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Mr. O. ran the Disney Marathon in 2 hours 18 minutes. Remember a marathon is 26.2

miles. Show that at least twice he had to be running at a rate of 11 miles per hour.

Determine whether Mean Value Theorem can be applied. If so, find all values x=c that satisfy the theorem, or explain why not.

Calculus AB AP

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Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Time taken = 2 hours 18 minutes

18 / 60 = 0.3 hours

Hence, time taken = 2.3 hours

Speed = distance / time

Speed = 26.2 / 11.3 = 11.39 mi/hr

Hence, according to the mean value theorem ;

The range of time taken is (0, 2.3) whereby a certain time, t exist when the runner attains a speed of 11.39

Since initial and final velocity is 0 ;

The runner attains a speed of 11 mi/hr between :

(0, 2.3) and (t, 2.3)

Mr. O. ran the Disney Marathon the AB AP is  (0, 2.3) and (t, 2.3).

  • Given Data:
  • Time taken = 2 hours 18 minutes

        Time taken =18 / 60

        Time taken = 0.3 hours

Hence,

time taken = 2.3 hours

  •  Speed = distance / time

          Speed = 26.2 / 11.3

          Speed = 11.39 mi/hr

According to the mean value theorem ;

The range of time taken is (0, 2.3) whereby a certain time, t exist when the runner attains a speed of 11.39 Since initial and final velocity is 0 ;

The runner attains a speed of 11 mi/hr between : (0, 2.3) and (t, 2.3)

Thus, the AB and AP is (0, 2.3) and (t, 2.3)

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