Use the function f(t) = -16t^2 + 60t + 16 to answer parts A, B, and C.

(Look at the image!)

Answer:

shape a is 20 cm squared

Step-by-step explanation:

shape a is a parallogram, A =b×h. 5x4=20

shape b is a trapezoid. The picture is cut off but here are the steps for you to solve. A=0.5h(base1+base2) count the number of squares on the top and bottom of the shape. I can see the top is 2, you will need to tfind the length of the bottom base.then count the height, how far to get from the bottom to top, here it is 4.

area=0.5*4(2+bottom base) simply and that's your answer! Don't forget your units

The variance of first n even natural numbers is n²-1/12. So, the correct option is (a) .

The first n even natural numbers can be represented as 2, 4, 6, ..., 2n. The mean or expected value of this sequence is given by:

mean = (2 + 4 + 6 + ... + 2n) / n

= 2(1 + 2 + 3 + ... + n) / n

= 2n(n+1)/2n

= n+1

The variance of a sequence is the average of the squared differences from the mean, so we need to calculate:

Var = [(2- (n+1))² + (4- (n+1))² + (6- (n+1))² + ... + (2n- (n+1))²] / n

Simplifying the expression inside the brackets and using the formula for the sum of the first n integers, we get:

Var = [4(1² + 2² + 3² + ... + n²) - 4(n+1)(1 + 2 + 3 + ... + n) + n(n+1)²] / n

Substituting the formula for the sum of the first n squares and the sum of the first n integers, we get:

Var = [4n(n+1)(2n+1)/6 - 4(n+1)n(n+1)/2 + n(n+1)²] / n

Simplifying and factoring out (n+1), we get:

Var = (n+1)(n² - 1) / 3

Thus, the correct option is (a) n²-1/12.

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For the Following the product function is f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7} and rate of change of function is f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}

For g(x) = 9e^{-x} + ln(x) and h(x) = 4x^{2.7}, we have:

(a) The product function is: f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7}

(b) The rate-of-change function is:

f'(x) = g'(x) * h(x) + g(x) * h'(x)

where g'(x) and h'(x) are the derivatives of g(x) and h(x), respectively.

Taking derivatives, we have:

g'(x) = -9e^{-x} + 1/x

h'(x) = 10.8x^{1.7}

Substituting into the formula for f'(x), we get:

f'(x) = (-9e^{-x} + 1/x) * 4x^2.7 + (9e^{-x} + ln(x)) * 10.8x^{1.7}

Simplifying, we get:

f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}

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a) To find the total surface area of the cuboid, we need to find the area of each face and then add them up.

Area of one face = length x width

Area of top and bottom faces = 1.1 m x 0.55 m = 0.605 m² (2 faces)

Area of front and back faces = 2.2 m x 0.55 m = 1.21 m² (2 faces)

Area of side faces = 2.2 m x 1.1 m = 2.42 m² (2 faces)

Total surface area = (2 x 0.605) + (2 x 1.21) + (2 x 2.42) = 7.7 m²

Each tin of varnish covers 20 m², so Emma needs:

Number of tins = (total surface area x number of coats) / coverage per tin

Number of tins = (7.7 x 3) / 0.02 = 1155

Emma needs to buy 1155 tins of wood varnish.

b) The cost of each tin of varnish is $3.99 for 100 ml. To find the cost of 1155 tins, we first need to convert the volume of varnish needed into liters.

Volume of varnish needed = (total surface area x number of coats) / coverage per litre

Volume of varnish needed = (7.7 x 3) / 20 = 1.155 liters

The number of tins required to make up 1.155 liters of varnish is:

Number of tins = (1.155 / 0.1) = 11.55

So Emma needs to buy 12 tins of varnish. The total cost is:

Total cost = cost per tin x number of tins

Total cost = $3.99 x 12 = $47.88

The total cost of the wood varnish is $47.88.

