The total number of animals in the farm is given by 200
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: The number of cows is 30 and they form 15% of the total animals on the farm.
Let the number of animals in the form be x then
15% of x=30
x=30×100/15
x=200
Hence, The total number of animals in the farm is given by 200
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ1
5x - 4y = 27; - 2x + y = 3
Answer: x=-13, y=-23
Step-by-step explanation:
y in terms of x
-2x+y=3
y=3+2x
Substitute in other equation:
5x-4(3+2x)=27
5x-12-8x=27
-3x=39
x=39/-3
x=-13
Solve for y, substitute for x:
-2(-13)+y=3
26+y=3
y=-23
elvis and costello bought 36 lemmons to make lemmondae elvid squxed 1/3 of them costello squezzed 4/9 their mom did the rest how many lemmons did the mom sqeze
Their mom squeezed 8 lemons and Elvis and Costello bought 36 lemons.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's represent the number of lemons Elvis squeezed "E", the number of lemons Costello squeezed "C", and the number of lemons their mom squeezed "M".
We know that:
E + C + M = 36 (because they bought 36 lemons in total)
E = (1/3) x 36 = 12 (because Elvis squeezed 1/3 of the lemons)
C = (4/9) x 36 = 16 (because Costello squeezed 4/9 of the lemons)
We can use the first equation to find the value of M:
M = 36 - E - C
Substituting in the values we know:
M = 36 - 12 - 16
M = 8
So their mom squeezed 8 lemons.
Learn more about the equation here:
brainly.com/question/10413253
#SPJ1
Evaluate geometric series sigma1^12 10×4^n-1
The value of the sigma notation is 55924050
How to evaluate the sigma notationFrom the question, we have the following parameters that can be used in our computation:
sigma1^12 10×4^n-1
Express properly
So, we have the following representation
[tex]\sum^{12}_{1} 10*4^{n-1[/tex]
The sum of the geometric series can be calculated using the formula:
S = a(1 - r^n)/(1 - r)
From the sigma notation, we have the following parameters
a = 10,
r = 4
n = 12.
Substituting these values, we get:
S = 10 * (1 - (4)^12) / (1 - 4)
Evaluate the expression
S = 55924050
Hence, the sum is 55924050
Read more about sequence at
https://brainly.com/question/6561461
#SPJ1
What is the limit of the function?
Select True or False for each limit statement
Answer:
all are True
Step-by-step explanation:
You want to know if the end behavior is properly described for the polynomial functions shown in the table.
-2x³ at -∞A function of odd degree with a positive leading coefficient has a graph that has a generally positive slope (/).
When the leading coefficient is negative, the slope is generally negative (\). In this case, the sign of the end behavior is opposite the sign of x.
x → -∞, -2x³ → ∞ . . . . . True
2x⁴ at ∞A function of even degree with a positive leading coefficient has a graph that generally opens upward (U). The sign of the end behavior will match the sign of the leading coefficient.
x → ∞, 2x⁴ → ∞ . . . . . True
-9x⁵ at ∞This function is of odd degree with a negative leading coefficient. The sign of the end behavior is opposite the sign of x.
x → ∞, -9x⁵ → -∞ . . . . . True
All the Limit statement are True
Explain about the limit of the function?
If the polynomial functions indicated in the table's final behavior are appropriately explained, you wish to know.
-2x³ at -∞
The graph of an odd-degree function with a positive leading coefficient has a generally upward slope (/).
The slope is often negative when the leading coefficient is negative. The sign of the end behavior is thus the opposite of the sign of x.
x -, -2x3 -∞ are True
2x⁴ at ∞
The graph of an even degree function with a positive leading coefficient typically opens upward (U). The final behavior's sign will coincide with the leading coefficient's.
x, 2x4 ∞ are True
To learn more about limit of the function refer to:
https://brainly.com/question/23935467
#SPJ1
i currently average a 7 over the first 3 test of the year. what do i need to average over the 4 test in order to bring my overall to an 8?
Answer:
11
Step-by-step explanation:
You have an average of 7 on 3 tests, and you want to know the score required of the 4th test to make the average be 8.
AverageThe average is the sum, divided by the number.
If you have an average of 7 on the first 3 tests, the sum of those scores is ...
average = sum/number
7 = sum/3
21 = sum
If you want an average of 8 on 4 tests, the sum of the scores must be ...
