An object in equilibrium has three forces exerted on it. a 42 n force acts at 90° from the x-axis and a 46 n force acts at 60° from the x-axis. what are the magnitude and direction of the third force? n ° (counterclockwise from the +x direction)

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

The pressure proportional to the area a- inversely b- directly c- increase d-decrease

Aspring has a natural length of 8 m. if a 12-n force is required to keep it stretched to a length of 10 m, how much work w is required to stretch it from 8 m to 16 m? (round your answer to two decimal places.)