Day 2, July 18 Modeling Problems Homework
1. The following problem is a typical homework problem from a precalculus book.
Similar to our classroom explorations of the box and circle problems I would like you to first identify and explore varying relationships; then determine what varying relationships should be modeled to respond to this question.
Problem Statement: You have 40 (linear) feet of fencing with which to enclose a rectangular space for a garden. Find the largest area that can be enclosed with this much fencing. Find the dimensions of the corresponding garden.
2. A tank is made from two hollow globes that are connected by a hollow stem, as shown in the figure to the right. Water is being poured into the globes from the top.
a. Sketch a graph that shows the height of water in this configuration as a function of the water’s volume in it.
b. A twisted, flat, rod will be placed into the configuration so that it stands at the bottom of the lower globe and ends at the top of the upper globe. A float, slotted in the middle, that cannot turn moves up the rod, so that the rod turns as the float moves upward. The rod must have a total twist of 360° as the water raises the float from the bottom to the top of the tank. Sketch a graph of “amount of turn” as a function of the water’s volume so that the rod turns at a constant rate with respect to the volume of water in the tank.