Constants as planets with a wide variety of properties are being discovered outside our solar system, astrobiologists are considering whether and how life could evolve on planets that might be very different from earth. one recently discovered extrasolar planet, or exoplanet, orbits a star whose mass is 0.70 times the mass of our sun. this planet has been found to have 2.3 times the earth's diameter and 7.9 times the earth's mass. for planets in this size range, computer models indicate a relationship between the planet's density and composition: density compared with that of the earth composition 2-3 times mostly iron 0.9-2 times iron core with a rock mantle 0.4-0.9 times iron core with a rock mantle and some lighter elements, such as (water) ice < 0.4 times hydrogen and/or helium gas based on s. seager et al., "mass-radius relationships for solid exoplanets"; arxiv: 0707.2895 [astro-ph]. observations of this planet over time show that it is in a nearly circular orbit around its star and completes one orbit in only 9.5 days how many times the orbital radius r of the earth around our sun is this exoplanet's orbital radius around its sun? assume that the earth is also in a nearly circular orbit

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?

Explain why electric current cannot exist if a current doesn't have a voltage source.

Two loudspeakers, 5.5 m apart and facing each other, play identical sounds of the same frequency. you stand halfway between them, where there is a maximum of sound intensity. moving from this point toward one of the speakers, you encounter a minimum of sound intensity when you have moved 0.33 m . assume the speed of sound is 340 m/s.part a) what is the frequency of the sound? part b) if the frequency is then increased while you remain 0.21 m from the center, what is the first frequency for which that location will be a maximum of sound intensity? express your answer to two significant figures and include the appropriate units.