Abead, under the influence of gravity, slides along a frictionless wire whose height is given by the function y(x). assume that at position (x; y) = (0; 0), the wire is tilted downward at an angle θ, and that the bead passes this point with a given speed v . what should the shape of the wire be (that is, what is y as a function of x) so that the horizontal speed remains constant at all times?