College Algebra Chapter 1 Equations and Inequalities Section 1.5 Applications of Quadratic Equations Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Concepts Solve Applications Involving Quadratic Equations and Geometry Solve Applications Involving Quadratic Models

Concept 1 Solve Applications Involving Quadratic Equations and Geometry

Example 1 (1 of 2) 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 (2 of 2) 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?

Skill Practice 1 A box is to be formed by taking a sheet of cardboard and cutting away four 2 in. by 2 in. squares from each corner. Then the sides are turned up to form a box that holds 56 in.3 If the length of the original piece of cardboard is 3 in. more than the width. find the dimensions of the original sheet of cardboard.

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 π = 3.14 and round your answer to the nearest foot.

Example 5 (1 of 3) 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."

Example 5 (2 of 3) 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?

Example 5 (3 of 3) 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?

Skill Practice 2 A sail on a sailboat is in the shape of two adjacent right triangles. The hypotenuse of the lower triangle is 10 ft, and one leg is 2 ft shorter than the other leg. Find the lengths of the legs of the lower triangle.

Concept 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. Determine the average weekly earnings in 2007. In what year will the average weekly earnings reach $638?

Solve Applications Involving Quadratic Models If an object has an initial vertical position and initial velocity straight upward or downward, then the vertical position s of the object is given by

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

Skill Practice 3 A fireworks mortar is launched straight upward from a pool deck 2 m off the ground at an initial velocity of 40 m/sec. Write a model to express the height of the mortar is (in meters) above ground level. Find the time(s) at which the mortar is at a height of 60 m. Round to 1 decimal place. Find the time(s) at which the rocket is at a height of 100 m.