Please answer this calculus question:

The length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

Using the formula obtained from Pythagoras' theorem, distance can be computed.

The distance formula in coordinate geometry is:

(P, Q) = √ (x2 – x1)² + (y2 – y1)².

Given points: (5, 4) and (−3, −1)

d = √ (-3 - 5)² + (4 + 1)²

d = √ 64 + 25

d = √ 89

d = 9.43

Thus, the length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

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The measure of side AC of the right triangle is 7.2 units.

The figure in the image is the of a right triangle.

To solve for the measure of side AC, we use trigonometric ratio.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Tangent = Opposite / Adjacent

tan( A ) = BC / AC

Plug in the values and solve for side AC.

tan( 51° ) = 8.9 / AC

AC = 8.9 / tan( 51° )

AC = 8.9 / 1.234897

AC = 7.2

Therefore, side AC has a value of 7.2 units.

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As an example, the 78-mph speed limit in the United States is equivalent to the 130 km/h restriction in Germany.

How quick is that speed?

A connection with a speed of 100 Mbps or higher is considered fast internet. Broadband internet speed is defined by the federal communications regulator (FCC) as 25 Mbps for downloading and 3 Mbps for upload.

We can increase each number by 0.6 to convert overall speed limitations from kilometers per hour into miles per hour. Here is the revised table:

Country Speed Limit (km/h)  Speed Limit (mph)

Germany         130                    78

France             110                     66

Italy                 150                     90

Japan              100                      60

Australia          110                       66

United Kingdom 113              67.8

Hence, Because one kilometer is equivalent to 0.6 miles, it is evident that speed limits in the form of miles per hour were lower than those in kilometers per hour.

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these two events are dependant because the probability of the second event depends on the probability of the first event

The sum of all the edges in the solid shape is 24 unit.

Length is a measurement οf distance οr size. It can refer tο the physical extent οf an οbject, the size οf an area, οr the amοunt οf time sοmething takes. Length is measured in units such as centimeters, meters, feet, inches, yards, miles, and sο οn. Length is an impοrtant cοncept in mathematics and physics, used tο measure distances and calculate speed and οther quantities.

The sum οf all the edges in the sοlid shape is 24. This is calculated by adding the 4 edges οf the square (4 x 1 = 4) plus the 12 edges οf the 4 equilateral triangles (12 x 1 = 12).

Therefοre, 4 + 12 = 24.

Since all the sides οf the triangles and the square are equal in length, it can be said that all the edges in the sοlid shape are equal. This means that the length οf each edge is equal tο 24/24, οr 1. This means that the length οf each edge οf the sοlid shape is 1 unit.

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Complete question:

The solid shape below is made up four equilateral triangles and a square. What is the sum of all the edges in the solid shape?​

[Given each side is 1 unit]

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Answer:

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

Answer:

9 54 divided by 9 = 6  72 - 18 = 54

Step-by-step explanation:

The function g(x) is translation of f(x) 9 units up. The solution has been obtained by using transformation.

An operation known as a transformation involves moving a polygon or other two-dimensional object on a plane or coordinate system.

We are given that the function g(x) is a translation of the function

f(x) = x².

In the graph, we can see that the vertex of the parabola is at (0, 9).

This means that the function g(x) is 9 units up from the function f(x).

So, g(x) = x² + 9

Hence, the function g(x) is translation of f(x) 9 units up.

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The model of the exponential function is y = 3.40(1.86)^x

From the question, we have the following parameters that can be used in our computation:

(6, 140) and (7, 260)

The exponential function for the model can be expressed as:

y = ab^x

Where

b = 260/140

b = 1.86

So, we have

y = a(1.86)^x

Substitute the known values in the above equation, so, we have the following representation

140 = a(1.86)^6

This gives

a = 140/(1.86)^6

Evaluate

a = 3.40

This means that

y = 3.40(1.86)^x

Hence, the function is y = 3.40(1.86)^x

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The domain and range of h(n) are the set of whole numbers

The domain and the range of h(n)

Given that

The function h(n), represents the count of houses.

Both n and h(n) can take only whole values.

So, we have the domain and range to be the set of whole numbers

Evaluating h(5) and h(11)

The number of houses is the same as the figure number

This means that

h(5) = 5 and h(11) = 11

The explicit function of h(n)

By the computations above, we have the formula of h(n) to be:

h(n) = n

The values of s(4) and s(7)

Given that

The function s(n), represents the count of segments.

