SOLUTION: 1. Find the dimensions of the rectangle whose perimeter is 40 inches and whose area is a maximum.
2. An open box is formed from a piece of cardboard 12 inches square by cutting
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-> SOLUTION: 1. Find the dimensions of the rectangle whose perimeter is 40 inches and whose area is a maximum.
2. An open box is formed from a piece of cardboard 12 inches square by cutting
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Question 649421: 1. Find the dimensions of the rectangle whose perimeter is 40 inches and whose area is a maximum.
2. An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way.
3. A closed box, whose length is twice its width, is to have a surface area of 192 square centimetres. Find the dimensions of the box when the volume is maximum.
4. What is the least amount of material needed to make an open right cylindrical can of volume 8 cubic inches?
5. Find the dimensions of the right circular cone whose volume is 3000 cubic centimetres if its lateral area is a minimum.
6. Find two numbers whose sum is 10 and the sum of the squares is a minimum.
7. Divide 20 into two parts such that the product of one part and the square of the other is maximum.
8. The electrical potential at a point (x,y) on the line extending from (0, 3) to (2, 0) is given by . At what point on this segment is the potential a minimum?
9. A man wishes to heat his basement by plugging a long extension chord connected to a number of heaters into a 120-volt socket at the house. The power P in watts radiated by the 30-omhs heater is given by , where n is the number of heaters plugged in. What would be the maximum amount of heat?
10. The power P generated by a 120-volt generator of internal resistance 5 ohms is given by watts, where is the current in amperes. For what current does the generator produce maximum power?
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