8 = sum/4
32 = sum
In order to increase the sum of scores from 21 to 32, you must have a score of ...
32 -21 = 11
You need to score 11 on the 4th test to bring the average to an 8.
__
Alternate solution
The difference between the scores you have and the average you want is ... 3(7 -8) = -3.
In order to bring your average up to 8, you need to have a total of 3 more points than that average on your 4th test: 8 + 3 = 11. (This brings the total of differences from average to zero: (-1) +(-1) +(-1) +(3) = 0.)
Your 4th test must have a score of 11 to bring your average on 4 tests up to 8.
What is the answer to this question?
The unknow angle in the isosceles triangle is as follows:
m∠C = 80 degrees.
How to find the angles of an isosceles triangle?An isosceles triangle is a triangle that has two of its sides equal to each other and also have two if its angles equal to each other.
The base angles of the isosceles triangles are equal and the legs of the triangle are equal.
Therefore, in ΔABC
AB = BC
Hence,
m∠A ≅ m∠C
The angle A and angle C are the base angles. This makes them congruent to each other.
Therefore,
m∠C = 80 degrees
learn more on isosceles triangle here: https://brainly.com/question/2456591
#SPJ1
The equation of the plane passing through the point (-8,3,7) and parallel to the plane 4x + 8y ~ 2z = 45, is given by 4x - 8y - 2z = -22 4x + 8y + 2z = -22 4x + 8y _ 2z = -22 4x + 8y - 2z = 22
The equation of the plane passing through the point (-8,3,7) and parallel to the given plane will be 4x + 8y - 2z = -22.
The given equation of the plane is 4x + 8y - 2z = 45.
To find the equation of the plane which passes through the point (-8,3,7) and is parallel to the given plane, we need to calculate the values of x, y and z in the given equation.
We have x = -8, y = 3 and z = 7 in the given point.
Substituting these values in the given equation, we get
4(-8) + 8(3) - 2(7) = 45
-32 + 24 - 14 = 45
-22 = 45
This is not possible.
Hence, the equation of the plane passing through the point (-8,3,7) and parallel to the given plane will be 4x + 8y - 2z = -22.
Learn more about equation of the plane here:
https://brainly.com/question/27190150
#SPJ4
A two member beach volleyball team decided they wanted new uniforms. The
swimsuits cost $58 and the visors cost $24 each. What is the total cost of the new
uniform for all of the members?
O $58
O $82
O $116
O $164
the expression \root(4)(10mn) and (10mn)^((1)/(4))are equivalent or not equivalent
The expression \root(4)(10mn) and (10mn)^((1)/(4)) are equivalent
What are index forms?Index forms are described as that number written in the form of an exponential expression.
It is also described as a single number raised to another number.
The exponent of an exponential expression explains how many times to multiply the base by itself to simply the expression.
Standard forms and scientific notation are other names for index forms.
It is important to note that the fourth root of a number or variable is the biquadratic root.
From the information given, we have that;
[tex]\sqrt[4]{10mn}[/tex]
[tex](10mn)^1^/^4[/tex]
Note the following;
√2 = 2^1/2
∛2 = 2^1/3
Hence, the expressions are equivalent
Learn about index forms here:
https://brainly.com/question/15361818
#SPJ1
TRAVEL Marion is travelling 500 miles by car. She drives 250 miles at an average rate of x miles per hour the first day and the remaining 250 miles at an average rate of x−5
miles per hour. Select the expression that represents the amount of time Marion spent traveling the 500 miles. (Hint: Write out the units to determine how to solve the problem.)
Multiple choice question.
A)
x(x−5)/500x−1250
B)
62,500/x(x−5)
C)
500x−1250/x(x−5)
D)
500/2x−5
Answer:
C) (500x - 1250)/x(x - 5)----------------------------------
We know that the equation for the time is:
time = distance / speedFind the time at travel in the first day:
250/xFind the time at travel in the second day:
250/(x - 5)To find the total time add app the two expressions we got above:
250/x + 250/(x - 5) = 250[1/x + 1/(x - 5)] = 250(x - 5 + x)/x(x - 5) = 250(2x - 5)/x(x - 5) = (500x - 1250)/x(x - 5)There matching choice is C.
