More Modeling with Functions

Each of the problems below is a link. If you click on the problem, it will take you to a YouTube video of a full, step-by-step solution for the problem. You may try these problems as practice and use the videos to check your answer, or you can just watch the videos to see more worked-out example problems.

1. Two ships leave port at the same time. One sails south at 15 miles per hour, and the other sails east at 20 miles per hour. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.
2. A right triangle has one leg twice as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.
3. A rectangle is inscribed in a semicircle of radius 10. Find a function that models the area A of the rectangle in terms of its height h. Then use a graphing calculator to find the maximum possible area of the rectangle.