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Concept explainers
Statuary Hall is an elliptical room in the United States Capitol in Washington, D.C. The room is also called the Whispering Gallery because a person standing at one focus of the room can hear even a whisper spoken by a person standing at the other focus. This occurs because any sound emitted from one focus of an ellipse reflects off the side of the ellipse to the other focus. Statuary Hall is 46 feet wide and 97 feet long.
(a) Find an equation that models the shape of the room.
(b) How far apart are the two foci?
(c) What is the area of the floor of the room? (The area of an ellipse is
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Chapter 4 Solutions
Bundle: College Algebra, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's College Algebra, 10th Edition, Single-Term
- Find the equation of the ellipse shown.arrow_forwardA person in a whispering gallery standing at one focus of the ellipse can whisper and be heard by a person standing at the other focus because all the sound waves that reach the ceiling are reflected to the other person. If a whispering gallery has a length of 120 feet, and the foci are located 30 feet from the center, find the height of the ceiling at the center.arrow_forwardFind the equation of the parabolic arch formed in the foundation of the bridge shown, Write the equation in standard form.arrow_forward
- Explain in your own words, the difference between a vertex and a focus of the ellipse.arrow_forwardDefine an ellipse in terms of its foci.arrow_forwardIn your own words, define an ellipse and write the equation of an ellipse centered at the origin in standard form. Draw a sketch of the ellipse labeling the center, vertices and major and minor axes.arrow_forward
- ?Write the equation of the parabolic arch formed in the foundation of the bridge shown. Write the equation in standard form.arrow_forwardGraph the ellipse given by the equation (x4)236+(y2)220=1 . Identify and label the center, vertices, co-vertices, and foci.arrow_forwardA planet moves in an elliptical orbit around its sun. The closest the planet gets to the sun is approximately 20 Au and the furthest is approximately 30 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below, use the graph to write an equation for the elliptical orbit of the planet.arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
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