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Answer:

Step-by-step explanation:

√4x^2=2x

Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

the total cost will be minimized when the loads are distributed in the following way:

5 loads in the small truck (total capacity of 5 * 50 = 250 cubic yards)

4 loads in the large truck (total capacity of 4 * 70 = 280 cubic yards)

This will result in a total of 9 loads and a total capacity of 530 cubic yards, which meets both the daily minimum delivery requirement of 350 cubic yards and the union contract requirement of 9 loads per day.

The total cost can be calculated as follows:

Cost of 5 loads in small truck = 5 * $87 = $435

Cost of 4 loads in large truck = 4 * $73 = $292

Total cost per day = $435 + $292 = $727

Therefore, Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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The volume of the cone is approximately one-third the volume of the

cylinder

:V(cone) ≈ 1/3 V(cylinder) = 1/3 (9.4) ≈ 3.1 cubic feet.

The volume of a cone with the same height and radius as the given

cylinder, we can use the formula:

[tex]V = 1/3 πr²h[/tex]

where V is the volume, r is the radius, and h is the height.

Since the cylinder has a volume of approximately 9.4 cubic feet, we can

use the formula for the volume of a cylinder

:V = πr²hand solve for the radius:

[tex]r = √(V/πh) = √(9.4/πh)[/tex]

Now we can substitute this expression for the radius into the formula for

the volume of a cone:

[tex]V = 1/3 π(√(V/πh))²h[/tex]

Simplifying this expression gives:

[tex]V = 1/3 π(V/πh)hV = 1/3 V[/tex]

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The dimensions of the cylinder that minimize the production cost are:

radius = approximately 2.78 cm

height = 600 / (πr^2) ≈ 7.14 cm

paper top radius = 2.5 cm

Let's start by finding the formula for the cost of the container in terms of its dimensions.

The volume of the cylinder is given as 600 cubic centimeters, so we have:

πr^2h = 600

where r is the radius of the cylinder and h is its height. Solving for h, we get:

h = 600 / (πr^2)

The surface area of the cylinder is given by:

A = 2πrh + 2πr^2

Substituting h in terms of r, we get:

A = 2πr(600/(πr^2)) + 2πr^2

= 1200/r + 2πr^2

The cost of the container is the sum of the cost of the styrofoam sides and bottom and the cost of the paper top. Let's call the radius of the paper top R, and assume that the height of the cylinder is greater than or equal to the radius of the paper top, so that the top can be completely covered with paper. Then the cost of the container is:

C = 0.04(2πrh + πr^2) + 0.05(πR^2)

Substituting h in terms of r, we get:

C = 0.08πr(600/(πr^2)) + 0.04πr^2 + 0.05πR^2

= 4.8/r + 0.04πr^2 + 0.05πR^2

To minimize the cost, we need to find the values of r and R that minimize the cost function C. To do this, we take the partial derivatives of C with respect to r and R, and set them equal to zero:

dC/dr = -4.8/r^2 + 0.08πr = 0

dC/dR = 0.1πR = 0

Solving for r and R, we get:

r = ∛(60/π) ≈ 2.78 cm

R = 2.5 cm

We can check that these values give us a minimum by checking the second derivatives:

d^2C/dr^2 = 9.6/r^3 + 0.08π > 0 (minimum)

d^2C/dR^2 = 0.1π > 0 (minimum)

Therefore, the dimensions of the cylinder that minimize the production cost are:

radius = approximately 2.78 cm

height = 600 / (πr^2) ≈ 7.14 cm

paper top radius = 2.5 cm

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Answer: AB = 16.4

Step-by-step explanation:

You can use tan x = opposite/adjacent

tan 38 = AB/21

21 tan 38 = AB

AB = 16.4

our final estimate for the area under the curve f(x)=1/x on [1,2] using 4 approximating rectangles and taking the average of the left and right endpoints is 0.76.

