What evidence showed archaeologists that an ancient civilization had existed in the Indus Valley?

An open box with a square base is to be built for $48. The sides of the box will cost$3 per square meter, and the base will cost $4 per square meter. Express the volume of the box as a function of the length of its base.

A rectangular poster contains 25 square centimeters of print surrounded by margins of 2 centimeters on each side and 4 centimeters on the top and bottom. Express the total area of the poster (printing plus margins) as a function of the width of the printed portion.

A cylinder of radius r and height h has volume $V=\pi r^{2} h$ and lateral (side) surface area $S=2 \pi r h.$ A circular disk of radius r has area $A = \pi r^2.$ A cylindrical can with no top has been made from $27 \pi$ square inches of metal. Express the volume of the can as a function of its radius.

What is the maximum possible volume of a cylindrical can with no top that can be made from $27 \pi$ square inches of metal?

A cylindrical can is to hold $4 \pi$ cubic inches of frozen orange juice. The cost per square inch of constructing the metal top and bottom is twice the cost per square inch of constructing the cardboard side. What are the dimensions of the least expensive can?

A cylinder of radius r and height h has volume $V=\pi r^{2} h$ and lateral (side) surface area $S=2 \pi r h.$ A circular disk of radius r has area $A = \pi r^2.$ A closed cylindrical can has a radius r and height h. a. If the surface area A of the can is a constant, express the volume V of the can in terms of S and r. b. If the volume V of the can is a constant, express the surface area S in terms of V and r.

A cylinder of radius r and height h has volume $V=\pi r^{2} h$ and lateral (side) surface area $S=2 \pi r h.$ A circular disk of radius r has area $A = \pi r^2.$ A closed cylindrical can has surface are $120 \pi$ square inches. Express the volume of the can as a function of its radius.

A cylinder of radius r and height h has volume $V=\pi r^{2} h$ and lateral (side) surface area $S=2 \pi r h.$ A circular disk of radius r has area $A = \pi r^2.$ A soda can holds 12 fluid ounces (approximately $6.89 \pi$ cubic inches). Express the surface area of the can as a function of its radius.

Julia can sell a certain product for $110 per unit. Total cost consists of a fixed overhead of$7,500 plus production costs of $60 per unit. a. Express Julia's total revenue, total cost, and total profit in terms of x, the number of units sold. Sketch the total revenue and total cost functions on the same set of axes. b. How many units must be sold for Julia to break even? c. What is Julia's profit or loss if 100 units are sold? d. How many units must be sold for Julia to realize a profit of$1,250?

A furniture manufacturer can sell dining room tables for $500 each. The manufacturer's total cost consists of a fixed overhead of$30,000 plus production costs of $350 per table. a. How many tables must the manufacturer sell to break even? b. How many tables must the manufacturer sell to make a profit of$6,000? c. What will be the manufacturer's profit or loss if 150 tables are sold? d. On the same set of axes, graph the manufacturer's total revenue and total cost functions. Explain how the overhead can be read from the graph.

Producers will supply x units of a certain commodity to the market when the price is p = S(x) dollars per unit, and consumers will demand (buy) x units when the price is p = D(x) dollars per unit, where S(x) = 2x + 15 and $D(x)=\frac{385}{x+1}$ a. Find the equilibrium production level $x_e$ and the equilibrium price $p_e.$ b. Draw the supply and demand curves on the same graph. c. Where does the supply curve cross the y axis? Describe the economic significance of this point.

A truck is hired to transport goods from a factory to a warehouse. The driver's wages are figured by the hour and so are inversely proportional to the speed at which the truck is driven. The cost of gasoline is directly proportional to the speed. Express the total cost of operating the truck as a function of the speed at which it is driven.

At a certain factory, setup cost is directly proportional to the number of machines used and operating cost is inversely proportional to the number of machines used.Express the total cost as a function of the number of machines used.