Describe two different ways to obtain the image below.

Caden's speed is 10 mph and Rahquez's speed is 16 mph faster, which is 16+6 = 32 mph

Let's use the formula: distance = rate x time

Since Caden and Rahquez are traveling towards each other, their combined distance will be 208 miles. Let's call Caden's speed "x" and Rahquez's speed "x+6", since Rahquez is traveling 6 mph faster than Caden.

Using the formula above, we can set up the equation:

208 = (x + x + 6) * 8

Simplifying, we get:

208 = (2x + 6) * 8

208 = 16x + 48

160 = 16x

x = 10

Therefore, Caden's speed is 10 mph and Rahquez's speed is 32 mph.

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Answer:

Factor 64h^3+216k^9

Step-by-step explanation:

The given expression is a sum of two terms:

[64h^3+216k^9

Notice that each term has a common factor. For the first term, the greatest common factor (GCF) is 64h^3, and for the second term, the GCF is 216k^9. So we can factor out these GCFs to get:

64h^3+216k^9 = 64h^3(1 + 3k^6)

This expression cannot be factored any further, so the final answer is:

64h^3+216k^9 = 64h^3(1 + 3k^6)

If you can, give me brainliest please!

The geometric sequence is 9 + 2 + 20 = 29.

The smallest number the third term in the geometric sequence can be is 29.

This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,

the third term of the geometric sequence is 9 + 2 + 20 = 29.

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The decision that most clearly reflects a lack of understanding of the concept of sunk costs is "You study eight hours for a final exam even though there is no way now that you can pass the course".

Sunk costs refer to any costs that have already been incurred and cannot be recovered. Sunk costs are irrelevant in decision-making because they are already gone and cannot be recovered. Decision-makers must only consider future costs and benefits when making decisions.

A lack of understanding of sunk costs may result in individuals making decisions based on past costs rather than future costs and benefits. Decision-making that is influenced by sunk costs may result in inefficient resource allocation and lost opportunities.

Individuals must ignore sunk costs and instead focus on future costs and benefits to make effective decisions.

In the given options, "You study eight hours for a final exam even though there is no way now that you can pass the course" is the decision that most clearly reflects a lack of understanding of the concept of sunk costs.

Even though the student has already spent 8 hours studying, the sunk costs are irrelevant because the student cannot pass the course now. The student should focus on future costs and benefits and use the remaining time to study for other courses.

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Answer:

x^2 +6x+7

Step-by-step explanation:

for roots a and b

x^2 - (a+b)x + ab = (x-a)(x-b)

in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

How to calculate the rate?

To answer these questions, we need to calculate the population and food supply at different points in time and compare them.

Let's first calculate the population after t years:

Population after t years = 2,000,000 * (1 + 4%) raise to the power t

And the food supply after t years:

Food supply after t years = 4,000,000 + 0.5 million * t

Now, let's answer the first question:

If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur?

If the country doubles its initial food supply, the new food supply would be 8,000,000, and it would still increase at a rate of 0.5 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%)^t = 8,000,000 + 0.5 million * t

Solving for t, we get t ≈ 17.77 years.

So, in approximately 18 years, the population would exceed the food supply, even if the country doubles its initial food supply and maintains a constant rate of increase in the supply adequate for an additional 0.5 million people per year.

Now, let's answer the second question:

If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?

If the country doubles the rate at which its food supply increases, the new rate would be 1 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%) raise to the power t  = 16,000,000 + 1 million * t

Solving for t, we get t ≈ 21.96 years.

So, in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

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Answer:

The first one

Step-by-step explanation:

Use the pythagoras theorem=a ^2+b^2 =c^2

Use a is 9 b is 40 because the largest value is always the hypotenuse and the hypotenuse is always c.

so you do 9 squared add 40 squared to find c squared.

Square root the answer and you get 41 so it is a pythagoras triple

There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.

Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability

The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.

Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:

Experimental probability = Number of bassists / Total number of musicians

Experimental probability = 15 / 89

Experimental probability = 0.1685 or approximately 16.85%

As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.

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Answer:

Step-by-step explanation:

To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.

First, we need to convert 1 1/4 to an improper fraction:

1 1/4 = (4 x 1 + 1)/4 = 5/4

Then, we can multiply the fractions:

5/7 x 5/4 = 25/28

As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.

 π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .

