How would you go about solving this problem?
(IDK how to solve because there are 2 variables. The height and the second base.
A 10 ft sectionis of gutter is made from a 12 in wide strip of sheet metal by folding up 4 in strips on each side so that they make the same angle with the bottom of the gutter. Determine the depth of the gutter that has the greatest carrying capacity
2007-10-04 04:53:43 · 1 answers · asked by Frank C 1 in Science & Mathematics ➔ Mathematics
The only variable is the angle the sides make with the bottom of the gutter, call it x. Depth is 4 sin x, and the other base is 4 + 2( 4 cos (π-x)) = 4 - 8 cos x. So you want to maximize the cross-sectional area which of course is depth times average of the bases, [4 sin x][4 - 4 cos x] = 16(sin x)(1 - cos x) = 16 sin x - 8 sin 2x.
2007-10-04 05:14:20 · answer #1 · answered by Philo 7 · 0⤊ 0⤋