There is NO net electric charge inside the box, but the space in and around the box is filled with a nonuniform electric field of the following form: E(x, y,z) = c1z2i + c2xyj + c3x2k, where c1 = 4.35 N/(Cm2), c2 = 3.16 N/(Cm2), c3 = 5.55 N/(Cm2), are constants. What is the electric flux through the top face of the box? (Remember that we define positive flux pointing out of the box.)

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 number of passengers who arrive at the platform of a subway station for the 10 am train is a random variable with a mean of 120 and a variance of 16. find the lower bound of the probability that there will be between 100 and 140 passengers (round off to second decimal place).

Asilver dollar is dropped from the top of a building that is 1324 feet tall. use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) determine the position and velocity functions for the coin. s(t) = v(t) = (b) determine the average velocity on the interval [1, 2]. ft/s (c) find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) find the time required for the coin to reach the ground level. (round your answer to three decimal places.) t = s (e) find the velocity of the coin at impact. (round your answer to three decimal places.) ft/s