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

Someone help me pls!

You can buy 3 apples at Quick Mart for $1.17. You can buy five of the same apples at Shop & Save for $2.40

How much will you save per apple if you buy them at the cheaper store?

Answers

Answer:

$0.09 or 9 cents

Step-by-step explanation:

1.17/3=0.39

2.4/5=0.48

0.48-0.39=0.09

Answer:

Well you can divide them by each

1.17/3 which is 0.39 (quick mart)

2.4/5 Which is 0.48 (stop and save)

39 cent is what you pay at the cheaper store

9 cents is what you would save

-also you go to bay academy?

I haven’t seen Jupiter ed in so long hahah

Help me please!
Mathematics

Answers

Answer:

x=12

Step-by-step explanation:

i'm assuming the numbers are the lengths of each segment. 8/24 = 1/3, so 4/x=1/3, cross multiply to get x=12

Can someone help with this please?

Answers

Answer:

900

Step-by-step explanation:

Might wanna double check. I rushed

(7m-2m^2n)^2

-42+144

900

what is 5 taken away from the product of 4 and a number. ​

Answers

Answer:

3

Step-by-step explanation:

Not sure, but let's take 32 to be the answer

4(5+x)=32

4×5= 20

4×x= 4x

20-4x=32

4x=32-20

4x=12

12÷4

x=3

Answer:

4n - 5

Step-by-step explanation:

let the number be n then the product of 4 and this number is 4n

Subtract 5 from 4n gives

4n - 5

Use the properties of multiplication to solve.

(4 x 13) x 25

Answers

1300 because you times 4 by 13 to get 52 and times that by 25
1300 bc I times then add

299 divided by 21 step by step

Answers

Step 1:
Start by setting it up with the divisor 21 on the left side and the dividend 299 on the right side like this:

2 1 ⟌ 2 9 9

Step 2:
The divisor (21) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:

0
2 1 ⟌ 2 9 9

Step 3:
Multiply the divisor by the result in the previous step (21 x 0 = 0) and write that answer below the dividend.

0
2 1 ⟌ 2 9 9
0

Step 4:
Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.

0
2 1 ⟌ 2 9 9
- 0
2

Step 5:
Move down the 2nd digit of the dividend (9) like this:

0
2 1 ⟌ 2 9 9
- 0
2 9

Step 6:
The divisor (21) goes into the bottom number (29), 1 time(s). Therefore, put 1 on top:

0 1
2 1 ⟌ 2 9 9
- 0
2 9

Step 7:
Multiply the divisor by the result in the previous step (21 x 1 = 21) and write that answer at the bottom:

0 1
2 1 ⟌ 2 9 9
- 0
2 9
2 1

Step 8:
Subtract the result in the previous step from the number written above it. (29 - 21 = 8) and write the answer at the bottom.

0 1
2 1 ⟌ 2 9 9
- 0
2 9
- 2 1
8

Step 9:
Move down the last digit of the dividend (9) like this:

0 1
2 1 ⟌ 2 9 9
- 0
2 9
- 2 1
8 9

Step 10:
The divisor (21) goes into the bottom number (89), 4 time(s). Therefore put 4 on top:

0 1 4
2 1 ⟌ 2 9 9
- 0
2 9
- 2 1
8 9

Step 11:
Multiply the divisor by the result in the previous step (21 x 4 = 84) and write the answer at the bottom:

0 1 4
2 1 ⟌ 2 9 9
- 0
2 9
- 2 1
8 9
8 4

Step 12:
Subtract the result in the previous step from the number written above it. (89 - 84 = 5) and write the answer at the bottom.

