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

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)

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something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).