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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You can get a vertical asymptote at x=1 using y = 1/(x-1)
You can generate a hole at x=3 by multiplying by (x - 3/(x - 3) which is undefined at x=3 but otherwise equals 1
You can move the horizontal asymptote up to y=2 by adding 2
y = (x - 3)/((x - 1)(x - 3)) + 2
Answer:
answer is (d) 4/3
Step-by-step explanation:
-x+3/7=2x-25/7
25/7+3/7=2x+x
28/7=3x
4=3x
x=4/3
Shelters found for dogs = 12,308
Shelters found for cats = 7,953
Total number of shelters found
= Shelters found for dogs + Shelters found for cats
= 12,308 + 7,953
= 20,261 shelters
Therefore, the total number of shelter found for both dogs and cats last year is 20,261 shelters
Answer:
(a) 
and 
are indeed mutually-exclusive.
(b) 
, whereas 
.
(c) 
.
(d) 
, whereas 
Step-by-step explanation:
<h3>(a)</h3>
means that it is impossible for events and to happen at the same time. Therefore, event and are mutually-exclusive.
<h3>(b)</h3>
By the definition of conditional probability:
.
Rearrange to obtain:
.
Similarly:
.
<h3>(c)</h3>
Note that:
.
In other words, and are collectively-exhaustive. Since and are collectively-exhaustive and mutually-exclusive at the same time:
.
<h3>(d)</h3>
By Bayes' Theorem:
.
Similarly:
.
