Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

In a whispering gallery, a person standing at one focus of the ellipse can whisper and be heard by another person standing at the other focus, because all sound waves that reach the ceiling from one focus are reflected to the other focus. A hall 120 feet in length is to be designed as a whispering gallery. Of foci are located 40 feet from the center, how high will the ceiling be at the center

Sagot :

Answer:

Hence, the height of the ceiling at the center is 44.72 feet.

Explanation:

Consider that a whispering gallery has a length of 120 feet, and the foci are located 40 feet from the center.

Assume that the shape is a horizontal semi-ellipse with a center (0,0) and has the equation,

[tex]\frac{x^{2} }{ a^{2} } + \frac{y^{2} }{b^{2} } =1[/tex]  where a>b,

so,

2a = 120

a = 60

and

c = 40

Therefore, the equation of the ellipse is,

[tex]c^{2} = a^{2} -b^{2} \\\\40^{2} = 60^{2} -b^{2}\\\\b^{2} =2000\\\\b= 44.72.[/tex]

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.