Calculator A particle moving in the XY-plane has position (x(t), y(t)) at time t ≥ 0, where x(t) …

Calculator A particle moving in the XY-plane has position (x(t), y(t)) at time t ≥ 0, where x(t) = tcos(t) and y(t) = tsin(t). At time t = 0, the particle is at position (4, 2). The figure above shows the path of the particle for 0 ≤ t ≤ 2. (a) Find the position of the particle at time t. (b) Find the slope of the line tangent to the particle #x27;s path at time t = 2. (c) Find the speed of the particle at time t = 2. (d) Consider a rectangle with vertices at points (0, 0), (x(t), 0), (x(t), y(t)), and (0, y(t)) at time t ≥ 0. For 0 ≤ t ≤ 2, what time is the perimeter of the rectangle maximum? Justify your answer.

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