The given series [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] is convergence and the sum of the series is 33/28.
In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.
The given series is [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex].
Firstly we check the convergence of the given series.
When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.
We can write the series as:
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex]
As |0.3|<1 and |0.2|<1
Then [tex]\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n[/tex] is convergent.
So [tex]\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex] is also convergent.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right[/tex]
Series [tex]\sum_{n=1}^{\infty}(x)^{n-1}[/tex] converges to 1/x-1 for |x|<1.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}[/tex]
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}[/tex]
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 10/7 - 1/4
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 33/28
Hence, the sum of the given series is 33/28.
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The right question is:
Determine whether the series is convergent or divergent.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex]
If is is convergent, find the sum. (If the quantity diverges, enter diverges.)
The bottom of a swimming pool is 12 feet below the surface of the water.
What is the pool's depth in feet?
Enter your answer as an integer.
If it is negative, enter it like this: -42"
Find the slope of the line that passes through (6, 6) and (3, 13). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer: -3/7
Step-by-step explanation:
So the fomula for slope is m=x2-x1/y2-y1
if (6,6) is our first coordinate and (3,13) is our second that means 6 is x1 and 3 is x2. 6 will be y1 and 13 will be y2. now we plug in the numbers
m=3-6/13-6
m= -3/7
In a circle, an angle measuring 7.1 radians intercepts an arc of length 2.4. Find the radius of the circle to the nearest 10th.
The radius of the circle with arc length of 2.4 and subtended angle at the center, 7.1 radians is 0.3
What is an arc of a circle?The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.
length of arc = 2.4
if 7.1 rad is the angle subtended by the intercepts of the arc
But [tex]\pi[/tex] rad = 180°
so 7.1 rad in degree = [tex]\frac{7.1}{\pi }[/tex] x 180 which is [tex](\frac{1278}{\pi } )^{} }[/tex] degree which is [tex]\alpha[/tex]
Length of an arc = [tex]\frac{\alpha }{360} * 2\pi r[/tex]
2.4 = [tex](\frac{1278}{\pi } )^{} }[/tex] x [tex]\frac{1}{360}[/tex] x 2 x [tex]\pi[/tex] x r
The equation reduces to
2.4 = 7.1r
r = 2.4 ÷ 7.1
r = 0.334 which is 0.3
In conclusion the radius of the circle is 0.3
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In a coordinate plane, a line has two points A and B with the coordinates A(4,n) and B(10,6n). In the same coordinate plane, a different line has two points C and D with coordinates C(−3,−6) and D(9,8n). For what value of n are the two lines parallel?
For the two lines to be parallel, the value of n must be 3
How are two lines parallel in a coordinate?When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line. If the slopes are the same then the lines are parallel.
The slope of each line is calculated as (y2-y1)/x2-x1
for line AB, the slope = (6n-n)/10-4 = 5n/6
for line CD, the slope= 8n-(-6)/9-(-3)=( 8n+6)/12
for AB and CD to be parallel,
5n/6 = (8n+6)/12
multiply both sides by 12
10n= 8n+6
collect like terms
10n-8n= 6
2n= 6
n= 6/2= 3
therefore for the value of n= 3 line CD and AB are parallel.
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Given the inequality 3(n − 6) < 2(n 12), determine which integer make the inequality fale. S:{−5}
S:{3}
S:{12}
S:{42}
The FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
So, we have the inequality: 3(n − 6) < 2(n + 12)
Now, verify the false inequality as follows:
(A) S:{−5}
3(n − 6) < 2(n + 12)
3(-5 − 6) < 2(-5 + 12)
3(-11) < 2(7)
-33 < 14: TRUE
(B) S:{3}
3(n − 6) < 2(n + 12)
3(3 − 6) < 2(3 + 12)
3(-3) < 2(15)
-9 < 30: TRUE
(C) S:{12}
3(n − 6) < 2(n + 12)
3(12 − 6) < 2(12 + 12)
3(6) < 2(24)
18 < 48: TRUE
(D) S:{42}
3(n − 6) < 2(n + 12)
3(42 − 6) < 2(42 + 12)
3(36) < 2(54)
108 + 108: FALSE
Therefore, the FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.
