Question

The function f(t) = 3 cos(pi over 6t) + 5 represents the tide in Blastic Sea. It has a maximum of 8 feet when time (t) is 0 and a minimum of 2 feet. The sea repeats this cycle every 12 hours. After nine hours, how high is the tide? 12 feet 5 feet 4.5 feet 2.5 feet

Answer 1

Answer:

5 feet

Step-by-step explanation:

$f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}$