The area of a square with a side 2.4m in length
Answer:
Below
Step-by-step explanation:
Squares have equal side lengths
area = side X side
= 2.4 m X 2.4 M = 5.76 m^2
C Question 2 (SO3, AC1, AC2, AC3, AC4) Harry intends to complete a BSc degree. He has to take either Mathematics A or Physics A in his first year. If he takes Mathematics A, he can take chemistry A or Mathematics B in His second year. If he takes Physics A, he has to take Mathematics A in his second year. When Harry has to make a choice between two subjects both are likely to be chosen 1. Draw a decision tree to illustrate the above situation. 2. What is the probability that he will take Mathematics A during the two years? 3. What is the probability that he will take Mathematics A and B during the two years? [6 [2 (2
The overall probability that Harry will take Mathematics A during the two years is (0.5 * 0.5) + (0.5 * 1) = 0.75
The probability that Harry will take Mathematics A and B during the two years is (0.5 * 0.5) = 0.25
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
The probability that Harry will take Mathematics A in his first year is 50%. If he takes Mathematics A in his first year, there is a 50% chance he will take it again in his second year. If he takes Physics A in his first year, he has to take Mathematics A in his second year. So the overall probability that Harry will take Mathematics A during the two years is (0.5 * 0.5) + (0.5 * 1) = 0.75The probability that Harry will take Mathematics A and B during the two years is (0.5 * 0.5) = 0.25To learn more about Probability, Visit
https://brainly.com/question/24756209
#SPJ1
Many people say they want to be rich. What are some legitimate ways you can become financially wealthy as an adult? Your own words!
Answer:
see below
Step-by-step explanation:
1. study hard and go to a good college and then find a good job.
2. be intelligent on spending and save money to invest in the financial markets
3. buy a few life insurance policies with living benefits.
4. find a niche on social media and create contents to attract followers, and then invest the earnings in stock market or bond market.
5. invest in real estate
6. start a small business and then grow into franchise.
From 1994 to 2003, the amount of athletic equipment E (in millions of dollars) sold domestically can be modeled by E(t) = -10t^3 + 140t^2 - 20t + 18,150where t is the number of years since 1994. Use the following steps to find the year when about $20,300,000,000 of athletic equipment was sold. a. Write a polynomial equation that can be used to find the answer. b. List the possible whole-number solutions of the equation in part (a) that are less than 10.c. Use synthetic division to determine which of the possible solutions in part (b) is an actual solution. Then calculate the year which corresponds to the solution.
In a synthetic polynomial , the real solution of 2 is found; the year is 1996, and $20,300,000,000 was sold.
a. 20,300,000,000 = -10t^3 + 140t^2 - 20t + 18,150
b. Suggestions for the problem: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
b. To solve, use synthetic division; the solution is 2; the year is 1996.
In order to discover the year in which the specified quantity of sporting equipment was sold, we must create a polynomial equation. E(t) = -10t3 + 140t2 - 20t + 18,150, where t is the number of years since 1994, is the equation given in the problem. We must rewrite the equation so that the right side equals 20,300,000,000 in order to determine the year in which $20,300,000,000 worth of sporting equipment was sold. After that, the equation is 20,300,000,000 = -10t3 + 140t2 - 20t + 18,150, which needs to be solved. The equation can have whole-number solutions that are less than 10, including 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We may use synthetic division to identify which of these answers is the true solution. this method, the coefficients of the equation are divided by the coefficient of the equation with the highest degree, and the quotient is then multiplied by the solution. Until the last portion is identified, this process is repeated. The answer is the quantity that equals the remainder.
Learn more about polynomial here
https://brainly.com/question/11536910
#SPJ4
Find the 45th term of the arithmetic sequence an = 2 + 4(n − 1).
Group of answer choices
182
178
145
264
Step-by-Step Explanation:
n = 45
Therefore, 2 + 4(n - 1)
Putting n = 45, we have
2 + 4(45 - 1)
= 2 + 4 × 44
= 2 + 176
= 178
Answer:
B) 178
Hope it helps.
If you have any query, feel free to ask.
Find the volume of the solid of revolution obtained by rotating the region bounded by the curve
y=3xâx2 and the line y=2x about the y-axis.
The region enclosed by the curve y=3x-x2 and the line y=2x can be rotated about the y-axis to determine the volume of the solid of revolution. The cylindrical shell method can be used to determine this volume.
The cylindrical shell method can be used to determine the volume of the solid of revolution created by rotating the area enclosed by the curve y=3x-x2 and the line y=2x about the y-axis.
We must first determine the region's boundaries.
At x=2 and y=4, y=2x.
When y=3x-x2, x=0, and y=0.
As a result, the region's boundaries are x=0 to x=2 and y=0 to y=4.
The following formula determines the solid's volume:
Volume equals b a 2 y r2 d y
where x is a constant and r is the cylindrical shell's radius.
As a result, the solid of revolution's volume is given by:
Volume = 4.002y x 2.2dy
= 2π ∫4 0 (3x2-x3)dx
= 2π [x3-x4/4]
4 0
= 2π (16/4)
Learn more about volume here
https://brainly.com/question/16134180
#SPJ4
Identify the type of sampling used in this example.
A researcher randomly selected 50 of the nation's middle schools and interviewed all of the teachers at each school. a. random
b. cluster
c. stratified
d. systematic
The type of sampling used in this example is a. random sampling
One of the most straightforward methods for gathering information from the entire population is random sampling. Every member of the subset has an equal chance of being chosen as part of the sampling process when using random sampling. For instance, if an organization employs 300 people overall, a sample group of 30 workers will be chosen to participate in the survey. In this instance, the population is the entire workforce of the organization, and the sample is 30 employees. Since all of the employees who were picked to participate in the survey were chosen at random, every worker has an equal chance of getting chosen.
To know more about random sampling visit :
https://brainly.com/question/29852583?referrer=searchResults
#SPJ4
Based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). Which of the following statements is true?
answer choices
90% of the time, the mean amount of money that all students spend on lunch at this high school will be between $3.45 and $4.15.
90% of all students spend between $3.45 and $4.15 on lunch at this high school.
90% of all random samples of 50 students obtained at this high school would result in a sample mean amount of money students spend on lunch between $3.45 and $4.15.
90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.
Approximately 45 of the 50 students in the random sample will spend between $3.45 and $4.15 on lunch at this high school.
The right answer is that a 90% confidence interval containing the actual mean amount of money kids spend on lunch would be produced by 90% of all random samples of 50 students collected at this high school.
It is given that the 90% confidence interval for the mean amount of money students spend on lunch time at a high school is ($3.45,$4.15)
A 90% confidence interval interprets that, 90% of the random samples will result in a 90% confidence interval that contain the true value of the population parameter.
In other words, 90% of the random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.
Thus, the correct answer is option (D) or The right answer is that a 90% confidence interval containing the actual mean amount of money kids spend on lunch would be produced by 90% of all random samples of 50 students collected at this high school.
To know more about confidence interval click here:
brainly.com/question/24131141
#SPJ4
Write an equivalent expression by distributing the "-" sign outside the parentheses:
-(-3.4c + 1)
Answer: 3.4c - 1
Step-by-step explanation:
multiply each part within the parentheses by the negative sign
so -3.4c x -1 = 3.4c
and 1 x -1 = -1
add those two together and we get 3.4c - 1
Calculate the volume of the Surface Area of pyramid 12cm height and 12cm base and 14cm weights
The volume of the pyramid is, 72 cm³.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Height of pyramid = 12 cm
Base of pyramid = 12 cm
Weight of pyramid = 14 cm
Now, We know that;
⇒ Volume of pyramid = 1/2 × Base × Height
Substitute all the values, we get;
⇒ Volume of pyramid = 1/2 × 12 × 12
⇒ Volume of pyramid = 6 × 12
⇒ Volume of pyramid = 72 cm³
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ1
PLEASE HURRY!!!! FOR 30 POINTS!!
Mr. Snow made snacks in separate gift bags. He gave one each to the 536 sixth-grade students going on the field trip. Then he gave 30 bags to the students in Mrs. Bond’s class for decorating the trophy cases. Next he gave 25 to the students in Mrs. Fuller’s class for helping during the school play. Mr. Snow had 3 snacks left. How many snacks did he make?