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Correct question:
Given the inequality 3(n − 6) < 2(n + 12), determine which integer makes the inequality false.
a. S:{−5}
b. S:{3}
c. S:{12}
d. S:{42}
out of 240 racers who started the marathon, 209 completed the race, 22 gave up, and 9 were disqualified. what percentage did not complete the marathon?
The percentage of racers that did not complete the marathon is 12.9 %
What is arithmetic?
Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots
Main Body:
Total racers = 240
racers that completed race = 209
so racers that did not complete the marathon = 240 - 209
= 31
percentage of racers that did not complete the marathon = (31/240)*100
= 12.9 %
Hence percentage of racers that did not complete the marathon is 12.9%
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Help me please
Use the line information to determine the slope and y-intercept
The slope and y-intercept of the given equations of line are shown below.
What is the slope intercept form of an equation ?When any equation is represented in the y = mx +c form, it is called the slope intercept from of the equation.
Here m is slope and c is constant.
(1)
y = 3x + 3
Slope m = 3
y intercept, at x =0,
y = 3
(2)
y = 3x - 3
Slope m = 3
y intercept, at x =0,
y = - 3
(3)
y = (1/3)x + 3
Slope m = 1/3
y intercept, at x =0,
y = 3
(4)
y = -(1/3)x + 3
Slope m = -1/3
y intercept, at x =0,
y = 3
(5)
y = (1/3)x - 3
Slope m = 1/3
y intercept, at x =0,
y = -3
(6)
y = -(1/3)x - 3
Slope m = -1/3
y intercept, at x =0,
y = -3
(7)
y = -3x + 3
Slope m = -3
y intercept, at x =0,
y = 3
(8)
y = -3x - 3
Slope m = -3
y intercept, at x =0,
y = - 3
The slope and y-intercept are shown above.
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Function g can be thought of as a translated (shifted) version of f(x) = x2.
++
-7-6-5-4-3-2
ल
1
उक्त
-2-
-3-
-5-
-6-
Write the equation for g(x).
9 (x) = [
9
+2
2 3 4 5 6 7
Answer: 3
Step-by-step explanation:
How can the triangles be proven similar by the SAS similarity theorem? I give brainiest
Answer:
Show that the ratios UV/XY and WV/ZY are equivalent, and ∠V ≅ ∠Y.
Please answer asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
I would be C
Step-by-step explanation:
lookup here
r+r+r+r+r in algebraic simplified
Answer:
5r
Step-by-step explanation:
r+r+r+r+r=5r
the sum of the height and radius of a right cylinder is 12 inches. what is the maximum volume of this cylinder
The maximum volume of this cylinder = 256π cubic inches
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
Let h be the height and r be the radius.
Then, h+r = 12
=> h=12-r
Volume of the cylinder (V):
V=πr²h
=> h= πr² ( 12-r )
=> h= π ( 12r² - r³ )
Differentiate with respect to r , we get
dv/dr = 24 πr - 3πr²
Find r by taking dv/dr=0
24 πr - 3πr² = 0
3π ( 8r - r² ) = 0
8r = r²
r=8
Again differentiating, we get
d²V/dr² = 24π - 6 π r
When r=8, 24π - 48 π <0
So, V is maximum at r= 8 inches
And h= 12-8= 4 inches
Hence, the required volume of the cylinder = π8²*4 = 256π cubic inches
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An employee at a paint manufacturing plant is mixing highly pigmented paint with some paint that is less pigmented. In addition to a large supply of 27%-pigment paint, he also has 160 liters of 12%-pigment paint. How many liters of the 27%-pigment paint should he add to the 12%-pigment paint to generate a batch of 15%-pigment paint?.
