A rancher has 200 feet of fencing to enclose two adjacent corrals
1 answer:
Answer:
a) Each corral should be 33⅓ ft long and 25 ft wide
b) The total enclosed area is 1666⅔ ft²
Step-by-step explanation:
I assume that the corrals have identical dimensions and are to be fenced as in the diagram below
Let x = one dimension of a corral
and y = the other dimension
(a) Dimensions to maximize the area
The total length of fencing used is:
4x + 3y = 200
4x = 200 – 3y
x = 50 - ¾y
The area of one corral is A = xy, so the area of the two corrals is
A = 2xy
Substitute the value of x
A = 2(50 - ¾y)y
A = 100 y – (³/₂)y²
This is the equation for a downward-pointing parabola:
A = (-³/₂)y² + 100y
a = -³/₂; b = 100; c = 0
The vertex (maximum) occurs at
y = -b/(2a) = 100 ÷ (2׳/₂) = 100 ÷ 3 = 33⅓ ft
4x + 3y = 100
Substitute the value of y
4x + 3(33⅓) = 200
4x + 100 = 200
4x = 100
x = 25 ft
Each corral should measure 33⅓ ft long and 25 ft wide.
Step 2. Calculate the total enclosed area
The enclosed area is 50 ft long and 33⅓ ft wide.
A = lw = 50 × 100/3 = 5000/3 = 1666⅔ ft²
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The answer is Option B
Step-by-step explanation:
Step 1: Group the given cubic polynomial into two sections.
So polynomial can be grouped as
Step 2:Find what's the common in each section.
In section the come term is
In section (8x + 48) the come term is 8
Step 3:Factor the commonalities out of the two terms.
Factoring out from the first section
, we get
Factoring out 8 from the second section(8x + 48) , we will get 8(x + 6).
Step 4: Combine the factors together for terms contains the same factor,
Combining we get,