1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nignag [31]
3 years ago
5

Suppose a rectangular pasture is to be constructed using 1 2 linear mile of fencing. The pasture will have one divider parallel

to one pair of sides and two dividers parallel to the other pair of sides, so that there are six congruent enclosures. What is the maximum total area of such a pasture, in square feet?
Mathematics
1 answer:
timama [110]3 years ago
6 0

Answer:

\displaystyle A=\frac{1}{192}

Step-by-step explanation:

<u>Maximization With Derivatives</u>

Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.

We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.

The two divisions parallel to x have lengths y, thus the fencing will take 4x. The three dividers parallel to y have lengths x, thus the fencing will take 3y.

The amount of fence needed to enclose the external and the internal divisions is

P=4x+3y

We know the total fencing is 1/2 miles long, thus

\displaystyle 4x+3y=\frac{1}{2}

Solving for x

\displaystyle x=\frac{\frac{1}{2}-3y}{4}

The total area of the pasture is

A=x.y

Substituting x

\displaystyle A=\frac{\frac{1}{2}-3y}{4}.y

\displaystyle A=\frac{\frac{1}{2}y-3y^2}{4}

Differentiating with respect to y

\displaystyle A'=\frac{\frac{1}{2}-6y}{4}

Equate to 0

\displaystyle \frac{\frac{1}{2}-6y}{4}=0

Solving for y

\displaystyle y=\frac{1}{12}

And also

\displaystyle x=\frac{\frac{1}{2}-3\cdot \frac{1}{12}}{4}=\frac{1}{16}

Compute the second derivative

\displaystyle A''=-\frac{3}{2}.

Since it's always negative, the point is a maximum

Thus, the maximum area is

\displaystyle A=\frac{1}{12}\cdot \frac{1}{16}=\frac{1}{192}

You might be interested in
I have no idea!!! Help??
Savatey [412]

Answer:

x<5

Open circle at 5  going to the left

x >1

Open circle at 1 going to the right

Step-by-step explanation:

7x -19 < 16

Add 19 to each side

7x -19 +19< 16+19

7x< 35

Divide by 7

7x/7 < 35/7

x<5

Open circle at 5  going to the left

9+3x>12

Subtract 9 from each side

9-9 +3x >12-9

3x >3

3x/3 >3/3

x >1

Open circle at 1 going to the right

3 0
3 years ago
What is the significance of a correlation coefficient of 0.88?
AleksandrR [38]
The maximum positive value that the correlation coefficient can have is 1.
Thus, 0.88 is pretty close, indicating a positive slope for the regression line and points lying close to that line.


6 0
3 years ago
Find the value (64)3/2
faltersainse [42]
(64)^3/2 = (sqrt(64))^3 = 8^3 = 512.
3 0
3 years ago
I need help with question 2c
Step2247 [10]

Answer:

c

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Simplify the following: 3(-3 + 5x) -1 (4 - 4x)
Gnesinka [82]

3(-3 + 5x) -1 (4 - 4x)

Simplify each term by first using the distributive property with each set of parenthesis:

3*-3 + 3*5x - 1*4 -1* -4x

Now do the multiplications:

-9 + 15x -4 + 4x

Combine like terms

15x +4x - 9 -4

19x - 13

8 0
3 years ago
Other questions:
  • A population of 40 rats living near a restaurant dumpster is growing at a monthly rate of 50%
    14·1 answer
  • A shopper bought shoes marked $40.<br> The sales tax is 8%. How much did the<br> shopper pay in all?
    7·2 answers
  • TELE
    13·1 answer
  • For the function f defined b f(x)=x^2+2x+3 find f(-x), -f(x), and -f(-x).
    5·1 answer
  • What is the answer to this problem? Please help me
    7·1 answer
  • Which transformation of y = f(x) moves the graph 7 units to the left and 3 units down?
    7·1 answer
  • If AABC = ADFE determine the values of x and y.
    10·1 answer
  • ning Attempt 1 of 3 SECTION 3 OF 4 QU Use the rule y=-x+ 7 to fill in the blank. If (1, .y) is on the graph, then y=​
    6·1 answer
  • Find the measure of angle b.<br> 40°<br> A) 140°<br> C) 40°<br> B) 50°<br> D) 136°
    14·1 answer
  • Determine the slope of the line represented by y=5x-7 ?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!