The position function of an object moving along a straight line is given bys = f(t). the average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. a ball is thrown straight up with an initial velocity of 112 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 112t − 16t2.(a) what is the average velocity of the ball over the following time intervals? [3,4] ft/sec[3,3.5] ft/sec[3,3.1] ft/sec(b) what is the instantaneous velocity at time t = 3?

Which units can be used to measure length or distance? check all that apply. gram meter kilometer liter inch

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?

Two rigid transformations are used to map δhjk to δlmn. the first is a translation of vertex h to vertex l. what is the second transformation? a reflection across the line containing hk a rotation about point h a reflection across the line containing hj a rotation about point k