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Vocabulary: Read through the following vocabulary. Knowing these words will help with understanding the context of the problem. . Ski run: a track on a mountain slope for skiing, a ski slope . Chairlift: a series of chairs used for carrying people up and down a mountain . Cross-section: the shape created when cutting through an object . Recommendation: a suggestion as to the best course of action Background: A new Ski Resort called \"Penta Ski Resort\" has five mountains that will be used for ski slopes. Before the resort opens, park constructors need to set up ski runs and decide on the level of difficulty for each ski mn. Surveyors have graphed cross-sections of the 5 mountains: Mt. Zacry, Mt. Arbour, Mt. Tango, Mt. Boston and Mt. Fairweather. It is yourjob to use these crossrsections, your knowledge of functions, gradients and calculus, in order to make recommendations for the proposed ski runs. Note: |m| (the \"absolute value" of m) means to give the value of m as positive. e.g. |-3.1| = 3.1, |2| = 2 Note: For numerical answers, give exact values unless otherwise specified. Where exact value answers are not possible, answers should be rounded to 3 decimal places unless instructed differently. Question 1 Ski runs can be classied in the following categories: Beginner, Intermediate, and Expert. Below is a table stating the angle range ofthe mountain slope for each category. Run classication Angle of incline of the mountain Gradient range slo -e, 9 Intermediate (medium) 20 3 angle 5 35 5 1m] 5 ' Expert (hard) angle > 35 ' lmi > Using the angle measurements, calculate the gradient (m) range for each an classification. Fill your answers in the table above. Use m = tan 9. Page50f13 Question 2 Below is a graph representing part of the cross-section of Mount Arbour. The y-axis represents the vertical height (in metres), above the base of the mountain. The xaxis represents the horizontal distance (in metres), from the origin. Mount Arbour 1000 2000 3000 4000 a) Write a hybrid function f (x) to represent the graph of Mount Arbour. b) Hence, state the steepest gradient for Mount Arbour. Thus, if a ski run is constructed on top of Mount Arbour, state the most appropriate run classification (Beginner, Intermediate, or Expert). Base your recommendation on the classification range calculated in Question 1. c) Assuming the entire mountain is used to make a ski run, what is the length of the run, to the nearest metre? Hint: Use your knowledge of Pythagoras' Theorem and right-angle triangles to help nd the lengths of the angled sectlons. Page6 of13 Question 3 Below is a graph representing part of the cross-section of Mount Boston. The y-axis represents the vertical height (in metres), above the base of the mountain. The xaxis represents the horizontal distance (in metres), from the origin. Mount Boston 12 10 a) The cross-section graphed above can be written in the form f (x) : Ax2 + Bx + C. Find the values of A, B, and C and hence, find x) in this form. b) Find f'(x). c) Use the gradient function f '(x) to determine the steepest gradient. Hence, if a ski run is constructed on Mount Boston, state the most appropriate run classification (Beginner, Intermediate, or Expert). Page? of13