A toy boat is bobbing in the water.

Its distance D(t) (in m) from the floor of the lake as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a×sin(b×t) + d.

At t=0, when the boat is exactly in the middle of its oscillation, it is 1 m above the water's floor. The boat reaches its maximum height of 1.2 m after pi/4 seconds.

Find D(t).

Step-by-step explanation:

The sinusoidal expression has the following form:

Where:

- Initial distance from the floor of the lake, in meters.

- Amplitude of oscillation, in meters.

- Angular frequency, in radians.

Now, each coefficient is derived as follows:

Initial distance from the floor of the lake

Amplitude of oscillation

Angular frequency

From the statement it is known that boat reaches its maximum height in a quarter of its oscillation. Then, the angular frequency is:

The expression is:

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step-by-step explanation: