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lara [203]
1 year ago
13

a person in a whispering gallery standing at one focus of the ellipse can whisper and be heard by a person standing at the other

focus because all the sound waves that reach the ceiling are reflected to the other person. if a whispering gallery has a length of 130 feet, and the foci are located 30 feet from the center, find the height of the ceiling at the center. round your answer to 4 decimal places. submit questionquestion 9
Mathematics
1 answer:
Lynna [10]1 year ago
7 0

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 \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

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

brainly.com/question/19507943

#SPJ4

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Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.

The distances:

  • from perihelion to the sun in terms of ellipse is a-c;
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Then

\left\{\begin{array}{l}a-c=741,000,000\\a+c=817,000,000\end{array}\right.

Add these two equations:

2a=1,558,000,000 \\ \\a=779,000,000

and subtract first equation from the second:

2c=76,000,000 \\ \\c=38,000,000.

Note that b=\sqrt{a^2-c^2}, thus

b=\sqrt{779,000,000^2-38,000,000^2}=\sqrt{605,397,000,000,000,000}.

The equation for the planet's orbit is

\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\Rightarrow \dfrac{x^2}{606,841,000,000,000,000}+\dfrac{y^2}{605,397,000,000,000,000}=1.

7 0
3 years ago
What is 4 1/3= 1/3 x _/_ = 4 _/_
Oxana [17]
4 1/3 = 13/3 = 1/3 x 13/1 = 4 1/3
3 0
3 years ago
Jimmy has $88 in his piggy bank. He is saving his
skelet666 [1.2K]

Answer:

88/15=5.86666666667

Step-by-step explanation:

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6 0
3 years ago
Why does the equation (x-4)^2-28=8 have two solutions?
Aliun [14]
<h3>Answer:</h3>

For your first answer it is because they are two different ways to solve the equation

<h3>Step-by-step explanation:</h3>

For Example!

<h2>Solution 1:</h2>

(x-4)² – 28 = 8The 8 is positive making it a different equation (this is like absolute value). (I am assuming you know the answer to the probelm)

<h2>Solution 2:</h2>

(x-4)² – 28 = -8

The 8 could be negative meaning that when you add the 28 to the right side it is -8+28 which will be a negative!

<h3>I hope this helps</h3><h2>IF IT DOES HELP PLEASE GIVE IT A BRAINLIEST!</h2>
4 0
2 years ago
Read 2 more answers
PLEASE HELP!! Question is below
maria [59]

Answer:

C

Step-by-step explanation:

Complementary means that the angles have a sum of 90° so we can write:

m∠A + m∠B = 90° → 3x + 2 + 8x = 90

11x + 2 = 90

11x = 88

x = 8 which means that m∠B = 8x = 8 * 8 = 64°.

Supplementary means that the angles have a sum of 180° so m∠C = 180° - m∠B = 180° - 64° = 116°.

8 0
3 years ago
Read 2 more answers
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