Related Rates.notebook
February 25, 2014
A point moves along the curve in such a way that the y­value is decreasing at the rate of 2 units per second. At what rate is the x changing when x = 4?
Related Rates.notebook
February 25, 2014
A water tank has the shape of an inverted right circular cone with an altitude of 12 ft and radius 6 ft. If water is being pumped into the tank at a rate of 10 gal/min, approximate the rate at which the water level is rising when it is 3 ft deep. (1 gal ≈ 0.1337 ft3)
Related Rates.notebook
February 25, 2014
A light is at the top of a 16 foot pole. A boy 5 feet tall walks away from the pole at a rate of 4 ft/sec. At what rate is the tip of his shadow moving when he is 18 feet from the pole? At what rate is the length of his shadow increasing?
Related Rates.notebook
February 25, 2014
For a certain rectangle the length of one side is always three times the length of the other side.
a) If the shorter side is decreasing at a rate of 2 inches/minute, at what rate is the longer side decreasing?
b) At what rate is the enclosed area decreasing when the shorter side is 6 inches long and is decreasing at a rate of 2 inches/minute?
Related Rates.notebook
February 25, 2014
Describe the motion of a particle moving along the curve s(t) = 5t2 ­ 10t on the time interval [­1,2]. Provide a verbal description as well.
Related Rates.notebook
February 25, 2014
Related Rates:
1) A snowball is melting at a rate of 2 ft3 per hour. If it remains spherical, at what rate is the radius changing when the radius of the snowball is 20 inches?
2) A car is traveling west on the interstate. A highway patrolman is parked 90 feet north of the interstate. The patrolman takes a radar reading and finds that the car is 150 feet from his position, and the distance separating them is increasing at a rate of 72 ft/sec. Find the speed of the car at that moment.
3) A child is standing still and flying a kite. The kite remains at an altitude of 30 feet above the child's hands while traveling parallel to the ground at a rate of 10 feet per second. When the kite is 50 feet away from the child, how fast is the kite string leaving the child's hand?
4) A car is 30 miles north of town, heading north at 25 miles per hour. At the same time, a truck is 40 miles east of town, traveling east at 50 miles per hour. At what rate is the distance between the two vehicles changing?