coldfoam
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a hall 100 feet in length is to be designed as a whispering gallery. If the foci are located 25 feet from the​ center, how high will the ceiling be at the​ center?

Respuesta :

granol4

Answer:

how high will the ceiling be at the center? ≈43.3 ft above the center

Step-by-step explanation:

standard form of equation for an ellipse with horizontal major axis and center at the origin:

x^2/a^2+y^2/b^2=1, a>b

for given problem:

a=50

a^2=2500

c=25

c^2=625

c^2=a^2-b^2

b^2=a^2-c^2=2500-625=1875

b=√1875≈43.3 ft

≈43.3 ft above the center

Height of celling from center is 43.3 feet (Approx.)

Given that;

Length of hall = 100 feet

Foci length from center = 25 feet

Find:

Height of celling from center

Computation:

Half length of hall = 100 / 2 = 50 feet

Height of celling from center = √Half Length of hall² - Foci length from  center²

Height of celling from center = √50² - 25²

Height of celling from center = √2500 - 625

Height of celling from center = √1875

Height of celling from center = 43.3 feet (Approx.)

Learn more:

https://brainly.com/question/10726356?referrer=searchResults

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