To estimate the area under the curve f(x)=1/x on [1,2], we can use 4 approximating rectangles.

a) Using left endpoints, the width of each rectangle is (2-1)/4 = 0.25. The left endpoints of the rectangles are 1, 1.25, 1.5, and 1.75. The height of each rectangle is f(x) evaluated at the left endpoint.

So, the heights are f(1) = 1/1 = 1, f(1.25) = 1/1.25 = 0.8,

f(1.5)=1/1.5 = 0.67, and f(1.75) = 1/1.75 = 0.57.

The area of each rectangle is width times height, so the areas are

0.25*1 = 0.25, 0.25*0.8 = 0.2, 0.25*0.67 = 0.1675, and 0.25*0.57 = 0.1425.

Adding these areas together, we get an estimate of the total area under the curve as

0.25 + 0.2 + 0.1675 + 0.1425 = 0.76.

b) Using right endpoints, the width of each rectangle is the same as before. The right endpoints of the rectangles are

1.25, 1.5, 1.75, and 2.

The heights are f(x) evaluated at the right endpoint. So, the heights are

f(1.25) = 0.8, f(1.5) = 0.67, f(1.75) = 0.57, and f(2) = 0.5.

The areas of the rectangles are the same as before, so adding them up, we get an estimate of the total area as

0.2 + 0.1675 + 0.1425 + 0.25 = 0.76,  

which is the same as before.
c) To get the average of the two estimates, we add them together and divide by 2:

(0.76+0.76) / 2 = 0.76.

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"It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn." refers projection (option c).

To understand projection in mathematical terms, we can think of it as a function f(x), where x represents the individual's own thoughts or emotions. The output of the function, f(x), represents the projection of these thoughts or emotions onto someone else.

In the case of arguments, the person who is most difficult to convince may have a high value of x, indicating that they are feeling stubborn. However, instead of accepting this feeling, they project it onto others, resulting in a high value of f(x) for those around them.

Projection is just one example of the many defense mechanisms that humans use to protect themselves from unpleasant thoughts or emotions. Understanding these mechanisms can help us to better navigate difficult situations, including arguments, and improve our communication skills.

Hence the correct option is (c).

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Answer:..

Step-by-step explanation:Use the distance formula to find the length of each side and then add the lengths.

Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.

Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.

Use the distance formula to find the length of the sides, and then multiply two of the side lengths.

The average price of milk in 2018 was $6.45 per gallon.

The average price of milk in 2021 was $189.15 per gallon.

When x = 0 (which represents the year 2018), the function becomes:

3.55 + 2.90(1 + 0)³

= 3.55 + 2.90(1)³

= 3.55 + 2.90

= 6.45

The average price of milk in 2018 was $6.45 per gallon.

When x = 3 (which represents the year 2021), the function becomes:

3.55 + 2.90(1 + 3)³

= 3.55 + 2.90(4)³

= 3.55 + 2.90(64)

= 3.55 + 185.6

= 189.15

The average price of milk in 2021 was $189.15 per gallon.

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Answer:  B   28√15

Step-by-step explanation:

They want you to find the Area of the quadrilateral.  But if you can find the area of 1 trangle then you can double it because the 2 triangles are congruent.

We know the 2 triangles are congruent from the theorem  (see diagram

We also know that  QR=TR=SR  They are all radius

Let's solve for triangle PRS

PR = hypotenuse = 10+7 =17

SR=7  radius

Use pythagorean to find PS

c²=a²+b²

17²=7²+b²

289 = 49 + b²

b²=289 -49

b² = 240

b=√240

b=[tex]\sqrt{16*15}[/tex]

b= 4√15  This is PS

Area of triangle = 1/2 bh       b=PS   h=7

Area of triangle = 1/2 (4√15)(7)

Area of triangle = (2√15)(7)

Area of triangle = 14√15

Area of quadrilateral = 2 (14√15)        > 2 triangles make the quadrilateral

Area of quadrilateral =  28√15

The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.

Let's denote the length of the bookmark as L and the width as W.

The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.

