Problem Name

Problem Description

Notes

algebra_apps_1

An oval athletic field is in the shape of a rectangle with semicircles at its opposite ends, as shown in the diagram. The rectangular section of the field is 300 feet long and 120 feet wide. Find the total area of the field and the distance around it.

algebra_apps_2

Find the volume and the surface area of a sphere inches in diameter.

algebra_apps_3

Find the volume of the object shown in the diagram. Its dimensions are given in inches.

algebra_apps_4

From a 36-inch-square piece of cardboard, 6-inch square corners are cut as shown in the diagram, and the resulting flaps are folded up to form an open box. Find the volume of the resulting box.

algebra_apps_5

Somewhere on the high seas there is a ship whose boiler was replaced sometime after the ship was launched. The sum of the ages of the ship and its replacement boiler is 49 years. The ship is twice as old as the boiler was when the ship was as old as the boiler is. What are the ages of the ship and its boiler?

algebra_apps_6

The weekly revenue for a product is given by

and the weekly cost is

where is the number of units produced and sold.

a. How many units will give maximum profit?

b. What is the maximum possible profit?

algebra_apps_7

An electric utility company determines the monthly bill by charging 76.7 cents per kilowatt hour (KWh) used plus a base charge of $16.37 per month.

algebra_apps_8

An $828,000 building is depreciated for tax purposes by its owner, using the straight-line depreciation method. The value of the building after months of use is given by dollars.

a. Find and interpret the -intercept of the graph of this function;

b. Find and interpret the -intercept of the graph of this function;

c. Use the intercepts to graph the function for non-negative - and -values.

algebra_apps_9

A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455 and the profit from 250 units is $895.

algebra_apps_10

To earn an A in a course, a student must get an average score of at least 90 on five tests. If her first four test scores are 92, 86, 79, and 96, what score does she need on the last test to obtain a 90 average?