1. (8 points) A man, who is 28 feet away from a 30 foot tall street lamp, is sinking into quicksand. (See diagram below.) At the moment when 6 feet of his body is above the ground, his height above the ground is shrinking at a rate of 2 feet/second. Street lamp (30 feet tell) (a) (3 points) How long will the man's shadow (shown in bold in the diagram above) be at the moment when 6 feet of his body is above the ground? (b) (5 points) At what. rate is the length of the man's shadow changing at the moment 6 feet of his body is above the ground? ls his shadow growing or shrinking at that moment? 2. (7 points] Sam is pouring concrete into a hole in the shape of a triangular prism. The hole is 4 meters wide, 4 meters long. and 6 meters deep at its deepest point. A partially lled hole with the correct. dimensions is shown below. Sam is looking down into the hole and observes that the rectangular top surface of the concrete is growing at a rate of 0.8 meters squared per minute. Note that the length of the rectangle top surface does not change as the concrete is poured into the hole. 4 '1 lAN (a) (3 points) How fast is the width of the rectangular top surface increasing at this time? (b) [4 points) Find the rate at which the depth of the concrete is growing