Where the segment is twice the figure number

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

By the statement above, we have the growth pattern to be a proportional equation with a constant rate of change

The explicit function of s(n)

Based on the statements above, we have

s(n) = 2n

Complete the table for f(5) and f(7)

From the table, we can see that

As n increases, the value of f(n) is divided by 2 to get the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

The domain of f(n)

The possible values of n are real numbers

So, we have

Domain: All set of real numbers

The observation of the function

Above, we have

As n increases, the value of f(n) is divided by 2 to get the next term

This means that

As n gets larger and larger, the value of f(n) get halved

The value of g(4)

From the question, we have

First term, a = 9

Common ratio, r = 2

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

Completing the statements

Based on the function definitions, the statements when completed are

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

Divide the equations

g(24)/g(21) = 729

Hence, the value of the ratio is 729

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When given the area of a rectangle, and one of the sides, the unknown measure of the rectangle would be 40 meters

To find the area of a rectangle, you can use the formula:

A = l x w

where A is the area of the rectangle, l is the length of the rectangle, and w is the width of the rectangle.

Seeing as you were given the area to be 2, 800 square meters and one of the sides measures 70 meters, the unknown measure of the rectangle would be:

70x Unknown = 2, 800

Unknown = 2, 800 / 70

Unknown measure = 40 meters

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Full question is:

Area = 2,800 square meters

Side A = 70 meters

Find the unknown measure of the rectangle

Step-by-step explanation:

$60÷8=$7.50

divide by 8 because 5+3=8

each book should of cost $7.50

Answer: 32 presents can be wrapped with 8 yards of ribbon

Step-by-step explanation:

Convert yards to inches

1 yard = 36 inches

8 yards = 288 inches

Divide 288 inches by 9 inches

288/9 = 32

Answer: You can wrap 32 presents with 8 yards.

Step-by-step explanation:

So, first, you need to know how many inches are in a yard. There are 36 inches in 1 yard.

Then, do 36 inches times 8 yards to figure out how many yards are in 8 yards. So in 8 yards, there are 288 inches.

Finally, do 288 divided by 9 to figure out how many present you can wrap with 8 yards (288 inches).

You can wrap 32 presents with 8 yards.

I hope this helped!

Answer:

Step-by-step explanation:

We can use the distributive property and basic algebraic operations to multiply the given expression:

(2x+3)(x^2 - 6x - 2)

= 2x(x^2 - 6x - 2) + 3(x^2 - 6x - 2) // Distribute 2x and 3

= 2x^3 - 12x^2 - 4x + 3x^2 - 18x - 6 // Multiply each term

= 2x^3 - 9x^2 - 22x - 6 // Combine like terms

Therefore, (2x+3)(x^2 - 6x - 2) simplifies to 2x^3 - 9x^2 - 22x - 6.

The figure is a composite figure compromising of a rectangle OHKN, two triangles ∆LMN and ∆HJK, and a semicircle of arc HP, hence the total area will be derived by the sum of area for each basic shapes.

We can observe from the figure that the lines OL and HK are parallel, likewise the lines OH and NK, so OHKN is a rectangle and its area can be simply derived by multiplying its length by the width.

LMN and HJK are two different triangles and their area can be derived by half of the multiple of their base and height.

we will be left with a semicircle of arc HP and the area is derived using the formula πr²/2, where r is the radius.

In conclusion, the area of the figure will derived by the sum of area for each basic shapes(rectangle OHKN, triangles ∆LMN and ∆HJK, and semicircle of arc HP).

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Answer:

Plain burgers: 12

Double cheeseburgers: 9

Regular cheeseburgers: 12

Step-by-step explanation:

Let's use P, D, and R to represent the number of plain burgers, double cheeseburgers, and regular cheeseburgers, respectively.

Each plain burger requires 1 patty and 1 bun, so we can make a maximum of 12 plain burgers (since we have 12 buns).

Each double cheeseburger requires 2 patties, 1 bun, and 2 slices of cheese, so we can make a maximum of 9 double cheeseburgers with the available patties, buns, and cheese. (We have enough patties and buns for 18 burgers, but each double cheeseburger uses twice as many patties, so we divide the total number of patties by 2 to get the maximum number of double cheeseburgers we can make.)

