An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive terms is always the same.
This common difference is called the common ratio of the arithmetic progression. The general form of an arithmetic progression is a, a + d, a + 2d, ..., where a is the first term and d is a common difference.
The nth term of an arithmetic progression can be found by using the formula: a_n = a + (n-1)d, where a is the first term, d is a common difference, and n is the position of the term in the progression.
If a, b, and c are in arithmetic progression, then the common difference is (b-a) = (c-b).
If d, e, and f are also in arithmetic progression, then the common difference is (e-d) = (f-e).
If a, d are the same and b, e are the same, then c = f.
so the common difference between both progressions is the same, and c = f
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let , and be arithmetic progressions. if and , then what is ? let , and be arithmetic progressions. if and , then what is the common difference
PLEASE HELP FINAL QUESTION TO UNIT TEST
A company makes cars at two factories. Some of the cars need repairs in the first year and some do not. This two-way frequency table shows the proportion of cars at each factory that need repairs or do not need repairs in the first year.
Which conclusions can be made from this table?
Select each correct answer.
Responses
Compared to Factory A, Factory B has a larger percentage of cars that do not need repairs.
Compared to Factory A, Factory B has a larger percentage of cars that do not need repairs.
More cars from Factory B need repairs than do not need repairs in the first year.
More cars from Factory B need repairs than do not need repairs in the first year.
For both factories, more cars need repairs than do not need repairs in the first year.
For both factories, more cars need repairs than do not need repairs in the first year.
Among cars from Factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
Among cars from Factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
Need repairs in first year Do not need repairs in first year
Factory A 0.05 0.95
Factory B 0.02 0.98
The conclusions that can be made from this table include:
Compared to Factory A, B has a larger percentage of cars that do not need repairs.Among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first yearHow to explain the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
From the information, factory A for those who need repairs is 0.05 in the first year. In this case, among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
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A) BCD is a straight line.
Triangle ABC is equilateral.
CE = DE
E
Not drawn
accurately
32
A
X
B
C
D
Work out the size of angle x.
(4)
+
PLEASE HELP ME I AM REALLY STUCK!!!
The size of angle x = 46 degree.
Now, According to the question:
A triangle in which at least two sides are equal is called an isosceles triangle. Following this fact, if two sides of a triangle are equal, then the angles opposite to those sides are also equal.
"Information available from the question"
Since Δ ABC is equilateral then interior angles = 60°
Since CE = DE then Δ CDE is isosceles and the base angles are congruent,
So,
∠ ECD = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74 degree
BCD is a straight line, then the 3 angles on it sum to 180°, that is
60° + 74° + x = 180°
134° + x = 180° ( subtract 134° from both sides )
Hence, The size of angle x = 46°
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in any 15-minute interval, there is a 20% probability that you will see at least one shooting star. what is the probability that you see at least one shooting star in the period of an hour
So, the probability that you see at least one shooting star in the period of an hour is 59.04%.
The probability of seeing at least one shooting star in a 15-minute interval is 20%, so the probability of not seeing a shooting star in that interval is 80%. The probability of not seeing a shooting star in an hour-long period is the product of the probability of not seeing a shooting star in each of the four 15-minute intervals, which is 0.8 * 0.8 * 0.8 * 0.8 = 0.4096 or 40.96%. Therefore, the probability of seeing at least one shooting star in an hour-long period is 1 - 0.4096 = 59.04%.
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In an isosceles triangle, the length of sides b and c are 8. The length of median B is 7. Find the length of the base of the triangle
The length of the base is 2√15 units. The median of an isosceles triangle divides the triangle into two equal parts.
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.
A median in a triangle is a line that runs from one corner (or vertice) to the centre of the other side. Triangle congruence makes it easy to demonstrate an isosceles triangle's property that the median to the base is perpendicular to the base.
According to the Pythagorean theorem,
AD² + BD² = AB²
7² + BD² = 8²
BD² = 64 - 49
BD² = 15
BD = √15
The median divides the base into two equal parts.
The length of the base is 2√15.
