A farmer with 1000 feet of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What is the largest area that can be enclosed? Round to the nearest whole number.

41,666.67m2

Step-by-step explanation:

Call W the Width and L the Length with 3 pieces.

The total length will be 2W + 3L

The Area is L*W

so,

A = L*W

2W+3L = 1000

Solve for L

3L = 1000-2W

L = (1000-2W)/3

subtitute for L into the first equation

A = L*W

A = W*(1000-2W)/3

A = (1000W - 2W^2)/3

Now, to find the max, set the 1st derivative = 0. I don't know if you know what that means, but...

dA/dW = 1000/3 - 4W/3 = 0

1000 - 4W = 0

W = 250 meters

Solve for L

2W+3L = 1000

500 + 3L = 1000

3L = 500

L = 166.67 m

Area = 250*500/3 = 41,666.67m2.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180