0 1 4
2 1 ⟌ 2 9 9
- 0
2 9
- 2 1
8 9
- 8 4
5

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 299 divided by 21 calculated using Long Division is:

14
5 Remainder

slope of a line perpendicular to the line whose equation is 6x+4y=−56, fully reduced

Answers

Answer: Answer

1.0/5

1

angelinagalindo127

Ambitious

40 answers

2.2K people helped

Answer:

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.Step-by-step

Step-by-step explanation: |\   /|

\|_|/

/. .\

=\_Y_/=

{>o<}

(a) 3 - 2/3÷4/3 × 7
(b) [(2/3)/(5/6)]-2/5
(c) {(-3/4) +( 1/2)}/{(2/5)-(5/2)}

Answers

Step-by-step explanation:

a. (3 - 2/3) ÷ (4/3 x 7)

= [(3 x 3) / (1 x 3) - 2/3] ÷ 28/3

= (9/3 - 2/3) ÷ 28/3

= 7/3 x 3/28

= 21/84

= (21 x 1) / (21 x 4)

= 1/4

b. 2/3 ÷ 5/6 - 2/5

= 2/3 x 6/5 - 2/5

= 12/15 - 2/5

= (3 x 4) / (3 x 5) - 2/5

= 4/5 - 2/5

= 2/5

c. (- 3/4 + 1/2) ÷ (2/5 - 5/2)

= [- 3/4 + (1 x 12) / (2 x 2)] ÷ [(2 x 2) / (5 x 2) - (5 x 5) / (2 x 5)]

= (- 3/4 + 12/4) ÷ (4/10 - 25/10)

= 9/4 ÷ (- 21/10)

= 9/4 x - 10/21

= - 90/84

= (6 x - 15) / (6 x 14)

= - 15/14.

If you have any doubt, then you can ask me in the comments.

simpify 5 cubed to the power of 6
[tex]5 cubed to the power of 6[/tex]

Answers

[tex]\displaystyle (5^3)^6 = 5^{(3 \times 6)} = 5^{18}[/tex]

(5^3)^6 = 5^6x3 —> = 5^18

If one ream of bond paper costs (3x -4) pesos. How many reams can you buy for ( 6x4 -17x3 +24x2- 34x + 24) pesos?

Answers

Answer:

1 ream = (3x - 4) pesos

Price of n reams = (6x^4-17x^3+24x^2 34x+24) pesos

Solution:(pic1)

number of reams 3x-4

By using synthetic division,

3x-4=0

3x=4

x=4/3

6 -17 24 -34 24 | 4/3

8-12 16-24

6 -9 12-18 0

Final equation is:(pic2)

Which statement about the graphs of these two functions is true?

Answers

Answer:

Both graphs intersect the x-axis to the right of 0

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9

Answers

Answer:

think its a

Step-by-step explanation:

the slope is 2/1 but both y int are different

Emily spends $28 on food. This amount of 4/9 of her allowance, what is Emily’s allowance?


please help with explanation !

Answers

Answer:

$63

Step-by-step explanation:

so we want to find 9/9 of her allowance, which is 100%

we could use a proportion:

let 'a' = full allowance

[tex]\frac{28}{1}[/tex] ÷ [tex]\frac{4}{9}[/tex] = [tex]\frac{a}{1}[/tex] ÷ [tex]\frac{9}{9}[/tex]

when we divide fractions we multiply by the reciprocal to get:

28 x 9/4 = a

a = 252/4

a = 63

4 * 4 * 4 * 5 * 5
help please

Answers

Answer:

=1600

Step-by-step explanation:

=4*4*4*5*5

=16*4*25

=64*25

=1600

Hope this helps, have a nice day/night! :D

which problem solving strategy would be best to solve this problem?

To study for the spelling competition, Jose memorized 2 words from the list. The next day, Jose memorized 4 words from the list. The third day, Jose memorized 8 words from the list. If Jose continues, how many words will he memorize on the tenth day

A.look for a pattern

B.work backwards

C.write an equation

D.guess, check and revise​

Answers

Answer:

The best solving strategy is D. Finding a pattern would be decent, but D clearly is an better answer,

Step-by-step explanation:

Which of these are prime numbers 5,6,9,13,18

Answers

Answer:

5 and 13

Step-by-step explanation:

Answer:

13

is the answer

Hope it help u

Which street is perpendicular to 2nd Avenue and I also need to know what the slop would be of the new road be perpendicular to D street

Answers

Answer:

the answer is d street :)

sami is making necklaces for a craft show. each necklace is 33.4 cenimeters long. if she has 233.8 centimeters of cord, how many necklaces can sami make

Answers

Answer:

Sami can make 7 necklaces.

233.8cm ÷ 33.4 = 7

The power, P(watts), of a car engine is proportional to the square of its speed, s(m/s).
When s=45 P=2200.
Work out the speed (to 1 DP) when the power is 1890 watts

Answers

The speed of the car is 41.7 m/s when the power is 1890 watts.

What is Proportion?

Proportion is defined as an equation on which two or more ratios are made to be equal to each other.

It is given that the power, P is proportional to square of the Speed,s.

If P ∝ s², then P = k s², for some constant k.

When s = 45 m/s, P = 2200 watts

k = P / s² = 2200 / 45² = 1.086

∴ when P = 1890 watts,

1890 = 1.086 × s²

s² = 1740.331

s = 41.717 ≈ 41.7 m/s

Hence, if power is proportional to the square of the speed, then, the speed of the car engine is 41.7 m/s if the power is 1890 watts.

To learn more about Proportion, click:

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Solve 22 x 104 = ________. (1 point) A. 2,200,000 B. 220,000 C. 22,000 D. 2,200

Answers

Solution:

[tex]22 \times {10}^{4} \\ = 22 \times 10 \times 10 \times 10 \times 10 \\ = 22 \times 10000 \\ = 220000[/tex]

Answer:

B. 220,000

Hope it helps.

Do comment if you have any query.

22*10^4
22*10000
220,000

The answer is B

[tex](3a^{3} -7b^{3} )^{2}=[/tex]

Answers

Answer:

Step-by-step explanation:

1.02 = _____ hundredths

Yo the anwser is freaking 69

Se tiene la siguiente proporción 2/5=8/x cual es el valor de x para que esta sea verdadera?

Answers

Es 20 si divides 2/5 te da 0.4 y si divides 8/20 te da 0.4 lo que hace que 2/5 = 8/20 sea verdad

What is y x y x y simplified

Answers

Answer:

y x y x y is simplified as y³

Step-by-step explanation:

Hoped this helped.

Answer:
Y x Y x Y is simplified as y^3

Hope this helps!!!

PLEASE HELP ME ASAP TYSM

Answers

The sale price is 85% of the regular price.

-If regular price is 100% and there is a 15% discount, The sale price will be 85% of reg. price.

100-15=85

Answers:

- Sale price: $25.50

-85%of 100%

-Discount: 15%

-$4.50

You can check by the following:

30-25.5=4.5

30-4.5=25.5

4.5+25.5=30

25.5+4.5=30

100-15=85

100-85=15

85+15=100

15+85=100

(Brainliest?) ^^

Use parallelogram ABCD. What are the values of x and

y?

A

4y-3

B

x=

y =

3x-9

42

D

37

С

Answers

Answer:

the value of x is a number but you can say 1 when you are factorising quadratic expression with the terms

Answer:

x=17

y=10

Step-by-step explanation:

Find the quotient: 8,441 ÷ 21 = ________. (1 point)
400 r 12
400 r 20
401 r 12
401 r 20
Pls Help ASAP!!! Thank you!!

Answers

Answer:

401 r 20

Step-by-step explanation:

It would equal to 401 r 20.

Two numbers have a sum of 24 and a difference of 5. Use and algebraic method to find the two numbers.

Answers

Step-by-step explanation:

x, y are the 2 numbers

x + y = 24

x - y = 5

x = y + 5

and that in the first equation

y + 5 + y = 24

2y = 19

y = 9.5

x = y + 5 = 9.5 + 5 = 14.5

the 2 numbers are 9.5 and 14.5.

Explain relative dating and its relationship to the Law of Superposition

Answers

Answer:

its b i took the test

Step-by-step explanation:

its b


What’s the slope or fraction?

Answers

Two ways to do this
You can draw a triangle from (6,10) and (0,8), then count from vertical to horizontal: 2 triangles/6 triangles
The slope is 2/6 or 1/3

You can also use slope formula
First find any two points on graph
(0,8) and (3,9)
Remember: (y2-y1)/(x2-x1) = slope
(9-8)/(3-0) = 1/3

The slope is 1/3

4.) You paid $51 for four tickets to a play. What is the unit price?
O $12.75
$12.50
O $13.00
$12.00

Answers

Answer:

$12.75

Step-by-step explanation:

To find the unit price of something divide the cost by the amount of the Item

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