In order to use the Pythagorean theorem to find the magnitude of a resultant vector which must be true regarding two initial vectors?

A2-kg bowling ball is 2.5 meters off the ground on a post when it falls. just before it reaches the ground, it is traveling 7 m/s. assuming that there is no air resistance, which statement is true?

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.)

Ascientist notices that an oil slick floating on water when viewed from above has many different colors reflecting off the surface, making it look rainbow-like (an effect known as iridescence). she aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). the index of refraction of water is 1.3