A farmer decides to make three identical pens with 88 feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible?

Answers

Answer 1

Answer:

The long fence, AC = 44 feet

4 shorter segments at 11feet each = 44 feet

Area = 484 ft^2

Step-by-step explanation:

The three pens will share one fence section parallel to the barn, we'll call it AB.  Each pen will need two side fence segments, from the front fence to the barn.  We'll call those portions AC.  We need four of them:  two for the outer sides and two more to divide up the space equally among the three pens.  The total area would be AB*AC.

We know that AC + 4AB = 88 feet.

or AC = (88feet - 4AB)

Area = AB(88feet - 4AB)

Area = 88AB - 4AB^2

To maximize the area, we can take the first derivative and set it equal to zero:

Area' = 88 - 8AB

0 = 88 - 8AB

AB = 11 feet

AC = (88 - 4AB)

AC = (88 - 44)

AC = 44 feet

The fours segments of fence:  

AC + 4AB = 88 feet

(44) + 4(11 feet) = 88feet

Area = 44' x 11 ft' = 484 ft^2


Related Questions

for these two rates, calculate the unit rate and determine if these two rates are proportional

Answers

Yes because both equal 1.5 per pound

Tina needs 36 flowers for her next project. The flowers are sold in bunches
of 5.How many bunches will she need?

Answers

She will need at least 8 bunches

is y =6x a linear function

Answers

Answer:

Yes

Step-by-step explanation:

Here is the graph!

Yes.

y = 6x is a linear function because it makes a straight line on the graph. Also, the degree is 1.

____

Hope it helps ⚜

Raymond has 3 pounds of birdseed. He has 5 bird feeders in his yard. How much seeds can he put in each feeder?

Answers

Answer:

The answer is 0

Step-by-step explanation:

Based on the given conditions, formulate: 3 ÷ 5

Evaluate the equation/expression: 0.6

Find the largest integer less than or equal to : 0.6 : 0

Answer: 0

Use a calculator to solve this question. This cube has volume 50cm cube. Work out the length of the side of the cube to 2 dp.​

Answers

Let the length of the side of the cube be a.We know, volume of a cube = [tex] {a}^{3} [/tex]Volume of the cube = 50 cm cube.Therefore, length of the side of the cube

[tex] \sf \: = \sqrt[3]{50} \: \:cm \\ \sf \: = 3.68 \: cm[/tex]

So the length of the side of the cube is 3.68 cm.

Answer:

3.68 cm

Hope you could get an idea from here.

Doubt clarification - use comment section.

Calculate the volume of a sphere with radius 2.5 meters.
36.81 m3
65.45 m3
8.18 m3
26.18 m3

Answers

volume = the second answer = 65.45 m3

[tex]\huge \bf༆ Answer ༄[/tex]

Let's calculate the volume of sphere with :

radius = 2.5 m

[tex] \sf \: vol = \dfrac{4}{3} \pi {r}^{3} [/tex]

Now, plug the value of radius (r) and find volume ~

[tex] \sf \dfrac{4}{3} \times 3.14 \times 2.5 \times 2.5 \times 2.5[/tex]

[tex] \sf \dfrac{12.56}{3} \times \dfrac{25 \times 25 \times 25}{1000} [/tex]

[tex] \sf \dfrac{12.56 \times 15625}{3} \times \dfrac{1}{1000} [/tex]

[tex] \sf \approx65416.67 \times \dfrac{1}{1000} [/tex]

[tex] \approx65.416[/tex]

The value closest to it is 65.45

Therefore, that's the most appropriate choice ~

[tex] ꧁  \large \rm{kaul} \: ꧂[/tex]

Please help me!!!!!

Answers

Answer:

y = - [tex]\frac{2}{5}[/tex] (x - 5)² + 7

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (5, 7 ) , then

y = a(x - 5)² + 7

To find a substitute (10, - 3 ) into the equation

- 3 = a(10 - 5)² + 7 ( subtract 7 from both sides )

- 10 = 5²a = 25a ( divide both sides by 25 )

[tex]\frac{-10}{25}[/tex] = a , that is

a = - [tex]\frac{2}{5}[/tex]

y = - [tex]\frac{2}{5}[/tex] (x - 5)² + 7 ← in vertex form

Solve for g.
f=1/3(g+h-k)

help it’s timed

Answers

Answer:

g = 3f - h + k

Step-by-step explanation:

hope this helps! :D

have a miraculous day, and brainliest is immensely appreciated!! <3

Write an inequality that represents the graph

Answers

Step-by-step explanation:

first step is to define the line, and then, secondly find the right direction of the inequality.

