# math

McDougal's Restaurant has a play area for children under and around their giant arch ( in the shape of parabola with negative orientation). They plan to set up a new activity that allows children to bungee jump from the arch. The manager, upon hearing of your team's expertise, hires you to calculate the maximum stretch of the rope that will keep the kids safe. The arch is 50 feet high and 40 feet wide at the base. The jumping location will be 5 horizontal feet away from the axis of symmetry of the arch.

A. Write an equation to model the shape of the arch.

1. 👍
2. 👎
3. 👁
1. let the x-axis be the ground and the y-axis the axis of symmetry
Make a sketch, your jump will be when x = 5

equation is y = ax^2 + 50
but (20,0) is the x-intercept , the other is (-20,0)
so 0 = a(20^2) + 50
400a = -50
a = -1/8

y = (-1/8)x^2 + 50
when x = 5
y = (1/8)(25) + 50 = 46.875 ft

max stretch is 46.875 ft, (it will "touch" the ground)

1. 👍
2. 👎

## Similar Questions

1. ### Math

Tickets for a play cost Php 250 for adults and Php 200 for children.The sponsor of the show collected a total amount of not more than lhp 44,000 from more than 150 adults and children who watched the play. A. What mathematical

2. ### physic

You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 7.37 ° above the

3. ### Algebra

The arch of the bridge below is half an ellipse, a "semi-ellipse". The arch is 148m long and has a height of 48m at the center. The height of the arch is 10m at point p. What is the distance from p to the center?

4. ### Trigonometry

An elliptical arch is constructed which is 6 feet wide at the base and 9 feet tall in the middle. Find the height of the arch exactly 1 foot in from the base of the arch. looking for direction with what ellipse equation is and how

1. ### math

A childrens play area is triangular. The sides of the play area measure 90m ,225m and 255m respectively . Calculate the area of the play area?

2. ### algebra

You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y=-0.000475x^2+0.851x, where x and y are in feet. How high above the river is the bridge(the top of the

3. ### Algebra 1

The arch support of a bridge can be modeled by y=-0.0012x^2 where x and y are measured in feet. Find the height and width of the arch. I don't know how to even attempt to solve this... If you know how, can you PLEASE help asap!!

4. ### Supportive learning environment

Which of the following activities most closely fits with the definition of play described in the textbook? A. The children are divided into small groups, and each child is given finger paint to create a picture. B. Children rotate

1. ### Math

The rainbow bridge of Utah is a natural arch that is approximately parabolic in shape. The arch is about 88m high. It is 84m across the base. Determine a quadratic relation, in standard form, that models the shape of the arch My

2. ### Algebra 2

The arch of the Gateshead Millennium Bridge forms a parabola with equation y=-0.016(x-52.5)^2+45 where x is the horizontal distance(in meters) from the arch's left end and y is the distance (in meters)from the base of the arch.

3. ### creative expression and play

A preschool teacher wants to support children’s creativity and play in her classroom. How can she provide these opportunities for them? A. Designate time in the daily schedule for free play, centers, and other activities that

4. ### physics

You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 7.31 ° above the