March 21st, 2009 | 
Author:
Polynomial function question?
One explanation for this problem would be appreciated. A piece of rectangular sheet metal is 16 inches wide. Is in fact a channel from the rain by the return of the edges to form the parallel sides equal. Let x be the length of each of the parallel sides. For what value of x the cross-sectional area of a maximum (and thus maximize the amount of water that the creek is expected)? If necessary, return to 2 decimal places. A) 8 B) 32 C) 64 D) 4 I already know the answer is D, but do not know how to get there. Thank you.
Cross section is a rectangle. Area determined by the length * width. Length = 16 – 2x (each turn-on the side is x) = x width Area = (16-2x) * x = 16x – 2x ^ 2 First, the area must be greater than 0 16x-2x ^ 2> 0 16x> 2x ^ 2 divided by 2x 8> x Therefore, x must be less than 8. the only option for this value is D) 4
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