2) The radius of a right circular cone is increasing at a rate of 1.8 - while its height is decreasing at a rate of 2.5- At what rate is the volume of the cone changing when the radius is 120 in and the height is 140 in? 3) Radiation intensity follows the Inverse Square Law, meaning it varies with the inverse of the square of the distance from the radiation source. In other words, it is proportional to =, where d is the distance from the source. This means if a radiation source is located at the origin, we can model the radiation intensity at a point by the function k I(x, y =) = for some constant value k. Suppose an object follows a path relative to this radiation source defined by (t) = (+2 - 1,2t - 1,t - 2) Find the rate at which the intensity of the radiation is changing as a function of t (substitute for x, y, and = and simplify), and at t = 0. In both cases your answer will be relative to the constant k. 4) Find the directions in which the directional derivative of f(x, >) = ye"at the point (0,2) has the value 1. 5) Show that for any k > 0, the volume of the tetrahedron formed in the first octant bounded by the coordinate planes and a tangent plane to the surface xy= = k at any point in the first octant depends only k and not on the coordinates of the point