Quiz 3††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† Name:†† †††††††††††††† Key†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††
Show all work, and be sure to include units in your answers where appropriate
1. What is the average value of the function
2. A cable, with a mass of 2 kg / meter, is used to lift 20 kg of water from a well 6 meters deep.
How much work is done?
At a depth of x meters, the combined mass of the cable and the water is (2x+20)kg, which has a weight of
† To lift this a small amount, say dx meters, requires (2x+20)(9.8)dx Joules
The total work is therefore
†††† $ ††††††††††††††††††††††††††††††† Number
††††††††††††††††††††††††††††††† Number sold (demand)
3. †For the demand function shown, what is the consumerís surplus if 600 units are sold at $20 each?
The consumerís surplus is the area of the region above the horizontal dashed line, and below the demand curve.† This is a triangle with area (1/2)(600