The braking distance required for a car to stop depends on numerous variables such as the speed of the car, the weight of the car, reaction time of the driver, and the coefficient of friction between the tires and the road. For a certain vehicle on one stretch of highway, the braking distances d ( s ) (in ft) are given for several different speeds s (in mph). s 30 35 40 45 50 d ( s ) 109 134 162 191 223 s 55 60 65 70 75 d ( s ) 256 291 328 368 409 a. Use regression to find a quadratic function to model the data. b. Use the model from part ( a ) to predict the stopping distance for the car if it is traveling 62 mph before the brakes are applied. Round to the nearest foot. c. Suppose that the car is traveling 53 mph before the brakes are applied. If a deer is standing in the road at a distance of 245 ft from the point where the brakes are applied, will the car hit the deer?
The braking distance required for a car to stop depends on numerous variables such as the speed of the car, the weight of the car, reaction time of the driver, and the coefficient of friction between the tires and the road. For a certain vehicle on one stretch of highway, the braking distances d ( s ) (in ft) are given for several different speeds s (in mph). s 30 35 40 45 50 d ( s ) 109 134 162 191 223 s 55 60 65 70 75 d ( s ) 256 291 328 368 409 a. Use regression to find a quadratic function to model the data. b. Use the model from part ( a ) to predict the stopping distance for the car if it is traveling 62 mph before the brakes are applied. Round to the nearest foot. c. Suppose that the car is traveling 53 mph before the brakes are applied. If a deer is standing in the road at a distance of 245 ft from the point where the brakes are applied, will the car hit the deer?
Solution Summary: The author calculates the quadratic function for the given set of data using the Ti- 83 graphing calculator.
The braking distance required for a car to stop depends on numerous variables such as the speed of the car, the weight of the car, reaction time of the driver, and the coefficient of friction between the tires and the road. For a certain vehicle on one stretch of highway, the braking distances
d
(
s
)
(in ft) are given for several different speeds s (in mph).
s
30
35
40
45
50
d
(
s
)
109
134
162
191
223
s
55
60
65
70
75
d
(
s
)
256
291
328
368
409
a. Use regression to find a quadratic function to model the data.
b. Use the model from part (a ) to predict the stopping distance for the car if it is traveling 62 mph before the brakes are applied. Round to the nearest foot.
c. Suppose that the car is traveling 53 mph before the brakes are applied. If a deer is standing in the road at a distance of 245 ft from the point where the brakes are applied, will the car hit the deer?
A research study in the year 2009 found that there were 2760 coyotes
in a given region. The coyote population declined at a rate of 5.8%
each year.
How many fewer coyotes were there in 2024 than in 2015?
Explain in at least one sentence how you solved the problem. Show
your work. Round your answer to the nearest whole number.
Answer the following questions related to the following matrix
A =
3
³).
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