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rewona [7]
2 years ago
6

A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of

the tunnel is 25 feet. What is the height of the tunnel 5 feet from the edge? Round your answer to the hundredths place.
9.99 feet
13.82 feet
24.65 feet
25.01 feet
Mathematics
1 answer:
rusak2 [61]2 years ago
5 0

The height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

<h3>What is an ellipse?</h3>

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

A tunnel is constructed with a semi-elliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet.

2a = 60 (width of the tunnel is 60 feet)

a = 30

And the maximum height at the center of the tunnel is 25 feet

b = 25

Let's assume the center of the ellipse is at the origin.

So the equation of the ellipse:

\rm \dfrac{x^2}{30^2}+\dfrac{y^2}{25^2}=1

Now plug x = a - 5 = 30 - 5 = 25

\rm \dfrac{25^2}{30^2}+\dfrac{y^2}{25^2}=1

After solving:

\rm \dfrac{y^2}{25^2}=1-\dfrac{25}{36}

\rm y^2=\dfrac{6875}{36}

y = ±13.819 ≈ ±13.82

Height cannot be negative

y = 13.82 feet

Thus, the height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

Learn more about the ellipse here:

brainly.com/question/19507943

#SPJ1

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Using the numbers 5 8 and 24 create a problem using no more than four operations addition subtraction multiplication division sq
lubasha [3.4K]

Answer:

(\frac{24}{8})^{2} gives rational solution and \sqrt{5} gives an irrational solution.

Step-by-step explanation:

We are given the numbers 5 , 8 , 24.

Using these numbers and maximum four operations given, we need to find the problem having a rational and irrational solution.

Now, applying two operations namely division and squaring, we define the following problem having a rational solution.

i.e. (\frac{24}{8})^{2} = (\frac{12}{4})^{2} = 3^{2} = 9, being an integer, it is a rational number.

Further, applying only one operation namely square root, we define the problem having an irrational solution.

i.e. \sqrt{5} , which is an irrational number.

Hence, the problems (\frac{24}{8})^{2} gives a rational solution and \sqrt{5} gives an irrational solution.

4 0
3 years ago
Please this is due at 11/00 pm help me please
Serga [27]

Answer and Step-by-step explanation:

The answer is 54.

We see that each time, the number is being multiplied by 1.5.

54 times 1.5 = 81 * 1.5 = 108

54 times 2 = 108

<u>54 is the starting number, because when you multiply 54 by 1, you get 54 for y.</u>

<u />

<u />

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

4 0
3 years ago
Read 2 more answers
What is the solution to the equation -2(1 + 5a) = -6(a + 3) <br> a=
Yuliya22 [10]
-2(1+5a)=-6(a+3)
Expand the brackets:
-2-10a=-6a-18
Add 10a to each side:
-2=4a-18
Add 18 to each side:
16=4a
Divide each side by 4:
4=a

Hope this helps :)
6 0
3 years ago
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