Auditorium Lights
The lights in an auditorium are 24-pound discs of radius 18 inches. Each disc is supported by three equally spaced cables that are L inches long (see figure).
(a) Write the tension T in each cable as a function of L. Determine the domain of the function.
(b) Use a graphing utility and the function in part (a) to complete the table.
L |
20 |
25 |
50 |
35 |
40 |
45 |
50 |
T |
(c) Use a graphing utility to graph the function in pan (a). Determine the asymptotes of the graph.
(d) Confirm the asymptotes of the graph in part (c) analytically.
(e) Determine the minimum length of each cable when a cable is designed to carry a maximum load of 10 pounds.
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