Your company was contacted by a client who wants to construct a passage tunnel which is either in the shape of a parabola or semi-ellipse. Given that the passage is to be constructed for one-way or two-way traffic and with a height of 16 − 24 feet and width of 34 − 58 feet along the ground (each group will be given specific values), help the client decide on what shape to use. For this project, we assume that the dimensions of the cross-section of the bus are 8 feet by 10 feet and 4 inches. There is a 2 feet space between the buses if they are entering the tunnel in the same direction. For the two-way tunnel, there will be a 4 feet space in between the buses that are in opposite directions. Solve for the standard form and general form of a parabolic and semi-elliptic tunnel. Then graph both. Given: Tunnel Height: 18ft Width along the Ground: 38ft
Your company was contacted by a client who wants to construct a
passage tunnel which is either in the shape of a parabola or semi-ellipse.
Given that the passage is to be constructed for one-way or two-way
traffic and with a height of 16 − 24 feet and width of 34 − 58 feet along
the ground (each group will be given specific values), help the client
decide on what shape to use. For this project, we assume that the
dimensions of the cross-section of the bus are 8 feet by 10 feet and 4
inches. There is a 2 feet space between the buses if they are entering the
tunnel in the same direction. For the two-way tunnel, there will be a 4
feet space in between the buses that are in opposite directions. Solve for the standard form and general form of a parabolic and semi-elliptic tunnel. Then graph both.
Given:
Tunnel Height: 18ft
Width along the Ground: 38ft
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- Diagrams or graphs showing the points at which each arch passes through.
- The equation of the parabola and ellipse, in standard form and general form, with the given dimensions.
- Detailed computation for the number of vehicles (specifically buses) with a given size that can pass through each tunnel.
- Recommendation for the shape to be used by a client for the project.
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