Find the a unit vector perpendicular to the surface
Z=x^2+y^2-z
at (1 ,2,3)

In a system, when potential energy decreases, then entropy also decreases. true false

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.)

Atriangle with equal sides of length 10 cm has -2.5-nc charged objects at each corner. part a determine the direction of the electrical force exerted on the object at the top corner due to the two objects at the horizontal base of the triangle. determine the direction of the electrical force exerted on the object at the top corner due to the two objects at the horizontal base of the triangle. horizontally rightward vertically downward vertically upward horizontally leftward