we see a few nice points with integer coordinates.

the one on the y-axis is particularly helpful (0, 1), as it gives up the y- intercept right away (1).

another point is (1, 3).

so, the slope is

x changes by +1 (from 0 to 1)

y changes by +2 (from 1 to 3)

so the slope is 2/1 = 2

that means our equation is

y = 2x + 1

the graph says that the inequality is everything bigger than the line value, and the line is not included (dashed line).

so, we get

y > 2x + 1

James is from Rochester. Today, he has to travel to Cannon Falls for a morning meeting and then to Austin for an afternoon meeting and then home again. Cannon Falls is 45 miles directly north of Rochester. Austin is 42 miles directly west of Rochester. There is a nice straight road from Cannon Falls to Austin. Calculate the total distance he will be driving. Round your answer to the nearest mile.
(Drawing a map may be helpful.)

Answers

Answer:

His total distance is 149 miles.

Step-by-step explanation:

Use the Pythagorean theorem to find the value of the straight road from cannon falls to austin.  Then add that value with 42 and 45.

You invest $4,300 in an account that pays you an interest rate of 8.5%, compounded continuously. Calculate the balance of your account after 10 years. Round your answer to the nearest hundredth.

Answers

Answer:

The amount is $8358.7 and the interest is $3858.7.

Explanation:

STEP 1: To find amount we use formula:

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

Step-by-step explanation:

Select all relations that represent function

Answers

the first three i believe represent a function

nineteen students named lacrosse as there favorite sport. explain how to use the circle graph for the total number of students? 20% chosr swimming 42% chose volleyball and 38% chose laccrosse

Answers

The total number of students is 50

The number of students that named lacrosse as their favorite sport is given as:

[tex]Lacrosse = 19[/tex]

From the circle graph, 38% chose lacrosse.

So, the proportion of students that represent lacrosse is:

[tex]Lacrosse = 38\% \times Students[/tex]

Substitute 19 for lacrosse

[tex]19= 38\% \times Students[/tex]

Multiply both sides by 100

[tex]1900 = 38 \times Students[/tex]

Divide both sides by 38

[tex]50 = Students[/tex]

Rewrite as:

[tex]Students = 50[/tex]

Hence, the total number of students is 50

Read more about circle graphs at:

https://brainly.com/question/24461724

1.0.2217.9-(4.1 + 1.8)] -0.22+ [7.9 - 0.224

Answers

Answer:

hhhhhhhhhhhhhh

Step-by-step explanation:

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

31. What are the perimeter and area
of AXYZ?
Х
5
W
Y
m
12
12
9
greater than
and less than
Z
=
A P= 28; A = 540
B P=42; A = 84
© P= 50; A = 216
DP= 54; A = 57

Answers

Answer:

tbh idek bc the pen pen duck duck duck goose I don't know I'm doing this for the beginning part

PLZ HELP ME
NO LINKS PLZ

Answers

Answer:

the domain is -11,10 but i didnt know if you wanted that or not

Step-by-step explanation:

I really need help!
If two noncollinear segments on a coordinate plane have a slope of 3, what can you conclude?

Answers

Answer:

Two non co-linear segments with a slope of 3 in a coordinate plane would mean that the two segments are parallel to each other and not attached to each other. Having the same slope is the definition of being parallel in the same plane.

Step-by-step explanation:

MAS CARDS
5. Determine if the equation has one solution, no solution, or infinite
solutions.
-2(x – 3) + 5 = -6(x + 1) + 4x

One solution
No solution
Infinite solutions

Answers

No solution

-2(x-3)+5=-6(x+1)+4x

Multiply to get rid of the parentheses

-2 x X = -2x
-2x-3=6

6 x X = 6x
6x1=6

New equation = -2x+6+5=-6x+6+4x

Add same

6+5=11
-6x + 4x = -2x

New equation = -2x+11=-2x+6

That just doesn’t work

Answer:

No solution

Step-by-step explanation:

-2(x-3)+5= -6(x+1)+4x

First Distribute:

-2x+6+5= -6x-6+4x

Then transfer all variables to one side and the rest to other side:*when transfer u turn to opposite number for example: -6x will transfer to 6x

6+5+6= -6x+4x+2x

Last solve

17=0

no solution

X
Multiply by taking
Multiply.
20 X 600
Stuck? Review related articles/videos or use a hint.

Answers

20 x 600 = 12000
…………

Describe the slope of the line with the equation
y = -4x + 10.

