a farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. if the fencing costs per linear foot to install and the farmer is not willing to spend more than , find the dimensions for the plot that would enclose the most area.

Answers

Answer 1

The constraint for the maximum enclosed area is the amount the farmer is

willing to spend on fencing.

The width of the plot that will give the most area, y = 83.[tex]\underline{\overline 3}[/tex] feet

The length of the plot that will give the most area, y = 125 feet

Reasons:

The given parameters are;

The cost of fencing per foot = $20

The maximum amount the farmer is willing to spend = $5000

Number of sides of fencing = 3 sides

Cost of the west side of the = Split with neighbor

Solution:

Let, y, represent the length of the fence, and let x represent the width of

the fence, we have;

Length of fence required = y + 2·x

Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x

Therefore;

Maximum amount to be spent on the fence, 5000 = 20·y + 30·x

[tex]\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x[/tex]

[tex]y = \mathbf{250 - \dfrac{3}{2} \cdot x}[/tex]

Area of a rectangle = Length × Width

The enclosed rectangular area of the fencing, A = y × x

[tex]\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2[/tex]

[tex]\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}[/tex]

The leading coefficient of the quadratic function of the area is negative,

therefore, the function only has a maximum point.

At the point of the most area, the slope, [tex]\dfrac{dA}{dx} = 0[/tex]

Finding the value of x at the maximum point, we get;

[tex]\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0[/tex]

Therefore;

[tex]\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}[/tex]

[tex]\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125[/tex]

The length of the plot that will give the most area, y = 125 feet

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Related Questions

Pls help me
On June 1, Mary had a balance of $50 in her bank account. During June she made the four transaction below.
Deposited $25.62
Withdrew $19.76
Wrote a check for $56.29
Paid a bank fee of $25

If there were no other transaction, what was the balance in Mary's account at the end of the month?

Answers

I got 137.15 by adding all the numbers

Answer:

The balance in Mary's account at the end of the month is $14.09

Step-by-step explanation:

Step 1: 50+25.62=75.62

Step 2: 75.62+19.76=95.38

Step 3: 95.38-56.29=39.09

Step 4: 39.09-25= $14.09

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Answer:

hexagonal prism

On a coordinate graph the following points of a rectangle are given. A(0,2) B (0,-2) C (3,-2) 4 Where do the coordinates of Dneed to be to form the rectangle? 0 (3,2) O (2, 3) 0 (1,3) 0 (3,1)​

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Answer:

(3, 2)

Step-by-step explanation:

Please mark me brainliest if this helped! :P

an electrician has 4.1 meters of wire.How many strips of 7 tenths can be cut?and how much wire will be left over?

Answers

If we’re talking about tenths, it would be .5 meters, with .6 meters of wire left over

0.5 meters per strip
0.6 meters left over

Which expression represents the area of this figure in square feet?

Answers

Answer:

(3×2) + (3×4)

Step-by-step explanation:

One box's area is 3×2 and the other box's area is 3×4, so when you add them, you get the total area.

Drag the numbers to order them from least to greatest.
0.7
-4.5
0.3
-0.5
2.3

Answers

Answer:

-4.5, -0.5, 0.3, 0.7, 2.3

Step-by-step explanation:

The higher the negative number the lower it really is.

Answer:

-4.5, -.5, .3, .7,2.3

Step-by-step explanation:

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Answers

Answer:

y = 5

Step-by-step explanation:

y = (1/4)x + 4

input (x) = 4

plug in 4 for x

y = (1/4)(4) + 4

y = 1 + 4

y = 5

URGENT!!!

Peggy sue decided to enter her famous “Five- Alarm chili” at her local chili cooking contest. Normally, she needs 5 tomatoes to make enough chili for her family of 7

A. How many tomatoes should she expect to use to make her famous recipe for 100 people?

b. When she gets to the contest, she realizes that she only packed 58 tomatoes. How many people can she expect to feed?

Answers

A. If she needs 5 tomatoes for a family of seven, then we need to find how many tomatoes it takes to feed only one person and then multiply that by 100z

5/7 = 0.714… tomatoes per person

Multiply this by one hundred

0.714 * 100 = 71.43 tomatoes.

Check:

5/7 = ?/100

Solve for ?

? = 71.43 tomatoes, but you technically can’t bring 0.43 tomatoes, so round that to 72 tomatoes

B. We would need to solve for

5/7 = 58/?

? = 81.2 people, but you should round down here because there isn’t enough chili for that 82 person, and there are not 20% of a person walking around looking for some chili.

What is the range of f(x)?

Answers

Answer:

{ f(x)| -∞ < f(x) ≤ 4 }

Step-by-step explanation:

The range of a function is the interval of every y-value represented on the function.  Since the highest this function goes on the y-axis is to y=4, we know that the upper limit of the range is 4, which is inclusive because the function actually reaches this value.  The function also appears to go down indefinitely on the right side, so the lower limit is -∞, which is non-inclusive because we will never reach that value.

The range is -∞ < f(x) ≤ 4

How much would it cost to buy three medium sodas and two hotdogs

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Answer:

depends how much they cost each

You have 4 cups of flour and you need to us 1 3/4 cups of flour for a cookie recipe.how much flour will you have left?

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That’s 4- 1 and 3/4. The answer is 2 and 1/4

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Answers

Answer:

x=3 and y= 4 / 3 (Fraction)

Step-by-step explanation:

Substitute x for 6y-5.

2(6y−5)−3y=2

Add 6y and 3y, and multiply 5 by 2/Simplify the equation.

9y−10=2

Add  10 to both sides, and then divide each side by 9.

9y−10+10=2+10

9y / 9 = 12 / 9

y = 4/3.

Repeat the process but replace y with 4/3!

Answer:

x=3

y= 4/3

Step-by-step explanation:

2(6y-5)-3y=2

y= 4/3

x=6x 4/3-5

x=3

Help needed, this is timed :’)

Answers

Answer:

Step-by-step explanation:

last answer

Which statement is an example of heat transfer by convection? Question 4 options: Jane's feet burned as she walked across the hot beach sand. Hot air from the sand rose and was replaced by cool air blowing in from the ocean as a sea breeze. The black asphalt of the parking lot was much warmer than the green grass surrounding the lot. People were scattered across the beach, sitting on chairs and towels, warming themselves in the bright sunshine.

Answers

Answer:

Step-by-step explanation

 Hot air from the sand rose and was replaced by cool air blowing from the ocean as a sea breeze.

A regular polygon has 45 sides.

Find the size of each of its exterior angles.

100 POINTS

Answers

Answer:

8

Step-by-step explanation:

360/45 = 8

We know

Sum of exterior angles of any polygon is 360°

Let every angle be x

[tex]\\ \sf\longmapsto 45x=360[/tex]

[tex]\\ \sf\longmapsto x=360/45[/tex]

[tex]\\ \sf\longmapsto x=8°[/tex]

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Answers

Answer:

No, they will need an additional £34 to stay the planned 10 nights.  

Step-by-step explanation:

Attached screenshot of a spreadsheet.

The cost for 10 nights for the 2 people is £100.

The tent site rental (over 10m^2) for 10 nights is £150.

Savings for the two over the 9 weeks is £216.

They will need an additional £34 to camp as planned.  

I suggest fibbing about the extra 0.5m^2 needed for the tent site.  That will reduce the bill by £30, so they are only £4 short.  Time to make a couple of friends.

The measures of angles x and y in the above figure is:

Answers

Step-by-step explanation:

sum of 2 angles on a straight line = 180°

therefore,

y + 120 = 180

y = 180 - 120 = 60

y = 60°

now apply angle sum property of triangle

now,

50 + x + y = 180

50 + x + 60 = 180

110 + x = 180

x = 180 - 110

x = 70

therefore, x = 70 & y = 60

hope this answer helps you dear! take care

Answer:

x = 70°

y = 60°

Step-by-step explanation:

hope it helps u

plzz plzz pLZZ MARK AS BRAINLIEST

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Answers

Step-by-step explanation:

a midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments (that create the midsegment triangle). A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side (due to similar triangles and their constant scaling factors, when one side of the similar triangle is half of the sys of the original triangle, then all its sides are half of their original counterparts).

the 3 sides of the main triangle are

2x + 5

3x - 1

5x

the perimeter of the main triangle is the sum of these :

2x + 5 + 3x - 1 + 5x = 10x + 4

since the sides of the midsegment triangle are all exactly half the length of the sides of the main triangle, also the perimeter of the midsegment triangle is half of the perimeter of the original triangle :

(10x + 4) / 2 = 5x + 2

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Answers

Answer:

21

Step-by-step explanation:

1) Simplify 1 + 2 to 3.

