A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensions of the pen that will maximize the area (100 PTS + BRAINLIEST)
Answers
Answer:
[tex]W_{max}=320m\\ L_{max}=160m[/tex]
Step-by-step explanation:
Since we know we only have 640 feet of fence available, we know that L + W + L = 640, [tex]\implies [/tex] 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L
Remember, the area of a rectangle is equal to the product of its width and length, therefore,
[tex]A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2[/tex]
Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.
recall,
[tex]x_{max}=-b/2a[/tex][tex]f(x)_{max}=f(x_{max})[/tex]Since our function is A(L)=640L-2L², we get
a=-2b=640plug in the value of a and b into the first formula:
[tex]L_{max}=-(640)/2(-2)\implies 160 [/tex]
[tex]A(L)_{max}=640(160)-2(160)^2\implies 51200 [/tex]
hence,the dimensions of the pen that will maximize the area are L=160m and W=51200/160=320m
and we're done!
Answer:
width (x) = 160 m
length (y) = 320 m
(refer to the attached diagram)
Step-by-step explanation:
**see attached diagram**
Let x = width of the pig pen
Let y = length of the pig pen
(where length > width)
Given:
Fence = 640 m4th side is the barn⇒ 2x + y = 640 m
⇒ y = 640 - 2x
Area of the pig pen = width × length
⇒ f(x) = xy
Substituting y for y = 640 - 2x:
⇒ f(x) = x(640 - 2x)
= 640x - 2x²
Now we have a function for the area of the pig pen, to find the value of x that will maximize the area, differentiate the function:
⇒ f'(x) = 640 - 4x
Set it to zero and solve for x:
⇒ f'(x) = 0
⇒ 640 - 4x = 0
⇒ 640 = 4x
⇒ x = 160
Substitute the found value of x into y = 640 - 2x to find the length:
⇒ y = 640 - 2(160) = 320
Therefore, the dimensions of the pen that will maximize the area are:
width (x) = 160 mlength (y) = 320 m
Related Questions
- At a school carnival, 8 out of 32 tickets sold were early-admission tickets. What
percentage of the tickets were early-admission tickets?
Answers
Answer:
25 Percent of tickets were early admission.
Step-by-step explanation:
We apply the percentage formula to solve this problem.
Total Ticket Amount * Percentage = Early tickets
We plug in our values
32 * x/100 = 8
Simplify
X=25
Answer:
25%
Step-by-step explanation:
8 out of 32 can be simplified to 1 early admission for every 4 tt (total tickets). 1/4 can be changed into a decimal which is .25, and .25*100 is 25%
Solve the equation for x.
-2x = 14
Enter the number that belongs in the green box.
x = [?]
Answers
Divide both sides by -2
X= -7
If the bottom row as a result of synthetic division is 3, 0, 4, 0, 1. then the quotient is what?
Answers
Answer:
[tex]a. \:\:3x^3 + 4x\:\:R1[/tex]
Step by step explanation:
Hope it helps you in your learning process.
Have a great day ahead.
The quotient and remainder for the last row of the synthetic division 3, 0, 4, 0, 1 are 3x³ + 4x, and 1 respectively.
The option representing this is, a. 3x³ + 4x R1.
What is synthetic division?Synthetic division is a short method of dividing a polynomial p(x) by another polynomial (x - c), to get the quotient and remainder.
The last row represents the quotient and remainder, the last digit being the remainder, and the others being the quotient multiplied by leading powers of x, starting from x⁰, starting from the second last term of the last row.
How to solve the question?In the question, we are given the last row of a synthetic division as 3, 0, 4, 0, 1, and we are asked to find the quotient of the division.
The last number, 1 represents the remainder and can be written as R1.
Now we move from the back to the front and multiply every number with the leading power of x, starting from x⁰.
0 gives 0 * x⁰ = 04 gives 4 * x¹ = 4x0 gives 0 * x² = 03 gives 3 * x³ = 3x³.Therefore, the quotient and remainder for the last row of the synthetic division 3, 0, 4, 0, 1 are 3x³ + 4x, and 1 respectively.
The option representing this is, a. 3x³ + 4x R1.
Learn more about the Synthetic Division at
https://brainly.com/question/24662212
#SPJ2
What is the simplified form of i^14?
A. -1
B. i
C. -i
D. 1
Answers
Answer:
-1
Step-by-step explanation:
Rewrite i14 as (i4)3×i2 If i=√−1, then i2=−1 .
Answer: (A. -1)
Step-by-step explanation: Rewrite i14 as (i4)3×i2 . If i=√−1, then i2=−1. I hope this helped!
a. Which cost category varies the least among the different types of colleges? Can you explain why this category varies so little?
b. Ignoring the "other expenses" category, the general trend is for all categories to cost more as you look down the chart from two-year public colleges to four-year private colleges. However, one category is an exception to this trend. Which category? Can you explain why?
Answers
The question indicated above speaks to expense analysis for anonymous colleges. See the details of the analyses below.
From the pictorial representation, which cost category varies the least among the different types of colleges?The cost category that varies the least amongst the various types of colleges is Books and supplies. Notice that at no point did it go below 1,097, nor above, 1,350.
The categories that do not cost more as one goes down the chart (apart from other expenses) are:
Books and supplies and Transportation.Books and supplies went from: $1,350 to $1,107, to 1,107, and then to 1097. Hence decreasing gradually over time.
Transportation also decreased over time starting out from $2,152, to $2,099, to 2,099 and then flatting out at $1,571.
It may be explained that the cost of books is on the decline as more and more people prefer online reading while the cost of transportation is declining as more and more students use their cars or vehicles to the college, hence driving down the cost of transportation.
Learn more about expense analyses at:
https://brainly.com/question/199821
i really need helps with this i dont understannd it
Answers
Answer:
A < C < B = 0.2 < 0.222 < 0.25
Step-by-step explanation:
the best way to do these least to greatest questions is to get them all in the same units so you can compare.
A = [tex]\sqrt{\frac{1}{25} }[/tex]which is [tex]\sqrt{0.04}[/tex] = 0.2
B= 1/4 = 0.25
c=0.22222222.....
now that they are in the same units we see A is the smallest, then C, and then B
Which congruence theorem can be used to prove △WXS ≅ △YZS?
Triangles W X S and Y Z S are connected at point S. Angles W X S and S Z Y are right angles. Sides X S and S Z are congruent.
SSS
ASA
SAS
HL
Answers
Answer:
SSS
Step-by-step explanation:
XS=SZ
WS=SY
WX=ZY
I hope this is useful.
The congruence theorem that can be used to prove △WXS ≅ △YZS is SSS. ; option A.
Which are congruence theorems?Congruence theorems are theorems which are used to prove congruency in triangles.
The congruence theorems include:
SSSASASASRHSIn the given triangle;
XS = SZ WS = SY WX = ZYTherefore, the congruence theorem that can be used to prove △WXS ≅ △YZS is SSS.
Learn more about congruence theorems at: https://brainly.com/question/2102943
#SPJ9
Question is in picture
Answers
A business owner wants a smaller version of the logo (picture attached) to be on the door of her business. The door is 7 feet tall and 3 feet wide There should be 6 inches of empty space to the left side of the logo and 6 inches of empty space on the right side of the logo.
Based off the logo (picture attached), what should be the total width, in feet, of the logo on the door?
Based off the logo (picture attached), what should be the total height, in feet, of the logo on the door?
Answers
Answer:
Clair, since there isn't an attached picture, we don't know some info
Step-by-step explanation:
but here is how you can figure this out....
they tell use to give 6 inches on each side of the door, so the total width of the logo can be 2 feet wide. Because the door is 3 feet wide. Now use that to find the height. find the height to width ratio of the logo, so if the logo is 4 feet wide and 6 feet tall it's 6/4 or 1.5 ratio, use that and multiply by the 2 that we know the width can be on the door. so 2*1.5 = 3. the height of the logo would be 3 feet tall and 2 feet wide on the door. see?
just find the ratio of the logo, and multiply that by 2 :) to find the height on the door, got it?
If A is the center of the circle, then which statement explains how segment GH is related to segment FH?
Circle A with inscribed triangle EFG; point D is on segment EF, point H is on segment GF, segments DA and HA are congruent, and angles EDA and GHA are right angles.
segment GH ≅ segment FH because arc EF ≅ arc GF
segment GH ≅ segment FH because the inscribed angles that create the segments are congruent.
segment GH ≅ segment FH because the tangents that create the segment FG share a common endpoint.
segment GH ≅ segment FH because segment FG is perpendicular to a radius of circle A.
Answers
Statement fourth the segment GH ≅ segment FH because segment FG is perpendicular to a radius of circle A if Circle A with inscribed triangle EFG; point D is on segment EF, point H is on segment GF, segments DA and HA are congruent, and angles EDA and GHA are right angles.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have AH as the radius and FG as a chord
AH is perpendicular to FG, AH⊥FG
As we know that a line passing through the center and perpendicular to the chord, bisects the chord.
