An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 127 ft at an angle of 31.0° above the horizontal. it then moves 127 ft at an angle of 46.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

6–55 refrigerant-134a enters the condenser of a residential heat pump at 800 kpa and 358c at a rate of 0.018 kg/s and leaves at 800 kpa as a saturated liquid. if the compressor consumes 1.2 kw of power, determine (a) the cop of the heat pump and (b) the rate of heat absorption from the outside air.

10 points! will mark brainiest! in a heat engine if 1,000 j of heat enters the system and the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2,000 j 1: write the equation 2: list out your known variables 3: plug the numbers into the equations 4: solve 5: write your solution statement that includes initial energy and final energy added you so much!