This project is intended as a "capstone" activity for our course. This means that it includes material from different units of the course that you have to use together to complete the project. There is more than 1 way to solve the problem but there is only 1 correct answer. You will need a picture to help understand what is happening and you need to include the picture with your solution. If you drawing that is "to scale" you can't find the answer by measuring on your drawing. You must show your work in order to receive full marks. You can do it!

The Problem

A bridge is supported by an arch that has the shape of a parabola. The base of the arch is a piece of flat ground 6.00 m wide and the top of the arch is 3.00 m above the base. A 160 cm diameter pipe is to pass under the bridge. The pipe is to be supported on a frame made of vertical supports on either side of the arch that are joined together by diagonal pieces. The vertical supports are 1.80 m high with the bottom resting on the ground and the top touching the arch. The pipe will rest on the diagonals. Find the length of the diagonal pieces, the distance from the bottom of the pipe to the meeting point of the diagonals and the distance from the top of the pipe to the top of the arch. Include a picture with your solution labelled with the location and size of the 3 required values. Report all values in mm to the nearest mm.

Bonus

Convert the length of the diagonal piece into binary.

Convert the distance from the top of the pipe to the top of the arch into hexadecimal.