∴ AH bisects FG
∴ FH = GH
Thus, the segment GH ≅ segment FH because segment FG is perpendicular to a radius of circle A if Circle A with inscribed triangle EFG; point D is on segment EF, point H is on segment GF, segments DA and HA are congruent and angles EDA and GHA are right angles.
Learn more about circle here:
brainly.com/question/11833983
#SPJ1
A restaurant did a survey among 100 customers to find their food preferences. The customers were asked about their preferences for pasta or rice. Out of the total 30 people who liked pasta, 10 also liked rice. There were 40 people who liked rice.
Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)
Like pasta Do not like pasta Total
Like rice A B C
Do not like rice D E F
Total G H I
Part B: What percentage of the survey respondents did not like either pasta or rice? (3 points)
Part C: Do the survey results reveal a greater dislike for rice or pasta? Justify your answer. (2 points)
Answers
Answer:Part A: Like pasta Do not like pasta TotalLike rice 10 30 40Do not like rice 20 40 60Total 30 70 100Part B: When we look at the table above, we can see that 40 people do not like rice or pasta, so 40 out of 100 = 40%, so 40% of the people surveyed don't like either. Part C: People surveyed have a greater dislike for pasta than rice. Reason: 60 people do not like rice and 70 people do not like pasta, and 70>60 so people dislike pasta more.
Step-by-step explanation:https://brainly.com/question/2141081
Brainliest if correct
Answers
Answer:
1 1/7
Step-by-step
E is on the 1 1/7 point on the number line
Answer:
[tex]1\frac{3}{20}[/tex]
Step-by-step explanation: Each space equals =.15. Count by the spaces not the lines. 15/100 simplifies to 3/20.
of the students at Wayland High School in
he first quarter, 48% made honor roll, 30%
had perfect attendance, and 25% both
made the honor roll and had perfect
attendance. If a student is chosen at
andom, what is the probability that they
have perfect attendance, given they made
he honor roll?
Answers
Using conditional probability, it is found that there is a 0.521 = 52.1% probability that they have perfect attendance, given they made he honor roll.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Student made the honor roll.Event B: Student has perfect attendance.The probabilities are given by:
[tex]P(A) = 0.48, P(A \cap B) = 0.25[/tex]
Hence the conditional probability is given by:
[tex]P(B|A) = \frac{0.25}{0.48} = 0.521[/tex]
0.521 = 52.1% probability that they have perfect attendance, given they made he honor roll.
More can be learned about conditional probability at https://brainly.com/question/14398287
#SPJ1
The distance between two towns is 120 kilometers. There are approximately 8 kilometers in 5 miles. How many miles are between the two towns?
Answers
Answer:
15 miles
Step-by-step explanation:
You know that there are 8 kilometres in 5 miles, so:
120/8=15
. Predict how the display may look after another 20 minutes.
erature
Answers
Answer:
creature
Step-by-step explanation:
it's definitely creature
Help picture below problem 19
Answers
Answer:
I think the amswer is C not 100% shere
Step-by-step explanation:
7. If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is?
Answers
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x[-0.699] = 0.3010.
x= 0.3010/-0.699.
x= = -0.4306….
x= = -0.4.
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x[-0.699] = 0.3010.
x = 0.3010/-0.699
x = -0.4306
x= -0.4 (nearest tenth)
Help would be appreciated:)
Answers
Answer:
19%
Step-by-step explanation:
Bottles manufactured in march = 4100×107% = 4387 bottles
bottles manufactured in April= 4387+500 = 4887 bottles
difference in bottles from Feb to April= 4887-4100 =787 bottles
percentage increase from Feb to April= (787/4100)×100 = 19.2%
rounded off= 19%
4. What is the difference between 34.062 And 2.87
M. 31.192
P. 31.292
R. 32.192
S. 33.775
Answers
Answer:
m. 31.192
explanation 34.062-2.87
Fundamental theorem of calculus
[tex]g(s)=\int\limits^s_6 {(t-t^4)^6} \, dt[/tex]
Answers
Answer:
[tex]\displaystyle g'(s) = (s-s^4)^6[/tex]
Step-by-step explanation:
The Fundamental Theorem of Calculus states that:
[tex]\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)[/tex]
Where a is some constant.
