Aparticle’s velocity (in m/s) in a gas is a random variable (let it be v ) with pdf fv (v) = av2 e −bv, v > 0, where b is a constant that depends on the temperature of the gas and the mass of the particle. answer the following questions. (a) what should a be for this to be a valid pdf as a function of b? (b) what is the probability the velocity of the particle is between 10 and 100 meters per second? (c) the kinetic energy of a particle is w = 1 2mv 2 , where v is the speed. what is the pdf of w? (d) what is the mean kinetic energy of a particle as a function of constant b?

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water

a skateboard rolling across the street - apex

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y