1. A flower bed is to be shape of a circular sector of radius r and central angle θ. Find r and θ if the area is fixed and the perimeter is a minimum.
2. Suppose that the position of a particle on a straight line at time t is s(t) = at - (1 + a^4)t^2. Show that the particle moves forward initially when a is positive but ultimately retreats. Show also that for different values of a the maximum possible distance that particle can move forward is 1/8.
thx in advance
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