Train Tracks are made of metal. They expand when it is warm and shrink when it is cold. When riding on a train you hear the clickety-clack of the wheels going over small gaps left in the tracks to allow for expansion. Suppose someone lay the track and forgot to put in the gaps so that the track is 1 mile long and firmly fixed at each end. On a hot day, suppose the track expanded by a total of 2 feet and therefore buckled in the middle creating a triangle. How high would the midpoint be?

The specific heat of silver is 0.057 calories/gram°c. if 10.0 grams of silver were heated and the temperature of the sample changed by 20.0°c, how many calories of heat energy were absorbed by the sample?

Acombination reaction is when two or more combine to form one product. a decomposition reaction is when a substance breaks down into two or more simpler substances in a chemical reaction.

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)