An analogy makes a comparison between objects based on their similar qualities. cassidy wanted to create an analogy for the motion of atoms in solids, liquids, and gases, so she compared them to marbles in a tray.

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.)

There are two-speed cameras, one in an are where the speed limit is 30 km/h and another where the speed limit is 50 km/h. in which will there be a smaller time interval between the photographs? explain your answer.

Under the action of a constant force an object accelerates at 7.8 m/s2. what will the acceleration be if (a) the force is halved? (b) the object's mass is halved? (c) the force and the object's mass are both halved? (d) the force is halved and the object's mass is doubled?