From the given information, we have two equations:

Equation 1: A = 150 square centimeters

Equation 2: P = 62 centimeters

Substituting the formulas for area and perimeter, we get:

Equation 1: L * W = 150

Equation 2: 2L + 2W = 62

To solve these equations, we can use substitution or elimination. Let's solve by substitution:

From Equation 1, we can express one variable in terms of the other:

L = 150 / W

Substituting this into Equation 2:

2(150 / W) + 2W = 62

300 / W + 2W = 62

300 + 2W^2 = 62W

2W^2 - 62W + 300 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

[tex]2W^2 - 62W + 300 = 0[/tex]

(W - 10)(2W - 30) = 0

This gives us two possible solutions:

W - 10 = 0 -> W = 10

2W - 30 = 0 -> W = 15

Since the width cannot be longer than the length, we discard the solution W = 15.

So, the width of the bookmark is W = 10 centimeters.

Now, we can substitute this value into Equation 1 to find the length:

L * 10 = 150

L = 150 / 10

L = 15

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Marlene will need to buy approximately 44 feet of fencing to enclose her circular vegetable garden.

To determine the amount of fencing Marlene needs, we'll need to calculate the circumference of her circular vegetable garden. Here's a step-by-step explanation:

1. Given the diameter of the garden is 14 feet, we can find the radius by dividing the diameter by 2: Radius = Diameter / 2 = 14 feet / 2 = 7 feet.

2. Now, we will use the formula for the circumference of a circle, which is: Circumference = 2 * pi * radius.

3. Plug in the radius value we found in step 1: Circumference = 2 * pi * 7 feet.

4. Calculate the circumference: Circumference ≈ 2 * 3.1416 * 7 feet ≈ 43.98 feet.

5. Since fencing is sold by the linear foot, Marlene needs to buy approximately 44 linear feet of fencing to enclose her circular vegetable garden and keep the rabbits away.

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If kawan paints the visible outside faces of her shed, she paints two rectangle faces and two triangle faces then the total surface area that she paints is 88ft².

The area of a triangle of altitude h and base b is given by;

A = 0.5bh

Therefore the area of one triangle face ;

At = 0.5 × 8 × 5

At = 20ft²

Area of a rectangle of length l and breadth b is;

A = lb

Therefore the area of a rectangle face;

Ar = 8 × 3

Ar = 24ft²

We have 2 triangle faces and 2 rectangle face, therefore total surface area as;

A = 2At + 2Ar

A  = 2×20 + 2×24

A = 40 + 48

A = 88ft²

Therefore the answer is; 88ft².

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Answer:

image dosent load

Step-by-step explanation:

Answer:

a = 80°, b = 100°, c = 80°, d = 100°

Step-by-step explanation:

You know a + b + c + d = 360°.

Plugging b + c + d = 280° into the formula above:

a + 280° = 360°.

a = 80°.

You know a + d = 180° because of angles on a straight line. Solve for d:

80° + d = 180°.

d = 100°.

For the same reason, you know a + b = 180°. b must be equal to d, which is 100°.

Lastly, c + d = 180° because they make up the second line. Solve for c:

c + 100° = 180°.

c = 80°.

a = 80°, b = 100°, c = 80°, d = 100°.

1) Leke pay $4.938 for his meal after a 40% discount.

2) -5 belongs to integers, rational numbers, and real number sets.

3) Target sells the shirt for $5.6 after they mark it up for 40%

1) Bill = 8.23 , discount coupon = 40 %

The total amount paid by leke after the discount coupon = 8.23 - (40 % of 8.23)

Total amount = 8.23 - ( 8.23 × 40/100 )

Total amount = 8.23 - 3.292

The total amount paid by Leke is $4.938

2) -5 is an integer because it is a negative whole number.

-5 is a rational number because it can be written in the form of a fraction.

-5 is a real number because it is a rational number .

-5 belongs to integers, rational numbers, and real number sets.

