A bead P of mass m slides down a smooth wire fixed in a vertical plane, which is bent into the form of the catenary S= c tanψ, with its axis is vertical and its vertex at its lowest point. The bead is given a velocity along the tangent when at its highest point. Prove that the velocity of the bead is given by and the bead will leaves the wire when cos ψ = 2/3

70 points ! pls 2. given the following two sets of data what is the union of the two sets and what is the intersection of the two sets. set a = {1, 2, 3, 4, 5, 6, 7, 8, 9} set b = {2, 4, 6, 8, 10, 12, 14} 3. given a regular deck of cards. describe a way of pulling cards that would create a dependent event and then one that would create an independent event. 4. what is the probability of drawing a red card and then drawing a spade without replacing the card that was drawn first?