College Algebra Chapter 1 Equations and Inequalities Section 1.5 Applications of Quadratic Equations

1. Solve Applications Involving Quadratic Equations and Geometry 2. Solve Applications Involving Quadratic Models

Example 1: Dmitri is having a fish tank constructed to fit in a niche in his wall. The width must be 12 inches, while the length is twice the height decreased by 8 inches. The total volume of the tank must be 6840 cubic inches. What are the dimensions of the tank?

Example 1 continued:

Example 1 continued: If 1 gallon of water measures 231 cubic inches and weighs 8.345 pounds, what will be the weight of the water in the tank?

Example 2: The three sides of a right triangle are represented by three consecutive integers. What are the integers?

Example 3: As the minute hand on the face of a clock sweeps around once, it covers an area of 114 square inches. What is the length of the minute hand? Round your answer to the nearest inch.

Example 4: Morris is designing a new sign for his ice cream shop to be placed by the exit from a nearby highway. The sign needs to be big. Really big. He plans on making the height of the bottom triangle 3 times the height of the semicircle on top and having a total area of 74 square feet. If the county will not allow any signage taller than 15 feet, will Morris be allowed to put up his cone? Use and round your answer to the nearest foot.

Example 4 continued:

Example 5: Quilters can create an astonishing variety of patterns using basic geometric shapes. The card trick quilt pattern is built from squares, half-triangles, and quarter-triangles. The finished pattern looks like overlapping "cards." card trick block

Example 5 continued: If each small square measures 3 inches by 3 inches, what is the length of the full diagonal of the 9 square pattern to the right? card trick block

Example 5 continued: Anne Marie is making a quilt from 9 inch square card trick blocks. The quilt will be 2 blocks wide, 3 blocks long and have a border of width x all the way around. What should the width of the border be so Anne Marie's quilt measures 682 square inches?

Example 5 continued:

1. Solve Applications Involving Quadratic Equations and Geometry 2. Solve Applications Involving Quadratic Models

Example 6: The average weekly earnings E in dollars, for a group of workers can be approximated by where x represents the number of years since 2004. a. Determine the average weekly earnings in 2007.

Example 6 continued: b. In what year will the average weekly earnings reach $638?

Solve Applications Involving Quadratic Models

Example 7: An arrow is shot from a height of 6 feet straight upward with an initial speed of 20 ft/sec. a. Write a model to express the arrow's height (in feet) above the ground after t seconds

Example 7 continued: b. How long will it take the arrow to land?