There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).​

There Is 1500 Ft Of Fencing Available To Make 6 Identical Pens. Find The Maximum Area For EACH Pen (meaning

Answers

Answer 1

Answer:

The maximum area is therefore is 93750 ft²

Step-by-step explanation:

The given parameter are;

The a]length of fencing available = 1500 ft.

The perimeter of the figure = 9·x + 4·y

Therefore, 9·x + 4·y = 1500 ft.

The area of the figure = 6 × (x × y) = 3·x × 2·y

From the equation for the perimeter, we have;

9·x + 4·y = 1500

y = 1500/4 - 9/4·x = 375 - 9/4·x

y = 375 - 9/4·x

Substituting the value of y in the equation for the area gives;

Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²

Area = 2250·x - 27/2·x²

The maximum area is found by taking the derivative and equating to zero as follows;

d(2250·x - 27/2·x²)/dx = 0

2250 - 27·x = 0

x = 2250/27 = 250/3

x = 250/3

y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5

The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²

The maximum area is therefore = 93750 ft.²


Related Questions

Kyra observed that 85% of the students at a library liked reading mystery stories. If 30 students at the library did not like reading mystery stories, the number of students at the library who liked mystery stories was _____. (only put numeric values, no other symbols)​

Answers

Answer:

The first thing we must do is find the percentage of students who do not like to read mystery stories.

We have then:

Then, to find the number of students who like to read mystery stories, we can make the following rule of three:

15% ----------------> 30 students

85% ----------------> x

From here, we clear the value of x.

We have then:

the number of students at the library who liked mystery stories was 170

HELPPPPPP PLSSSSSSSSSS ASP HELPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

if it helps please mark brainliest!

Step-by-step explanation:

essays= x

quizzes=y

2x=60

x=30 1 essay per 30 days

4y=40

y=10 1 quiz every 10 days

120/30=4

120/10= 12

so 4 essays and 12 quizzes in 120 days

if it helps please mark brainliest!

4. f(x) = 1/2x - x?
f(8) =
a. 64
b. -68
C. 68
d. -60

Answers

Answer:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee hi

Step-by-step explanation:

What is the coefficient of this expression?

3 + 4y +5

Your answer:

3


4


5


x

(Need nOw!!)

Answers

Answer:

4

Step-by-step explanation:

Define coefficient:

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy).

Hope this helped.

i need help for this question. can someone help me

Answers

Answer:

the missing angle is 130

Step-by-step explanation:

180-50=130

130 is the answer

the straight line must add up 180, so if one angle is 50, 180-50= 130

Question 8 (1 point)
(03.02 MC)
Given the function f(x) = 2(x + 6), find x if f(x) = 22. (1 point)
56
Ob
Сл.
38

Answers

22= 2(x+6)
divide on both sides by 2
11= x+6
subtract by 6
5=x
i’m not sure if I read the question right though

Answer:

1 question: Question 8 (1 point) (03.02 MC) Given the function f(x) = 2(x + 6), find x if f(x) = 22. (1 point) 56 Ob Сл. 38

Step-by-step explanation:

The nth term of a different sequence is 10n^2+5 work out the 5th term of this sequence

Answers

Answer:

255

Step-by-step explanation:

10n^2+5

where n=5

10×5²+5

10×25+5

250+5

255

The 5th term of Sequence is 255.

What is Sequence?

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).

Given:

10n² +5

Now for 5th term put n= 5 we get

10n² +5

= 10(5)² +5

= 10 x 25 + 5

= 250+ 5

= 255

hence, the 5th term is 255.

Learn more about Sequence here:

https://brainly.com/question/21961097

#SPJ2

Sean adds up all the even integers from 2 to 500, inclusive. Julie adds up all the integers from 1 to 250, inclusive. What is Sean's sum divided by Julie's sum?

Answers

Answer:

Sean's sum divided by Julie's sum is 2.

Step-by-step explanation:

The sum of an arithmetic sequence is:

[tex]\frac{n}{2}(2a+(n-1)d)[/tex]

In Sean's sequence, a = 2, n = 250, and d = 2

In Julie's sequence, a = 1, n = 250, and d = 2

[tex]\frac{\frac{250}{2}(2(2)+(250-1)2)}{\frac{250}{2}(2(1)+(250-1)1)}\\= 2[/tex]

The Sean's sum divided by Julie's sum gives the 2.

