3. A 420-kg piano slides 3.25 m down a 30° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. Determine: a. The force exerted by the man. (10pts) b. The work done on the piano by the man. (10pts) c. The work done on the piano by the force of gravity. (10pts) d. The net work done on the piano. Ignore friction. (10pts)

In september, lee ran in the run rabbit run 50 mile race in steamboat. the race is an out-and-back course, meaning that you start and run out from the base of steamboat ski resort up to rabbit ears, and then turn around and retrace your path to the finish. the table below provides the timed splits through the various aid stations along the course. time aid state (distance traveled from start) 0: 00: 00 start (0 miles) 1: 21: 51 mount werner aid station (6.4 miles) 2: 22: 52 long lake aid station (13.2 miles) 3: 34: 36 base camp trailhead aid station (18.4 miles) 4: 05: 34 dumont aid station (22.3 miles) 4: 45: 25 rabbit ears (25 miles) 5: 13: 17 dumont aid station (27.7 miles) 6: 02: 43 base camp trailhead aid station (31.6 miles) 7: 07: 11 long lake aid station (36.8 miles) 8: 41: 37 mount werner aid station (43.6 miles) 9: 29: 13 finish (50 miles) (a) explain if the table represents a function. if it does not, provide evidence supporting that it is not a function. if it is a function, describe the relationship between the independent variable and dependent variable in this scenario. (b) construct a graph that depicts the relationship between time and the total distance traveled in the race. (c) construct a graph that depicts the relationship between time and displacement from start/finish (relative distance to start/finish). (d) construct a graph that depicts the relationship between time and lee’s speed running. (e) what can we infer about lee’s speed at time 4: 05: 34? explain your reasoning.