A square plane mirror of side length s s hangs on a wall such that its bottom edge is a height h h above the floor. The wall opposite the mirror is a distance d d away. Marco, whose eyes are at the exact height of the center of the mirror, stands directly in front of the mirror at the center of its width. Derive an expression for the maximum distance x x that Marco can stand from the mirror and still see the reflection of the bottom of the wall behind him. Assume that s < 2 h .

Three archers each fire four arrows at a target. joe’s four arrows hit at points 10 cm above, 10 cm below, 10 cm to the left, and 10 cm to the right of the center of the target. all four of moe’s arrows hit within 1 cm of a point 20 cm from the center, and flo’s four arrows hit within 1 cm of the center. the contest judge says that one of the archers is precise but not accurate, another archer is accurate but not precise, and the third archer is both accurate and precise. which description applies to which archer? explain

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.)

The experiment was repeated many years later but the gases were mixed in a different type of container. a white solid was obtained which was xenon fluoride. predict whether you think 1) krypton and 2) radon will react with fluorine. explain reasons for your predictions