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Please help me, I need the inequality only
The solution of the inequality is x < 60 and graph is shown in the image attached
How to solve and graph an inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.
Let x represent the number of days.
Since 25 tables is being shipped daily and we want to find how many days will there be fewer than 1500 tables, we can write:
25x < 1500
x < 1500/25
x < 60
Note: fewer than means less than i.e. <
The graph is shown in the image attached
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I got 2 different answers. 1 or 100% and also 0.2962... can i please get clarification on which of these i did is correct?
The probability that the first item is not the first to be delivered is 0.6667
How to determine the probabilityRepresent the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.
The probability that the first item arrives is 1/3.The probability that the second item arrives is 1/3,The probability that the third item arrives is 0.So, the probability that one of the other two items arrives first is
1/3 + 1/3 = 2/3.
The probability that the first item is not the first to be delivered is
1 - 2/3 = 1/3
Evaluate
1 - 2/3 = 0.6667
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A cylindrical candle is sold in a gift box
that is a square-based prism. What is
the volume of empty space in the box?
Radius 8 cm
Height 16 cm
The volume of empty space in the box will be 220cm³
The diameter of the candle is equal to the width of the box (the length of the side of the square base of the box), and the height of the box is equal to the height of the candle, assuming that the candle fits tightly inside the box without wasting any room.
You may compute the prism's volume by multiplying it by the square base's area (height).
The area of the circular base can be used to compute the volume of the candle's cylinder (height).
The square box base's side measures 8 cm long, hence its area is equal to that measurement= 8cm²=64cm²
The candle's diameter is two times its radius, hence the radius is 8cm/2=4cm
area of the circular base thus Equals (A = π r²).
=πx4²
=16π²
Since the height of the candle and of the box is 16cm, the difference in volume is 1024-256π
=220cm³
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2. Your boss has decided to make room for new models of digital cameras by discounting old models. In order to sell them quickly, she wants to sell them at the store’s original cost before markup. She asks you to change the price tags and make signs with the percent of discount. Knowing that the stores’ percent of markup on digital cameras in 40%, and the original price of a camera is $175.50. What was the store's original cost on this camera?
Knowing that digital camera merchants typically mark up their products by 40%, even when a camera's actual cost is $175.50 The price of one rupee is $438.75.
What does cost price mean in math?Your boss has chosen to give old models of digital cameras a discount in order to make place for new ones. She wants to offer them for sale at the store's original price, without a markup, in order to move them quickly. You are requested by her to alter the price tags and create signage indicating the percentage of the reduction. A digital camera costs $175.50 at the manufacturer's suggested retail price, with shops adding 40% to that figure.
cost = ($175.50 / 40 ) × 100 = $438.75
In mathematics, the cost price formula, often known as C.P., is used to determine an object's exact price.The price that a buyer pays for a good, service, or commodity, according to the definition of C. P.In the estimation of profit and loss calculations for a specific purchase, it is frequently utilized.
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Dirt being hauled by two trucks to a construction site is modeled by the expression xS+yRS+R. Truck 1 can haul x cubic yards and truck 2 can haul y cubic yards. Truck 1 makes S trips to the construction site, while truck 2 makes R trips. Which TWO statements are correct?
S + R represents the total trips done by these trucks.
What is volume?Volume is defined as the amount of space occupied by an object that is bound by a boundary. It must be noted that the volume is a mathematical term that is only applicable to 3D (three-dimensional) objects or spaces. As such, the units commonly used for volume are cubic units, that is, m3, cm3, in3, etc.
Two dump trucks hauling rock to a construction site is given by the expression. xS + yR
S +R
Truck 1 can haul x cubic yards
Truck 2 can haul y cubic yards.
Truck 1 makes P trips to the construction site, while truck 2 makes R trips.
Hence the trips made by truck 1 and truck 2 should be the addition of the trips made by the trucks individually.
So the total trips is represented by S + R
Therefore, S + R represents the total trips done by these trucks.
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a rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. the photograph measures $8$ inches high and $10$ inches wide. what is the area of the border, in square inches?
