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

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?

Found 2 solutions by lynnlo, ralhp09:
Answer by lynnlo(4176) (Show Source): You can put this solution on YOUR website!
10 questions, have you tried to do any of them
Answer by ralhp09(3) (Show Source): You can put this solution on YOUR website!
x+y=10
RELATED QUESTIONS
How do you find the dimensions of a rectangle whose perimeter is inches and whose area is (answered by Theo)
Find the dimensions of a rectangle whose perimeter is 46m and whose area is... (answered by checkley77)
Find the dimensions of a rectangle whose width is 1 inches less than half its length an... (answered by CubeyThePenguin)
Find the dimensions of a rectangle whose perimeter is 26 meter and whose area is 40... (answered by atique.ah)
Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40... (answered by KnightOwlTutor,jojo14344)
Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40... (answered by mananth)
FIND THE DIMENSIONS OF A RECTANGLE WHOSE PERIMETER IS 76CM THAT WILL GIVE THE MAXIMUM... (answered by palanisamy)
Find the dimensions of a rectangle whose area is 60cm squared and whose perimeter is... (answered by nabla)
How do you find the maximum area of a rectangle whose perimeter is 60 inches (answered by rfadrogane)