# Answer: Construction A roofing contractor is fabricating gutters from 12-inch aluminum

**Chapter 2, Problem 99**

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Construction A roofing contractor is fabricating gutters from 12-inch aluminum sheeting. The contractor plans to use an aluminum siding folding press to create the gutter by creasing equal lengths for the sidewalls (see figure). (a) Let represent the height of the sidewall of the gutter. Write a function that represents the cross-sectional area of the gutter. (b) The length of the aluminum sheeting is 16 feet. Write a function that represents the volume of one run of gutter in terms of (c) Determine the domain of the function . (d) Use a graphing utility to construct a table that shows the sidewall heights and the corresponding volumes Use the table to estimate the dimensions that will produce a maximum volume. (e) Use the graphing utility to graph Use the graph to estimate the value of for which is a maximum. Compare your result with that of part (d). (f ) Would changing the length of the aluminum sheet affect the value of for which is a maximum? Explain.

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