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

Mathematics

Daniel

23 May, 07:24

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)

Know the Answer?

Philip Arnold · Answer 1

1.25 seconds

Kiera Reynolds · Answer 2

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