The Problem. A waterway in a theme park has a semicircular section with a diameter of 11 ft. The boats that are going to be used in this waterway have rectangular cross-sections and are found to submerge 1 ft into the water. If the waterway is to be filled with water 4.5 ft deep, what is the maximum possible width of the boats? 11 ft 4.5 ft From the problem, fill in the blanks. 1. The center is at (0,0). The radius of the circle is 2. Using the answer in #1 above, give the equation of the circle: (_)2 + _)? = 3. If the center is at the origin, and let y=-1 as the level of the water surface, then the base of the boat will be at y =

College Algebra (MindTap Course List)
12th Edition
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Author:R. David Gustafson, Jeff Hughes
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Chapter7: Conic Sections And Quadratic Systems
Section7.1: The Circle And The Parabola
Problem 84E: Building tunnels A construction firm plans to build a tunnel whose arch is in the shape of parabola....
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The Problem. A waterway in a theme park has a semicircular section with a
diameter of 11 ft. The boats that are going to be used in this waterway have
rectangular cross-sections and are found to submerge 1 ft into the water. If the
waterway is to be filled with water 4.5 ft deep, what is the maximum possible width
of the boats?
11 ft
4.5 ft
From the problem, fill in the blanks.
1. The center is at (0,0). The radius of the circle is
2. Using the answer in #1 above, give the equation of the circle: (_)² + _)² =
L)?.
3. If the center is at the origin, and let y=-1 as the level of the water surface, then
the base of the boat will be at y = _
4. From result in #3 above, by substitution, our formula becomes x² +
5. Solving for x in #4, the boat's maximum possible width is
II
Transcribed Image Text:The Problem. A waterway in a theme park has a semicircular section with a diameter of 11 ft. The boats that are going to be used in this waterway have rectangular cross-sections and are found to submerge 1 ft into the water. If the waterway is to be filled with water 4.5 ft deep, what is the maximum possible width of the boats? 11 ft 4.5 ft From the problem, fill in the blanks. 1. The center is at (0,0). The radius of the circle is 2. Using the answer in #1 above, give the equation of the circle: (_)² + _)² = L)?. 3. If the center is at the origin, and let y=-1 as the level of the water surface, then the base of the boat will be at y = _ 4. From result in #3 above, by substitution, our formula becomes x² + 5. Solving for x in #4, the boat's maximum possible width is II
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