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# The displacement of a buoy, in metres, in the water is described by the function b(t) = 5sin(30t) at time t seconds.

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Question: The displacement of a buoy, in metres, in the water is described by the function b(t) = 5sin(30t) at time t seconds. If the buoy starts at the center, when is the second time that the buoy will be back at the center?

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The buoy will be back at the center whenever the sine function equals zero. The sine function equals zero at nπ, where n is an integer. Here, we have b(t) = 0 when 30t = nπ. Given that the buoy starts at the center, this means that time t=0 seconds is the first time it's at the center. Solving the equation, we get: 30t = π (for n = 1, which is the next time it will be at the center after the start time) So, t = π / 30 ≈ 0.1047 seconds (which is the second time it will be at the center) Then, we find the next time: 30t = 2π (for n = 2, which is the next time it will be at the center after t = π / 30) So, t = 2π / 30 = π / 15 ≈ 0.2094 seconds. Therefore, the second time that the buoy will be back at the center is approximately at t=0.2094 seconds.

July 20, 2023, 9:16 a.m.

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