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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
To know more about Ellipse here
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Answer:
Step-by-step explanation:
<h3><u>Question 12</u></h3>Find the slope of the line by substituting two points from the given table into the slope formula.
<u>Define the points</u>:
- Let (x₁, y₁) = (2, 7)
- Let (x₂, y₂) = (3, 13)
Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:
Given:
- f(4) = 3
- f(0) = -2
Therefore, two points on the line are:
- (4, -3)
- (0, -2)
The y-intercept is the y-value when x = 0.
Therefore, the y-intercept of the line is -2.
Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for <em>m</em> to find the slope:
Therefore, the equation of the line is: