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

The ratio of taxis to buses to bikes
is 12:5:18.
How many buses are there if there
are 72 bikes?

Answers

Answer:

20 buses

Step-by-step explanation:

Using the given ratio, we can see that for every 12 taxis, there are 5 buses and 18 bikes.

To get from 18 bikes to 72 bikes, we multiply by 4. Therefore, to figure out the number of buses, we multiply it by 4.

5 * 4 = 20

Hope this helps! :D

What is the probability of rolling an even number on a number cube and flipping a tails on a coin?

Answers

Answer:

25% or 1 in 4 chance.

Step-by-step explanation:

The chances for rolling an even number are 3/6, because there are 6 numbers total, and 3 are even.

3/6 can be re-written as 1/2.

The chances of landing tails are also 1/2, because there are 2 sides and tails is one of them.

So then, multiply 1/2 by 1/2 to get 1/4.

please help quick

Which equation has only two solutions: x=3
and x=−3
?

A
x2=6

B
x3=27

C
x2=9

D
x3=9

Answers

Answer:

x^2 = 9

Step-by-step explanation:

Both 3 and -3 are 9 when squared.

Will give BRAINLIEST

Answers

Answer:

Point B is

Step-by-step explanation:

Answer:

B (-2,-4)

Step-by-step explanation:

help plz (asap) ..............................................................................

Answers

Answer:

oof u alone kid

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

(08.06 MC)
Based on the graph, what is one solution of the equation f(x) = g(x)?
f(x)
(
g(x)

A x=-3.5
b x=-1
c x = 0.25
d x=-2

Answers

Answer:

A:  X= -3.5  

I just took the test, and I chose -1 and got it wrong and I looked back on the answer and that's what the answer said. Sorry if I was late, but good luck.

What is the slope from the equation: 2x + 9

Answers

Answer:

If you want a angle the angle is positive and the answer is M=2

Step-by-step explanation:

The answer is M=2

The base area of a box is 36 square inches. If the volume of the box is 108 cubic inches, what is the height of the box?

Answers

The height of a box that has a base area of 36 sq. in. and a volume of 108 cubic inches is: 3 inches.

Recall:

The formula for the volume of a box = base area × height

Given the following dimensions:

base area of box = 36 sq. in.

Volume = 108 cubic inches.

Required: height of the box

Plug in the given values into the formula for the volume of a box

108 = 36 × height

Divide both sides by 36

height = 108/36

height = 3 inches

Learn more about the Volume of a box on:

https://brainly.com/question/14957364

h(x) = 4x + 3; Find h(1)

Answers

Answer:

h(1) = 7

Step-by-step explanation:

h(x) = 4x + 3

h(1) = 4(1) + 3

h(1) = 4 + 3

h(1) = 7

A 16-ounce can of mixed nuts includes 6 ounces of cashews and 10 ounces of almonds. What is the ratio of almonds to mixed nuts in this can of nuts?

Answers

Step-by-step explanation:

Total=16 ounces

Ratio of almonds to mixed nuts

almonds:mixed nuts

10 : 16

5 : 8

At a restaurant, 30% of customers donate to charity in exchange for a coupon. Estimate the probability that it will take at least four customers to find one who donates.

Answers

Answer:

75.99%

Step-by-step explanation:

To calculate this, we can use complements. We can find, instead the probability that at least one will donate, the probability that not none of them will donate.

First, we can find the probability that none will donate, which will be (70%)^4, since the chance each will not donate is the same. From this we get 24.01%.

To find the probability that at least one donates, we do the complement:

100%-24.01%=75.99%

Solve the system with elimination:
5x - y =1
10x + 3y = 7

Answers

Answer:

X = 2/5

y = 1

Is this what your looking for?

Step-by-step explanation:

Solve the system with elimination:
5x - y =1
10x + 3y = 7

Answer x= 1

120% of what number is
54?

Answers

Answer:

45

Step-by-step explanation:

Help on these two please

Answers

Answer:

21

Step-by-step explanation:

CANT SEE THEM

Which ordered pair is a solution to the line whose equation is 2y=-3x-2
A.(2, -3) C. (2, -4)
B. (-3, 2) D. (-4, 2)

Answers

Answer:

The solution would be C. (2, -4)

Step-by-step explanation:  Equation: 2y = -3x - 2

1. (2, -3)

  2(-3) = -3(2) - 2

  -6 = -6 - 2

  -6 = -8   (Not a solution)

2. (-3, 2)

   2(2) = -3(-3) - 2

   4 = 9 - 2

   4 = 7   (Not a solution)

3. (2, -4)

   2(-4) = -3(2) - 2

   -8 = -6 - 2

   -8 = -8   (Solution)

4. (-4, 2)

   2(2) = -4(-4) - 2

   4 = 12 - 2

   4 = 10   (Not a solution)

-4-(-8) divided by 4

Answers

Answer:

1

Step-by-step explanation:

-4 minus -8 is the same as 8 - 4 which is 4 and 4 divided by 4 is 1.

Answer:

8

Step-by-step explanation:

2. The wholesale price of the skirt is $12 and the retail price is $24.
How much is the markup?
nah
So ein
What percent of the wholesale price is the markup?

Answers

With the sale price being $12 and the retail price being 24, it is a 12 dollar markup or 50% considerably.

Katie earns 15$ each hour. Round to total time katie worked to the nearest hour and estimate her pay by using mulitplacation

Answers

Answer:

How long did she work for though?

