Trig

A bridge is built in the shape of a parabolic arch. The bridge has a span of s= 160 feet and a maximum height of h= 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.

10=
30=
50=

  1. 👍
  2. 👎
  3. 👁
  1. If it has a span of 160', then the equation of the parabola is
    f(x)=ax(160-x)
    where a is a constant, and x=0 and x=160 are the zeroes which correspond to points where the arch reaches ground/water.
    The constant "a" can be found by the fact that f(80)=25.
    Post your answer for a check if you wish.

    1. 👍
    2. 👎
  2. 10 feet= 24.61 ft
    30 feet= 21.48 ft
    50 feet= 15.23 ft

    1. 👍
    2. 👎
  3. Yes, the answers are all correct.
    You have also correctly taken the origin at the centre of the span, which is logical since the question requires the height at distances from the centre.

    Check that at negative distances the heights are the same.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math math

    the arch of a concrete bridge is a semi ellipse having a span of 60 ft and a central height of 20 ft. if the roadway is 25 ft above the base. find at 10 ft intervals the distance from the arch to the roadway. ( im completely lost

  2. Language Arts PLEASE HELP

    John Roebling the designer of the Brooklyn Bridge, A.was a civil engineer who invented the twisted wire-rope cable ✗ B.also worked on the design of the George Washington Bridge ? C.took over the building of the bridge after his

  3. Math

    the arch of a concrete bridge is a semi ellipse having a span of 60 ft and a central height of 20 ft. if the roadway is 25 ft above the base. find at 10 ft intervals the distance from the arch to the roadway. (Im completely lost

  4. Math

    The bridge will span a section that is 35 meters wide, with ends of the bridge set back 2.5 m from each river bank. The engineer must apply right angle relationships because one river bank is 9 m higher than the other. What is the

  1. algebra

    Have a few questions can someone please help me figure them out? 1) You research the cost of a gallon of gasoline over several years to look for a trend. The table shows your data. What is a line of best fit for the data? Based

  2. Math

    The cable of a suspension bridge has supporting towers which are 50 ft high and 400 ft apart and is in the shape of a parabola.If the lowest point of the cable is 10 ft above the floor of the bridge, find the length of a

  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. 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

  1. 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!!

  2. mathematics

    Find the angle of depression of a boat from the bridge at a horizontal distance of 25 m from the bridge if the height of the bridge is 25 m

  3. Grade 10 Math

    The Brooklyn Bridge in New York City is a suspension bridge that crosses the East River and connects Brooklyn to the island of Manhattan. If the origin is placed at the top of one of the cable suport towers, as shown, the shape of

  4. math

    The main span of a suspension bridge is the roadway between the bridge's towers. The main span of the Walt Whitman Bridge in Philadelphia is 2000 feet long. This is 600 feet longer than two-fifths of the length of the main span of

You can view more similar questions or ask a new question.