Quiz7_09 - opposite bank but 4500m downstream is a power...

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Honors Calculus I Quiz 7 1. A wire of length 100 cm is cut into two pieces. One piece is bent into a circle, the other into a square. Where should the cut be made to maximize the sum of the areas of the square and the circle? To minimize that sum? 2. An athletic Feld is to be built in the shape of a rectangle x m long capped by semicircular regions of radius r m at the two ends. The Feld is to be bounded by a 400-m running track. What values of x and r will give the rectangle the largest possible area? 3. A farmer wants to hire workers to pick 900 bushels of beans. Each worker can pick up 5 bushels per hour and is paid $1.00 per bushel. The farmer must also pay a supervisor $10 per hour while the picking is in progress, and he has additional miscellaneous expenses of $8 per worker. How many workers should he hire to minimize the total cost? What will then be the cost per bushel picked. 4. A factory is located on one bank of a straight river that is 2000 m wide. On the
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Unformatted text preview: opposite bank but 4500m downstream is a power station from which the factory draws its electricity. Assume that it costs three times as much per meter to lay an underwater cable as to lay an aboveground cable. What path should a cable connecting the power station to the factory take to minimize the cost of laying the cable? 5. A box with no top is to be made from a rectangular piece of cardboard two feet wide and four feet long by cutting out equal squares from the four corners and folding up the sides. What size squares should be cut out to maximize the volume of the box? 6. A typical 6 oz. can of tuna has a height h = 3.5 cm , and the diameter of its base is d = 8.5 cm . Thus, the volume of a can is V = ! d 2 h 4 . This is approximately 200 cm 3 . What should the dimensions of the can having the same volume V to minimize its surface area....
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