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The entrance to a tunnel is in the shape of a semiellipse over a 24-ft by 8-ft rectangular opening. The height at the center of the opening is 14 ft. 6 ft 8 ft 24 ft a. Determine the height of the opening at a point 6 ft from the edge of the tunnel. Round to 1 decimal place. b. Can a 10-ft-high truck pass through the opening if the truck's outer wheel passes at a point 3 ft from the edge of the tunnel? C. Set up a coordinate system with the origin placed on the ground in the center of the roadway. Write a function that represents the height of the opening h(x) (in ft) as a function of the horizontal distance x (in ft) from the center.

The entrance to a tunnel is in the shape of a semiellipse over a 24-ft by 8-ft rectangular opening. The height at the center of the opening is 14 ft. 6 ft 8 ft 24 ft a. Determine the height of the opening at a point 6 ft from the edge of the tunnel. Round to 1 decimal place. b. Can a 10-ft-high truck pass through the opening if the truck's outer wheel passes at a point 3 ft from the edge of the tunnel? C. Set up a coordinate system with the origin placed on the ground in the center of the roadway. Write a function that represents the height of the opening h(x) (in ft) as a function of the horizontal distance x (in ft) from the center.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 48E
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The entrance to a tunnel is in the shape of a semiellipse over a 24-ft by 8-ft rectangular opening. The height at the center of the opening is 14 ft. 6 ft 8 ft 24 ft a. Determine the height of the opening at a point 6 ft from the edge of the tunnel. Round to 1 decimal place. b. Can a 10-ft-high truck pass through the opening if the truck's outer wheel passes at a point 3 ft from the edge of the tunnel? C. Set up a coordinate system with the origin placed on the ground in the center of the roadway. Write a function that represents the height of the opening h(x) (in ft) as a function of the horizontal distance x (in ft) from the center.
Transcribed Image Text:The entrance to a tunnel is in the shape of a semiellipse over a 24-ft by 8-ft rectangular opening. The height at the center of the opening is 14 ft. 6 ft 8 ft 24 ft a. Determine the height of the opening at a point 6 ft from the edge of the tunnel. Round to 1 decimal place. b. Can a 10-ft-high truck pass through the opening if the truck's outer wheel passes at a point 3 ft from the edge of the tunnel? C. Set up a coordinate system with the origin placed on the ground in the center of the roadway. Write a function that represents the height of the opening h(x) (in ft) as a function of the horizontal distance x (in ft) from the center.
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