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:
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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
Answer:
Point slope is ( Y+4) = 1/2(x+3)
Slope intercept is Y = 1/2(x) -5/2
Step-by-step explanation:
For the point slope form.
Given the point as (-3,-4)
And the gradient m = 1/2
Point slope form is
(Y - y1) = m(x-x1)
So
X1 = -3
Y1 = -4
(Y - y1) = m(x-x1)
(Y - (-4)) = 1/2(x -(-3))
( Y+4) = 1/2(x+3)
For the slopes intercept form
Y = mx + c
We can continue from where the point slope form stopped.
( Y+4) = 1/2(x+3)
2(y+4)= x+3
2y + 8 = x+3
2y = x+3-8
2y = x-5
Y = x/2 - 5/2
Y = 1/2(x) -5/2
Where -5/2 = c
1/2 = m
Equilateral, because the sides are equal
Answer:
11
Step-by-step explanation:
There are more than eleven cards in a deck but there can only be one outcome because there are only 11 letters in the word PERSONALITY.