When variables and coefficients are combined using arithmetic procedures like addition, subtraction, multiplication, and non-negative integer exponents, the result is a mathematical expression known as a polynomial. Any numerical value may be represented by the variables, and the expression's coefficients are constants that combine the variables.

given

A =  πr², where r is the circle's radius, is the method for calculating a circle's surface area. The area of one circle can be expressed as follows if the radius of each circle is (4a–6):

A₁ = π(4a-6)²

If we condense this phrase, we get:

A₁ = π(16a² - 48a + 36)

A₂ = π(4a-6)²

A₂ = π(16a² - 48a + 36)

A₃ = π(4a-6)²

A₃ = π(16a² - 48a + 36)

A₄ = π(4a-6)²

A₄ = π(16a² - 48a + 36)

We can add up the areas of each of the four circles to determine their combined area:

A1 + A2 + A3 + A4 Equals A total

A total is equal to π (16a2 - 48a + 36) +  π(16a2 - 48a + 36) +  π(16a2 - 48a + 36).

 π(64a2 - 192a + 144) = A total

 π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .

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Let's denote the width and length of the pool by “w” and “l” respectively. Then, the width of the pool and deck combined would be:So the equation that represents the total area of the pool and deck as binomials is [tex]: A = 2(L + 8)(2L + 8)[/tex]

Let's start by drawing a diagram of the rectangular pool and the surrounding deck:

 ___________  Pool Length (L)

|           |

|           |

|           |

|           |

W|___________|

| Deck Width|

|    = 4ft  |

|___________|

We know that the width of the pool (W) is twice its length (L), so we can write:

[tex]W = 2L[/tex]

We also know that the deck is 4ft wide on each side, so the total width of the pool and deck is:

[tex]W_total = W + 8 = 2L + 8[/tex]

And the total length of the pool and deck is:

[tex]L_total = L + 8[/tex]

The total area of the pool and deck can be found by multiplying the total width by the total length:

[tex]A = W_total \times L_total[/tex]

Substituting our expressions for W_total and L_total, we get:

[tex]A = (2L + 8) * (L + 8)[/tex]

Expanding the brackets, we get:

[tex]A = 2L^2 + 24L + 64[/tex]

So the equation that represents the total area of the pool and deck is:

2L^2 + 24L + 64

To represent the sides of the shape as binomials, we can factor out a common factor of 2 from the quadratic expression:

[tex]A = 2(L^2 + 12L + 32)[/tex]

Then we can write the sides of the shape as:

[tex]L + 8[/tex]   and [tex]2L + 8[/tex]

Therefore, So the equation that represents the total area of the pool and deck as binomials is: [tex]A = 2(L + 8)(2L + 8)[/tex]

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x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.

The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².

It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.

Given,

DF = 24

DE = 25

Using Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

25² = x² + 24²

x² = 25² - 24²

x² = 625 - 576

x² = 49

x = √49

x = 7

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The number of ways to form an 8-person committee with 4 men and 4 women is 9,180. The number of ways to form a committee with at least 2 men is 70,320. The number of ways to form a committee with more women than men is 7,620. This can be solved by the concept of  Permutation and Combination.

If the committee must contain four men and four women, there are 7,425 ways to form the committee. If there must be at least two men, there are 58,275 ways to form the committee. If there must be more women than men, there are 26,207,700 ways to form the committee.

To find the number of ways to form a committee with four men and four women, we can use combinations. The number of ways to choose 4 men out of 12 is 495, and the number of ways to choose 4 women out of 15 is 1,365.

To get the total number of ways, we can multiply these numbers:

495 x 1,365 = 7,425.

To find the number of ways to form a committee with at least two men, we need to consider two cases: 2 men and 6 women, and 3 men and 5 women. For the first case, we can choose 2 men out of 12 in 495 ways, and 6 women out of 15 in 5,005 ways. For the second case, we can choose 3 men out of 12 in 2,190 ways, and 5 women out of 15 in 3,003 ways.

To get the total number of ways, we can add these numbers:

495 x 5,005 + 2,190 x 3,003 = 58,275.

To find the number of ways to form a committee with more women than men, we can use a different approach. We can count all the possible committees with 1 man, 2 men, 3 men, and 4 men, and then subtract the committees that have more men than women. There are 15 ways to choose 1 man, 330 ways to choose 2 men, 3,960 ways to choose 3 men, and 12,870 ways to choose 4 men.

To count the committees with more men than women, we can use the complement rule. This means we need to count the committees with 4 men and 0, 1, 2, or 3 women, the committees with 3 men and 0 or 1 women, the committees with 2 men and 0 women, and the committee with 1 man and 0 women.

Adding these numbers gives us the total number of committees with more women than men:

15 + 330 + 1,320 + 2,772 + 330 + 15 = 26,207,700

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There are 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.

To calculate this, we can use a combination formula. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the size of the group and r is the number of people in the committee.

In this case, n = 15 and r = 3.

Using this formula, we can calculate that there are 15! / (3! * (15 - 3)!) = 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.

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Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.

Interest earned in First Oak account after 5 years at 6% simple interest:

= 0.06 x $800 x 5

= $240

Interest earned in West United account after 5 years at 5% compounded annually:

= $800 x (1 + 0.05)^5 - $800

= $800 x 1.27628 - $800

= $221.02

Total interest earned in both accounts:

= $240 + $221.02

= $461.02

Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.

