1. The altitude of a triangle is increasing at a rate of 33 centimeters/minute while the...

1. The altitude of a triangle is increasing at a rate of 33 centimeters/minute while the area of the triangle is increasing at a rate of 4.54.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 11.511.5 centimeters and the area is 8686 square centimeters?

2. Gravel is being dumped from a conveyor belt at a rate of 30 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 19 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by using the volume formula?

3. 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.

4. At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 20 knots and ship B is sailing north at 20 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.

5.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 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?

6.An inverted pyramid is being filled with water at a constant rate 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 height is 5 cm.
Find the rate at which the water level is rising when the water level is 3 cm.

7.A circle is inside a square.

The radius of the circle is decreasing at a rate of 2 meters per day and the sides of the square are increasing at a rate of 2 meters per day.
When the radius is 3 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 ____________ square meters per day.

8. A police car is located 40 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 200 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 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 _________ feet per second

Expert Solution

milcah answered 2 years ago

The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area...

The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8 centimeters and the area is 82 square centimeters?

The area of a square is increasing at a rate of 2 square feet per minute....

The area of a square is increasing at a rate of 2 square feet per minute. How fast is the perimeter changing in feet per minute when the area of the square is 64 square feet?

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