For the demand function q = D(p) = 314-p, find the following. K a) The elasticity b) The elasticity at p=93, stating whether the demand is elastic, inelastic or has unit elasticity c) The value(s) of p for which total revenue is a maximum (assume that p is in dollars)
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- Water is leaking out of an inverted conical tank at a rate of 9400.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 13.0 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 28.0 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Let "R" be the unknown rate at which water is being pumped in. Then you know that if is the volume of water,dv/dt=R-9400.0. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by1/3 pi r^2hA spring in equilibrium has length 1 meter. If ittakes 40 joules (i.e., kg-msec2 ) of work to stretch the spring toa length of 3 meters, how much work does it take to stretchthe spring from a length of 3 meters to a length of 5 meters?A ball with mass 0.15 kg is thrown upward with initial velocity 20 m/s from the roof of a building 30 m high. Neglect air resistance. a.Find the maximum height above the ground that the ball reaches. b.Assuming that the ball misses the building on the way down, find the time that it hits the ground. c. Plot the graphs of velocity and position versus time.