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Chapter 7 Review Exercises

Chapter 7 Review Exercises
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  • 17. Golden Gate Bridge

    The Golden Gate Bridge is a suspension bridge that spans the opening of the San Francisco Bay into the Pacific Ocean. It has two main suspension cables that pass over the tops of two main towers at 500 feet above the roadway. Each of the main cables has a diameter of about 3 feet. The table shows the heights of the main cables above the roadway relative to the distance from the middle of the bridge.

    Describe the pattern in the table.

    data folder

    • Worked-Out Solution

      Enter the data into a spreadsheet. Because the second differences are equal, the pattern is quadratic.

      data folder

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      ______     ___      _____      ___      ______  
     /_   _//   / _ \\   |__  //    / _ \\   /_   _// 
     `-| |,-   | / \ ||    / //    | / \ ||    | ||   
       | ||    | \_/ ||   / //__   | \_/ ||   _| ||   
       |_||     \___//   /_____||   \___//   /__//    
       `-`'     `---`    `-----`    `---`    `--`     
                                                      
    
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  • 18. Golden Gate Bridge

    The Golden Gate Bridge is a suspension bridge that spans the opening of the San Francisco Bay into the Pacific Ocean. It has two main suspension cables that pass over the tops of two main towers at 500 feet above the roadway. Each of the main cables has a diameter of about 3 feet. The table shows the heights of the main cables above the roadway relative to the distance from the middle of the bridge.

    Use a spreadsheet to graph the data in the table. Does the graph appear to be linear or quadratic? Explain your reasoning.

    data folder

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                 ___      _____    _    _     _  _   
        ___     / _ \\   / ____|| | || | ||  | \| || 
       /   ||  / //\ \\ / //---`' | || | ||  |  ' || 
      | [] || |  ___  ||\ \\___   | \\_/ ||  | .  || 
       \__ || |_||  |_|| \_____||  \____//   |_|\_|| 
        -|_|| `-`   `-`   `----`    `---`    `-` -`  
         `-`                                         
    
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  • 19. Golden Gate Bridge

    The Golden Gate Bridge is a suspension bridge that spans the opening of the San Francisco Bay into the Pacific Ocean. It has two main suspension cables that pass over the tops of two main towers at 500 feet above the roadway. Each of the main cables has a diameter of about 3 feet. The table shows the heights of the main cables above the roadway relative to the distance from the middle of the bridge.

    Use the graph from Exercise 18 to predict the height of the cables 2500 feet from the middle of the bridge. Is your prediction possible? Explain your reasoning.

    data folder

    • Worked-Out Solution

      By extending the spreadsheet as shown, you can see that the height of the cables 2500 feet from the middle of the bridge will be about 708 feet. This is not possible because the main towers are only 500 feet above the roadway.

      data folder

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     _____       ___      _  __    _____      _____  
    |  __ \\    / _ \\   | |/ //  |  ___||   / ___// 
    | |  \ ||  / //\ \\  | ' //   | ||__     \___ \\ 
    | |__/ || |  ___  || | . \\   | ||__     /    // 
    |_____//  |_||  |_|| |_|\_\\  |_____||  /____//  
     -----`   `-`   `-`  `-` --`  `-----`  `-----`   
                                                     
    
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  • 20. Dropped Paintbrush

    A maintenance worker is painting a main cable when he accidently drops a paintbrush. The table shows the heights of the paintbrush at various times. Is the pattern in the table linear, exponential, quadratic, or none of these? Explain your reasoning.

    data folder

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     ______     ______   __   __   __   __    _  __  
    |      \\  /_   _//  \ \\/ //  \ \\/ //  | |/ // 
    |  --  //   -| ||-    \   //    \ ` //   | ' //  
    |  --  \\   _| ||_    / . \\     | ||    | . \\  
    |______//  /_____//  /_//\_\\    |_||    |_|\_\\ 
    `------`   `-----`   `-`  --`    `-`'    `-` --` 
                                                     
    
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  • 21. Dropped Paintbrush

    A maintenance worker is painting a main cable when he accidently drops a paintbrush. The table shows the heights of the paintbrush at various times.

    Use a spreadsheet to graph the data. Describe the graph.

    data folder

    • Worked-Out Solution

      The graph shows a quadratic pattern. From the spreadsheet, you can see that with each additional half second, the speed of the falling paintbrush is increasing.

      data folder

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      ______     ___                ______    _____   
     /_   _//   / _ \\      ___    /_   _//  /  ___|| 
     `-| |,-   | / \ ||    /   ||   -| ||-  | // __   
       | ||    | \_/ ||   | [] ||   _| ||_  | \\_\ || 
       |_||     \___//     \__ ||  /_____//  \____//  
       `-`'     `---`       -|_||  `-----`    `---`   
                             `-`                      
    
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  • 22. Dropped Paintbrush

    Use the graph from Exercise 21 to predict how long it takes the paintbrush to reach the water.

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     __   _     _____     ______     ___     _    _   
    | || | ||  |  ___||  /_____//   / _ \\  | \  / || 
    | '--' ||  | ||__    `____ `   | / \ || |  \/  || 
    | .--. ||  | ||__    /___//    | \_/ || | .  . || 
    |_|| |_||  |_____||  `__ `      \___//  |_|\/|_|| 
    `-`  `-`   `-----`   /_//       `---`   `-`  `-`  
                         `-`                          
    
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