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# Mathmatical modelling

The first question, 1, rquires determining which roller coaster, te Giant or Feeling the Fear modelled by and respectively, i bigger. I order to achieve this, te minimum and maximum heights of bother roller coasters is determined, agraph is then drawn, ad finally, fr the Feeling the Fear coaster, adetermination is made of when the coaster is at ground level, wile for the Giant coaster, adetermination is made of where the ride begins. Fr the Feel the Fear coaster, agraph is made and the height of the time, through to is determined.

Acording to the graph, te Feel and Fear roller coaster is at ground level when this happens at three different instances, wen. Gven the equation and using the factor theorem in which we divide by, w can check whether or not the coaster reaches the ground level at instanceThe first part of the question involves illustrating that the area of the enclosure can be calculated by. I this case, w assume the width to x meters, ad the length to meters. I te area of the enclosure is given by: Te piece of cardboard is 40cm by 40cm; te goal is to determine what dimensions would give a box of maximum volume if squares from each corner of the cardboard are removed and then the sides are folded up.

T do this, w assume that the length of the cardboard after removing squares of side x will be: Uing mathematical modelling, w have been able to solve four different real world problems, abeit in theory. Uing the differentiation and quadratic w been able to determine the maximum and minimum heights of each roller coaster; mximum height of 36 at t=8, ad minimum height of 14.

8at, fr the Feel and Fear coaster. Mximum height of 36. 4at t=1. 8 and minimum height of -96. 4at, fr the Giant coaster; te ride begins at h=0. Fr the Feel and Fear Coaster, te report indicates that the coaster is at ground level at times, t2, t5, ad t=10; tis successfully confirmed using the factor theorem. Fr the third question, te confirms, uing modelling, tat the area of the enclosure is given by A = 102x – x2.

Trough differentiation, w have successfully determined the value of x that would give the maximum value to be and thus, te maximum possible area to be. Fnally, trough mathematical modelling, w determine, fr Q4, tat for a cardboard of 40cm by 40cm, te dimensions that would give the maximum volume are height, ...

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