Quiz1Solution

# Quiz1Solution - MAC1105 Quiz 1(2 pages Name SOLUTION 1...

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Unformatted text preview: MAC1105 Quiz 1 (2 pages) Name: SOLUTION 1. Write the following set in set-builder notation (3 points): {−7, 0, 7, 14, 21} Answer: {7x| x is an integer s.t. −1 ≤ x ≤ 3 } 2. Write the following sets in interval notation (1.5 points each) a) { x|12 < x ≤ 32} b) The negative Real Numbers Answers: a) b) (12, 32] (−∞, 0) 3. Write the following number in decimal form (3 points)(ACTUALLY WRITE AS A FRACTION) 7.¯ 4 Answer: 7.¯ = 7 + 0.¯ 4 4 Let x = 0.¯ and 4 10x = 4.¯ 4 10x = 4 + 0.¯ 4 10x = 4 + x 9x = 4 x= 4 9 multiply this expression by 10 on both sides So from the beginning we know that: 7.¯ = 7 + 0.¯ 4 4 7.¯ = 7 + x 4 Now using the fraction form of x we derived above (x = 7.¯ = 7 + 4 4 9 7.¯ = 67 4 9 can be written as 1 4 9 ) and plugging in that value in 7.¯ = 7 + x. 4 We obtain: 4. Evaluate the following expression (3 points): 4x2 2y √ −3 Answer: 4x2 2y 4x2 2y 4x2 2y 4x2 2y 4x2 2y 4x2 2y √ −3 √ −3 √ −3 √ −3 √ −3 √ −3 y y + 5π for x = −2 2 + 5π = 4(−2) − 3 2(4) √ 4 and y=4 + 5π 5π = 4(4) − 32 + 5π 8 16 5π = 8 − 9 + 5 π y + y + y + 5 π =2 − 9 + 5 π y + 5 π = −7 + 5 π y + 5π =5π − 7 5. Find the steps to make the following expressions equivalent (3 points) 42 5x + 2y − 3xz = 3y − 3xz ⇐⇒ 4x2 − 5y = 0 Answer: 42 5x + 2y − 3xz = 3y − 3xz −3xz to both sides (additive cancellation property) 42 x + 2y = 3y 5 Add −3y to both sides (additive cancellation property) 42 5x − y = 0 Multiply both sides by 5 (multiplicative cancellation property) 4x2 − 5y = 0 Add 2 ...
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Quiz1Solution - MAC1105 Quiz 1(2 pages Name SOLUTION 1...

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