Exam 2: Extension G: Limits and Derivatives

Gravel is being dumped from a conveyor belt at a rate of ft/min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.How fast is the height of the pile increasing when the pile is ft high? Round the result to the nearest hundredth.

The top of a ladder slides down a vertical wall at a rate of m/s .At the moment when the bottom of the ladder is 3 m from the wall,it slides away from the wall at a rate of 0.2 m/s .How long is the ladder?

Two carts,A and B,are connected by a rope 39 ft long that passes over a pulley (see the figure below).The point Q is on the floor 12 ft directly beneath and between the carts.Cart A is being pulled away from Q at a speed of 2 ft/s.How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q?

A plane flying horizontally at an altitude of 1 mi and a speed of mi/h passes directly over a radar station.Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

If a snowball melts so that its surface area decreases at a rate of , find the rate at which the diameter decreases when the diameter is 35 cm.

If two resistors with resistances and are connected in parallel,as in the figure,then the total resistance measured in ohms ( $\Omega$ ),is given by If and are increasing at rates of and respectively,how fast is changing when and ? Round the result to the nearest thousandth.

Two cars start moving from the same point.One travels south at mi/h and the other travels west at mi/h.At what rate is the distance between the cars increasing 2 hours later? Round the result to the nearest hundredth.

A baseball diamond is a square with side 90 ft.A batter hits the ball and runs toward first base with a speed of 32 ft/s.At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth.

Two sides of a triangle are m and m in length and the angle between them is increasing at a rate of rad/s.Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat.If the rope is pulled in at a rate of 1 m/s how fast is the boat approaching the dock when it is 7 m from the dock? Round the result to the nearest hundredth if necessary.