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
During an alpine skiing event, the times of four skiers were listed below. Time is measured in seconds.
Salsk061 [2.6K]
Skier c's time would be different
6 0
3 years ago
Kwan said that the product of 5/6 × 2 1/3 is 10/3. how can you tell that his answer is wrong?
seropon [69]
5/6 of a number cannot be greater than the number
6 0
3 years ago
Read 2 more answers
What’s the work for 6.2 x 88.01?
nekit [7.7K]

Answer:

545.662

Step-by-step explanation:

          88.01

        <u>  x   6.2    </u>

          17602

    <u>  52806        </u>

      545.662

3 0
3 years ago
A bag of backed chips advertises that it now has 1/4 fewer calories than the old recipe.What is the percent of calories were rem
Mrrafil [7]

Answer:

25%

1/4 * 25 = 25/100

25/100=25%

7 0
3 years ago
Help I’m not sure how to answer this
Drupady [299]

Answer:

option A is the correct choice

Step-by-step explanation:

The trigonometric equation you are using has a general form

y = A* tan w*(x - r)

Where

A is the amplitude of the function

w is the frequency rad/s

r  is the phase shift

In your case

A = 2

B = w = 3

r = pi/2

y = 2* tan 3*(x - pi/2)

8 0
3 years ago
Other questions:
  • Which angle description represents an angle that is greater than ninety degrees?
    5·1 answer
  • How many 5-person committees are possible from a group of 9 people if:
    12·1 answer
  • George has $23 to spend on art supplies he wants to buy markers papers and glue if the total cost of markers and papers is more
    12·1 answer
  • Three times the difference of a number and 2
    15·1 answer
  • PLEASAE HELp
    6·1 answer
  • Please my new and old friends on here please help i already said how i was feeling and some people made me feel better so yay ju
    6·1 answer
  • The sum of ages of Nira before 10 years and after 10 years is 60.find her present age.
    8·2 answers
  • Which equation represents the line shown on the coordinate grid below?
    6·1 answer
  • Please yall im crying this is hard
    13·1 answer
  • 8:11:11 PM
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!