What is arithmetic sequence?

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is ; T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is T_{n+1} - T_n for all positive integer values of n

The sum of an arithmetic sequence is;

[tex]= \dfrac{n}{2}[2a + (n-1)d ][/tex]

In Sean's sequence, a = 2, n = 250, and d = 2

[tex]= \dfrac{250}{2}[2(2) + (250-1)2 ]\\[/tex]

In Julie's sequence, a = 1, n = 250, and d = 2 then;

[tex]= \dfrac{250}{2}[2(1) + (250-1)2 ]\\[/tex]

Therefore, the Sean's sum divided by Julie's sum gives the 2.

Learn more about arithmetic sequence here:

https://brainly.com/question/3702506

#SPJ2

Randy, Sandy and Todd are my cousins and their combined age is 87 years. Randy is four times as old as Sandy, but Todd is actually 15 years older than Sandy. How old are each of my cousins

Answers

Answer:

Randy is 48 years old

Sandy is 12 years old

Todd is 27 years old

Step-by-step explanation:

Given

Represent their ages with the first letters of their names:

[tex]R + S + T = 87[/tex]

[tex]R = 4 * S[/tex]

[tex]T = 15 + S[/tex]

Required

Determine their individual ages

We'll solve the above equations using substitution method of simultaneous equations

Substitute 15 + S for T and 4 * S for R in [tex]R + S + T = 87[/tex]

This gives:

[tex]4 * S + S + 15 + S = 87[/tex]

[tex]4 S + S + 15 + S = 87[/tex]

Collect Like Terms

[tex]4 S + S + S = 87 - 15[/tex]

[tex]6S = 72[/tex]

Divide through by 6

[tex]S = 72/6[/tex]

[tex]S = 12[/tex]

This implies that Sandy is 12 years old

Substitute 12 for S in [tex]R = 4 * S[/tex] and  [tex]T = 15 + S[/tex]

[tex]R = 4 * 12[/tex]

[tex]R = 48[/tex]

[tex]T = 15 + 12[/tex]

[tex]T = 27[/tex]

This implies that Randy is 48 years old and Todd is 27

help!!!!!!!!!!!!!!!!!

Answers

Answer:

5.2

Step-by-step explanation:

√27 = 5.1962 (5s.f.) = 5.2 (2s.f.)

Answer:

i hope 5.2 is the answer

Step-by-step explanation:

i m not sure

what is the slope of the line?
plss answer now

Answers

Answer:

y= -3 I think but the next person will answer this for you

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Hint :

Slope of horizontal lines is

zero (( 0 )) .

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Thus ;

[tex]slope = 0[/tex]

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d) A company increased the monthly salary of its employees by 20%. If an employee
gets Rs 6000 now, find his previous salary.​

Answers

Answer: 4800
______________
Explanation:

6000* 20/100= 1200
6000-1200= 4800

A jar contains 12 caramels, 8 mints and 7 dark chocolates. What is the probability of selecting a mint? simplify if possible.

ME PUEDEN AYUDAR ES PARA HOY

Answers

Answer:

8/27

Step-by-step explanation:

Ms. Baker makes 9 out of 10 free throws. Mrs. S. Brown makes 10 out out of every 12 free
throws. Who is better at making free throws?

Answers

Answer:

ms baker

Step-by-step explanation:

9/10 = 90%

10/12= 83

Answer:

Ms.Baker

Step-by-step explanation:

9/10 > 10/12 or 0.9 > 0.833333. Next time try to make equivalent fractions with the same denominator or convert to decimal then compare.

PLEASEEEEE HELPPPP ASPPPPPPP

Answers

Answer:

The answer is A because a number on it's own is a constant (30) and a number with a variable is a coefficient (12h)

ill give you'll brain list

Answers

Answer:

I can’t see. Pic is not readable

Step-by-step explanation:

I can’t answer number 2 but number 1 is

H:2,5
i:4,8
J:8,7
K:8,3
L:4,2

x - 2y = 4
3x +2y = 4

Answers

Answer:

tje answer is (2,-1) to this

One tree can produce 175 avocados. The avocados are packed in boxes of 24. How many boxes are needed?

