There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).
Answers
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
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.
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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
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.
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 )
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!
d) A company increased the monthly salary of its employees by 20%. If an employee
gets Rs 6000 now, find his previous salary.
Answers
______________
Explanation:
6000* 20/100= 1200
6000-1200= 4800
i need help for this question. can someone help me
Answers
Answer:
the missing angle is 130
Step-by-step explanation:
180-50=130
the straight line must add up 180, so if one angle is 50, 180-50= 130
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
x - 2y = 4
3x +2y = 4
Answers
Answer:
tje answer is (2,-1) to this
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.
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
The amount of money in my account went from being $5 to $8, what is the percent increase?
Answers
0.2(10-5c)=5c-16
solve the iniquality
Answers
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
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.
Slope of (2,8) and (2,6)
Answers
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:
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.
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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
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:
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
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
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!
ill give you'll brain list
Answers
Answer:
I can’t see. Pic is not readable
Step-by-step explanation:
H:2,5
i:4,8
J:8,7
K:8,3
L:4,2
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:
help me please, thx
Answers
Answer:
C.
F.
Please mark brainliest hit the crown thanks :)
HELP ME PLEASE!!!!!!!!!!!!
Answers
Answer: linear
Step-by-step explanation: cus when u connect the points it forms a straight line
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.
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
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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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)