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3. An arch in the form of semi – ellipse is 50 feet wide at the base and has a height of 16 feet. How wide is the arch at the height 8 feet above the base?

3. An arch in the form of semi – ellipse is 50 feet wide at the base and has a height of 16 feet. How wide is the arch at the height 8 feet above the base?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 36E
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Answer question number 3. Show your solution.

B.Situational Problems Involving Conic Sections 1. A Ferris wheel is elevated 1 m above ground. When a car reaches the highest point on the ferris wheel, its altitude from ground level is 31 m. How far away from the center, horizontally, is the car when it is at an altitude of 25 m? 2. A truck has to pass under an overhead parabolic arch bridge which has a span of 20 meters and is 16 meters high. If the tank is 14 meters wide, is placed in the truck with its sides vertical, and the top of the tank is 7.5 meters above the street level, what is the smallest clearance from the top of the tank so that the truck can pass under the bridge? 3. An arch in the form of semi – ellipse is 50 feet wide at the base and has a height of 16 feet. How wide is the arch at the height 8 feet above the base? 4. A yacht is travelling on a course parallel to and 80 kilometers from the straight shoreline of Palawan. Two transmitting stations are located 180 kilometers apart on the shoreline. By timing radio signals from stations, the yacht's navigator determines that the yacht is between the two stations and 60 kilometers closer to station A than to station B. Find the distance from the yacht to each station.
Transcribed Image Text:B.Situational Problems Involving Conic Sections 1. A Ferris wheel is elevated 1 m above ground. When a car reaches the highest point on the ferris wheel, its altitude from ground level is 31 m. How far away from the center, horizontally, is the car when it is at an altitude of 25 m? 2. A truck has to pass under an overhead parabolic arch bridge which has a span of 20 meters and is 16 meters high. If the tank is 14 meters wide, is placed in the truck with its sides vertical, and the top of the tank is 7.5 meters above the street level, what is the smallest clearance from the top of the tank so that the truck can pass under the bridge? 3. An arch in the form of semi – ellipse is 50 feet wide at the base and has a height of 16 feet. How wide is the arch at the height 8 feet above the base? 4. A yacht is travelling on a course parallel to and 80 kilometers from the straight shoreline of Palawan. Two transmitting stations are located 180 kilometers apart on the shoreline. By timing radio signals from stations, the yacht's navigator determines that the yacht is between the two stations and 60 kilometers closer to station A than to station B. Find the distance from the yacht to each station.
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