Answer:huh,

Step-by-step explanation:I don’t understand you’re saying

The subtraction of the polynomials (3.1x + 2.8z) - (4.3x - 1.2z) is -1.2x + 4x

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

(3.1x + 2.8z) - (4.3x - 1.2z)

open parenthesis

3.1x + 2.8z - 4.3x + 1.2z

combine like terms

3.1x - 4.3x + 2.8z + 1.2z

-1.2x + 4x

Ultimately, -1.2x + 4x is the results of the subtraction of the polynomial.

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ARMY DISBANDED MEANS SOLDIERS WERE RELEASED FROM SERVICE

When George Washington became president in 1789, the army he had

commanded in the American Revolution had disbanded. This means that

the soldiers were released from service and the military units were

dissolved after the end of the war.He pursued two intertwined interests:

military arts and western expansion. At 16 he helped survey Shenandoah

lands for Thomas, Lord Fairfax. Commissioned a lieutenant colonel in 1754,

he fought the first skirmishes of what grew into the French and Indian War.

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The area of the equilateral triangle is 36√3 square units

What is area of the equilateral triangle?

Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.

In an equilateral triangle, the center, the centroid, and the circumcenter coincide.

The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.

The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.

So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.

The area of an equilateral triangle with side length s is given by:

A = (s² * √3) / 4

Substituting s = 12, we get:

A = (12² * √3) / 4

= 36√3

Therefore, the area of the equilateral triangle is 36√3 square units.

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Answer: 239

Step-by-step explanation:

Darius wrote 2 integers 256 and -17. The question is asking you to solve how much larger is 256 than -17. This means you will subtract 256 by -17 which will give you 239 (256-17). The answer remains positive because 256 is larger

Hope this helps

Answer: They are exactly 273 places away.

Step-by-step explanation:

If a number is larger than another number then you need to subtract it to get the distance. In this case, you look at the subtraction to see how far away they are.

Hope this helps!

Have a blessed day!

The angle of rotation in standard form is 251.5651 degrees.

The length of arc S is approximately 20.94 feet.

If the point (-1, -3) is on the circle x² + y² = 10, then we can substitute these values for x and y in the equation to obtain:

(-1)² + (-3)² = 10

1 + 9 = 10

So, the point (-1, -3) satisfies the equation of the circle.

To find the angle of rotation in standard form, we need to use the formula:

tan(θ) = y/x

where θ is the angle of rotation.

In this case, x = -1 and y = -3, so we have:

tan(θ) = (-3)/(-1)

tan(θ) = 3

θ = tan⁻¹(3)

Using a calculator, we find:

θ ≈ 1.2490 radians or 71.5651 degrees

To express in standard form, add 180 degrees to the angle in order to obtain an angle between 0 and 360 degrees:

θ ≈ 71.5651 + 180 ≈ 251.5651 degrees

To find the length of an arc S given the radius r and the central angle θ, we use the formula:

S = (θ/360) x 2πr

In this case, r = 15 ft and θ = 1.396 radians

Substituting the values:

S = (1.396/2π) x 2π(15 ft)

S ≈ 1.396 x 15 ft

S ≈ 20.94 ft

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Complete question:

Consider the point (-1, -3), which is on the circle x² + y² = 10. Find the angle of rotation in standard form

Find the length of the arc S when r = 15 ft and θ = 13.96°

The area of the figure rounded to the nearest square meter is 97 m². So correct option is A.

With five equal sides and five equal angles, a regular pentagon is a polygon. In other words, a regular pentagon's sides and angles are all congruent. It is a closed, two-dimensional object that is categorized as a sort of polygon since it is constructed of straight line segments.

Regular pentagons have a number of distinctive features, including:

A regular pentagon has 108 degree internal angles that are all equal.

A standard pentagon's outside angles are all 72 degrees in angle.

A regular pentagon is divided along its diagonals into three smaller triangles, two of which are congruent.

Regular pentagons are prevalent in a variety of fields, including geometry, architecture, and the arts.

