Question 3 [20 marks] The distance a tyre can travel (d) in kms can be related to the pressure of the tyre (p) in kPa as follows: d = ap~ + bp+ c; where a, b, and c are constants for a particular tyre. To determine a, b, and c, a research team for Wheels USQIM makes the following three measurements on a specific tyre. . when p = 100 kPa, d = 20.4 x 10* km; . when p = 300 kPa, d = 36.4 x 10* km; and . when p = 200 kPa, d = 38.4 x 10 km. 6 marks a) Write in matrix form the set of equations that must be solved to determine a, b, and c from these measurements. 4 marks b) Show that: 20000 20000 10000 70 -200 3 -3 is the inverse of: 1002 100 3002 3 200- 200 6 marks c) Using the result of Q3a, determine the values of a, b, and c for this particular tyre. Verify that the solution satisfies the measurements made by the WheelsUSQTM team. 4 marks d) Hence, or otherwise, determine the pressure which maximises the tyre life