You are building an open-top aquarium with a square base with side length x ft. Material...

You are building an open-top aquarium with a square base with side length x ft. Material for the base costs $20 per square foot, while glass for the sides costs $30 per square foot. The volume of the aquarium needs to be 200 cubic feet. To find the dimensions of the cheapest suitable aquarium, which function should you minimize?

Expert Solution

milcah answered 2 years ago

A rectangular tank with a square base, an open top, and a volume of 1372 ft...

A rectangular tank with a square base, an open top, and a volume of 1372 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.

Suppose a tin box is to be constructed with a square base, an open top and...

Suppose a tin box is to be constructed with a square base, an open top and a volume of 32 cubic inches. The cost of the tin to construct the box is $0.15 per square inch for the sides and $0.30 per square inch for the base. The minimized cost of the tin box is: A. $3.50 B. $$4.82 C. none of the answers D. $9.07 E. $$\$0$$

A rectangular box with a square base and an open top and a volume of 1ft^3...

A rectangular box with a square base and an open top and a volume of 1ft^3 is to be made. Suppose the material used to build the sides cost $4 per ft^2 and the material used to build the bottom costs $1 per ft^2. Determine the dimensions (i.e. the side-length of the base and the height) of the box that will minimize the cost to build the box. Note: if we let x denote the side-length of the base and...

A box with a square base and open top must have a volume of 32000 cm3....

A box with a square base and open top must have a volume of 32000 cm3. We wish to find the dimensions of the box that minimize the amount of material used. Find the following: 1. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula...

A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=9 ft

A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=9 ft and width=6 ft by cutting a square piece out of each corner and turning the sides up as shown in the picture. Determine the length x of each side of the square that should be cut which would maximize the volume of the box.

A box with a square base and open top must have a volume of 32000 cm^3....

A box with a square base and open top must have a volume of 32000 cm^3. Find the dimension of the box that minimize the amount of material used. (show all work)

A company plans to design an open top rectangular box with square base having volume 4...

A company plans to design an open top rectangular box with square base having volume 4 cubic inches. Find the dimension of the box so that the amount of materiel required for construction is minimal. (a) Find the dimension of the box so that the amount of materiel required for construction is minimized. (b) What is the minimized material required for the construction?

There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the....For the following exercises, use a calculator to find the length of each side to four decimal places.

For the following exercises, use a calculator to find the length of each side to four decimal places.There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the top of the building is measured to be 40°. From the same location, the angle of elevation to the top of the antenna is measured to be 43°. Find the height of the antenna.

A square plot of land has a building 70 ft long and 60 ft wide at...

A square plot of land has a building 70 ft long and 60 ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 10,200 ft2, what are the dimensions of the entire plot of land? A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what...

The 12-ft wall shown here stands 28 ft from the building. Find the length of the...

The 12-ft wall shown here stands 28 ft from the building. Find the length of the shortest straight beam that will reach to the s

Question