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A designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 30 ft, which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guests to stand to experience his whisper chamber will be 4 ft from the center of the warehouse space, which will act as the foci. How far out from the center, along the minor axis, should he build his whisper chamber?


29.7 ft

28.9 ft

14.5 ft

7.2 ft

Sagot :

Answer:

The extent to which he should build the whisper chamber along the minor axis is approximately;

14.5 ft

Step-by-step explanation:

The question examines the relationship between the dimensions of the focus, half the length of the minor axis and half the length of the major axis

let, 'c', represent the length of the focus from the center of the ellipse, let 'a', represent half the length of the major axis, and let 'b', represent half the length of the minor axis, we have;

a² = b² + c²

The given parameters are;

The length of the major axis, 2·a = 30 ft.

The distance of the focus from the center, c = 4 ft.

Therefore, we have;

a = 30 ft./2 = 15 ft.

a = 15 ft.

From a² = b² + c², we have;

b² = a² - c²

By plugging in the values, we have;

b² = (15 ft.)² - (4 ft.)² = 209 ft.²

b = √209 ft· ≈ 14.5 ft.

The distance from the center to the vertex of the minor axis of the elliptical whisper chamber, b ≈ 14.5 ft.

420976idn

Answer:

14.5 ft

Step-by-step explanation:

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