6. Miniature Golf A golfer is trying to make a hole-in-one on the miniature golf green shown. The golf ball is at the point (2.5, 2) and the hole is at the point (9.5, 2). The golfer wants to bank the ball off the side wall of the green at the point (x,y). Find the coordinates of the points (x,y). Then write an equation for the path of the ball.
1. Problem 6
0. What are the coordinates of the point (x,y)?
0. Give the equation for the path of the ball, showing all work. Explain why you do each step.
0. Include a screenshot of the graph of your equation (use Desmos.com), verifying that it goes through the given points.
10. Trip Time You are in a boat 2 miles from the nearest point on the coast (see figure). You plan to travel to point Q, 3 miles down the coast and 1 mile inland. You row at 2 miles per hour and walk at 4 miles per hour.
a) Write the total time T (in hours) of the trip as a function of the distance x (in miles).
b) Determine the domain of the function.
c) Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window.
d) Find the value of x that minimizes T.
e) Write a brief paragraph interpreting these values.
1. Problem 10
1. The total time T (in hours) of the trip as a function of the distance x (in miles). Make sure you show all your work to come up with this equation, and explain each step and what it represents.
1. The domain of the function. Explain why this domain makes sense, and show work as needed.
1. Graph the function using the graphing utility on Desmos.com. Take a screenshot and make sure it is included in your document. The graph should be focused over the domain of the function.
1. Find the value of x that minimizes T. Desmos.com will note this ordered pair for you automatically. If it does not, then you can click various points of the graph and it will display the ordered pair.
1. What does the ordered pair of the minimum for T represent in our situation? I.E. what does the value of x tell us, and what does the value of T tell us? Write a brief paragraph interpreting these values.