Step-by-step explanation:

Write an equation of the line that is parallel to the y-axis and goes through the point (-2, 5)

Answers

f it is parallel to the y-axis, it is a vertical line passing through (-2 ,5). The equation is just

x = -2

is -2x+3 the same as 2x-3

Answers

Answer:

no they are different numbers, however their signs are inverted

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

-2x+3 is not the same as 2x-3 because, let's say we set each equation equal to something...

-2x+3 = 10                   2x-3 = 10

     -3     -3                      +3    +3

------------------              -----------------

-2x = 7                        2x = 13

x = [tex]\frac{7}{2}[/tex]                               x = [tex]\frac{13}{2}[/tex]

x = 3.5                           x = 6.5

As we can see, these equations are not the same, because, when we set them equal to the same value, the answers are different.

Hope this helps! :D

What is the distance between the following points?



Answer choices


A 9


B 10


C square root of 21


D square root of 58

Answers

Answer: 9 is incorrect the anwser is acactually D . The square root of 58

Step-by-step explanation:

f (x) = 3 (x– 4)^2– 12

based on this value, select ALL that APPLY for the following function:

Answers

Answer:

see explanation

Step-by-step explanation:

Given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

Then the discriminant Δ = b² - 4ac informs us about the nature of the zeros

• If b² - 4ac > 0 then 2 real and irrational zeros

• If b² - 4ac > 0 and a perfect square then 2 real and rational zeros

• If b² - 4ac = 0 then 2 real and equal zeros

• b² - 4ac < 0 then zeros are not real

Given

f(x) = 3(x - 4)² - 12 ← expand factor using FOIL

     = 3(x² - 8x + 16) - 12 ← distribute parenthesis by 3

     = 3x² - 24x + 48 - 12

     = 3x² - 24x + 36 ← in standard form

with a = 3, b = - 24 , c = 36 , then

b² - 4ac

= (- 24)² - (4 × 3 × 36

= 576 - 432      

= 144 ← a perfect square

Then 2 zeros are real and rational  and produce 2 x- intercepts

Write the word sentence as an equation. Then solve.
19 more than a number c is 4.

Answers

[tex]19+c = 4\\\\\implies c = 4-19 = -15[/tex]

Average 8, 14, and 11

Answers

Answer:

Step-by-step explanation:

you add 8,14, and 11 to get 33 then you divide it by 3, because there are 3 numbers meaning the average is 11.

If that makes, all you have to do is add up all the numbers then divide by the amount of numbers you see to find the average of the numbers.

[tex]\huge\text{\bf Hey there!}[/tex]

[tex]\large\text{The word \underline{average} is basically the \boxed{\bf mean} of a data set. When you }\\\large\text{hear or see the word \underline{average} in math think of its asking you to \boxed{\bf find \ your \ total}}\\\large\text{in your data set.}[/tex]

[tex]\large\text{Here is the formula to make it easier to solve}\downarrow[/tex]

[tex]\mathbf{mean = \dfrac{sum\ of\ all\ terms}{number\ of\ terms}}}[/tex]

[tex]\large\text{YOUR EQUATION:}[/tex]

[tex]\mathbf{average = \dfrac{8 + 14 + 11}{3}}[/tex]

[tex]\mathbf{\dfrac{8 + 14 + 11}{3}}[/tex]

[tex]\mathbf{= \dfrac{22 + 11}{3}}[/tex]

[tex]\mathbf{= \dfrac{33}{3}}[/tex]

[tex]\mathbf{= \dfrac{33\div3}{3\div3}}[/tex]

[tex]\mathbf{= \dfrac{11}{1}}[/tex] [tex]\mathbf{\rightarrow 11\div1}[/tex]

[tex]\mathbf{= 11}[/tex]

[tex]\huge\boxed{\text{Therefore, your answer should be: \textsf{11}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

a. Examine the zeros of the graph, and write a function that models this situation.


b. After 10 minutes, the elevation model changes and is given by the function Use the Edmentum Graphing Tool to graph this function. Capture a screenshot of your graph, and paste it in the space provided.

Answers

Answer:

See below

Step-by-step explanation:

A) We have zeroes at (2,0) (3,0) (5,0) (9,0) and (10,0). Therefore, we can write the function as (x-2)(x-3)(x-5)(x-9)(x-10) = x⁵-29x⁴+311x³-1519x²+3360x-2700

B) View attached screenshot for reference

Given the graph below. What is the axis of symmetry (vertex)of the parabola?

Answers

Answer:

Answer:

safe speed for the larger radius track u= √2 v

Explanation:

The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.

Also given that r_1= smaller radius

r_2= larger radius curve

r_2= 2r_1..............i

let u be the speed of larger radius curve

now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=

r

1

mv

2

=

r

2

mu

2

................ii

form i and ii we can write

v^2= \frac{1}{2} u^2v

2

=

2

1

u

2

⇒u= √2 v

therefore, safe speed for the larger radius track u= √2 v

what is 12x⁸/3x² in simplest form, where x>0?

Answers

[tex] \frac{12 {x}^{8} }{3 {x}^{2} } \\ = \frac{12}{3} {x}^{8 - 2} \\ = 4 {x}^{6} [/tex]

Answer:

[tex] {4x}^{6} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

25 Points!! :D

Complete the interphase part of the data from your data table.

Answers

Answer: you should have gotten a pic that shows all the cells phases just count the interphase ones however in the interphase cells spend 90% of its life cycle in this phase

While working for a lawn service company, Austin figures he earns $5 for edging 20 feet of curb. If he edges 50 feet of curb at the same rate, how much will Austin earn?

Power Lawn Edger

x=13 1/2 or 13.50$
x=12 1/2 or $12.50
x=14 3/4 or 14.75
x=12 or 1/4 or $12.25

Answers

X= 12 is your answer explanation?
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