A: positive slope

B: negative slope

C: zero

D: undefined

Answers

[tex]\huge \tt༆ Answer ༄[/tex]

The given equation of the line is in slope intercept form, and if we equate the given equation with general equation of line (y = mx + c) , we will get slope (m) = -4

And therefore, the slope of the line is B

Negative


Here is a trapezium.
20 m
Jenny wants to work out the area of
the trapezium.
13 m
She writes:
13 m
N
12 m
area =-
ol
(20+30)(13)
+5 m
+5 m
=(10+30)(13)
= 40x13
= 520 m²
What two mistakes did Jenny make in her method?

Answers

Answer:

Jenny wants to work out the area of

the trapezium.

13 m

She writes:

13 m

N

12 m

area =-

Step-by-step explanation:

I AM ON MY LAST BRAINLY POINTS! NOBODY WILL HELP ME T-T! EVERYBODY SENDS ME RANDOM LINKS! IF U HELP ME U CAN GET THE CROWN
David mixed 5 3/8 cups of popcorn with 3 5/8 cups of pretzels. He then divided the snack into bags with 2/3 cups in each. After dividing, how many bags of snack bags will David have?

Answers

Answer: 13.5 bags

Explanation:

5 3/8 = 43/8

3 5/8 = 29/8

43/8 + 29/8 = 9

9 divided by 2/3 is 13.5

Hope this helps :)

Answer:

[tex]13 \frac{1}{2} [/tex]

Step-by-step explanation:

So first we can add the two snack together

So the

[tex]5 \frac{3}{8} + 3 \frac{5}{8} = 9[/tex]

Once we have that we can say 9÷2/3

And this will give us 13.5 or 13 and a half.

I really hope this helps

5. What linear function defines the following Arithmetic Sequence?
-4, -1, 2, 5, 8,...
an = 4 - 3(n-1)
an = -4 -3(n-1)
an = 4 + 3(n - 1)
an = -4 + 3(n - 1)

Answers

Answer

A

Step-by-step explanation:

The linear function defines the arithmetic sequence is an = -4 + 3(n - 1). The correct option is D.

What is an arithmetic progression?

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given series is -4, -1, 2, 5, 8. The common difference of the series is  calculated as,

d = -1 - ( -4 )

d = -1 + 4

d = 3

The equation will be written as,

an = a₁ + d(n - 1)

an = -4 + 3(n - 1)

Therefore, the linear function that defines the arithmetic sequence is an = -4 + 3(n - 1). The correct option is D.

To know more about arithmetic progression follow

https://brainly.com/question/6561461

#SPJ2

Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width. What is the perimeter of Janice's fence if the area of her garden s 5,670 square feet?

Answers

Answer:

P = 342 ft

General Formulas and Concepts:

Pre-Algebra

Evaluations

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Distributive Property

Algebra I

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Terms/Coefficients

Factoring/Expanding

Quadratics

Solving quadratic equationsStandard Form: ax² + bx + c = 0

Geometry

Area of a Rectangle Formula: A = lw

l is lengthw is width

Perimeter of a Rectangle Formula: P = 2w + 2l

l is lengthw is width

Step-by-step explanation:

Step 1: Define

Identify variables.

A = 5670 ft²

"Length that is 9 feet less than 3 times its width" → l = 3w - 9

Step 2: Find w

Substitute in variables [Area of a Rectangle Formula]:                                w(3w - 9) = 5670[Distributive Property] Expand:                                                                      3w² - 9w = 5670[Subtraction Property of Equality] Rewrite [Standard Form]:                      3w² - 9w - 5670 = 0[Quadratic] Factor:                                                                                          3(w - 45)(w + 42) = 0[Quadratic] Solve [Find roots]:                                                                      w = -42, 45

Since length/width cannot be negative, we know that w = 45 ft.

Step 3: Find l

Substitute in w [Length Formula]:                                                                   l = 3(45) - 9[Order of Operations] Evaluate:                                                                       l = 126 ft

Step 4: Find Perimeter

Substitute in variables [Perimeter of a Rectangle Formula]:                        P = 2(45 ft) + 2(126 ft)[Order of Operations] Evaluate:                                                                      P = 342 ft

∴ The perimeter of Janice's fence is 342 ft.