First, you would need to determine the side length of the regular hexagon. This can be done using the radius of the circumscribed circle, which is given as 5 meters. The side length of the hexagon can be calculated using the formula:

s = r * √(3)

where s is the side length and r is the radius of the circumscribed circle. Plugging in the given value for r, we get:

s = 5 * √(3)

simplifying, we get:

s ≈ 8.7 meters

Next, you would need to calculate the area of one of the congruent triangles. This can be done using the formula:

A = (1/2) * b * h

where A is the area of the triangle, b is the base, and h is the height. The base of the triangle is equal to one side of the hexagon, which we just calculated to be approximately 8.7 meters. To find the height, we can draw an altitude from one vertex of the triangle to the opposite side, creating a 30-60-90 right triangle. The height is equal to the shorter leg of this triangle, which can be calculated using the formula:

h = (1/2) * s * √(3)

Plugging in the value for s, we get:

h ≈ 7.5 meters

Now we can calculate the area of one of the triangles:

A = (1/2) * 8.7 * 7.5 ≈ 32.6 square meters

Finally, we can calculate the total area of the figure by adding the area of the hexagon to three times the area of one of the triangles:

A = 6 * (s²) * √(3)/4 + 3 * A

Plugging in the values we calculated, we get:

A ≈ 96.9 square meters

Rounding to the nearest square meter, we get:

A ≈ 97 square meters

Therefore, the answer is A. 97 m².

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Answer:

4t - 22

Step-by-step explanation:

To find:-

Answer:-

To find out the perimeter we can simply add all the side lengths of the given figure. Since the given figure here is a rectangle, we can add up all the four sides to find the perimeter.

The four sides given to us are t-6 , t-5 , t-6 and t-5 .

Hence the perimeter of the quadrilateral would be ,

Perimeter = t-5 + t-6 + t-5 + t-6

Perimeter = 4t - 10 - 12

Perimeter = 4t - 22

Hence the perimeter of the given figure us 4t - 22.

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{$\sf\large t-5$}\multiput(-1.4,1.4)(6.8,0){2}{$\sf\large t-6$}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture} [/tex]

Therefore , the solution of the given problem of unitary method comes out to be the parking lot has 60 trucks.

It is possible to accomplish the objective by using this widespread convenience, pre-existing variables, or all significant components from the initial Diocesan adaptable survey that adhered to a specific methodology. If it doesn't, both of the essential components of a term confirmation outcome will undoubtedly be lost, but if it is, there is going to be another opportunity to contact the entity.

Here,

Let's begin by giving the unknowns variables:

x = number of vehicles

Van count = 4 times

Since there are 205 cars overall, the number of lorries is equal to (205 - 11x).

The value of x can be determined using the second bit of knowledge:

=> 4x/3 = (205 - 11x)/2

When we simplify this solution, we obtain:

=> 8x = 3(205 - 11x)

=> 8x = 615 - 33x

=> 41x = 615

=> x = 15

We can now determine the quantity of vans:

Van count = 4x = 4(15) = 60

Consequently, the parking lot has 60 trucks.

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Answer:

the area ot the triangle is half the area of the rectangle, so the area of the triangle is what sqauare units

Answer: It's  much easier to form a rectangle and multiply the width and the length and then divide it by 2  

a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

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the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).To find the location of the receiver, we first need to determine the equation of the paraboloid.

The standard equation for a paraboloid of revolution with a vertical axis is:

z = [tex](x^2 + y^2)[/tex]/(4f)

Where:

z is the height at any point (x, y) on the paraboloid.

x and y are the horizontal coordinates of the point.

f is the focal length of the paraboloid, which is half the depth of the dish.

In this case, the dish is 6 feet across at its opening, so the diameter is 6 feet and the radius is 3 feet. Therefore, the maximum value of x and y is 3 feet. The depth of the dish is given as 2 feet.

Using these values, we can solve for the focal length:

2 = [tex](3^2 + 3^2)[/tex]/(4f)

2 = 18/(4f)

f = 18/8 = 9/4 = 2.25 feet

Now that we have the value of f, we can find the location of the receiver, which is placed at the focus of the paraboloid. The focus is located at (0, 0, f).

Therefore, the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).

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Answer: $ 46.50

First divided 31 by 2

Which equals...

15.50

Then add 15.50 to 31.

46.50

The answer is $46.50

As a result, the circumference of the circular walkway is approximately 367.06 square feet.

A circle is a geometric shape made up of all points that are equally spaced apart from the center. It is a flat, two-dimensional object whose radius or diameter serves as its sole defining characteristic. A circle's circumference is the distance around it, while the area of the circle is the amount of space inside it.

given

We must deduct the area of the smaller circle from the size of the larger circle in order to determine the area inside the circular path. Let's use the abbreviations "r" for the smaller circle's radius and "R" for the larger circle's radius. We are aware that the circumference of the smaller circle, which is 132 feet, is equal to the distance around the circular path.

The wider circle's circumference is 132 feet.

2πR = 132

R = 21

The breadth of the circular path, which is equal to the difference between the radii of the two circles, can now be used to calculate the radius of the smaller circle:

R - r = diameter of the circle

21 - r = diameter of the circle

r = 18

The smaller circle therefore has a radius of 18 feet.

Inside the arc of the path, there is:

R2 - r2 equals (21 - 18) = (44 - 324) = (117) 367.06 square feet.

As a result, the circumference of the circular walkway is approximately 367.06 square feet.

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