With the help of unitary method , we can say that ,To create a batch of 15%-pigment paint, he needs to mix 98.57 liters of the 27%-pigment paint with the 12%-pigment paint.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
Paint volume times pigment concentration equals pigment amount.
or
V × c = P
If the three options are referred to as 1, 2, and 3, then
P₁ + P₂ = P₃
V1c1 = V2c2 + V3c3
Let x equal the paint's 11% volume.
Then
230 × 21 % + x × 11 % = (230 +x) × 18 %
Add 4830 plus 11x to get 4140 plus 18x, then take 4140 away from each side.
690 + 11x = 18x Take 11 times off of each side.
Divide each side of 690 by 7 to get the answer.
x = 98.57 L
The worker needs to add 98.57 L of the paint with a 21% pigment.
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help answer right answers only
Answer:
3. 70 degrees
4. 110 degrees
Step-by-step explanation:
3. The angles are mirrored on both sides
4. A straight line is equal to 180 degrees so if <AED is 70 degrees then you would do 180-70 to get 110 degrees
B. If I go to be early, then I sleep well.
Converse:
Inverse:
Contrapositive:
The converse, inverse and contrapositive statements for the given conditional statement are :
Converse: if I sleep well, then I go to be early
Inverse: if I don't go to be early, then I don't sleep well
Contrapositive: if I don't sleep well, then I don't go to be early.
What is conditional statement?A conditional statement is a part of mathematical reasoning which is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning.
Given is a conditional statement, "If I go to be early, then I sleep well", we need to form its converse, inverse and contrapositive statements,
The rules for the given conditional statement are ;
Let p and q be the parts of the statement,
1) Converse statement = if p then q, converse = if q then p.
Therefore,
Converse: if I sleep well, then I go to be early.
2) Inverse statement = if p then q, inverse = if not p then not q.
Therefore,
Inverse: if I don't go to be early, then I don't sleep well.
3) Contrapositive statement = if p then q, Contrapositive = if not q then not p.
Therefore,
Contrapositive: if I don't sleep well, then I don't go to be early.
Hence, the converse, inverse and contrapositive statements for the given conditional statement are :
Converse: if I sleep well, then I go to be early
Inverse: if I don't go to be early, then I don't sleep well
Contrapositive: if I don't sleep well, then I don't go to be early.
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Solve for x on [0, 2pi]
secx-cscx=0
I know what the answer is but can someone help me with the process of finding it?
The required solution to the trigonometry equation is x = π/4 + π n.
The equation of trigonometry functions is given in the question as
secx - cscx = 0
We have to determine the solution to the given equation
As per the question, we have
⇒ secx - cscx = 0
⇒ 1/cosx - 1/sinx = 0
⇒ (-cosx + sinx)/cosxsinx = 0
Using property : f(x)/g(x) = 0 ⇒ f(x) = 0
⇒ -cosx + sinx = 0
Divided by cosx into the equation,
⇒ -1 + tanx = 0
⇒ tanx = 1
The general solution for tan tanx = 1 is
⇒ x = π/4 + π n
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donnell is doing market research for a major brand by surveying customers at a local mall the probability of a customer agreeing to take the survey is 22% what is the probability that one of the first five sustomers agrees to take the survey
The probability that one of the first five customers agrees to take the survey is 71%
Here we have to use binomial distribution.
What is binomial distribution?
A common probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It provides a summary of the number of trials when each trial has an equal chance of producing a particular result.
A binomial distribution with the following formula could be used to represent the proportion of clients who agree to participate in the survey out of 5:
X ~ Bin (n = 5, p = 0.22)
Thus the probability is computed as:
P(X >= 1) = 1 - P(X = 0) = [tex]1 - (1-0.22)^5[/tex]
= 0.71
The required probability in this case is therefore 71%.