A . 600 snacks
B. 596 snacks
C. 594 snacks
D. 584 snacks
In the cuboid below all lengths are in centimetres. The cuboid has a volume of 196cm cubed. Find the value of k.
The value of k in the cuboid is 7 cm when the volume is 196cm³.
What is volume?The space taken up by any three-dimensional solid constitutes a volume, to put it simply. They can be a cube, cuboid, cone, cylinder, or sphere.
The volumes of various shapes vary. In three-dimensional geometry, we have examined a variety of solids and shapes that are defined in three dimensions, including cubes, cuboids, cylinders, cones, etc. We are going to learn to calculate the volume for each of these shapes.
The volume of cuboid = l × b × h
Here,
4 × k × k = 196cm³
k² = 196/4
k² = 49
k = √49
k = 7
Thus, The value of k in the cuboid is 7 cm when the volume is 196cm³.
Learn more about volume
https://brainly.com/question/13338592
#SPJ1
a study was conducted to help determine which of the top two political parties the general population would prefer to vote for in the up-coming election. in determining whom to include in the sample, two stages were involved. at the first stage, a random sample of 50 individuals was selected from each of the 20 regions in the country and then pooled into a combined sample of 1,000. at the second stage, these 1,000 individuals were divided into 5 income-level groups, and a random sample of 50 from each group was selected. Select all of the statements regarding the sampling design in the above scenario that are true:
The study does not involve a voluntary response.
The first stage creates a stratified random sample.
The whole study creates a multistage random sample.
The second stage involves simple random sampling only.
The true statements are the study does not involve a voluntary response, the first stage creates a stratified random sample and the whole study creates a multistage random sample.
In the given question, the study done ideally creates a multistage random sample. There are two parts to the sampling process for the study in the given question. Initially, a combined sample of thousand of individuals was assembled by combining a randomly selected sample of fifty individuals, that were from each of the 20 regions of each nation. The next step was to choose a random sample of fifty individuals from every one of the five income groups represented among those 1,000 individuals.
Additionally, because the study doesn't entirely rely on a discretionary answer, individuals were picked by a random sample approach rather than explicitly or through self-selection. A stratified random sample is also created during the initial step. This shows that a random sample was drawn from each subgroup after the dataset was separated into groups.
Read more about sample on:
https://brainly.com/question/26941429
#SPJ4
Andy buys x cakes.
Betty buy 4 times as much as Andy
Colin buy 3 times as much as Betty
Each cake costs 65p
The total cost was £52.65
How much cakes did each person buy?
Each person buys a number of cakes
Andy: 13Betty: 52Colin:16What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy
So,
Andy has = x Cakes
Betty have = 4x Cakes
Clin has = x +3 Cakes
Since each cake costs 65p and the total cost of the cakes is £52.65
thus,
0.65( x + 4x + x +3) = 52.62
x + 4x + x +3 = 81
6x = 78
x = 13
Therefore,
Andy has = 13 cakes
Betty has = 4x = 4*13 = 52 cakes
Colin has = x + 3 = 16 cakes
Learn more about Mathematical operations here:
https://brainly.com/question/20628271
#SPJ1
This funnel is in the shape of a cone.
Determine the volume of the following cone.
The height of the cone is 20 cm and the R is 5 cm
Answer:
Exact volume: 500π/3 cm³
Approximate volume: 523.6 cm³
Step-by-step explanation:
For a cone,
V = (1/3)πr²h
V = (1/3)π(5 cm)²(20 cm)
V = 500π/3 cm³ ≈ 523.6 cm³
convert the following unsigned binary numbers to hexadecimal. a. 1101 0001 1010 1111 b. 001 1111 c. 1 d. 1110 1101 1011 0010
Answer:
a. D1AF
b. 1F
c. 1
d. EDB2
Step-by-step explanation:
You want these unsigned binary numbers converted to hexadecimal.
a. 1101 0001 1010 1111
b. 0001 1111
c. 0001
d. 1110 1101 1011 0010
HexEach group of 4 bits can take on any of 16 different values. Conveniently, each of those corresponds to a hexadecimal digit, as shown in the attachment.
To do the conversion, we replace each group of 4 bits by its hexadecimal equivalent.
a. D1AF
b. 1F
c. 1
d. EDB2
__
Additional comment
A couple of the given numbers are one or more bits short of a group of 4 bits. You may want to check your actual problem statement to see if the numbers here are the same. The attached table applies in any event.
