\f(1 point) The altitude (i.e., height) of a triangle is increasing at a rate of 3.5 cm/minute while the area of the triangle is increasing at a rate of 5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 9 centimeters and the area is 100 square centimeters? The base is changing at 9.02 cm/min.(1 point) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of Im/s, how fast is the area of the spill increasing when the radius is 15m? Answer (in m=/s):(1 point) Air is being pumped into a spherical balloon so that its volume increases at a rate of 50cm /s. How fast is the surface area of the balloon increasing when its radius is 18cm? Recall that a ball of radius / has volume 1 = -a and surface area S = 4xp2. 16.67(1 point) Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 19 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V = far h. When the pile is 19 feet high, its height is increasing at 40 81 x feet per minute.A jogger runs around a circular track of radius 60 ft. Let (x, y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (36, 48), her x-coordinate is changing at a rate of 20 ft/s. Find dy/dt. dyldt = ftis(1 point) A spotlight on the ground is shining on a wall 12m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 0.8m/s, how fast is the length of her shadow on the building decreasing when she is 2m from the building? Answer (in meters per second): 0.8A 22 ft. ladder is leaning against a house while the base is pulled away at a constant rate of 1 ft./s. At what rate is the top of the ladder sliding down the side of the house when the base is: 1 foot from the house? Answer= 0.06825 5 feet from the house? Answer= 0.35 21 feet from the house? Answer=|4.8037 (Answers should be positive.)