3) Shirt price = $4 , price increased = 40%

selling price = 4 + (40% of 4)

selling price = 4 + (4 × 40/100)

selling price = 4 + 1.6

Target sell shirt for $5.6

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The parts of this equilateral triangle ABC are as follows:

The length of side x of the equilateral triangle is determined as follows:

AD = x

AB = 6

DB = 6/2 or 3

AB² = AD² + DB²

6² = x² + 3²

x² = 6² - 3²

x = 27

x = 3√3

Therefore, the length of the perpendicular bisector AD is 3√³ units

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Answer:

the length is 3√³ units

The difference between the outcomes when selected with or without replacement is B. 10 outcomes.

With Replacement:

When you select two coins with replacement, you put the first coin back in the jar before selecting the second coin. This means that there are 10 possibilities for each selection. So, the number of outcomes for selecting two coins with replacement is 10 x 10 = 100 outcomes.

Without Replacement:

When you select two coins without replacement, you don't put the first coin back in the jar before selecting the second coin. This means that after selecting the first coin, there are 9 coins left in the jar for the second selection. So, the number of outcomes for selecting two coins without replacement is 10 x 9 = 90 outcomes.

Difference = 100 outcomes - 90 outcomes

Difference = 10 outcomes

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Answer:

y=f(x) = log7x

Just trust me

The graph best represents the function y = f(x) = 7x, an exponential function.

The graph represents the function y = 7x, which is an exponential function. In an exponential function, the variable x is the base, and the exponent is a constant, which in this case is 7. This means that the function grows rapidly as x increases, creating a steep curve on the graph.

The other two options, y = f(x) = log7x and y = f(x) = x7, are not represented by the given graph.

The function y = f(x) = log7x is a logarithmic function, which has a different shape on the graph, with a horizontal asymptote and the x-axis acting as its asymptote.

The function y = f(x) = x7 is a polynomial function, where x is raised to the power of 7, and it would have a different pattern on the graph compared to the exponential function shown.

Thus, the graph best represents the function y = f(x) = 7x, an exponential function.

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Answer:  First, we need to find the composite function (fg)(x):

(fg)(x) = f(g(x))

= f(-4x-3)

= (-4x-3)^2 + (-4x-3) + 9 (substituting g(x) into f(x))

= 16x^2 + 24x + 18

Therefore, (fg)(x) = 16x^2 + 24x + 18.

Next, we need to find the quotient function (f/g)(x):

(f/g)(x) = f(x) / g(x)

= (x^2 + x + 9) / (-4x - 3) (substituting f(x) and g(x))

To simplify this expression, we can use polynomial long division or synthetic division. Using synthetic division, we get:

  -4 |   1    1    9

      |_____-4__ 12

      |  1  -3   21

Therefore, (f/g)(x) = -4x + 3 - 21 / (-4x - 3)

Simplifying further, we get:

(f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4))

Therefore, (f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4)).

Step-by-step explanation:

The sum of all edges of the regular quadrilateral prism is 108 cm.

To find the sum of all edges of a regular quadrilateral prism with height h = 11 cm and base edges b = 8 cm, follow these steps:

1. Determine the number of base edges: A quadrilateral has 4 edges, so there are 4 base edges for the top and 4 for the bottom, totaling 8 base edges.
2. Determine the number of height edges: There are 4 vertical edges connecting the top and bottom bases.
3. Add the number of base and height edges: 8 base edges + 4 height edges = 12 edges in total.
4. Calculate the sum of all edge lengths: (8 base edges (8 cm)) + (4 height edges (11 cm)) = 64 cm + 44 cm = 108 cm.

So, the sum of all edges of the regular quadrilateral prism is 108 cm.

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Clarissa needs a total of 251.25 square inches of construction paper for her project.

To find the total area of construction paper needed, we need to find the area of each rectangle and add them together.

The first rectangle has an area of 10 inches × 14.5 inches = 145 square inches.

The second rectangle has an area of 10.25 inches × 10.5 inches = 107.625 square inches.

Adding these two areas together, we get a total of 145 + 107.625 = 252.625 square inches.

