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:
Social security and medicare with 7.65% rate of gross pay $2355
=> Deduction amount: 2355 x 7.65/100 = $180.16
=> Option A is correct
Hope this helps!
:)
Answer:
32+q=x
Step-by-step explanation:
32(jakes) + q (molly) = x(total)
Answer:
2/3
Step-by-step explanation:
Use rise over run, (y2 - y1) / (x2 - x1)
Plug in the points, then simplify:
(y2 - y1) / (x2 - x1)
(-1 + 7) / (4 + 5)
6/9
= 2/3
So, the slope of the line is 2/3
Answer:
9 TV ads and 20 radio ads
Step-by-step explanation:
He has $37,000 to spend. He has to sum that amount of money between the TV and radio ads. Each TV ad costs $3000 while each radio ad costs $500, so the equation that represents that is 37000 = 3000x + 500y
The same happens with the amount of voters he needs to reach, the equation is 130000 = 10000x + 2000y
The system that represents this is
And the augmented matrix is
![\left[\begin{array}{cc|c}3000&500&37000\\10000&2000&130000\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D3000%26500%2637000%5C%5C10000%262000%26130000%5Cend%7Barray%7D%5Cright%5D)
First we divide the first row by 3000 and the second by 10000:
![\left[\begin{array}{cc|c}1&1/6&37/3\\1&1/5&13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C1%261%2F5%2613%5Cend%7Barray%7D%5Cright%5D)
Then we multiply the second row by (-1) and we add the first row:
![\left[\begin{array}{cc|c}1&1/6&37/3\\0&-1/30&-2/3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C0%26-1%2F30%26-2%2F3%5Cend%7Barray%7D%5Cright%5D)
Now we multiply the second row by -30:
![\left[\begin{array}{cc|c}1&1/6&37/3\\0&1&20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C0%261%2620%5Cend%7Barray%7D%5Cright%5D)
Finally, to the first row we add the second one multiply by (-1/6):
![\left[\begin{array}{cc|c}1&0&9\\0&1&20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%260%269%5C%5C0%261%2620%5Cend%7Barray%7D%5Cright%5D)
So, x = 9 and y = 20
That means 9 TV and 20 radio ads will contact 130,000 voters using the allocated funds