We can let:
[tex]\displaystyle g(t) = (t-t^4)^6[/tex]
By substitution:
[tex]\displaystyle g(s) = \int_6^s g(t)\, dt[/tex]
Taking the derivative of both sides results in:
[tex]\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right][/tex]
Hence, by the Fundamental Theorem:
[tex]\displaystyle \begin{aligned} g'(s) & = g(s) \\ \\ & = (s-s^4)^6\end{aligned}[/tex]
Help me I don’t know how to do this
Answers
The starting point which is on the left then in a different color the end point
Then you need to just figure out the rotation and transformation that got you from the start point to the end
Example
Solve the quadratic equation
x² - 6x +13=0
Answers
[tex]x^2-6x+13=0\\\\\implies x^2-6x =-13\\\\\implies x^2 -2\cdot 3 \cdot x+3^2 -3^2 =-13\\\\\implies (x-3)^2 -9 = -13\\\\\implies (x-3)^2 = -13 +9 = -4\\\\ \implies x-3 =\pm\sqrt{-4} \\\\\implies x -3 = \pm2i\\\\\implies x = \pm 2i +3\\\\\text{Hence,}~ x = 3 + 2i, ~~ x = 3-2i[/tex]
Which of the numbers listed below are solutions to the equation? Check all
that apply
x2 = 0
O A. -
B. 1
C. -2
IN D. O
E.2
F. None of these
Answers
Answer:
x=0
Step-by-step explanation:
x^2 =0
The only solution for x is
x=0
Please help! Determine the function which corresponds to the given graph.
Answers
By identifying that it is a translation of the natural logarithm, we see that the function is:
g(x) = ln(x - 5).
How to determine the function?
We can see that the function has a logarithmic behavior. We know that the function:
f(x) = ln(x)
Has an asymptote at x = 0, and is equal to 0 for x = 1.
For our function, we can see that the asymptote is at x = 5 and the zero is at x = 6. So the graphed function seems to be the natural logarithm translated 5 units to the right.
Then the function graphed is:
g(x) = f(x - 5) = ln(x - 5)
If you want to learn more about translations, you can read:
https://brainly.com/question/24850937
The cost of two hats and three bandanas is $114.25. The cost of five hats and two bandanas is $166.00. What is the cost of one hat?
(A) 18.75
(B) $21.75
(C) $22.50
(D) $24.50
(E) $51.75
Answers
Answer:
Step-by-step explanation:
I DONT UNDERSTAND THE EQUATION CAN SOMEBODY HELP ME PLEASE
Answers
Answer:
I dunno how do sorry mann
how a high prevalence of human rights violations can negatively impact a community?list 4 factors
Answers
The high prevalence of human rights violations can negatively impact a community in terms of:
Behavior and government structureArmed conflictPsychological factorsEconomic factorsWhat are human rights?These are the inherent rights of all human beings, such as the right to life, work and security, for example, without distinction of class, gender or any other characteristic. They exist to protect liberty and promote equity among individuals.
Therefore, a community with human rights violations will be harmed in relation to its social and economic structure.
Find out more about human rights here:
https://brainly.com/question/1261546
The mZAOB is 40 degrees. The mZDOF is 120 degrees.
FIND THE FOLLOWING:
m
m
Answers
80
60
REASON:
1)Any angles opposite eachother is a cross with straight lines are equal. Therefore angle DOE is also 40. We know DOF is 120 so EOF must be 120-40=80 (which is DOF-DOE). BOC is opposite EOF so it also equals 80.
2) We know that angles on 1 straight line equal to 180 degrees. And we have to angles on a straight line but we are missing one which is COD. So we do (180-BOC-the angle we are given) 180-80-40= 60
Make sure to tell me if there is anything you don't understand!
20 points please help me answer this
Answers
Answer:
171 Square Feet
Step-by-step explanation:
We first cut the figure up into smaller parts...
we then use the formula (L x W = A) to find the area
L = Lenth
W = Width
the first rectangle (1)...
15 x 5 = 75
the second figure (2)...
8 x 9 = 72
the third figure (3)...
6 x 4 = 24
now we have to add up all the values to find the area of the entire figure...
75 + 72 + 24 = 171
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!
John works at Klein’s Dry Cleaning. He earns $8.45 per hour. If John worked 39 hours this week, what is his pay?
Answers
Answer:
$329.55
Step-by-step explanation:
We simply just multiply the hours by the total cost he gets paid each hour.
Since he gets paid 8.45 each our and works 39 hours we do:
8.45 * 39 = 329.55
Answer:
$329.55
Step-by-step explanation:
8.35 times 39