Each regular cheeseburger requires 1 patty, 1 bun, and 1 slice of cheese, so we can make a maximum of 16 regular cheeseburgers with the available patties, buns, and cheese (since we have 16 slices of cheese).

To maximize our sales, we want to make as many of each type of burger as we can. Since we can only make 12 plain burgers, we should make all 12 of those. We can then make 9 double cheeseburgers (using 18 patties, 9 buns, and 18 slices of cheese), and 12 regular cheeseburgers (using 12 patties, 12 buns, and 12 slices of cheese).

So the final answer is:

Plain burgers: 12

Double cheeseburgers: 9

Regular cheeseburgers: 12

Answer:

Let's suppose that Mr. Lee puts "x" apples into each box.

According to the first statement, when he puts an equal number of apples into 8 boxes, he has one apple left. This can be represented by the equation:

8x + 1 = n, where n is the total number of apples Mr. Lee has.

Similarly, the second statement says that when he puts the same number of apples into 5 boxes, he has 7 apples left. This can be represented by the equation:

5x + 7 = n

Now we have two equations with two unknowns (x and n). We can solve for x by setting the two equations equal to each other:

8x + 1 = 5x + 7

Subtracting 5x from both sides, we get:

3x + 1 = 7

Subtracting 1 from both sides, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

So Mr. Lee puts 2 apples into each box. To find the total number of apples he has, we can substitute x = 2 into either of the two equations we started with:

8x + 1 = 8(2) + 1 = 17

So Mr. Lee has 17 apples

The ordered pair that would make the function true is option 4 (-1, -4).

As the name implies, an ordered pair is a set of items where the order in which they are placed is of particular significance. In coordinate geometry, ordered pairs are typically used to represent a point on a coordinate plane. They may also be used to depict aspects of a relationship.

The given equation of the graph is y = -0.25x - 2.

Substituting the coordinates in the options we have:

For (0, - 3):

y = -0.25x - 2

- 3 = -0.25(0) - 2

- 3 = -2 False.

For (4, 3)

y = -0.25x - 2

3 = -0.25(4) - 2

3 = -3 False

For (8, 4):

y = -0.25x - 2

4 = -0.25(8) - 2

4 = - 4

False.

For (-4, -1)

-1 = -0.25(-4) - 2

- 1 = -1

True.

Hence, the ordered pair that would make the function true is option 4 (-1, -4)

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Julian's timed lap after 4 weeks of training written in mixed fraction form is 58 1/10 seconds.

What are fractions?

Every number of equal parts is represented by a fraction, which also represents a portion of a whole. A single object or a collection of objects might be whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object. The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves. The number of parts into which the whole has been divided is shown by the denominator. How many sections of the fraction are displayed or chosen is shown in the numerator.

Given,

Number of metres run Julia runs each week = 400

Time taken to run 400m dash in the beginning = 59 7/10 seconds

                                                                                = 597/10 seconds

Since the time is given in fractions, we have to do fraction subtraction for the following weeks.

Time taken in week 1 = 597/10 - 0.6 seconds = 597/10 - 6/10 = 591/10 seconds

Time taken in week 2 = 591/10 - 1/4 = 2364 - 10 / 40 = 2354/40 seconds

Time taken in week 3 = 2354/40 + 0.1 = 2354/40 + 1/10 = 2358/40

Time taken in week 4 = 2358/40 - 17/20 = 2358-34 / 40 = 2324/40

                                                                             = 581/10= 58 1/10 seconds.

Therefore Julian's timed lap after 4 weeks of training written in mixed fraction form is 58 1/10 seconds.

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Answer:360

Step-by-step explanation:

The equation and solution for given situations are

Situation 1: 1.45x + 3.25 = 9.05; 4 pounds

Situation 2: 850 - 15a = 805; 3 days

Situation 3: 12.50 + 1.50r = 39.50; 18 times

Situation 4: 29.95x + 5.95 = 185.65; 6

Situation 5:  y = x - 5; 37 inches

The linear equation is a mathematical statement that is used to find an unknown quantity or number in a given situation. In this, we used different types of variables to represent the unknown value.

To solve the following situations use different variables and solve them for the value of variables.

