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.
Express d in terms of r and h. Then substitute your answer from Exercise 78 for h. Factor out r.
(Reference Exercise 78)
Use a right triangle to relate r, h, and θ . Solve for h.
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