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• f(x):
=
6-4x
4x+x
dy u uv-uvi
=
dx v
22
Blaste
Love
Answer:
Step-by-step explanation:
fx+35+lovebased2=94
some stickers were divided among avea, brianna, and carson in the ratio 1:3:4. brianna recieved 21 stickers. how many stickers did ava receive?
Avea received 28 stickers when brianna, and carson in the ratio 1:3:4 and brianna received 21 stickers.
What is a ratio?The ratio is defined as the comparison of two or more quantities of the same units, which shows how much bigger one quantity is than another.
Equating the ratios :Given,The ratio of the distribution of stickers among Avea, Brianna and Carson is 1:3:4
The number of stickers Briana received is 21
Let us consider x as the common factor of the given ratio then, The number of stickers received by the girls are
Avea = xBriana = 3x
Carson = 4x
As we know 3x = 21 x
= 21/3
= 7
then,4x
= 4×7
= 28
The number of stickers that Avea received is 28. Hence, the answer is 28
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In winter, apple prices suddenly increase by €0.75 per kilogram. Sam bought 3 kilograms of apples for the new price of €5.88.
Answer:
p represents the original per pound price
3p represents the cost of three pounds
3p + 3(0.75) = 5.88 multiply
3p + 2.25 = 5.88 subtract 2.55 from both sides
3p = 3.63 divide both sidesby 3
p = 1.21
The original price was $1.21 per pound.
1.21 = 0.75
1.96
3(1.96)
5.88
help help help help help me
What grade is that?
Step-by-step explanation:
find the mean, median and mode of these numbers: 9, 10, 9, 9, 11, 9, 10, 9, 9, 10 round all answers to the hundreth place.
The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is
Mean =9.5
Median = 11 or 9
Mode is 9
Given that,
The data is 9,10,9,9,11,9,10,9,9,10
The data's mean, median, and mode must be determined.
We know that,
The arithmetic mean of the provided data is another name for mean. If the data are grouped and sorted in ascending order, the median is the value that falls in the middle of the set of grouped data. The value that dominates the data is known as the mode. The Mean, Median, and Mode formulas are described independently for the group of data in the sections that follow.
The data is 9,10,9,9,11,9,10,9,9,10
Mean = 9+10+9+9+11+9+10+9+9+10/10 =95/10=9.5
Median = 11 or 9
Mode is 9
Therefore, The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is
Mean =9.5
Median = 11 or 9
Mode is 9
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there are a cup of milk and a cup of water. take one teaspoon of milk, put into the water cup; mix well. take one teaspoon of the mixture in the water cup and put into the milk cup then mix well. which is higher: the percentage of water in the milk cup or the percentage of milk in the water cup ?
The percentage of water in the milk cup and the percentage of milk in the water cup are same.
What is milk?
A white liquid meal called milk is generated by mammals' mammary glands. Before they can digest solid food, it is the main source of nutrition for young mammals. Milk immunity is influenced by immune components and immune-modulating elements.
Given:
There are a cup of milk and a cup of water.
Take one teaspoon of milk, put into the water cup; mix well.
Take one teaspoon of the mixture in the water cup and put into the milk cup then mix well.
Suppose the percentage of water cup are 'p' and the percentage of milk cup are 'q'.
When we add one teaspoon of milk and put into water cup then the percentage of water cup are 'p + 1'.
And the percentage of milk cup are 'q - 1'.
Again one teaspoon of mixture in the water cup put into the milk cup.
So, the percentage of milk cup are, q - 1 + 1 = q.
And the percentage of water cup are p + 1 - 1 = p.
The percentage will be same for both milk cup and water cup.
Hence, the percentage of water in the milk cup and the percentage of milk in the water cup are same.
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A radio station had 198 tickets to a concert. They gave away 5 times as many tickets to listeners as to employees. How many tickets did they give away to employees?
The number of tickets that they give away to employees is 33.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenarios.
Let the number of employees be x
Therefore, number of listener = 5x
Total number of people = 198
Therefore, this will be illustrated thus:
x + 5x = 198
6x = 198
Divide
x = 198/6
x = 33
Therefore 33 tickets are given to employees.
