212 Math Exam 2 Spring 00 Kerckhove
Name Pledge
1. Two farmers, husband and wife, wish to purchase a eld in which to grow yams. The eld is rectangular in shape and lies in a valley between a riverbed and a hillside. The Farmers estimate that land located x feet from the edge of the eld nearest the river has value 250 0.15x dollars per square foot. The edge of the eld nearest the river is 1000 feet long while the edge perpendicular to the river is 1500 feet long. Use the information above to set up an integral for the total value of the eld. A clear diagram of the eld as viewed from above should be helpful to you. Do not bother to evaluate your integral.
2. Mr Farmer has recently purchased a Pivot Master irrigation sprinkler for watering the 1 yam eld. The sprinkler delivers 1+r2 gallons of water per hour per square foot of eld at distance r feet from the sprinkler head. Use the information above to set up an integral for the total amount of water delivered in one hour to a circular region centered on the sprinkler and having radius 100 feet. A clear diagram of the circle as viewed from above should be helpful to you. Do not bother to evaluate your integral.
3. The Farmers specialize in growing cone-shaped yams. When harvest time comes, work must be done in order to transfer the yams from the ground into the back of the Farmers atbed truck. Here is the relevant information for this problem: The average yam sits in the ground with its pointed end downward, much like a carrot. The yam is 0.5 feet long, a with radius of 0.1 feet at the top. The distance from the top of the yam to the bed of the truck is 4 feet. The density of the yam is 72 pounds per cubic foot. Use the information above to set up an integral for the total amount of work done by Mrs Farmer in lifting an average size yam onto the truck. A clear diagram of the yam should be helpful to you. Do not bother to evaluate your integral.
4. When Mr Farmer removes hot yams from the oven they obey Newtons Law of Cooling. The initial temperature of the yams is 200 , the temperature of the kitchen is 70 and the temperture of the yams after 10 minutes is 110 . Use the information above to nd the value of the proportionality constant for cooling in the farmers kitchen. You may leave your answer in terms of logarithms.
5. While eating their yams, the farmers consider the population of yam pests (tiny bugs related to potato beetles) in their eld. S...