1 + 2 + 3 ×  ( 3 + 3 )

2) Simplify 3 + 3 to 6.

1 + 2 + 3 × 6

3) Simplify 3 × 6 to 18.

1 + 2 + 18

4) Simplify 1 + 2 to 3.

3 + 18

5) Simplify.

21

in the inequality 4> -4 which number appears farther right on a number line and why?

Answers

Answer:

4

Step-by-step explanation:

It is a positive number meanwhile -4 in negative.

The theater manager needs to set up 54 chairs for a show each row can be holed up to eight chairs the manager puts as many chairs in each row as possible how many rolls will the manager set up

Answers

Answer:

7 not 7 full rows though

Step-by-step explanation:

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Answers

Answer:

21

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

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Answers

Answer:

27 / 4x^6y^8.

Step-by-step explanation:

= 4 * 3^3 x^6 y^12 / 16 x^12 y^20

= 4*27 / 16 x^6y^8

= 4*27/ x^6y^8

= 27 / 4x^6y^8

reorder the steps of the proof to make sure that steps that are logically dependent on prior steps are in the proper order.


Given:

A

B





C

D



AB



CD

and

B

C





A

D



.

BC



AD

.


Prove:

A

C



AC

bisects

B

D



BD

.

Answers

Answer: a

Step-by-step explanation:

what is (x-2) (3x-4)=
a.3x² - 6x-8
b.3x² - 2x - 8
c.3x² + 10x + 8
d.3x² - 10x + 8

Answers

Answer:

D. 3x^2-10x+8

Step-by-step explanation:

[tex] \: \: \: \: \: [/tex]

D. 3x²- 10x + 8

hope it helps

refer to the attachment

[tex] \: \: \: \: \: [/tex]

Solve the equation by completing the
square. Enter the smallest solution first
and round to the nearest tenth.
s2 - 10s - 23 = 0
-
s = [?]
=

Answers

Answer:

s ≈ - 1.9 , s ≈ 11.9

Step-by-step explanation:

s² - 10s - 23 = 0 ( add 23 to both sides )

s² - 10s = 23

To complete the square

add ( half the coefficient of the s- term )² to both sides

s² + 2(- 5)s + 25 = 23 + 25

(s - 5)² = 48 ( take square root of both sides )

s - 5 = ± [tex]\sqrt{48}[/tex] ( add 5 to both sides )

s = 5 ± [tex]\sqrt{48}[/tex]

Then

s = 5 - [tex]\sqrt{48}[/tex] ≈ - 1.9 ( to the nearest tenth ) ← smaller solution

s = 5 + [tex]\sqrt{48}[/tex] ≈ 11.9 ( to the nearest tenth ) ← larger solution

-3 and -5 what is less, greater than , and or equal

Answers

Answer:

-3 is less and -5 is greater

Step-by-step explanation:

Answer:

less than

Step-by-step explanation:

because -5 would be less than -3 because it is bigger

Answer this middle school math equation for 30 points lol

Answers

Answer:

n

Step-by-step explanation:

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

Multiply both sides by -5:

[tex]-\frac{1}{5} (x-4)=-2[/tex]:

[tex]-\frac{1}{5} (x-4)*-5=-2*-5[/tex]

[tex]1(x-4)=10[/tex]

[tex]x-4=10[/tex]

Add 4 to both sides:

[tex]x-4+4=10+4[/tex]

[tex]x=14[/tex]

what is the unknown number to ( 6 x 2) + (6 x 3) = 6 x __

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Answer:

6

Step-by-step explanation:

6

I need help please !

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Answer:

y column: 1st = -7 , 2nd = -5 , 3rd = -3 , 4th = -1 , 5th = 1

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