The area of the border is 72 square inches - 80 square inches = -8 square inches.
What is rectangle ?
A rectangle is a four-sided geometric shape with four right angles. The opposite sides of a rectangle are of equal length and parallel to each other, and the opposite angles are equal. The length and width of a rectangle are its two dimensions, with the length being the longer side and the width being the shorter side.
To find the area of the border, subtract the area of the photograph from the total area of the photograph and the frame. The total area of the photograph and the frame is the area of the frame (which is just the border) plus the area of the photograph.
The area of the photograph is 8 inches * 10 inches = 80 square inches
The area of the frame is the perimeter of the photograph (28 + 210) multiplied by the width of the border, which is 2 inches. So the area of the frame is 2*(28 + 210) = 2*36 = 72 square inches.
Therefore, the area of the border is 72 square inches - 80 square inches = -8 square inches.
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use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class.
(a)The class width = 3
(b) The class midpoint of the first class = 51
(c) The class boundaries of the first class = (49.5, 52.5)
Consider the frequency distribution in the following image.
We know that in frequency distribution the class width is nothing but the distance between the lower limits of consecutive classes.
Whereas the range is the difference between the maximum and minimum data entries.
The smallest number is 50, and the largest is 62.
So the range is 62 - 50 = 12
We know that the formula for the class width:
Class width= upper limit – lower limit +1
So, the class width = 52 - 50 + 1
= 3
The formula for the midpoint of each class:
midpoint = (lower limit of class + upper limit of class)/2
Let us assume that m be the midpoint of the first class.
Using above formula of midpoint:
m = (50 + 52)/2
m = 51
We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.
So, the class boundaries of the first class = (49.5, 52.5)
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The ratio of the measures of the angles of a triangle is 5:7:9. How many degrees is the largest angle? Round answer to the nearest whole number.
please help giving 20 points
Answer:
well the best I can say is maybe multiply all of the numbers
Step-by-step explanation: The first stepunderstanding[tex]5 \times 7 \times 9 = x \div 3[/tex]
second stepproving35*9=x÷3
315÷3
just do the 315÷3 and you should get an answer
Ricardo has 2 cases of video games with the same number of games in each case. He gives 4 games to his brother. Ricardo has 10 games left. How many video games were in each case?
Answer:7 games
Step-by-step explanation:2 cases= x games
you give 4 or 2 from each case
divide 10 by 2 and get 5 them add 2 to your answer and get 7 GAMES
BOOM!!
Part 3: Put It All Together- The table below lists the costs and prices for four businesses involved in
making, distributing, and selling bread. Use the information to answer the questions below.
Cost of Inputs
$0
$0.50
$1.50
$2.25
Price of Output
$0.50
$1.50
Farmer Fred
Baker Bob
Trucker Tom
$2.25
Retail Rob
$3.50
16. Calculate the GDP using value-added approach. Explain how you got your answer.
The GDP using value added approach is $3.50
How to calculate the GDP?GDP using value added approach is calculated by obtaining the sum total of value added by each production unit.
Value added by Farmer Fred = Price of output - Cost of inputs = $0.50 - $0 = $0.50
Value added by Baker Bob = Price of output - Cost of inputs = $1.50 - $0.50 = $1.00
Value added by Trucker Tom = Price of output - Cost of inputs = $2.25 - $1.50 = $0.75
Value added by Retail Rob = Price of output - Cost of inputs = $3.50 - $2.25 = $1.25
GDP = Value added by Farmer Fred + Value added by Baker Bob + Value added by Trucker Tom + Value Added by Retail Rob
GDP = $0.50 + $1.00 + $0.75 + $1.25
GDP = $3.50
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In a certain city, each block is about 275
meters long. If the post office is 13 blocks
away from the library, approximately how
many miles is it from the post office to the
library? Round your answer to the nearest
tenth. Step-by-step
If the post office is 13 blocks away from the library and each block is 275 meters, approximately, the distance from the post office to the library, in miles, is 2.2 miles.
