SEDE TASK: You are tasked with analyzing a design that has been drawn for a bridge over an existing two-lane road. The a

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Sede Task You Are Tasked With Analyzing A Design That Has Been Drawn For A Bridge Over An Existing Two Lane Road The A 1 (50.09 KiB) Viewed 46 times

Sede Task You Are Tasked With Analyzing A Design That Has Been Drawn For A Bridge Over An Existing Two Lane Road The A 2 (37.16 KiB) Viewed 46 times

SEDE TASK: You are tasked with analyzing a design that has been drawn for a bridge over an existing two-lane road. The arch over the road is in the shape of a half-ellipse that is 40 feet wide at the base of the arch and it is 15 feet tall at the center of the arch. The bridge must have a 13-foot clearance for vehicles on the road. The 22- foot-wide road is centered directly beneath the highest point of the arch. a. Using the information given above, write an equation that represents the arch of the bridge. b. Using the equation listed as an answer for part (a), convert it to an inequality that defines the set of ordered pairs in the coordinate plane that could freely pass beneath the bridge. c Vehicles of various heights and sizes will drive under the arch. Knowing that vehicles can drive along any part of each lane, including along the extreme outer edges, think about a 13-foot-tall semi-truck passing under the bridge. You need to know with certainty that the outer edge of the truck won't hit the arch. If the truck is driving in the right-hand lane, what ordered pair would describe the highest point on a 13-foot tall semi-truck that is the farthest to the right on the two-lane road? d. Test your mathematical model. Does the semi-truck fit? Take the ordered pair found in partc and test it in the inequality written for part b. Does the point satisfy the inequality?
e. Will the current bridge design allow 13-foot tall vehicles to pass on the road beneath it? Explain the reasoning for your answer. Yes! Explain. (Then, go to part 1.) No. Explain. (Then, go to parte) f. If you said yes, the semi-truck will be able to pass under the bridge, then find the maximum height of a vehicle that can freely pass beneath the bridge. This information is needed for the maximum clearance signs that are posted on bridges. Skip to part 1 8. If you said no, the semi-truck will NOT be able to pass under the bridge, it is time to make an adjustment. You will need to modify the design of the bridge. Keep the arch shape as half an ellipse, and the base as 40 feet wide. You may adjust the bridge's arch up to 18 feet above the center line of the two-lane road below, but no more than that because of restrictions concerning the road crossing over the bridge. Give a new equation for the ellipse that represents your modified design. h. Test the equation you now have from part g in the inequality from part b to confirm the design works. Then find the maximum height of a vehicle that can freely pass beneath the bridge that would be posted on the maximum clearance sign. 1. Is it possible to have more than one option that fits within the parameters of the restrictions? If so, explain why you chose the equation you used. And then explain why other equations would not be as preferable, even if they pass the inequality test.