Here we have

Situation 1:

A freight company charges $ 1.45 per pound plus a handling fee of $ 3.25. A customer was charged $ 9.05 to ship a package  

Let 'x' be the weight of the package

=> 1.45x + 3.25 = 9.05

=> 1.45x = 5.8

=> x = 4

∴ weight of the package is 4 pounds

Situation 2

A tenant is charged $ 850 for rent on the 5th of the month. For every day they are early, they can deduct $ 15 from the rent. The tenant pays $ 805

Let the tenant pay the rent 'a' number of days early

=> 850 - 15a = 805

=> 15a = 45

=>  a = 3

∴ The tenant paid 3 days early.

Situation 3

Jordan pays $ 12.50 for a city bus pass lowering his bus fare to $ 1.50 per ride. In March, Jordan spent $ 39.50 to ride the city How many times did he ride the bus

Let Jordan ride for 'r' time

=> 12.50 + 1.50r = 39.50

=> 1.5r = 27

=> r = 18

∴  Jordan ride the bus 18 times

Situation 4

Jung purchased several video games priced at $ 29.95 and the shipping cost is $ 5.95. His total purchase is $ 185.65

Let Jung buy 'y' number of games

=> 29.95x + 5.95 = 185.65

=> 29.95x = 179.7

=> x = 6

∴ Jung purchased 6 video games.

Situation 5:

Milo is five inches shorter than his brother, Jayce. Milo is 42 inches tall

Let Jayce is 'x' inches and Milo is 'y' inches

=> y = x - 5

=> 42 = x - 5   [ From the data ]

=> x = 37 inches

Therefore,

The equation and solution for given situations are

Situation 1: 1.45x + 3.25 = 9.05; 4 pounds

Situation 2: 850 - 15a = 805; 3 days

Situation 3: 12.50 + 1.50r = 39.50; 18 times

Situation 4: 29.95x + 5.95 = 185.65; 6

Situation 5:  y = x - 5; 37 inches

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Answer: $41.62

Step-by-step explanation:

let the price of the jacket be X

then the price of belt will be X-8.61

according to question

X + X-8.61 = 91.85

2X - 8.61 = 91.85

2X = 91.85 + 8.61

2X = 100.46

X = $50.23

cost of jacket = $ 50.23

cost of belt = $ 41.62

Hope this helps!!!

Answer: $41.62

Step-by-step explanation:

*j = jacket*  *b = belt*
belt + jacket = 91.85 (the total cost of the belt and jacket)
belt = jacket - 8.61 (the price of the belt is $8.61 less than the jacket)

We can use substitution to solve for the value of b.
Substitute the second equation into the first equation:
(j - 8.61) + j = 91.85

Simplify by combining like terms:
2j - 8.61 = 91.85
Add 8.61 to both sides:
2j = 100.46
Divide both sides by 2:
jacket = 50.23

b = j - 8.61

b = 50.23 - 8.61

b = 41.62

The number of men needed to complete the same job in 16 days working 6 hours a day is given as follows:

28 men.

The number of men is obtained applying the proportions in the context of the problem.

The rule of three is given as follows:

n/48 = 8/6 x 7/16.

(the time is inverse proportional to the number of men, hence the fractions are inverted).

Thus:

n/48 = 56/96

Applying cross multiplication, the number of men is obtained as follows:

96n = 48 x 56

n = 48 x 56/96

n = 28 men.

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the values of a, m, and x will be √5, 3√5, and 2 respectively.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, A big right triangle has three other right triangles in it.

Since, In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem

For the smallest right triangle,

Hypotenuse = 3

thus,

3² = 2² + a²

a² = 9 - 4

a² = 5

a = √5

For the medium size triangle,

Hypotenuse = 3 + 6 = 9

Other side = 2 + 4 = 6

Base = m

Thus,

9² = 6² + m²

m² = 81 - 36

m² = 45

m = 3√5

For the biggest triangle,

hypotenuse = 3 + 6 + 3 = 12

Height = 2 + 4 + x = 6 + x

base = 5

Since the given triangle is congruent to the smallest triangle,

(6 + x)/ 12 = 2/3

6 +x = 8

x = 2

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The x-intercepts and y-intercepts of the graph include the following:

x-intercept: B. -1.

y-intercept: D. none.

The equations for all vertical and horizontal asymptotes are as follows;

Vertical asymptote: x = 1.

Horizontal asymptote: y = 4.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).

