The equation d=11cos (8pi/5 t) models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance. 0.625 seconds 0.8 seconds 1.25 seconds 1.6 seconds

Question

Jaime Madden

Mathematics

25 June, 17:08

The equation d=11cos (8pi/5 t) models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance. 0.625 seconds 0.8 seconds 1.25 seconds 1.6 seconds

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Answers (2)

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Nathanael Wong · Answer 1

1.25 seconds

Step-by-step explanation:

Cosine is a maximum at cos (0) = 1, and a minimum at cos (π) = - 1.

At the maximum:

8π/5 t = 0

t = 0

At the minimum:

8π/5 t = π

t = 5/8

t = 0.625

The time from maximum to minimum is 0.625 seconds. Therefore, the time from minimum back to maximum is also 0.625 seconds. So the total time is:

0.625 + 0.625 = 1.25

Amara Marsh · Answer 2

1.25 seconds