Determine the width of the strip so that each labourer mows the same area using this equation
(44-2x)(32*2x)= 704m^2
To determine the width of the strip, we need to solve the equation
(44-2x)(32*2x) = 704m^2
First, let's simplify both sides of the equation.
(44-2x)(32*2x) = 704
(44-2x)(64x) = 704
2816x - 128x^2 = 704
Rearranging the equation to a quadratic form:
128x^2 - 2816x + 704 = 0
Dividing the entire equation by 16 to simplify:
8x^2 - 176x + 44 = 0
Now, let's solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 8, b = -176, and c = 44.
x = (-(-176) ± √((-176)^2 - 4*8*44)) / (2*8)
x = (176 ± √(30976 - 1408)) / 16
x = (176 ± √(29568)) / 16
x = (176 ± √(736*4*4)) / 16
x = (176 ± (4√(184))) / 16
x = (44 ± √(184)) / 4
Therefore, the potential solutions for the width of the strip are:
x = (44 + √(184)) / 4 and x = (44 - √(184)) / 4
These are the two possible values for the width of the strip that would result in each laborer mowing the same area.