CALCULUS
posted by diana on .
A PIECE OF SHEET METAL IS 2.6 TIMES AS LONGS AS IT IS WIDE.
IT IS TO BE MADE INTO A BOX WITH AN OPEN TOP BY CUTTING 3INCH SQUARES FROM EACH CORNER AND FOLDING UP THE SIDES.
IF THE VOLUME OF THE BOX MUST BE BETWEEN 600 AND 800 CUBIC INCHES, WHAT VALUES OF X WILL PRODUCE THIS RANGE OF VOLUMES?

width of sheet = x ??? I will assume
b, breadth of box = x  6
L = length of box = 2.6 x  6
height = 3
600 ≤ 3(x6)(2.6 x  6) ≤ 800
600 ≤ 7.8 x^2 64.8 x + 108 ≤ 800
492 ≤ 7.8 x^2  64.8 x ≤ 692
solve those quadratics (ignore negative solutions)
x = 13.1
x = 14.4