The horsepower, H (s), required for a racecar to overcome wind resistance is given by the function : H (s) = 0.003s^2+0.07s-0.027, where (s) is the speed of the car in miles per hours. What is the average rate of change in horsepower per unit speed if the race car increases in speed from 80 mph to 100 mph. A 1.64 B. 0.61 C. 12.2 D. 20.0

Question

Mathematics

Vivian Myers

30 March, 11:46

The horsepower, H (s), required for a racecar to overcome wind resistance is given by the function : H (s) = 0.003s^2+0.07s-0.027, where (s) is the speed of the car in miles per hours. What is the average rate of change in horsepower per unit speed if the race car increases in speed from 80 mph to 100 mph. A 1.64 B. 0.61 C. 12.2 D. 20.0

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Fisher · Answer 1

Average rate of change = [H (100) - H (80) ] / (100 - 80)

H (100) = 0.003 (100) ^2 + 0.07 (100) - 0.027 = 0.003 (10000) + 0.07 (100) - 0.027 = 30 + 7 - 0.027 = 36.973

H (80) = 0.003 (80) ^2 + 0.07 (80) - 0.027 = 0.003 (6400) + 0.07 (80) - 0.027 = 19.2 + 5.6 - 0.027 = 24.773

Average rate of change = (36.973 - 24.773) / (100 - 80) = 12.2/20 = 0.61

Answer: B