Arancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 3 identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. find the dimensions that maximize the enclosed area. write your answers as fractions reduced to lowest terms

Let x be the shorter side, and y be the longer side

There would be 4 fences along the shorter side, and 2 fences along the longer side

4x + 2y = 800

Rewrite in terms of y:

y = 400 − 2x

The area of the rectangular field is

A = x*y

Replace Y with the equation above:

  A = x(400 − 2x)

  A = − 2x^2 + 400x

The area is a parabola that opens downward, the maximum area would occur at the parabola vertex.

At the vertex

x = −b/2a

  = −400/[2(−2)]

  = 100

y = 400 −2x

y = 400 -2(100)

y = 400-200

y = 200

The dimension of the rectangular field that maximize the enclosed area is 100 ft x 200 ft.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

0/5 is 0, 2/0 is undefined, and 0/0 is indeterminate.

step-by-step explanation:

hope my answer has you!