You have 1200 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. what are the largest dimensions of this enclosure that you could build?

step-by-step explanation: problem n' solution

you have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. what are the largest dimensions of this enclosure that you could build?

answer provided by our tutors

make a drawing and denote:

x = half of the length of the enclosure

2x = the length of the enclosure

y = the width of the enclosure

p = 800 ft the perimeter

the perimeter of the two enclosures can be expressed p = 4x + 2y thus

4x + 3y = 800

solving for y:

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y = 800/3 - 4x/3

the area of the two enclosure is a = 2xy.

substituting y = 800/3 - 4x/3 in a = 2xy we get

a = 2x(800/3 - 4x/3)

a =1600x/3 - 8x^2/3

we need to find the x for which the parabolic function a = (- 8/3)x^2 + (1600/3)x has maximum:  

x max = -b/2a, a = (-8/3), b = 1600/3

x max = (-1600/3)/(2*(-8/3))

x max = 100 ft

y = 800/3 - 4*100/3

y = 133.33 ft

2x = 2*100

2x = 200 ft

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it has the same slope and a different y-intercept

hope this : )

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.