Hi there, I am a student. I am working on designing a rollercoaster for an investigation that is a part of Year 11 Mathematics Methods Investigation. It requires multiple functions to make the whole roller coaster. For any tangent for the function, the slope of the ascent must be 0.7 and the slope of the descent must be -1.8. This applies for all hills I make for my rollercoaster. I am required to make 4 functions joining g(x) and 5 functions joining h(x). I don't know how to complete h(x). I am not sure whether we need a motor, because I thought it would be nearly impossible to end at the same point where we had started. I am attaching some documents for context. Thanks!

4. You must determine equations (minimum of 5) for the section on the left to join g(x) and equations (minimum of 4) from h(x) to the exit point, ensuring a smooth transition between points; show detailed working, equations, constraints, reasons for the choices etc. The start and exit point of your ride must be horizontal lines. You must carefully consider: -length and height constraints -using a range of functions in your design -consider different techniques for generating the functions 5. Include a discussion of any assumptions, limitations and improvements in the design of your roller coaster. Your answers should be written up as an investigational report. Outlined below is how your report should be formatted Investigation Report The format of the investigation report should include: . An outline of the problem and context The method required to find a solution, in terms of the mathematical model or strategy used The application of the mathematical model or strategy, including - relevant data and/or information mathematical calculations and results, using appropriate representations - the analysis and interpretation of results, including consideration of the reasonableness and limitations of the results The results and findings in the context of the problem.Designing a Roller Coaster Using the links below investigate what makes a 'good' roller coaster. http://www.funderstanding.com/educators/roller-coaster-game/ Through research, it is found that for a roller coaster to be safe whilst still being fun for patrons, the slope of any ascent must be 0.7 and the slope of any descent must be -1.8. f(x) g (x) For the track to be smooth there can't be abrupt changes ". .. in direction. To ensure smooth transitions between the inear segments and the parabola g(x) and h(x) need to h(x) be tangents to the parabola, f (x) at the transition points P and Q. quevala world To simplify the equations, you decide to place the origin at P. Furthermore, the horizontal distance between P and Q is 16 metres. 1. ) Find the equations of the three segments of track indicated below for the given greaney domains, showing all appropriate steps of logic: than a) g(x ) = mix + k, for x 16 make sense in the graph. 2. Using the website https://www.desmos.com/calculator plot the equations for the given domains, to check your answers. Ensure you create an account so you can save your graphs 3. After conducting some research on roller coaster specifications, your task is to design a roller coaster and specify the equations for your roller coaster track from the starting point (entrance on the left) to its finish point (exit on the right). The three segments of track from part 1 must be included in your track.Mathematics Methods Rollercoaster Investigation X https://www.desmos.com/calculator + . . . Mathematics Methods Roll... Save desmos C ? + # x>16} X 50 0.05x2 + 2.2x + 11.25 {-40 Sx- X b X -0.036x2 - 4.68x - 126.35 {-40 RCTW X 0.045x- + 5.85x + 215.875 {-85 19 31x2 X -150 -100 -50 50 7 500 500 - 9.45x - 393.43: b y = 80.417 {-143 > > 140} X + EN 4:43 PM O 28.C Sunny call's ENG 29/08/2021