The table provides data on the distance (in yards) of a dog from a park entrance as a function of the number of seconds since the dog entered the park. | Change in the number of seconds since the dog entered the park | The number of seconds since the dog entered the park | The distance (in yards) of a dog from the park entrance | Change in the distance (in yards) of a dog from the park entrance | Average rate of change of the dog’s distance with respect to time ||---------------------------------------------------------------|------------------------------------------------------|-----------------------------------------------------------|--------------------------------------------------------------|---------------------------------------------------------------|| 0 | 0 | 0 | | || 3 | 3 | 26.25 | | || | 3.2 | 30.976 | | || | 4.5 | 77.344 | | || | 7 | 271.25 | | |Tasks:a. Complete the table of values above.b. Sketch a graph of the number of yards the dog is from the park entrance in terms of the number of seconds since the dog entered the park. (Be sure to label your axes).c. Describe what these average rates of change tell you about how the distance of the dog from the park entrance is changing over the time interval from $ t = 0 $ to $ t = 7 $ seconds.d. Is your graph concave up, concave down, or some combination of both on the interval $ 0 < t < 7 $? Justify your answer from part (a) and (c).

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The average rate of dog's distance (d'(t)) is obtained as follows:Let say ∆d(t) = change in distance…

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14. The values in the table below represent the distance (measured in yards) of a dog from a park entrance as a function of the number of seconds since the dog entered the park. Change in the number of seconds since the Average rate of change of the dog's distance with respect to time The number of seconds since the The distance (in yards) of a dog distance (in yards) from the park entrance Change in the dog entered the park dog entered the park of a dog from the park entrance 26.25 3.2 30.976 4.5 77.344 7 271.25 a. Complete the table of values above. b. Sketch a graph of the number of yards the dog is from the park entrance in terms of the number of seconds since the dog entered the park. (Be sure to label your axes). c. Describe what these average rates of change tell you about how the distance of the dog from the park entrance is changing over the time interval from t = 0 to 1 = 7 seconds. d. İs your graph concave up, concave down, or some combination of both on the interval 0 < t< 7? Justify your answer from part (a) and (c).

14. The values in the table below represent the distance (measured in yards) of a dog from a park entrance as a function of the number of seconds since the dog entered the park. Change in the number of seconds since the Average rate of change of the dog's distance with respect to time The number of seconds since the The distance (in yards) of a dog distance (in yards) from the park entrance Change in the dog entered the park dog entered the park of a dog from the park entrance 26.25 3.2 30.976 4.5 77.344 7 271.25 a. Complete the table of values above. b. Sketch a graph of the number of yards the dog is from the park entrance in terms of the number of seconds since the dog entered the park. (Be sure to label your axes). c. Describe what these average rates of change tell you about how the distance of the dog from the park entrance is changing over the time interval from t = 0 to 1 = 7 seconds. d. İs your graph concave up, concave down, or some combination of both on the interval 0 < t< 7? Justify your answer from part (a) and (c).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

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Question

The table provides data on the distance (in yards) of a dog from a park entrance as a function of the number of seconds since the dog entered the park.

| Change in the number of seconds since the dog entered the park | The number of seconds since the dog entered the park | The distance (in yards) of a dog from the park entrance | Change in the distance (in yards) of a dog from the park entrance | Average rate of change of the dog’s distance with respect to time |
|---------------------------------------------------------------|------------------------------------------------------|-----------------------------------------------------------|--------------------------------------------------------------|---------------------------------------------------------------|
| 0 | 0 | 0 | | |
| 3 | 3 | 26.25 | | |
| | 3.2 | 30.976 | | |
| | 4.5 | 77.344 | | |
| | 7 | 271.25 | | |

Tasks:
a. Complete the table of values above.

b. Sketch a graph of the number of yards the dog is from the park entrance in terms of the number of seconds since the dog entered the park. (Be sure to label your axes).

c. Describe what these average rates of change tell you about how the distance of the dog from the park entrance is changing over the time interval from $ t = 0 $ to $ t = 7 $ seconds.

d. Is your graph concave up, concave down, or some combination of both on the interval $ 0 < t < 7 $? Justify your answer from part (a) and (c).

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