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quiz1-solutions

# quiz1-solutions - ing your work(a(3 points 3 5 Â log 2(32 3...

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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 finish. Showing your work may increase partial credit in case of mistakes. 1. (5 points) For 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 negationslash = 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) Factor 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 Â· log 2 (32 3 ) 5 = log 2 (32 3 ) = 3 log 2 (32) = 3 Â· 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) âˆ’ log 3 (27) = 4 âˆ’ 3 = âˆ’ 4 3 (c) (2 points) Suppose log k x = 8. Then log k ( x âˆš x ) = 12. This is because log k ( x âˆš 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 ) = âˆš 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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