I've been working on practice problems over the summer in preparation for next years AP calc class, and these problems are beyond my knowledge. Any help is highly appreciated.
1. Sketch the polar curve r=2-4sinθ and determine the values of θ which generate the inner loop. Give these angles in exact radian measure.
2. A closed can in the shape of a right circular cylinder is designed to hold 12 oz. soda. If the height of the cylinder is x in., write an equation in terms of x to represent the amount of material needed to construct the closed can. (1 fl. oz. = 1.805 in^3) Find the minimum amount of material needed.
3. Solve over the given interval: sin(x) - cos(2x)=0, -pi/2 ≤ x ≤ pi
4. Two particles move in the x-y plane. For t≥0 the position of a particle A is x=(t-2)^2 and y=t-2 and the position of particle B is x=(3/2)t - 2 and y= (3/2)t - 4. At what time do the particles collide?