A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below. A rectangular area consisting of two separated regions. A rectangular area consisting of two separated regions. If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the maximal area?
Answers
The dimensions of the region which enclose the maximal area will be 40.5 feet in length by width 27 feet.
How to find the dimensions of the areaGiven that the farmer has 162 feet of fencing, we will have:
2L + 3W = 162 feet
2L = 162 - 3W
L = 162 - 3W\2
L = 81 -3/2W Eqn 1
Given that the area of a rectangle is A = L × W we will call this equation 2
Now we substitute the first equation in the second one to give
A = (81 -3/2W) × W
A = 81W -3/2W²
When we take the derivative W will equal
81/3 = 27
Now we substitute in the second equation, we will have:
= 81 - 3/2(27)
= 81 - 40.5
= 40.5.
So the length will be 40.5 feet while the width will be 27 feet.
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Related Questions
HELP PLEASE PLEASE FAST PLEASE I WILL REWARD BRAINLYEST!
Answers
Answer:
good luck i would help bud i really don't know that
Answer:
14
Step-by-step explanation:
The area of the triangle is \(\frac{1}{2}\times4\times7 = 14\)
Need this ASAP PLZ .........................................:........
Answers
I don't now just need points
Picture in a school year book is a constant ratio of width to length 6cm to 9cm what would it be if the width was 8 cm
Answers
Answer:
12 cm.
Step-by-step explanation:
to find the answer, first find the scale factor. the scale factor is 4/3. Then, multiply with 9 to find the length. 9x4/3=12.
Find the area of the figure below using the given dimensions. Think about
creating two shapes from the figure!*
20
15 ft
20 ft
175 ft squared
125 ft squared
200 ft squared
150 ft squared
Answers
Answer:
200
Step-by-step explanation:
The solution for a kite is multiply the two diagonals which in this case are both 20 and then divide the answer by 2
What is the perimeter of the triangle?
Answers
what is 12/21 + 18/21 + 14/21
Answers
Answer:
44/21
Step-by-step explanation:
what is 12/21 + 18/21 + 14/21
having the same denominator just add the numerators leaving 21 as the denominator(12 + 18 + 14)/21 =
44/21
4) Which best summarizes the MAIN IDEA of this narrative? A) The most important thing in politics is to identify and support the victorious candidate. B) The most dangerous thing in politics is to be misled by the promises the candidates make. The most rewarding thing in politics is to be fully informed and fully involved in the process. D) The most surprising thing in politics is the way the news media focuses on unimportant details.
Answers
Answer:
The correct answer is C.
Step-by-step explanation:
"The most rewarding thing in polictics is being fully informed." I took a test and I got it right so you can trust me lol
Answer:
The answer is C) the most rewarding thing in politicsis to be fully informed and fully involved in the process.
Step-by-step explanation:
got this question on usa test prep
Suppose a triangle has vertices AA, BB and CC and has the following measurements:¯¯¯¯¯¯¯¯AB=23.5 cm ¯¯¯¯¯¯¯¯AC=87.2 cm ¯¯¯¯¯¯¯¯BC=64.8 cmStart by drawing a diagram of this triangle and labeling the known values.What is the degree measure of ∠C?m∠C= ° What is the degree measure of ∠A?m∠A= ° What is the degree measure of ∠B?m∠B= °
Answers
First let's draw this triangle:
First let's compare the square of the bigger side with the sum of squares of the other two sides, this way we can find out if the triangle is acute, right or obtuse:
\(\begin{gathered} 87.2^2=23.5^2+64.8^2 \\ 7603.84=522.25+4199.04 \\ 7603.84=4721.29 \end{gathered}\)Since the square of the bigger side is greater than the sum of squares, the triangle is obtuse.
In order to calculate the first angle, let's use the law of cosines, using angle A:
\(\begin{gathered} 64.8^2=23.5^2+87.2^2-2\cdot23.5\cdot87.2\cdot\cos (A) \\ 4199.04=522.25+7603.84-4098.4\cos (A) \\ \cos (A)=\frac{3927.05}{4098.4}=0.958_{} \\ A=16.63\degree \end{gathered}\)Now we can use the law of sines for angle B:
\(\begin{gathered} \frac{64.8}{\sin(16.63\degree)}=\frac{87.2}{\sin (B)} \\ \sin (B)=\frac{0.286\cdot87.2}{64.8}=0.385 \\ B=157.36\degree \end{gathered}\)Finally, for angle C:
\(\begin{gathered} \frac{64.8}{\sin(16.63\degree)}=\frac{23.5}{\sin (C)} \\ \sin (C)=\frac{0.286\cdot23.5}{64.8}=0.104 \\ C=5.95\degree \end{gathered}\)
what percent of 50 is 18?
