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The Height of the ceiling at the center is 57.6628 feet
In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base.
It has two focal points. The sum of the two distances to the focal point, for all the points in curve, is always constant.
The General form of ellipse is 
According to the question,
Length of whispering gallery is 130 feet
The foci are located 30feet from the center (0,0)
So, 2a = 130
=> a = 130/2
=> a = 65
and c = 30
As we know ,
=> c² = a² - b²
=> (30)² = (65)² - b²
=> 900 = 4225 - b²
=> b² = 4225 - 900
=> b² = 3325
=> b = 57.7 feet
Therefore , the height of the ceiling at the center is 57.6628 feet
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Answer:
Pasos para resolver una ecuación lineal
3x−2/4−2x+5/3=1−x/6
Multiplique ambos lados de la ecuación por 12, el mínimo común denominador de 4,3,6.
36x−3×2−24x+20=12−2x
Multiplica −3 y 2 para obtener −6.
36x−6−24x+20=12−2x
Combina 36x y −24x para obtener 12x.
12x−6+20=12−2x
Suma −6 y 20 para obtener 14.
12x+14=12−2x
Agrega 2x a ambos lados.
12x+14+2x=12
Combina 12x y 2x para obtener 14x.
14x+14=12
Resta 14 en los dos lados.
14x=12−14
Resta 14 de 12 para obtener −2.
14x=−2
Divide los dos lados por 14.
x=
14
−2
Reduzca la fracción
14
−2
a su mínima expresión extrayendo y anulando 2.
x=−
7
1
Step-by-step explanation: