151 A machine produces open boxes using square sheets of met

151. A machine produces open boxes using square sheets of metal. The figure illustrates that the machine cuts equal- sized squares measuring 2 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 200 cubic inches, find the length and width of the open box. 12 121 the en

Solution

21) box is cut by 2 inch on edges both sides.

So, length = x -2 -2 = x-4

width = x -2 -2

height of box = 2 inch

volume = l*b*w = (x-4)(x-4)*2

2(x-4)^2 = 200 ----> (x -4)^2 = 100

x -4 = 10 -----> x = 14 inches

So, length and width of box = 14 -4 = 10 inches

105 . 1/x +1/(x+2) =1/3

taking x( x+2) as lcd:

(x+2 +x)/x(x+2) = 1/3

3(2x+2) = x^2 +2x

x^2 +2x -6x -6 =0

x^2 -4x -6 =0

solve the quadratice using formula for roots:

x = (4 +/- sqrt(16 +24))/2 = (4 +/- sqrt40)/2

x = 2 +/- sqrt10