Problema 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:
........
click here to see all the equation solution steps
........
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
Answer:
A triangles angle always equal to 180 degrees. So if you add up what you already have which is 80+40=120
Even means g(-x)=g(x)
replace x with -x and see if it simplifies to original functin
g(-x)=(-x-1)²+1
g(-x)=((-1)(x+1))²+1
g(-x)=(x+1)²+1
nope
g(x)=2x²+1
g(-x)=2(-x)²+1
g(-x)=2x²+1
yep
we are done
answer is 2nd one
60% bc i just know these things
