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:
D. AC ≅ XZ
Step-by-step explanation:
To prove that two triangles are congruent by the Angle-Side-Angle theorem, both triangles must have two corresponding angles that are congruent to each other in each triangle, and also a corresponding included side in each triangle that are congruent.
Thus, we are given that,
<X ≅ <A and <Z ≅ <C, therefore, what is needed is a corresponding included angle in each triangle that are congruent to each other, which are,
AC and XZ
Therefore, what is needed is:
AC ≅ XZ
Answer: See explanation
Step-by-step explanation:
3.) Boys║5║<em>10 ║</em>60
Girls ║7║ 14 ║<em>84</em>
7 × 2 = 14
5 × 2 = 10
5 × 12 = 60
7 × 12 = 84
Hope I helped!
Answer:
14 dollars
Step-by-step explanation:
Answer:
f(x) = -3x + 6
Step-by-step explanation:
The general linear function is;
y = mx + b
it can also be written as (x , f(x))
f(x) = mx + b
where m is the slope and b is the y-intercept
so we have the points ;
(0,6) and (4,-6)
So we have;
for f(0) to be 6, it means that the y-intercept b is 6
This is because the value of x at the y-intercept is 0
So we have this as;
f(x) = mx + 6
Now, let’s substitute the other point so as to get m
For the other point;
x = 4 and f(x) = -6
that means;
-6 = 4m + 6
4m = -6-6
4m = -12
m = -12/4
m = -3
So we have the equation as;
f(x) = -3x + 6
