Work in 1-dimension for simplicity. let ф(2', t) %3dt(2", 2)ф(т, t), where t(',x) is called the "space translation operator from x to x". so that r' = x + dx. explain why the following form makes (a) consider an infinitesimal space translation, sense for the corresponding "infinitesimal space translation operator": idx t(xdr, x) 1 + ô+ (dx2) (b) hence show that o is the momentum operator. (c) explain why the full space translation operator is thus given by and comment on the relationship of this expression to the usual taylor series expansion of /(x',t) around the point r

An object weighs 40n in air, weighs 20n when submerged in water and 30n when submerged in a liquid of unknown density. what is the density of the liquid?

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.)

This punnett square shows the cross between two pants. one parent has round seeds (rr). and the other parent has wrinkled seeds (rr) which best describes their offspring as shown in this cross?