A closed box with square base is to be built to house an ant colony. the bottom of the box and all four sides are to be made of
material costing $2/ft2, and the top is to be constructed of glass costing $4/ft2. what are the dimensions of the box of greatest volume that can be constructed for $72? (enter the dimensions (in feet) as a comma separated list.)
Box has all sides same leinght(a). Area of that box is 6*a^2. Cost of material for bottom and 4 sides is 2$/ft^2. Area of bottom and sides is A=5*a^2 Cost of material for top is 4$/ft^2. Area of top of the box is T=a^2
A*2+T*4=72 5*a^2*2+a^2*4=72 a^2*(10+4)=72 a^2*14=72, a^2=72/14, a=root(72/14), a=2.267ft Dimensions of the box: leinght of sides 2.2ft. Area of hole box 30.835ft^2 Area of the bottom and sides: A=5*a^2=25.696ft^2 Area of the top : T=a^2=5.139ft^2 Check: A*2$+T*4$=71.95$
The movement of a roller coaster is accomplished by the conversion of potential energy to kinetic energy. The roller coaster cars gain potential energy as they are pulled to the top of the first hill. As the cars descend the potential energy is converted to kinetic energy.
