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find parametric equations and a parameter interval for the motion of a particle starting at point (3,0) and tracing the top half of the circle

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Final answer:

The parametric equations for the motion of the particle tracing the top half of a circle are x = 3cos(t) and y = 3sin(t), with a parameter interval of 0 <= t <= π.

Step-by-step explanation:

To find the parametric equations for the motion of a particle tracing the top half of a circle, we can use the equation of a circle. The equation of a circle with radius r centered at the origin is given by x = rcos(t) and y = rsin(t), where t is the parameter. In this case, the particle starts at point (3,0), so the equation becomes x = 3cos(t) and y = 3sin(t). The parameter interval for the motion of the particle can be any interval that covers the top half of the circle, such as 0 <= t <= π. These parametric equations succinctly outline the particle's x and y coordinates as it traverses the top arc of the circle, providing a clear mathematical description of its trajectory.

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