How is the distance or number of miles determined?To determine the distance or the number of miles from the post office to the library, we use unit conversions and mathematical operations (multiplication and division).
Using multiplication, the number of blocks is converted to meters.
The distance is converted from meters to miles by division.
The distance of a block in the city = 275 meters
The number of blocks from the library to the post office = 13 blocks
The distance from the post office to the library = 3,575 meters (13 x 275)
1,609.34 Meters = 1 Miles
The distance in miles from the post office to the library = 2.2 miles (3,575/1,609.34)
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Term to term rule is subtract 2 and multiply 4 the third term is 248 what is the two previous term
The two previous terms of 248 are 64 and 18.
A term-to-term rule is a rule that will describe calculating the following terms of a sequence given by the previous term.
In the given problem, the rule is to subtract 2 and multiply by 4.
Considering that the third term is 248. we can utilize the rule to figure out the subsequent term.
248 = (4 * (x - 2))
248 = 4x - 8
256 = 4x
x = 64
So the subsequent term is 64.
To find the initial term, we can utilize a similar rule once more
64 = (4 * (x - 2))
64 = 4x - 8
72 = 4x
x = 18
So the initial term is 18.
Therefore, the two previous terms of 248 are 64 and 18.
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Castanea received the first 2 of Christopher Paolini's books from the inheritance cycle and was very excited to start reading them over the winter break. The first book - Eragon - had 530 pages.
Castenea reads 1 page every 72 seconds How long in hours : minutes : seconds, did it take her to finish the book?
(Example: A total of 6264 seconds is equal to 1 hour 44 minutes 20 seconds)
Castanea finished Eragon on the 3rd day of her break and continued to the 2nd book "Eldest". If she continued to read at the same rate, and it took a total of 14 hours 8 minutes and 24 seconds to finish reading "Eldest", how many pages were in Eldest (the second book) ?
Using arithmetic operations it is found that -
It took Castenea 10 hours and 36 minutes to finish the first book Eragon.
The number of pages in Castenea's second book Eldest is 707.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The number of pages in Eragon is = 530 pages
The rate for Castanea's reading is = 1 page/72 seconds
The time taken by Castanea to finish the first book is -
Time Taken = Number of Pages × Time taken to read 1 page
Use the arithmetic operation of multiplication.
Substitute the values in the equation -
Time Taken = 530 × 72
Time Taken = 38160 seconds
To convert seconds into minutes use the arithmetic operation of division.
38160 / 60 = 636 minutes
To convert minutes into hour use the arithmetic operation of division.
636 / 60 = 10.6 hour
Therefore, it took Castanea 10 hours 36 minutes to finish the first book.
The time took by Castanea to finish the second book = 14 hours 8 minutes and 24 seconds
To convert hours into minutes use the arithmetic operation of multiplication.
14 × 60 = 840 minutes
To convert minutes into seconds use the arithmetic operation of multiplication.
848 × 60 = 50880 seconds
Use the arithmetic operation of addition to get the total seconds -
50880 + 24 = 50904 seconds
The rate for Castanea's reading is = 1 page/72 seconds
The number of pages in Castanea's second book is -
Number of Pages = Time Taken in total/Time taken to read 1 page
Use the arithmetic operation of division.
Substitute the values in the equation -
Number of Pages = 50904/72
Number of Pages = 707
Therefore, there were seven pages in the second book.
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Photo attached. Please help.
Answer:
There is no real solution set for this equation
Step-by-step explanation:
We have
[tex]\sqrt{2x-1}+7=4[/tex]
Move 7 to the right side:
[tex]\sqrt{2x-1}+7-7=4-7\\\\\sqrt{2x-1}=-3\\\\[/tex]
If we treat 2x - 1 as a function f(x) then we are getting
[tex]\sqrt{f(x)} = -3\\\\[/tex]
But the square root of a function cannot be negative for real values of x
Hence there is no real solution set
Solve the system of linear equations by substitution. 4x−2y=14 y=1/2x−1
4x−2y=14
Step-by-step explanation:
Answer:
The solution to the system of linear equations is x = 4, y = 1.
