 log k ( x ). 5. (3 points) Suppose that F and G are functions whose inputs and outputs are real numbers, deFned by F ( x ) = x 2 + 14 x and G ( x ) = √ x + 49. Compute the value of G ( F ( p )). G ( F ( p )) = G ( p 2 + 14 p ) = r p 2 + 14 p + 49 = r ( p + 7) 2 = p + 7 2...
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This note was uploaded on 11/08/2010 for the course 173 CS taught by Professor Fleck during the Spring '10 term at University of Illinois at Urbana–Champaign.

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quiz1-solutions - ing your work. (a) (3 points) 3 5 · log...

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