the equation $d = 11cos(\frac{8pi}{5}t)$ models the horizontal distance, $d$, in inches of the pendulum of a…

the equation $d = 11cos(\frac{8pi}{5}t)$ 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.\n0.625 seconds\n0.8 seconds\n1.25 seconds\n1.6 seconds

the equation $d = 11cos(\frac{8pi}{5}t)$ 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.\n0.625 seconds\n0.8 seconds\n1.25 seconds\n1.6 seconds

Answer

Explanation:

Step1: Identify the formula for period

The general form of a cosine - function is $y = A\cos(Bt - C)+D$, and its period $T$ is given by $T=\frac{2\pi}{|B|}$. In the given function $d = 11\cos(\frac{8\pi}{5}t)$, $B=\frac{8\pi}{5}$.

Step2: Calculate the period

Using the period formula $T=\frac{2\pi}{|B|}$, substitute $B = \frac{8\pi}{5}$ into it. Then $T=\frac{2\pi}{\frac{8\pi}{5}}$. When dividing by a fraction, we multiply by its reciprocal: $T=2\pi\times\frac{5}{8\pi}$. The $\pi$ terms cancel out, and $2\times\frac{5}{8}=\frac{10}{8}=1.25$ seconds.

Answer:

1.25 seconds