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What type of variable is required to construct a confidence interval for a population proportion?.
The confidence interval for a proportion should be constructed since the variable of interest is a person's opinion, which is a qualitative variable.
What is a qualitative variable?A trait that cannot be quantified is referred to as a categorical variable (also known as a qualitative variable).
Nominal or ordinal categorical variables are also acceptable.
Since the variable of interest is a person's opinion, which is a qualitative variable, the confidence interval for a proportion should be built.
Statistical Variables Qualitative variables also referred to as categorical variables are variables without a built-in sense of hierarchy.
As a result, they are quantified using a nominal scale.
For instance, a qualitative variable is a name as well as hair color (Black, Brown, Gray, Red, Yellow).
Therefore, the confidence interval for a proportion should be constructed since the variable of interest is a person's opinion, which is a qualitative variable.
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Aimee packs ice cream into an ice cream cone. She then puts a perfect hemisphere of ice cream on top of the cone that has a volume of 4 in.3 The diameter of the ice cream cone is equal to its height. What is the total volume of ice cream in and on top of the cone? Use the relationship between the formulas for the volumes of cones and spheres to help solve this problem. Show your work and explain your reasoning.
Answer:To help read it step by step until you understand trust me you will get it!
Step-by-step explanation:
The total volume of the ice cream in and on top of the cone is (16/3)πd³.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is 1/3 πr²h.
We have,
Volume of the hemisphere = 4 in³
The volume of ice cream.
= Volume of the hemisphere + Volume of the cone
= 4 + (1/3)π(d/2)²h
[ height = diameter ]
= 4 + (1/3) x π x d²/4 x d
= 4 + (1/3) x π x d³/4
= 4 + (4/3)πd³
= (16/3)πd³
Thus,
The volume of the ice cream is (16/3)πd³.
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Does the point (-7, 5) satisfy the inequality y > -3/7x +2
Answer:
Yes, the point (-7, 5) satisfies the inequality y > -3/7x + 2
Step-by-step explanation:
Plug in the values to the inequality and verify if it is true:
x = -7, y = 5
5 > (-3/7*-7) + 2
5 > (-3/-49) + 2
5 > 3/49 + 2
5 > 101/49
The inequality above is true (5 is greater than 101/49 [101/49 is about 2.06]), so the point (-7, 5) satisfies y > -3/7x + 2
Hurry please i have 24 hours to do this. The area of the triangle below is 29.25 square feet. What is the length of the base?
6.5 ft
Answer:
length of base = 9 feet
Step-by-step explanation:
b= base A= area h= height
[tex]b=2*\frac{A}{h} = 2*\frac{29.25}{6.5} = 9[/tex]
Kari's renter's insurance is set to increase by 10% per month after she files a theft claim. If her premium is $35 per month, what
will her new premium be?
$45 per month
$31.50 per month
$38 per month
$38.50 per month
Answer: $38.50 per month
Step-by-step explanation: We have to find 10% of 35 and add it to 35. This is because 10% of 35 is the amount that will increase so adding that to the original 35 will be her new premium. 10% of 35 is $3.50 and $3.50 + $35 is $38.50. This means her new premium is $38.50 per month.
a farmer wants to fence an area of 3750 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. what should the lengths of the sides of the rectangular field be so as to minimize the amount of fencing needed?
The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 3750, hence:
Area = length * width = x * y
3750 = xy
y = 3750/x
A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:
Amount of fencing needed (P) = x + x + y + y + y = 2x + 3y
Amount of fencing needed (P) = 2x + 3(3750/x) = 2x + 1800/x
To minimize the amount of fencing needed, dP/dx = 0, hence:
dP/dx = 2 - 1800/x²
2 - 1800/x² = 0
2 = 1800/x²
2x² = 1800
x² = 900
x = 30 feet
y = 600/x = 600/30 = 20 feet
Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet
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