Answers
Answer:
36 %
Step-by-step explanation:
Convert the fraction to a decimal, then multiply by 100 .
Answer:
36%
Step-by-step explanation:
The same explanation as she said
Oliver and Layla each built a rectangular prism with centimeter cubes. Both prisms have a volume of 24 cubic centimeters but they do not look the same. Give possible dimensions for each prism.
Answers
Possible Dimensions of one prism are; 2cm, 3 cm and 4cm
Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm
How to find the dimensions of a rectangular Prism?We are told that volume of both rectangular prisms is; V = 24 cm³
Now, formula for Volume of a rectangular prism is;
V = lwh
where;
l is length
w is width
h is height
Thus, to solve this, we have to look for multiples of 24 which are;
1, 2, 3, 4, 6, 8, 12, 24.
Now, we must pick 3 numbers from the above in which their products will be equal to 24.
Thus;
Possible Dimensions of one prism are; 2cm, 3 cm and 4cm
Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm
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Which of the following is the graph of 2x+3y=6
Answers
Taking point (0,-2) of graph one and replacing in the equation;
2x+3y=6
2(0)+3(-2)=6
-6=6
So graph isn't the required graph.
Taking point (0,2) of graph 2;
2x+3y=6
2(0)+3(2)=6
6=6
So, graph 2 is the required graph.
Answer:
nice
Step-by-step explanation:
which is bigger 100 kg or 1,000 grams
Please answer is for todayyyyy
Answers
100 kg becouse 1000 grams is egual 1 kg
Answer: A kilogram is 100 grams.
Step-by-step explanation: For every kilogram, there are 1000 grams. That means that the ratio between kilograms and grams is 1:1000. It also means 1 kilogram and 1000 grams are defined as being equal. Traditionally, grams are referred to as the base unit, so 1 g is bigger than kg.
A button machine produces one button in 0.15 seconds. How many buttons are produced in 48.6 seconds?
Answers
Answer: 324 buttons
Step-by-step explanation:
1 button in 0.15 seconds = x buttons in 48.6 second d
1 / 0.15 = x / 48.6 (cross multiplication )
48.6/0.15 = 324
please copy the picture or screenshot it then place the dots on the screen shot of the graph read the whole Question
Answers
The three points that are the solution set of the equation, x + 3y = -5, are shown in the graph below as: (-5, 0), (-2, -1), and (7, -4).
What is the Solution Set of the Equation of a Line?If a point is a solution to an equation of a line, it means the point lies on the line and its coordinate values will make the equation true if plugged into the equation.
Given the equation, x + 3y = -5, in slope-intercept form, it can be rewritten as y = -1/3x - 5/3.
This means that the line of this equation will have the following features:
The slope of the line = rise/run = -1/3
The y-intercept is -5/3.
The line is drawn in the graph as shown in the image below.
The solution set plotted on the line are: (-5, 0), (-2, -1), and (7, -4).
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Points A, B, C, D, and E are collinear and in
that order. Find AC.if AE = x + 50 and
CE = x + 32.
Answers
Points A, B, C, D, and E are collinear and in that order. The value of Ac is 18.
According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC.
Keep in mind that a line segment is a portion of a line that has two distinct end points. There are many points between the two end points that make up the object.
The segment addition postulate can be stated more simply by saying that if point B lies on line segment AC, then AB + BC will equal AC.
by the segment addition postulate,
AC + CE = AE so AC = AE - CE
AC = (x+50) - (x+32)
AC = x+50-x-32
AC = 18
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Please help me I need it bow
Answers
Answer:
C
Step-by-step explanation:
I'm pretty sure it's none..?
Two vacationing families leave New York at the same time. They take 20 and 6 days, respectively, to reach their destination and return to New York. The vacationing families each take continuous trips to and from New York. How many days will pass before the two vacationing families leave New York on the same day again?
Answers
Answer:
Step-by-step explanation: evagline has 3/5 of box of nuts.she uses it to fill 6 bowls
Question 10 please help and show step by step working out
Answers
Answer:
P and Q must have some relation f their integers but it doesn't give a value
Step-by-step explanation:
Answer:
The answer is
\(8 + \sqrt{48} \)
A company is going to make a water tank in the shape of a cylinder. As shown below, the tank will have a height of 3ft and a diameter of 8ft. The tank will be made from metal (including its top and bottom). If the metal costs $29 for each square foot, how much will the metal cost in total?
Answers
The total cost of the metal needed to cover the tank shaped like a metal is $5,099.36.
What is the total cost?In order to determine the total metal cost, we are to first calculate the total surface area of the tank. Since the tank is a closed cylinder, we are to determine the total surface area of a cylinder.
The total surface area of a closed cylinder can be determined by adding the area of all its faces.
