the beam from a lighthouse completes one rotation every two minutes. at time t, the distance d shown in the…

Explanation:

Step1: Calculate $d(0.2)$

Substitute $t = 0.2$ into $d(t)=3\tan(\pi t)$. So $d(0.2)=3\tan(0.2\pi)$. Since $\tan(0.2\pi)=\tan(36^{\circ})\approx 0.7265$, then $d(0.2)=3\times0.7265 = 2.18$ (rounded to two - decimal places).

Step2: Calculate $d(0.25)$

Substitute $t = 0.25$ into $d(t)=3\tan(\pi t)$. So $d(0.25)=3\tan(0.25\pi)$. Since $\tan(0.25\pi)=\tan(45^{\circ}) = 1$, then $d(0.25)=3\times1=3.00$.

Step3: Calculate $d(0.35)$

Substitute $t = 0.35$ into $d(t)=3\tan(\pi t)$. So $d(0.35)=3\tan(0.35\pi)$. Since $\tan(0.35\pi)=\tan(63^{\circ})\approx 1.9626$, then $d(0.35)=3\times1.9626 = 5.89$ (rounded to two - decimal places).

Answer:

$d(0.2)=2.18$ mi $d(0.25)=3.00$ mi $d(0.35)=5.89$ mi