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Answer:

↓ ↓ ↓

Step-by-step explanation:

Given: f(x)= x² -4x + 3

Find :-

a) f(1)

f(x)= x² -4x + 3

→ Substitute x with with 1:-

[tex]\tt f(1)=\left(1\right)^2-4\left(1\right)+3[/tex]

[tex]\tt f(1)=1-4\cdot \:1+3[/tex]

[tex]\tt f(1)=1-4+3[/tex]

[tex]\boxed{\tt f(1)=0}[/tex]

_______________________

b) f(3)

f(x)= x² -4x + 3

→ Substitute x with with 3:-

[tex]\tt f(3)=\left(3\right)^2-4\left(3\right)+3[/tex]

[tex]\tt f(3)=\left(3\right)^2-4\left(3\right)+3[/tex]

[tex]\tt f(3)=3^2-4\cdot \:3+3[/tex]

[tex]\tt f(3)=3^2-12+3[/tex]

[tex]\tt f(3)=3^2-9[/tex]

[tex]\tt f(3)=9-9[/tex]

[tex]\boxed{\tt f(3)=0}[/tex]

_______________________

c) f(-1)

f(x)= x² -4x + 3

→ Substitute x with with -1:-

[tex]\tt f(-1)=\left(-1\right)^2-4\left(-1\right)+3[/tex]

[tex]\tt f(-1)=\left(-1\right)^2+4\cdot \:1+3[/tex]

[tex]\tt f(-1)=1+4+3[/tex]

[tex]\boxed{\tt f(-1)=8}[/tex]

_______________________

d) -f(1)

f(x)= x² -4x + 3

→ -f(1)

[tex]\tt -f(1)=\left(1\right)^2-4\left(1\right)+3[/tex]

[tex]\tt -f(1)=1-4\cdot \:1+3[/tex]

[tex]\tt -f(1)=1-4+3[/tex]

[tex]\boxed{\tt -f(1)=0}[/tex]

_____________________

Hope this helps! :)

Given:-

To find:-

Answer:-

The given figure is made up of a cone and a hemisphere , so to find the total volume , we would find the volume of cone and hemisphere individually and add them up to find the net volume.

Finding volume of cone:

The data we have is ,

As we know that the volume of cone is given by,

[tex]\implies V =\dfrac{1}{3}\pi r^2 h \\[/tex]

on substituting the respective values,we have;

[tex]\implies V =\dfrac{1}{3}\times 3.14 \times (9in.)^2 \times 14in .\\[/tex]

[tex]\implies V = \dfrac{1}{3}\times 3.14 \times 81in.^2\times 14in. \\[/tex]

[tex]\implies V = 1186.92 \ in.^3 \\[/tex]

Finding the volume of hemisphere:

As we know that the volume of hemisphere is given by;

[tex]\implies V =\dfrac{2}{3}\pi r^3 \\[/tex]

And here ,

So that;

[tex]\implies V =\dfrac{2}{3}\times 3.14\times (9\ in.)^3 \\[/tex]

[tex]\implies V =\dfrac{2}{3}\times 3.14\times 729\ in.^3 \\[/tex]

[tex]\implies V = 1526.04 \ in.^3 \\[/tex]

Hence the total volume will be ,

[tex]\implies V_{prop} = (1526.04 + 1186.92 )in.^3\\[/tex]

[tex]\implies V = 2712.96 \ in.^3 \\[/tex]

[tex]\implies \underline{\underline{ V_{prop}= 2713\ in.^3 }} \\[/tex]

Hence the volume of prop is 2713 in.³

and we are done!

Answer:

2713.0 in³  (nearest tenth)

Step-by-step explanation:

To calculate the volume of the prop, sum the volume of the cone and the volume of the half-sphere.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]     [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=\dfrac{2}{3} \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

Therefore, the equation for the volume of the prop is:

[tex]V_{\sf prop}=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3[/tex]

From inspection of the given diagram:

Substitute the values of r, h and π into the equation and solve for V:

[tex]\begin{aligned}\implies V_{\sf prop}&=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3\\\\&=\dfrac{1}{3} (9)^2 (14)+\dfrac{2}{3} \pi (9)^3\\\\ &=\dfrac{1}{3} \pi (81) (14)+\dfrac{2}{3} \pi (729)\\\\ &=378 \pi+486 \pi\\\\ &=864 \pi\\\\&=864 \cdot 3.14\\\\&=2712.96\\\\&=2713.0\;\sf in^3\;\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the volume of the prop is 2,713.0 in³ to the nearest tenth.