Warmup 1) 2). 4.6: Related Rates They are related (Xmas 2013)

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Presentation transcript:

Warmup 1) 2)

4.6: Related Rates They are related (Xmas 2013)

Suppose that the radius of a sphere is changing at a rate of 0.1 cm/sec. The sphere has a radius of 10 cm to start Find the rate of change of the volume. (Possible if the sphere is a soap bubble or a balloon.) The sphere is growing at a rate of.

Air is being pumped into a balloon at a rate of 6 cubic feet per minute. Find the rate of change of the radius when the radius is 2 ft. Ex.

Steps for Related Rates Problems: 1. Draw a picture (sketch). 2. Write down known information. 3. Write down what you are looking for. 4. Write an equation to relate the variables. 5. Differentiate both sides with respect to t. 6. Evaluate.

A pebble gets dropped into a pool and the resulting ripples are concentric circles that expand from the center. The radius of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 3 feet, at what rate is the total area of the water changing?

All edges of a cube are expanding at a rate of 4 inches per second. How fast is the volume changing when each edge is (a) 1 inch, (b) 3 inches ?

Hot Air Balloon Problem: Given: How fast is the balloon rising? Find

Hot Air Balloon Problem: Given: How fast is the balloon rising? Find

B A Truck Problem: Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr. How fast is the distance between the trucks changing 6 minutes later?

B A Truck Problem: How fast is the distance between the trucks changing 6 minutes later? Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr.

Police chase problem (group): A police cruiser, approaching a right intersection from the north, is chasing a speeding car that has turned the corner and headed east. When the cruiser is 0.6 mi north of the intersection and the car is 0.8 mi to the east, the police determine the distance between them is increasing at 20 mph. If the cruiser is moving at 60 mph at the instant measurement, what is the speed of the car? ex. 3 from our book

Water runs into a conical tank at a rate of 9ft 3 /min. The tanks stands point down and has a height of 10ft and a base radius of 5ft. How fast is the water level rising when the water is 6ft deep? Ex. 4 p. 235

Water is draining from a cylindrical tank at 3 liters/second. How fast is the surface dropping? Find ( r is a constant.) (We need a formula to relate V and h. )

B) At what rate is the angle changing where the ladder meets the ground when the ladder is 10 feet from from the base of the wall.

The end