Please answer those math questions and show your steps and work that you did to get the answers for each question

Spiral Review 5 Linear and Sinusoidal Functions [30 marks] Name: 1. The diagram shows the straight line L1. Points A(9, 1),M(3. 2) and C are points on L1. a. Find the gradient ole. [2 marks] M is the midpoint ofAC. b. Find the coordinates of point C. [2 marks] Line L2 is perpendicular to L1 and passes through point M. c. Find the equation osz. Give your answer in the form ax + by + d = 0, where a, b, d E Z. [3 marks] The point N(k, 4) is on L2- d. Find the value of k. [2 marks] e. Find the distance between points M and N. [2 marks] f. Given that the length of AM is v45, find the area of triangle ANC. [2 marks] ............................2. The Texas Star is a Ferris wheel at the state fair in Dallas. The Ferris wheel has a diameter of 61.8m. To begin the ride. a passenger gets into a chair at the lowest point on the wheel, which is 2.7m above the ground, as shown in the following diagram. A ride consists of multiple revolutions, and the Ferris wheel makes 1.5 revolutions per minute. diagram not to scale ground The height ofa chair above the ground, It, measured in metres, during a ride on the Ferris wheel can be modelled by the function Mt) = acos(bt) + d, where t is the time, in seconds, since a passenger began their ride. Calculate the value of a. [2 marks] [2 marks] [2 marks] A ride on the Ferris wheel lasts for 12 minutes in total. d. Calculate the number of revolutions of the Ferris wheel per ride. [2 marks] For exactly one ride on the Ferris wheel, suggest e. an appropriate domain for h(t). [1 mark] f. an appropriate range for h(t). [2 marks] Big Tex is a 16.7 metre-tall cowboy statue that stands on the horizontal ground next to the Ferris wheel. diagram not to scale Big Tex statue platform 030 ground [Source: Aline Escobar., n.d. Cowboy. [image online] Available at: https://thenounproject.com/search/?q=cowboy&i=1080130 This file is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en [Accessed 13/05/2021]. Source adapted.]g. By considering the graph of h (t), determine the length of time during one revolution of the Ferris wheel for which the chair is higher than the cowboy statue. [3 marks] There is a plan to relocate the Texas Star Ferris wheel onto a taller platform which will increase the maximum height of the Ferris wheel to 65.2m. This will change the value of one parameter, a, b or d, found in part (a). h. Identify which parameter will change. [1 mark] i. Find the new value of the parameter identified in part (e) (i). [2 marks]