A light train made up of two cars is traveling at 90 km/h when the brakes are applied to both cars. Knowing that car A has a mass of 25 Mg and car B a mass of 20 Mg, and that the braking force is 30 kN on each car, determine (a) the distance traveled by the train before it comes to a stop, (b) the force in the coupling between the cars while the train is showing down.

According to social exchange theory, altruistic behaviors benefit the individual who performs them.

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Comedians like to joke that the reason we haven’t been visited by intelligent life from elsewhere in the universe is that aliens have been monitoring earth’s broadcasts of intellectually embarrassing tv programs, like gilligan’s island, fear factor, the jersey shore, and the jerry springer showand so consider us far too primitive to merit a visit. let’s check the assertion that aliens could have been receiving them. tv programs are broadcast at a frequency of about 100mhz with about 100kw of total power in 30frames per second, which emanatesroughly uniformly in all directions. assume that interstellar space transmits these broadcasts without attenuation. no matter how smart they are, aliens would require at least one photon per frame to interpret our signals. findthe number of photons per unit time per unit area reaching a receiver on a possible planet in the nearest star system, which is about 4 light-years away (a light-year is the distance light travels in a year). if aliens aimed a receiver or detector directly at earth, how big (in diameter) would it have to be to receive a photon per frame