Answers

Answer:

8 boxes

Step-by-step explanation:

Divide 175 by 24 since you have 175 avocados and 24 can be put in each box. This gives you 7.29166666667. You have to round up to get 8.

Answer:

8 boxes would be needed

Step-by-step explanation:

175/24 = 7 with a remainder of 7 and you cannot just leave out those 7 avocados, they will be lonely so therefor you will need another box and 7+1=8

On the coloring sheet find the ratio that is equivalent to 2/7

Answers

Answer:

Equivalent Ratios of 2 : 7

2 : 7    4 : 14    6 : 21    8 : 28    10 : 35    12 : 42    14 : 49    16 : 56    18 : 63    20 : 70    22 : 77    24 : 84    26 : 91    28 : 98    30 : 105    32 : 112    34 : 119    36 : 126    38 : 133    40 : 140    42 : 147    44 : 154    46 : 161    48 : 168    50 : 175 52 : 182    54 : 189    56 : 196    58 : 203    60 : 210

( Brainlyst helps my rank <3 )

0.2(10-5c)=5c-16
solve the iniquality

Answers

i’m pretty sure it’s c = 3? i think
Multiply both sides by 10
2(10 - 5c) = 50c -160
Distributive property
20 - 10c = 50c - 160
Add 160 to both sides
180 - 10c = 50c
Add 10c to both sides
180 = 60c
Divide by 60c
c = 3

help me please, thx​

Answers

90 degrees clockwise

Answer:

C.

F.

   Please mark brainliest hit the crown thanks :)

The length of x 200 feet​

Answers

Answer:

If the length of x is less than 200, then add <.

If the length of x is more than 200, then add >.

If the length of x is 200, then add =.

Step-by-step explanation:

how do you write 47,100 in scientific notations ?

Answers

Answer:

4.71 x 10^4

I did maf

Answer: It should be 4.71 x 104.

The amount of money in my account went from being $5 to $8, what is the percent increase?

Answers

I’ll tell u if u answer mine


Find the equation of the line that contains the point ( - 1. - 4) and is parallel to the line 2x + 3y = 5

Answers

Answer:

Answer: 2x+3y=-14

Y needs to be changed in order to maintain parallelism

Good luck!

A $136,000.00 home with 30yr mortgage with 1.1% fixed rate. 20% down down payment. How much is the down payment, the monthly payments, interest rate and the loan?

Answers

Answer:

down payment = home value x 20% = $136,000 x 20% = $27,200

loan = home value - down payment = $136,000 - $27,200 = $108,800

interest rate = 1.1% fixed (given) ≈ 0.09167% per month

duration of loan = 30 years or 360 months

monthly payment = present value of loan / PV annuity factor

PV annuity factor, 360 periods, 0.09167% = 306.5134 (I used an online annuity calculator)

monthly payment = $108,800 / 306.5134 = $354.96      

The average cost per unit c(x) to produce x units of lumber is given byc * (x) = 400/(x + 25) if the cost per unit is \$1.00 how many units have been produced if necessary round your answer to the nearest whole unit. the answer is 375

Answers

Answer:

The number of units of lumber that have been produced is 375

Step-by-step explanation:

From the question,

The average cost per unit c(x) to produce x units of lumber is given by

c(x) = 400/(x + 25).

Now, to determine how many units have been produced (that is, x) if the cost per unit is $1.00 (that is, c(x) = $1.00), we will put in the value into the given equation to determine x.

c(x) = 400/(x + 25)

c(x) = $1.00

∴ 1.00 = 400/(x + 25)

Then,

(x + 25) × 1.00 = 400

x + 25 = 400

x = 400 - 25

x = 375

Hence, the number of units of lumber that have been produced is 375.

Slope of (2,8) and (2,6)

Answers

no slope because the points are vertical.

What is the binary number for 16​

Answers

Answer:

Decimal Number 4-bit Binary Number Hexadecimal Number

14 1110 E

15 1111 F

16 0001 0000 10 (1+0)

17 0001 0001 11 (1+1

Step-by-step explanation:

hope this helped

HELP ME PLEASE!!!!!!!!!!!!

Answers

Answer: linear

Step-by-step explanation: cus when u connect the points it forms a straight line

Linear is the awnser CHUJVCFHHVF
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