the length of a box is 4 times its width, and its height is 2 feet more than its width, the volume of the box is 103^2 feet

Answer 1

L = 4w

h = w+2

Vo Lhw = 4w(w+2)w = 4w^3 + 8w^2 = 103 ft^3

4w^3 +8w^2 -103 = 0

max 1 positive real solution

max 2 negative real solutions

w =2, v=32+32-130 <0

w=3, v =4(27)+8(9)-103 >0

2 < w < 3

graph it and see where the curve intersects the x axis

it's somewhere between 2 and 3 feet for width

looks about 2.5 feet

4(2.5)^3 + 8(2.5)^2 -103

=62.5 + 50 -103 = 62.5 -53 = 9.5

width is slightly less than 2.5 feet

w = 2.41504 feet = width

L = 9.26016 feet = Length

h= 4.41504 feet = height

if volume = 103 ft^3

h =