Therefore, Clarissa needs a total of 251.25 square inches (rounded to two decimal places) of construction paper for her project.

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Let's assume that the hourly rate for loading and unloading is $x and the hourly rate for packing and unpacking is $y.

From the given information, we can form the following two equations:

[tex]8x + 6y = 890[/tex] ...(1) (for 8 hours of loading and unloading and 6 hours of packing and unpacking)

[tex]5x + 3y = 515[/tex] ...(2) (for 5 hours of loading and unloading and 3 hours of packing and unpacking)

To solve for x and y, we can use the method of elimination.

Multiplying equation (2) by 2, we get:

[tex]10x + 6y = 1030[/tex] ...(3)

Now, subtracting equation (1) from equation (3), we get:

2x = 140

Therefore, x = $70 per hour.

Substituting the value of x in equation (2), we get:

5(70) + 3y = 515

Simplifying, we get:

3y = 165

Therefore, y = $55 per hour.

Hence, the company's hourly rates are $70 per hour for loading and unloading and $55 per hour for packing and unpacking.

In summary, we can set up a system of equations to solve for the hourly rates of a moving team.

From there, using the method of elimination, we can solve for the hourly rates for both loading and unloading as well as packing and unpacking.

In this case, the hourly rate for loading and unloading is $70 per hour, and the hourly rate for packing and unpacking is $55 per hour.

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The full t-table will be:

Hours (x)                               Money (y)

  0                                           $0

  1                                            $7.5

  2                                           $15

  3                                           $22.5

  4                                           $30

  5                                           $37.5

Given that the neighbors paid $45 for 6 hours to babysit their children.

So the rate to babysit is = $45/6 = $7.50 per hour.

So the function rule for the situation is given by,

y = 7.50x, where y is the total earning by babysitting neighbors' children and x is the number of hour to babysit.

when x = 0, y = 7.5*0 = $0

when x = 1, y = 7.5*1 = $7.5

when x =2, y = 7.5*2 = $15

when x = 3, y = 7.5*3 = $22.5

when x = 4, y = 7.5*4 = $30

when x = 5, y = 7.5*5 = $37.5

So the t-table will be:

Hours (x)                               Money (y)

  0                                           $0

  1                                            $7.5

  2                                           $15

  3                                           $22.5

  4                                           $30

  5                                           $37.5

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Both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0

Know more about rational function,

First, let's rewrite the rational function f(x) more clearly and identify the two limits we need to find: f(x) =[tex](x + 6) / (x^2 + 20)[/tex]

a. lim (x→∞) f(x) b. lim (x→-∞) f(x)

To find these limits, we can use the following steps:

Step 1: Divide both the numerator and the denominator by the highest power of x in the denominator.

In this case, it is x^2. f(x) = [tex][(x + 6) / x^2] / [(x^2 + 20) / x^2][/tex]

Step 2: Simplify the function. f(x) =[tex][(1/x) + (6/x^2)] / [1 + (20/x^2)][/tex]

Step 3: Evaluate the limits.

a. lim (x→∞) f(x)

= [(0) + (0)] / [1 + (0)]

= 0 / 1 = 0

b. lim (x→-∞) f(x)

= [(0) + (0)] / [1 + (0)]

= 0 / 1 = 0

So, both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0

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The volume  33.5 cubic inches

To calculate the volume of the cylinder, we need to use the formula:

V = π[tex]r^2[/tex]h

where V is the volume, π is the constant pi, r is the radius of the base (which is half the diameter), and h is the height.

First, we need to convert the diameter of the cylinder to inches:

2 3/4 inches = (2*4 + 3)/4 inches = 11/4 inches

The radius of the cylinder is half the diameter, so:

r = (11/4)/2 = 11/8 inches

Now we can plug in the values into the formula:

V = π[tex](11/8)^2[/tex](11) cubic inches

V ≈ 33.5 cubic inches (rounded to the nearest tenth)

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