Let width be x ft

Length be 3x-9ft

Now

Area=Length ×Breadth5670=x(3x-9)5670=3x²-9x3x²-9x-5670=0

On solving we wI'll get x=-42,45

Take it positive

x=45width=45ftLength=3(45)-9=135-9=126ft

Now

Perimeter

2(Length+Width)2(45+126)2(171)342ft

No files please help me on this for math

Answers

Answer:

y=3x+8

Step-by-step explanation:

Answer:

y=1.5x+11

Step-by-step explanation:

A smoothie calls for of a peach, 8. of a banana, and a kiwi. What is the total quantity of fruits used for the smoothie​

Answers

No of banana and kiwi = 8

So,

= 8×8

=64

what does x equal?
3/4(x+21)=10 1/2

Answers

x= -7

Hope this helps :)

At the bakery shop, each baker works at his or her own speed, making the same number of cakes each day. Marissa makes 28 cakes in 2 weeks, Carlos makes 60 cakes in 20 days, and Shelby makes 5 cakes in 2 days.
When the shop owner graphs the relationship between the number of cakes made and days, who has the steepest graph? Explain.

Answers

Answer:

The rate of speed is Carlos

Step-by-step explanation:

M- 28 c in 14 days

C- 60 c in 28 days (2x as much as M)

S- 5 c in 2 days

Solve the inequality:
12+x≥3(x-6)​

Answers

Hello there! :)

The first step is to use the Distributive Property.

It states that

a(b+c)=ab+ac

Let's distribute 3, using this property:

3(x-6)=3x-18

Now, our inequality looks like so:

12+x≤3x-18

The next step is to move the variables to the left, using the opposite operation:

12+x-3x≤-18

12-2x≤-18

Now, move all the numbers to the right, using the opposite operation:

-2x≤-18-12

-2x≤-30

Divide both sides by -2 to isolate x.

Remember that when we divide by a negative variable, we change the inequality sign:

x≥15

Therefore, x≥15

Hope it helps.

~A lonely teen who helps others with a smile

-Grace :-)

Good luck.

what is the value of the 4 in the number 546210?
give your anwer in words

Answers

Answer:

1000

Step-by-step explanation:

Answer:

10000 or 40000 pls mark this answer as brain list

Other Questions
In physics, power is __________.a. how fast something does workb. how much force something can applyc. how strong something isd. how much work something can do Which are two molecular groups that distinguish proteins from carbohydrates? A circle has a radius of 15 centimeters and an area of 225 cm2. If the radius is multiplied by 3, what is the area of the new circle? What did the European conquerors and colonists bring to the Americas that made iteasier to subdue the Native American populations and then prompted them to lookfor slaves in Africa instead of the Americas?O FirearmsO SugarcaneO ChristianityO Diseases do you think that the third level was a medium of escape for charley ?why? Q.What may be the causes behind decreasing the export in foreign trade. Mention at least 5-6 causes. a race car is traveling at a speed of 80.0m/s on a circular race track of radius 450m what is the centripetal acceleration Convert -439 to radians In a paragraph of at least five sentences, answer the question: do you agree with picasso's claim that "the urge to destroy is also a creative urge"? include at least one specific reference to each excerpt in your response. Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x 3)?(0,6)(0,6)(6,0)(6,0) Select all the correct answers.What is the purpose of using subheadings as a text feature in your writing?increases reading comprehensionintroduces new informationorganizes the informationcondenses the essaydescribes keywords to know The height of a tennis ball tossed into the air is modeled by h(x) = 40x " 16x 2, where x is elapsed time in seconds. During what time interval will the tennis ball be at least 15 feet above the ground? x > 0. 5 seconds and x > 2. 04 seconds x > 0. 5 seconds and x 2. 04 seconds x 0. 5 seconds and x > 2. 04 seconds x 0. 5 seconds and x 2. 04 seconds. Laying fiber-optic cable is expensive. Cable companies want to make sure that if they extend their lines to less dense suburban or rural areas, there will be sufficient demand so the work will be cost-effective. They decide to conduct a survey to determine the proportion of households in a rural subdivision that would buy the service. They select a simple random sample of 5 blocks in the subdivision and survey each family that lives on one of those blocks.a. What is the name for this kind of sampling method?b. Give a possible reason why the cable company chose this method. some African American students sued their states for not providing a quality education. These students wanted public schools to 20.Cuando yo (tener) once anos, yo fui a Disney con mi familia. *1 pointtienetenatenamostuve If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books? Seven tickets for a Broadway show cost $385. How much will only 4 tickets cost? You see a whiteboard that has 8-10 years olds, interested in horses written on it. This is MOST likely a description of:A. data management.B. target users.C. GUI.D. iterative development. You find an infant in a safe environment who is not moving and not breathing normally. What would be the correct course of action? Based on the electron configuration of the twoatoms, predict the ratio of metal cationic (+) atomto nonmetal anionic (-) atom in the compound.Hydrogen 1sFluorine 1s22s22p5A. 2:3B. 1:2C. 1:1D. 3:2