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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
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13 votes
13 votes
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

User Hacksoi
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1 Answer

13 votes
13 votes

Answer:

5 feet

Explanation:


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

User Amir Shabani
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