For individual or collaborative investigation (Exercises 77–80) (Modeling) Measurin...

For individual or collaborative investigation (Exercises 77–80)

(Modeling) Measuring Paper Curl Manufacturers of paper determine its quality by its curl. The curl of a sheet of paper is measured by holding it at the center of one edge and comparing the arc formed by the free end to arcs on a chart lying flat on a table. Each arc in the chart corresponds to a number d that gives the depth of the arc. See the figure. (Source: Tabakovic, H., J. Paullet, and R. Bertram, “Measuring the Curl of Paper,” The College Mathematics Journal, Vol. 30, No. 4.)

To produce the chart, it is necessary to find a function that relates d to the length of arc L. Work Exercises 77–80 in order, to determine that function. Refer to the figure on the right.

Use a right triangle to relate r, h, and u . Solve for h.