Hello! I only need help with part 2. It should say Part 2 at the top of the screenshot. All the information needed is in the attached word document screenshots. Thanks!
Assignment Part 1: Write parametric equations to represent a mountain hiking trail. The table shows the estimated distances and elevation changes between a base camp and various locations along a popular mountain trail. The distance traveled along the trail is represented by x. the elevation is represented by y, and the time from the base camp to each location is represented by t. Location Distance from Base Cam - Elevation Travel Time from Base Cam - Base Cam 0 miles 6,990 feet 0 hours Camp | Cam || Camp Ill 4 miles 8.4 miles 11.4 miles 8,290 feet 10.875 feet 13,331 feet 10 hours 21 hours 28.5 hours Camp IV Summit 14.8 miles 17.2 miles 16,795 feet 19,675 feet 37 hours 43 hours 1. Use the data points about the distance and elevations of the camps to graph the data points where the x-coordinate is the total distance traveled from the base camp and the y-coordinate is the elevation. Use the grid below or include a screenshot of the data plotted from a calculator. (5 points) Elevation (ft) Distance from Base Camp vs. Elevation 20.000 15.000 10.000 5.000 O 5 ID 15 Distance from base camp (mi) 2. Describe the curve in the graph by completing the steps. 20 a) Find a reasonable interval for the values oft and explain its signicance. (10 points) OStS43. The significance of the values oft are that they dene the amount of time that is allotted to travel with respect to its vertical distance or in regards to the horizontal distance from base camp to the summit. b) Write a linear function. x(t), for the total distance in miles hiked in terms of total time hiking in hours using the data from the table. (5 points) x(t)=t12.5 0) Write a quadratic function, y(t), for elevation in terms of the total time hiking in hours using the data in the table. Find a system of three equations and three unknowns to write the equation. (10 points) t=0, y= 6990 6990=0)"'2+b*0+c 6990=0+0+c C=6990 T=10, y=8290 8290=a(1_a);2+b(10)+6990 1300=1DOa+10b 1300=1003+10b 1300-1 Dbl 1 00=a 13-.1b=a 3885=441(13D.1t_1);21b 3885=5733-44.1b+21b B=80 A=13-.1*80=5 Y(t)=5t"2+80t+6990 Part 2: Write and use the rectangular form of the parametric equations. 1. Using the equations from Part 1. eliminate the parameter. and write the rectangular form of the equation. (10 points) 2. Use the rectangular equation to show the elevation that a group can expect to reach after hiking 8 miles. Then determine the time it will take the group to get to that point on the mountain. (6 points) 3. Use the rectangular equation to show approximately how far a group can expect to hike before reaching an elevation of 12,000 feet. (4 points)
