1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
patriot [66]
3 years ago
8

A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find

the height of the arch at 10 feet from its center.

Mathematics
1 answer:
scoray [572]3 years ago
8 0

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, O(0,0) in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

x^2=4ay\;\cdots(i)

where a is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is A(83, -40) and B(-83, -40).

There is only one constant in the equation of the parabola, so, use either of one point to find the value of a.

Putting A(83,-40) in the equation (i) we have

83^2=4a(-40)

\Rightarrow a=-43.05625

So, on putting the value of a in the equation (i), the equation of bridge is

x^2=-172.225y

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, x=\pm 10 feet, put this value in equation (i) to get the value of y.

(\pm10)^2=-172.225y

\Rightarrow y=-1.72225 feet.

The point P_1(10,-1.72225) and P_2(-10,-1.72225) represent the point on the bridge at a distance of 10 feet from its center.

The distance of these points from the x-axis is d=1.72225 feet and the distance of the base of the bridge from the x-axis is h=40 feet.

Hence, height from the base of the bridge at 10 feet from its center

= h-d

=40-1.72225=38.27775 feet.

You might be interested in
Please help me I have been stuck
Mnenie [13.5K]
I think you have to pay attention in class for this
8 0
3 years ago
Y=3x^2+2x-8 in factored form
Phantasy [73]

Y=(3x-4)(x+2)

x=-2,4/3

7 0
3 years ago
(-2,-1) is a solution of the equation 4x + 5y = -13.
Art [367]

Answer:

true

Step-by-step explanation:

4x + 5y = -13.

Substitute the point in

4(-2) + 5(-1) = -13

-8+-5 = -13

-13 = -13

This is true so the point is a solution

5 0
3 years ago
Answer question in picture.
Andrews [41]

Answer:

Surface area ~ 197.33

<em>Hope that helps!</em>

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Which expression is a product of the factors 6xy(2x
Harman [31]

Answer:

A

Step-by-step explanation:

Process of elimination

4 0
3 years ago
Other questions:
  • Use the number line to name the fraction or decimal. (H)
    11·1 answer
  • What is the answer to 72 = 24 + w
    13·2 answers
  • one teacher wants to give each student 7/8 of a slice of pizza. If the teacher has 7 slices of pizza then how many students will
    12·2 answers
  • What are the restrictions for (x^2+10x+25)/(x^2-3x-28)<br><br> 0,14<br> -4,7<br> 0,7<br> 4,7
    13·1 answer
  • Solve each equation. Round your answers to the nearest ten-thousandth. Please show work. Part 3A​
    11·1 answer
  • Select the correct answer. If g = 8, what is the value of the expression g/8+2
    7·1 answer
  • (12x5+3x25)-8<br><br> 12x5=60<br> 3x25=75<br> 60+75=135<br> 135-8=127
    12·2 answers
  • Solve : 5(x−12)=260+4x
    6·2 answers
  • Help help help help help help
    9·1 answer
  • Find the solution for this system of equations. 12x 15y = 34 -6x 5y = 3 x = y =
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!