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Resource 2- Rate of Change and Kinematics-solutions

# Resource 2- Rate of Change and Kinematics-solutions -...

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nguyen (jn9656) – Resource 2: Rate of Change and Kinematics – balasubramanya – (1401111) 1 This print-out should have 53 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points At Memorial Hospital there were 571 births in 1986. In 1991, there were 526 births. Find the average rate of change. Correct answer: - 9 births / year. Explanation: The average rate of change was Δbirths Δyears = 526 - 571 1991 - 1986 = - 9 in births/year. 002(part1of2)10.0points An open box is made from an 8 inch × 9 inch rectangular piece of cardboard by cutting equal squares from the corners and turning up the sides as shown in the figure x x x x x x x x Determine the volume V of the box as a function of x . 1. V ( x ) = 72 x - 34 x 2 + 4 x 3 correct 2. V ( x ) = 144 x - 34 x 2 + 4 x 3 3. V ( x ) = 72 x + 34 x 2 + 4 x 3 4. V ( x ) = 72 x - 34 x 2 + 2 x 3 5. V ( x ) = 72 x - 34 x 2 - 4 x 3 Explanation: The length of one side of the base of the box is 8 - 2 x , while the length of the other side of the base is 9 - 2 x . Since the height of the box is x the volume will be V ( x ) = (length) × (width) × (height) = x (8 - 2 x )(9 - 2 x ) . Thus V ( x ) = 72 x - 34 x 2 + 4 x 3 cu ins 003(part2of2)10.0points What is the domain of V for a box that makes physical sense? 1. domain = (0 , 5) 2. domain = (0 , 4) correct 3. domain = (0 , 8) 4. domain = [0 , 4) 5. domain = (0 , 4] Explanation: Since all the dimensions in the expression V ( x ) = 2 x (4 - x )(9 - 2 x ) for the volume have to be positive for the box to make good physical sense, the domain of V is the solution set of the inequalities x > 0 , 4 - x > 0 , 9 - 2 x > 0 . Consequently, domain = (0 , 4) . 004(part1of2)10.0points Evaluate function f ( x ) = 8 x 2 - 5 x - 11 at a) x = 7; Correct answer: 346. Explanation:

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nguyen (jn9656) – Resource 2: Rate of Change and Kinematics – balasubramanya – (1401111) 2 f (7) = 8(7) 2 - 5(7) - 11 = 392 - (35) - 11 = 346 005(part2of2)10.0points b) x = 5. Correct answer: 164. Explanation: f (5) = 8(5) 2 - 5(5) - 11 = 200 - 25 - 11 = 164 006 10.0points Given f ( x ) = 6 x 2 + 2 x , find f (3). 1. None of these. 2. 59 3. 62 4. 63 5. 60 correct 6. 64 Explanation: f ( x ) = 6 x 2 + 2 x , so f (3) = 6(3) 2 + 2(3) = 54 + 6 = 60 007 10.0points The graph shown gives the weight of a certain person as a function of age. Find the age at which the person started an exercise program. 30 60 60 120 180 Age Weight 1. 50 correct 2. 40 3. 60 4. 100 5. 80 Explanation: 008 10.0points The number of horsepower y required to over- come wind drag on a certain automobile is approximated by y = 0 . 005 s 2 + 0 . 004 s + 0 . 033 , 0 s 100 where s is the speed in miles per hour. Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Correct answer: 44 . 3969 miles / hour. Explanation: 0 . 005 s 2 + 0 . 004 s - 0 . 033 = 10 5 s 2 + 4 s - 33 = 10000 5 s 2 + 4 s - 10033 = 0 a = 5 , b = 4 , c = 10033 s = - 4 ± radicalbig 4 2 - 4(5)( - 10033) 2(5) = - 4 ± 2 . 00676 × 10 5 10 ≈ - 45 . 1969 , 44 . 3969 .
nguyen (jn9656) – Resource 2: Rate of Change and Kinematics – balasubramanya – (1401111) 3 The maximum speed if power is not to exceed 10 horsepower is 44 . 3969 miles per hour.

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