A farmer wants to build a rectangular pen with 80 feet of fencing. The pen will be built against the wall of the barn, so one si
de of the rectangle won’t need a fence. What dimensions will maximize the area of the pen?
1 answer:
Answer:
20 ft out from the wall by 40 ft parallel to the wall
Step-by-step explanation:
Let x represent the length of fence in the direction parallel to the wall. Then the other dimension of the rectangular pen is (80 -x)/2. The area is the product of these dimensions:
area = x(80 -x)/2
This function describes a downward-opening parabola with zeros at x=0 and x=80. The vertex (maximum) is halfway between the zeros, at x=40.
The dimensions are 40 ft parallel to the wall and 20 ft out from the wall.
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The vector function is, r(t) =
Given two surfaces for which the vector function corresponding to the intersection of the two need to be found.
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Second equation is of the parabolic cylinder,
Now to find the intersection of these surfaces, we change these equations into its parametrical representations.
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Firstly, we will draw figure
Let's assume
length of AC=x
we have
AB : BC = 2 : 1
so,
Point D is on line AB
and
AD : DB = 3 : 2
so, we get
now, we can locate these values
Firstly, we will find DC
DC=DB+BC
now, we can plug values
we have got
now, we can find ratio
now, we can simplify it
so,
AD:DC=2:3...........Answer
