A rectangular lot is 125 yards long and 80 yards wide. Give the length and width of another rectangular lot that has the same perimeter but a larger area.

Step-by-step explanation:

perimeter=2(125+80)=2(205)=410 yards

let the length of new rectangle be x and y.

Perimeter=2(x+y)

2(x+y)=410

x+y=410/2=205 yards

y=205-x

area A=xy=x(205-x)=205x-x²

A is maximum at x=205/2

y=205-205/2=(410-205)/2=205/2

so x=205/2=102.5 yards

y=205/2=102.5 yards

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.