FC: Quadratic Word Problems Suspension Bridge By: Samantha Gomes
1: Question 20: In a suspension bridge such as the Golden Gate Bridge in California or the Verrazano-Narrows Bridge in New York, the roadway is supported by parabolic cables hanging from support towers. Vertical suspender cables connect parabolic cables to the roadway. Suppose that you work forOrnery & Sly Construction Company. Your job is to procure the vertical suspender cables for the center span of the new bridge to be built across Broad River. From the Design Department, you find the following information: i. The support towers are located at x=400 meters and x=2000 meters (making this span slightly longer than the Verrazano-Narrows Bridge.) The tops of the towers are 165 meters above the roadway, at y=165. ii. There are four parallel parabolic cables that go from the tower top to tower top. They are 5 meters above the roadway at their lowest points, halfway between the two towers. iii. The vertical suspender cables are spaces every 20 meters, stating at x= 420 and ending at x=1980. Each of the four cables has two suspender cables at each value of x. Demonstrate that you understand the above information by writing three ordered pairs for points on the parabolic cables. Find the equation of the parabolic cables. The success of the $700,000,000 project (and whether you keep your job!) depends on the correctness of you calculations. Demonstrate that your equation gives correct values of y by substituting the three values of x from the given ordered pairs in the first part. How many suspender cables are needed to complete the bridge? What is the average length of the suspender cables? What is the total length of suspender cable that will be used for the center span so that the Purchasing Department may buy the correct amount of cable. Support your answer.
2: The three ordered pairs i found in the given information are (400,165),(2000,165),and (1200,5) | Demonstrate that you understand the above information by writing three ordered pairs for points on the parabolic cables.
3: Find the equation of the parabolic cables. | The equation when rounded comes out to be 2.49x^2+-.599x+364.9. I found out this equation by typing in the ordered pairs into the stat edit key in my calculator. And then I chose the Quadreg equation button.
4: Demonstrate that your equation gives correct values of y by substituting the three values of x from the given ordered pairs in the first part. | With the full equation that was not rounded the ordered pairs come out correct. When you insert 400, y comes out to be165. When you insert 2000, y comes out to be 165. And when you insert 1200, y comes out to be 5.
5: To complete the bridge you would need to purchase 320 suspender cables.i found this by subtracting 2000 and 400. Then I divided that by 20. That comes out to 80 with that I multiplied by four because there are four parabolic cables. The average length of the cables is 54.7225 meters. I found this by subtracting 2000 and 400, dividing by 20. this is where each cable would be placed. Then when I found where each of the cables would be placed I added them up and divided by 40.
6: The total length of the suspender cable that would be used for the center span is 17511.2. I got this total by multiplying the average length of the suspenders and the total amount of suspenders needed.