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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.