Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 16 feet high? Recall that the volume of a right circular cone with heighth and radius of the base r is given by 1 V = = rh 3 ft min A rotating light is located 14 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 5 degrees from perpendicular to the wall. wall V light feet per second At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) knots A square tile is expanding as it is heated. Right now, the 22 inch tile is growing by 0.125 inches per minute. At what rate is the area of the tile changing? inches / minute Round your answer to the nearest hundredth. A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole? ft sec Water is leaking out of an inverted conical tank at a rate of 12800 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 6 meters. If the water level is rising at a rate of 23 centimeters per minute when the height of the water is 1 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. cm min A circle is inside a square. The radius of the circle is increasing at a rate of 2 meters per minute and the sides of the square are decreasing at a rate of 2 meters per minute. When the radius is 2 meters, and the sides are 22 meters, then how fast is the AREA outside the circle but inside the square changing? The rate of change of the area enclosed between the circle and the square is per minute. square meters A police car is located 30 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 190 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 80 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 feet per second An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 4 cm, and the height is 12 cm. Find the rate at which the water level is rising when the water level is 5 cm. cm/sec h b b A balloon is rising at a rate of 2 meters per second from a point on the ground 42 meters from an observer. Find the rate of change of the angle of elevation from the observer to the balloon when the balloon is 32 meters above the ground. radians/second 1. (5 pts.) Function y(x) is given implicitly: 3+2x = sin(x y). Find the derivative y'(x). 2. (5 pts.) A snowball melts so its surface area decreases at a rate of 1 cm/s . Find the rate at which the diameter decreases when the diameter is 10 cm. 3. (5 pts.) Two small planes approach an airport, one flying due west at 120 mi/hr, and the other flying due north, at 150 mi/hr. Assuming they fly at the same constant elevation, how fast is the distance between the planes changing when the westbound plane is 180 mi from the airport and the northbound plane is 225 miles from the airport? (Round your answer to the nearest whole number of miles/hr.) 4. (5 pts.) An oil rig springs a leak and oil spills in a circular patch around the rig. If the radius of the oil patch increases at a rate of 30 meters per hour, how fast is the area increasing when the radius is 100 m? Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 16 feet high? Recall that the volume of a right circular cone with heighth and radius of the base r is given by 1 V = = rh 3 ft min A rotating light is located 14 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 5 degrees from perpendicular to the wall. wall V light feet per second At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) knots A square tile is expanding as it is heated. Right now, the 22 inch tile is growing by 0.125 inches per minute. At what rate is the area of the tile changing? inches / minute Round your answer to the nearest hundredth. A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole? ft sec Water is leaking out of an inverted conical tank at a rate of 12800 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 6 meters. If the water level is rising at a rate of 23 centimeters per minute when the height of the water is 1 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. cm min A circle is inside a square. The radius of the circle is increasing at a rate of 2 meters per minute and the sides of the square are decreasing at a rate of 2 meters per minute. When the radius is 2 meters, and the sides are 22 meters, then how fast is the AREA outside the circle but inside the square changing? The rate of change of the area enclosed between the circle and the square is per minute. square meters A police car is located 30 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 190 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 80 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 feet per second An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 4 cm, and the height is 12 cm. Find the rate at which the water level is rising when the water level is 5 cm. cm/sec h b b A balloon is rising at a rate of 2 meters per second from a point on the ground 42 meters from an observer. Find the rate of change of the angle of elevation from the observer to the balloon when the balloon is 32 meters above the ground. radians/second 1. (5 pts.) Function y(x) is given implicitly: 3+2x = sin(x y). Find the derivative y'(x). 2. (5 pts.) A snowball melts so its surface area decreases at a rate of 1 cm/s. Find the rate at which the diameter decreases when the diameter is 10 cm. 3. (5 pts.) Two small planes approach an airport, one flying due west at 120 mi/hr, and the other flying due north, at 150 mi/hr. Assuming they fly at the same constant elevation, how fast is the distance between the planes changing when the westbound plane is 180 mi from the airport and the northbound plane is 225 miles from the airport? (Round your answer to the nearest whole number of miles/hr.) 4. (5 pts.) An oil rig springs a leak and oil spills in a circular patch around the rig. If the radius of the oil patch increases at a rate of 30 meters per hour, how fast is the area increasing when the radius is 100 m?