Sandra wants to buy an Apple iPad Pro (12.9-inch display) costing $900.00. Her parents have agreed to pay $5 for every $2 that Sandra saves. How much will each contribute?
To purchase the Apple iPad Pro, based on an equation, Sandra contributed $257 while her parents contributed $643.
What is an equation?An equation is a mathematical statement that states that two or more mathematical expressions are equal or equivalent.
Mathematical expressions are depicted as equations using variables, constants, numbers, and values and the equation symbol (=).
The total cost of the Apple iPad Pro = $900
The contribution of Sandra's parents per $2 = $5
The contribution of Sandra = $2
Let x = the variable contributed by each party
Equations:2x + 5x = 900
7x = 900
x = 128.57
Sandra's contribution = $257 (2 x 128.57)
Parents contribution = $643 (5 x 128.57)
Learn more about equations at https://brainly.com/question/2972832
#SPJ1
Elena wants to add (2.3×105)+(3.6×106) and writes (2.3×105)+(3.6×106)=5.9×106. Find Elena's mistake and fix it.
What was her mistake? I havent seen any comments saying anything about it.
The mistake of Elena is that the powers of the terms were not the same and the correct result is 3.83 ×10^6.
What was the mistake?We have to note that the addition of the exponents is not just like the addition of the ordinary numbers that we know. The operation of the addition of the exponents would require an extra care to ensure that the powers of the two terms to be added is exactly the same.
In the work of Elena; (2.3×10^5)+(3.6×10^6)=5.9×10^6. This is wrong because the powers of the terms on the right hand side are not the same. As such the correct approach would be;
0.23 × 10^6 + 3.6×10^6 = 3.83 ×10^6
Learn more about exponents:https://brainly.com/question/5497425
#SPJ1
You randomly choose one of the tiles shown. Select the favorable outcome(s) of choosing a 6.
Answer:
Step-by-step explanation:
I DONT UNDERSTAND
find the maclauvins series of f(x) = x ln(2x+1) what in the rc of the obtained seties
The Maclaurin series is xln(2x + 1) - x^2 + (2x^3)/3 - (2x^4)/4 + ... and the arc is (-1/2, 1/2).
How to determine the Maclaurin seriesFrom the question, we have the following parameters that can be used in our computation:
f(x) = x ln(2x+1)
The Maclaurin series of f(x) = x ln(2x + 1) can be found by using the power series expansion of the logarithm function and the definition of a derivative.
Starting with the power series expansion of ln(1 + x):
ln(1 + x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...
We can then substitute x = 2x + 1 - 1 to obtain the power series expansion of ln(2x + 1):
ln(2x + 1) = (2x + 1 - 1) - (2x + 1 - 1)^2/2 + (2x + 1 - 1)^3/3 - (2x + 1 - 1)^4/4 + ...
= 2x - x^2 + (2x^3)/3 - (2x^4)/4 + ...
Next, we use the definition of a derivative to find the Maclaurin series of f(x) = x ln(2x + 1):
f'(x) = d/dx (x ln(2x + 1)) = ln(2x + 1) + x * d/dx ln(2x + 1)
= ln(2x + 1) + x * (2 - 2x + 2x^2 - 2x^3 + ...)
= ln(2x + 1) + 2x - 2x^2 + 2x^3 - 2x^4 + ...
Therefore, the Maclaurin series of f(x) = x ln(2x + 1) is:
f(x) = ∫ f'(x) dx = ∫ (ln(2x + 1) + 2x - 2x^2 + 2x^3 - 2x^4 + ...) dx
= xln(2x + 1) - x^2 + (2x^3)/3 - (2x^4)/4 + ...
How to determine the arc of the seriesThe arc of a Maclaurin series refers to the range of values for x for which the series converges to the actual value of the function.
For the Maclaurin series above, the range of convergence depends on the function ln(2x + 1) which has a singularity at x = -1/2.
This implies that the Maclaurin series converges for all x such that |x| < 1/2.
Rewrite as
(-1/2, 1/2)
So, the arc of the series is (-1/2, 1/2).
Read more about Maclauring series at
https://brainly.com/question/3804324
#SPJ1