Step-by-step explanation:
Given system of linear equations:
[tex]\begin{cases}4x-2y=14\\y=\dfrac{1}{2}x-1\end{cases}[/tex]
To solve the system of linear equations by the method of substitution, substitute the second equation into the first equation:
[tex]\implies 4x-2\left(\dfrac{1}{2}x-1\right)=14[/tex]
Solve the equation for x:
[tex]\implies 4x-x+2=14[/tex]
[tex]\implies 3x+2=14[/tex]
[tex]\implies 3x=12[/tex]
[tex]\implies x=4[/tex]
Substitute the found value of x into the second equation and solve for y:
[tex]\implies y=\dfrac{1}{2}(4)-1[/tex]
[tex]\implies y=2-1[/tex]
[tex]\implies y=1[/tex]
Therefore, the solution to the system of linear equations is:
x = 4, y = 1On a team, 3 girls and 2 boys scored a total of 27 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 15. Each girl scored the same number of points, and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
Answer: Let x be the number of points scored by each girl and y be the number of points scored by each boy.
We know that:
3x + 2y = 27 (the total number of points scored by the 3 girls and 2 boys)
3x - 2y = 15 (the difference between the number of points scored by the girls and the number of points scored by the boys)
We can use the second equation to find the value of one of the variables and substitute it into the first equation.
3x - 2y = 15
3x = 15 + 2y
Substitute this into the first equation:
(15 + 2y) + 2y = 27
2y = 12
y = 6
Now that we know that each boy scored 6 points, we can substitute that back into the second equation to find the number of points each girl scored:
3x - 2y = 15
3x - 2(6) = 15
3x = 27
x = 9
So each girl scored 9 points and each boy scored 6 points.
Step-by-step explanation:
On a team have 3 girls and 2 boys
Let say each girl points scored=x
Let say each boy points scored=y
Total scored by 3 girls and 2 boys =27
3x +2y=27----------1
The difference between points of 3 girls and 2 boys =15
3x-2y=15---------2
Solve equation 1 and 2
From 2nd equation
we can rewrite as :
3x=15+2y---------3
Submit 3rd equation in 1st equation.
15+2y+2y=27
4y=27-15
4y=12
y=3
Therfore, each boy points scored=3
For find each girl scored points
Submit y=3 in 1st equation.
3x+2(3)=27
3x=27-6
3x=21
x=7
Therfore, each girl points scored=7
Therfore,number of points each boy scored by =3points
Therfore,number of points each girl scored by =7points
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(8.6 x 10-7) - (4.3 x 10-7)
Answer: 43
Step-by-step explanation:
Multiply 8.6 and 10 then subtract 7 then you do 4.3 times 10 then you subtract then subtract the values you get
how to find the y intercept of a polynomial function
To find the y intercept of a polynomial function solve the function for the input value of zero.
We know that a polynomial function is a function that contains only positive integer exponents of a variable.
The highest power of a polynomial function is the degree of polynomial function.
A polynomial is generally represented as P(x).
The domain of a polynomial function is entire real numbers (R).
We know that the y-intercept is the value of the function for which the function has an input value of zero.
To find the y intercept of a polynomial function P(x) we substitute x = 0 and solve the polynomial function.
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jacy arrnanged cans on a store shelf. there are 126 cans in all. jacy makes rows of 6 cans how many rows will she make?
Answer:
126 cans in total / 6 cans per row
126/6 = 21 rows of cans
a square is cut out of a circle whose diameter is approximately feet. what is the approximate area (shaded region) of the remaining portion of the circle in square feet? ( where )
The approximate area (shaded region) of the remaining portion of the circle in square feet is 55.94 ft².
We know that,
the side of square=2*[r*√2/2]=r*√2 that is being taken out.
diameter = 14 ft and radius , r = 7 ft.
the side of square=7*√2=9.89 ft
[area of the remaining portion of the circle]=[ area of a circle]-[area of a square]
[area of a square] = (7√2)²=98 ft²
[ area of a circle] = π*r²= π x 7^2 = 153.94 ft²
therefore,
[area of the remaining portion of the circle]=153.94 - 98=55.94 ft²
the answer is 55.94 ft².
