1. The altitude of a triangle is increasing at a rate of 33centimeters/minute while the area of the triangle is increasing ata rate of 4.54.5 square centimeters/minute. At what rate is thebase of the triangle changing when the altitude is 11.511.5centimeters and the area is 8686 square centimeters?
2. Gravel is being dumped from a conveyor belt at a rate of 30cubic feet per minute. It forms a pile in the shape of a rightcircular cone whose base diameter and height are always equal. Howfast is the height of the pile increasing when the pile is 19 feethigh? Recall that the volume of a right circular cone with heighth and radius of the base r is given by using thevolume formula?
3. A rotating light is located 14 feet from a wall. The lightcompletes one rotation every 4 seconds. Find the rate at which thelight projected onto the wall is moving along the wall when thelight's angle is 5 degrees from perpendicular to the wall.
4. At noon, ship A is 40 nautical miles due west of ship B. ShipA is sailing west at 20 knots and ship B is sailing north at 20knots. How fast (in knots) is the distance between the shipschanging at 5 PM? (Note: 1 knot is a speed of 1 nautical mile perhour.
5.A street light is at the top of a 12 ft tall pole. A woman 6ft tall walks away from the pole with a speed of 5 ft/sec along astraight path. How fast is the tip of her shadow moving when she is30 ft from the base of the pole?
6.An inverted pyramid is being filled with water at a constantrate of 45 cubic centimeters per second. The pyramid, at the top,has the shape of a square with sides of length 3 cm, and the heightis 5 cm.
Find the rate at which the water level is rising when the waterlevel is 3 cm.
7.A circle is inside a square.
The radius of the circle is decreasing at a rate of 2 meters perday and the sides of the square are increasing at a rate of 2meters per day.
When the radius is 3 meters, and the sides are 22 meters, then howfast is the AREA outside the circle but inside the squarechanging?
The rate of change of the area enclosed between the circle and thesquare is ____________ square meters per day.
8. A police car is located 40 feet to the side of a straightroad.
A red car is driving along the road in the direction of the policecar and is 200 feet up the road from the location of the policecar. The police radar reads that the distance between the policecar and the red car is decreasing at a rate of 95 feet per second.How fast is the red car actually traveling along the road?
The actual speed (along the road) of the red car is _________ feetper second
