Question 1070823
A trough at the end of a gutter spout is meant to direct water away from a house. 
 The homeowner makes the trough from a rectangular piece of aluminum that is 30 in.long and 14 in. wide. 
 He makes a fold along the two long sides a distance of X inches from the edge.
 If he wants the trough to hold 280 in. to the third power of water, how far from the edge should he make the fold?
:
let x = the fold distance from the edge
End view is something like this
x|__|x
then
(14-2x) = the width of the trough
:
Volume
x(14-2x)*30 = 280
(14x - 2x^2)*30 = 280
420x - 60x^2 = 280
A quadratic equation
-60x^2 + 420x - 280 = 0
Simplify, divide by -10
6x^2 - 42x + 28 = 0
Using the quadratic formula; a=6; b=-42; c=28
Two solutions
x = 6.2538
and
x = .7462 in, this is the reasonable solution (height of the trough)
:
;
Check this, find the volume using x = .7462
the width of the trough: 14 - 2(.7462) = 12.5076 in wide
Vol = 12.5076 * .7462 * 30
Vol = 279.99 ~ 280