4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially empty a...
4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially empty and rain enters the can during a 60-day period. The height of water in the can is modeled by the function S, where S(t) is measured in millimeters and t is measured in days for 0sts 60. The rate at which the height of water is rising in the can is given by S'(t) = 2 sin(0.03t) of the 60-day period? +1.5. According to the model, what is the height of the water in the can at the end 5) The rate (R) at which people enter an auditorium for a rock concert, is modeled by the function R where R(t) 1380t2 auditorium when the doors open (t: 675t3, and time (t) is measured in hours. No one is in the 0), and the doors close 2 hours later, when the concert begins (t 2). How many people are in the auditorium when the concert begins? 6) A sand bag originally weighing 144 lb was lifted at a constant rate. As it rose, sand leaked out at a constant rate. The sand was half gone by the time the bag had been lifted 18 ft. How much work (ft-lb) was done lifting the sand this far (neglect the weight of the lifting equipment and bag). 7) A rock climber is about to haul up 100N (about 22.5 lb) of equipment that has been hanging beneath her on 40 m of rope weighing 0.8 N/m. How much work will it take to lift all this? 8) A vertical cylindrical tank measures 30 ft high and 20 ft in diameter. It is full of kerosene weighing 51.2 lb/ft'. How much work (ft-lb) does it take to pump the kerosene to the level of the top of the tank (i.e to pump all the kerosene out the top of the tank).
4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially empty and rain enters the can during a 60-day period. The height of water in the can is modeled by the function S, where S(t) is measured in millimeters and t is measured in days for 0sts 60. The rate at which the height of water is rising in the can is given by S'(t) = 2 sin(0.03t) of the 60-day period? +1.5. According to the model, what is the height of the water in the can at the end 5) The rate (R) at which people enter an auditorium for a rock concert, is modeled by the function R where R(t) 1380t2 auditorium when the doors open (t: 675t3, and time (t) is measured in hours. No one is in the 0), and the doors close 2 hours later, when the concert begins (t 2). How many people are in the auditorium when the concert begins? 6) A sand bag originally weighing 144 lb was lifted at a constant rate. As it rose, sand leaked out at a constant rate. The sand was half gone by the time the bag had been lifted 18 ft. How much work (ft-lb) was done lifting the sand this far (neglect the weight of the lifting equipment and bag). 7) A rock climber is about to haul up 100N (about 22.5 lb) of equipment that has been hanging beneath her on 40 m of rope weighing 0.8 N/m. How much work will it take to lift all this? 8) A vertical cylindrical tank measures 30 ft high and 20 ft in diameter. It is full of kerosene weighing 51.2 lb/ft'. How much work (ft-lb) does it take to pump the kerosene to the level of the top of the tank (i.e to pump all the kerosene out the top of the tank).