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in a scientific research, a statistical test resulted in a -value of 0.026. match each value with the correct decision. (a) do not reject h0 (b) reject h0
Any p-value less than 0.05 is a cause to reject the null hypothesis.
What is Null Hypothesis?
The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.
In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).
Any p-value less than 0.05 is a cause to reject the null hypothesis.
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This figure consists of two squares. The length of each side is a whole number of feet. The combined area of the squares is 100 feet. What is the perimeter of the entire figure in inches?
The perimeter of the entire figure is 40 inches
How to determine the perimeter of the figureIt is important to note that the formula for area of a figure is expressed as;
A = a²
Where;
A is the area of the squarea is the length of side of the squareThe total area is 100 feetA + A = 100
a² = 100
Take the square root of both sides
a = √100
a = 10 inches
The formula for calculating the perimeter of a square is expressed as;
Perimeter = 4a
Substitute the value of a, we have;
Perimeter = 4(10)
expand the bracket
Perimeter = 40 Inches
Hence, the perimeter is 40 Inches
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Dan is a software salesman. His monthly salary is $1800 plus an additional $60 for every copy of English is Fun he sells.
Let S represent his total salary this month (in dollars), and let N represent the number of copies of English is Fun he sells. Write an equation relating S to N, and then graph your equation using the axes below.
The linear function relating S to N is given as follows:
S(n) = 1800 + 60n.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the amount earned for each extra copy.b is the intercept, representing the base monthly salary.The parameter values for this problem are given as follows:
m = 60, b = 1800.
Hence the function is defined as follows:
S(n) = 1800 + 60n.
The function is graphed on the image given at the end of the answer.
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A transformation is applied to a figure to create a new figure. Which transformation does not preserve congruence?
When a transformation is applied to a figure to create a new figure then Dilation do not preserve congruence but do preserve orientations.
Rotations, reflections, translations, and dilation are only a few of the many transformations. Dilation do not preserve congruence but do preserve orientations. Rotations, reflections, and translations all preserve congruence and are referred to as isometries.
Maintaining congruence refers to a transformation where the side lengths and angle measurements of the Image and Pre-Image are the same.
An object's orientation refers to how its related parts are ordered. As long as the components of an item remain in the same sequence, rotation and translation retain orientation. Orientation is not maintained by reflection.
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J and M are base angles of trapezoid JKLM. If measure J is 4x+1 and measure M is 12x-95, find measure K and show your work!
Since J and M are base angles of trapezoid JKLM, the measure of k is 168°.
What is an isosceles trapezoid?The base angles of an isosceles trapezoid are congruent and equal. This ultimately implies that, an isosceles trapezoid has base angles that are always equal in magnitude.
By equating the given base measures of isosceles trapezoid JKLM, we can determine the specific value of x and angle k as follows;
m∠J = m∠M
4x + 1 = 12x - 95
By re-arranging and collecting like terms, we have the following:
12x - 4x = 95 + 1
8x = 96
By dividing both sides of the equation by 8, we have the following:
x = 96/8
x = 12.
Therefore, the measure of k is given by:
m∠k = 180 - 12
m∠k = 168°.
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A circular plot of land has a diameter of 6ft. if the walkway around this piece of land has a width of 2x, what is the total area of the land and walkway combined?
The area of the circle, as a function of x, will be:
A(x) = 3.14*(3ft + 2x)²
What is the total area of the land and walkway combined?We know that for a circle of radius R, the area is:
A = pi*R²
Where pi = 3.14
In this case we have a circular plot of land with a diameter of 6ft, then the radius (half of that) is:
R = 6ft/2 = 3ft
And then we have a walkway with a width of 2x, then the radius of the circle that includes the walkway is:
R' = 3ft + 2x
Replacing that in the area equation we will get:
A(x) = 3.14*(3ft + 2x)²
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