Total surface area of the closed cylinder = 2πr(r + h)
Where:
r = radius = diameter / 2 = 8/2 = 4ft
h = height
π = pi = 3.14
(2 x 3.14 x 4)(4 + 3)
25.12 x 7 = 175.84 ft²
Total cost of the metal = $29 x 175.84 = $5,099.36
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Can someone help me do the long division of this please
Its
P-4 divided by 10p^3-45p^2+26p-33
Answers
Answer:
\(10p {}^{2} - 5p + 6 + \frac{ - 9}{p - 4} \)
Step-by-step explanation:
10p²-5p+6
p-4√10p³-45p²+26p-33
- 10p³-40p²
-5p²+26p
- -5p²+20p
6p-33
- 6p-24
-9
What is the answer of 3y=2x in a fraction?
Answers
Answer:
you cant simplify further
Step-by-step explanation:
On Tuesday , the wait to ride the roller coaster was 40 minutes. The roller coaster is the fastest ride at the fair .The line of people waiting was 100 meters long . How long would you expect to wait if the line 50 meters long.
Answers
Answer:
You would expect to wait 20 minutes if the line was 50 meters long.
Step-by-step explanation:
This question can be solved using a rule of three.
The line of people waiting was 100 meters, and the wait was 40 minutes. How long the wait would have been if the line was of 50 meters?
100m - 40 min
50m - x min
\(100x = 50*40\)
\(x = \frac{50*40}{100}\)
\(x = 20\)
You would expect to wait 20 minutes if the line was 50 meters long.
At a local pizza parlor, patrons have 3 choices of cheese and 5 choices of meat. In how many different ways can a patron choose 1 type of cheese and 1 type of meat? 10 30 o 15 0 8 o Termsat a local pizza parlor that runs has three choices of cheese and five choices of meat in how many different ways can a pageant use one type of cheese and what type of meat
Answers
Answer:15
Step-by-step explanation:
A nation can produce two products: tanks and autos. The table below is the nation's production possibilities schedule.
Production Possibilities
Product
Tanks
The total opportunity cost of three unit(s) of tanks is
A
0
1000
B
1
950
C
2
850
D
3
650
E
4
350
F
5
0
Answers
Using the it's formula, the total opportunity cost of three unit(s) of tanks is of 350 autos.
What is the opportunity cost formula?The opportunity cost formula is given by:
C = F - A.
In which:
F is the best return.A is the actual return.For this problem, we have that:
When no tanks are produced, 1000 autos can be produced, hence F = 1000.When 3 tanks are produced, 650 autos can be produced, hence F = 650.Thus:
F = 1000 - 650 = 350.
The total opportunity cost of three unit(s) of tanks is of 350 autos.
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Zev read 15% of his 56-page book. Kelly read 12% of her 64-page book. Marneisha read 14% of his 68-page book Aleisha read 10% of her 72-page book. what the grastest
Answers
Answer:
Marneisha with 9.52 pages.
Step-by-step explanation:
Zev: 56×0.15 = 8.4
Kelly: 64×0.12 = 7.68
Marneisha: 68×0.14 - 9.52
Aleisha: 72×0.10 = 7.2
write an equation of the line in the point- slope form that passes through the given points in the table. Then write the equation in slope-intercept form. (10,80) (5,65)
Answers
To write the equation of the line that passes through (10,80) (5,65)
we will use the formula;
\(y-y_1\text{ =}\frac{y_{2-}y_1}{x_2-x_1}(x-x_1)\)x₁ = 10 y₁ = 80 x₂ = 5 y₂ = 65
substituting the above into the formula;
\(y\text{ - 80 = }\frac{65\text{ - 80}}{5\text{ - 10}}(\text{ x - 10)}\)we will go ahead and simplify
\(y\text{ - 80 = }\frac{-15}{-5}(x-10)\)y- 80 = 3(x - 10)
y- 80 = 3x - 30
y -3x -80 + 30 = 0
y - 3x - 50 = 0
The above is the equation of the line.
To write in a slope-intercept form simply means to write it in the form;
y = mx + b
where m is the slope and b is the intercept
Hence;
y = 3x + 50
The above is the equation of the line in a slope-intercept form
how many tickets are there when it weighs 135 grams
Answers
Answer:
about like 4-5
Step-by-step explanation:
its 4 or 5
What is greater than 525.06 but less than 525.6?
Answers
Answer:
A
Step-by-step explanation:
Desperate Need Of Help
Answers
The domain and range of the graph above in interval notation include the following:
Domain = [-6, 3]
Range = [-3, 3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-6, 3] or -6 ≤ x < 3.
Range = [-3, 3] or -3 < y < 3
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Pleaseee hellllpppp!!!!
Answers
Answer:
I hope option D is write
I hope you help
Answer:
B. 32°
Step-by-step explanation:
The reference angle for 212°
=212°-180°
=32°
Hope it is helpful to you