These tables correspond to inputs and outputs. Select whether these input and output tables could represent a functions.

The volume of the solid is 29.865 cubic units.

We have,

To find the volume of the solid generated by revolving region R around the line y = 6, we can use the method of cylindrical shells.

The volume of the solid can be obtained by integrating the area of each cylindrical shell.

Each shell is formed by taking a thin vertical strip of width dx from region R and rotating it around the line y = 6.

Let's denote the radius of each cylindrical shell as r(x), where r(x) is the distance from the line y = 6 to the curve y = 2tan(\(x^5\)).

Since the shell is formed by revolving the strip around y = 6, the radius of the shell is given by r(x) = 6 - 2tan(\(x^5\)).

The height of each cylindrical shell is the difference in x-values between the curve y = 5 - x and the y-axis, which is given by h(x) = x.

The differential volume of each cylindrical shell is given by:

dV = 2π x r(x) x h(x) x dx.

To find the total volume of the solid, we integrate the differential volume over the interval where region R exists, which is determined by the intersection of the curves y = 2tan(\(x^5\)) and y = 5 - x.

The volume V is given by the integral:

V = ∫[a,b] 2π x (6 - 2tan(\(x^5\))) x dx

Setting the two equations equal to each other, we have:

2tan(\(x^5\)) = 5 -x

Let's use numerical approximation to find the intersection points.

Using a numerical solver, we find that one intersection point is approximately x ≈ 1.051.

Now, we can set up the integral to find the volume of the solid:

V = ∫[a,b] 2π  (6 - 2tan(\(x^5\))) x dx

Since we are revolving around the line y = 6, the limits of integration will be from x = 0 to x = 1.051.

V = ∫[0,1.051] 2π  (6 - 2tan(\(x^5\))) x dx

The integral does not have an elementary antiderivative, so we cannot find the exact value of the integral.

However, we can still approximate the value using numerical methods or software.

Using numerical approximation methods, the volume is approximately V ≈ 29.865 cubic units.

Thus,

The volume of the solid is 29.865 cubic units.

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Answer:

a=7

b=8

c=12

d=33

find e by adding up all numbers in the Venn diagram then subtract the total amount of people by total from the Venn diagram to find e

Answer:

For Line T:

\(m = \frac{5 - 14}{2 - 0} = - \frac{9}{2} \)

Since Lines T and R are perpendicular, the slopes of these two lines are negative reciprocals. So Line R has slope 2/9. We have:

\(3 = \frac{2}{9} (4) + b\)

\( \frac{27}{9} = \frac{8}{9} + b\)

\(b = \frac{19}{9} \)

\(y = \frac{2}{9} x + \frac{19}{9} \)

So the equation of Line R is

y = (2/9)x + (19/9)

Answer:

Step-by-step explanation: its 32

Answer:

Step-by-step explanation:

A + B + C = 180

A = 47

B = 62

C = ???

We don't know what "C" is??

So..

A + B + C = 180

C = 180 - A - B

C = 180 - 47 - 62

Subtract those numbers and you should get 71

Soo..

C = 71

we can also add up

47 + 62 + 71 = 180

so if you get 180 when you add them up then that's your correct answer!!

YOUR WELCOME FOR THE HELP!!!!!1

The simplified expression is \(\frac{1 - x - y}{x + y}\)and the restriction is \(y \ne -x\)

The expression is given as:

\(\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1\)

Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions

\(\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1\)

Rewrite the expression as products

\(\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1\)

Cancel out the common factors

\(\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1\)

Express 4x^2 - y^2 as (2x - y)(2x + y)

\(\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1\)

Cancel out the common factors

\(\frac{1}{x + y} -1\)

Take the LCM

\(\frac{1 - x - y}{x + y}\)

Hence, the simplified expression is \(\frac{1 - x - y}{x + y}\)and the restriction is \(y \ne -x\)

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Step-by-step explanation:

I'm not sure what has infinite x-intercepts

Answer:

The quadrant for angle 230 is quadrant 3

Step-by-step explanation:

quadrant 3

The requried width of the pathway around the garden is 4.27 meters.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Here,

Jamie has a garden that is 20 meters by 30 meters.
Area of the garden = 20 × 30 = 600 square meter
Let the offset in the form of width be x,

New length = 20 + 2x
New width of garden = 30 + 2x
New area =  old area + area of the offset pathway
(20 + 2x)(30 + 2x) = 600 + 500

By the simplification of the above expression, we get
x = 4.27 meter

Thus, the requried width of the pathway around the garden is 4.27 meters.

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The decimal positional number system is the one that is most frequently used.

The consistent representation of numbers using digits and other symbols is known as a number system.

Some key features of number system are-

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Answer:

1, 2, 5, 10

Step-by-step explanation:

1 × 10 = 10

2 × 5 = 10

10 ÷ 5 = 2

10 ÷ 2 = 5

10 ÷ 10 = 1

Answer:

6.75

Step-by-step explanation:

So basicly we know the area of the rectangle which really helpful.

So lets take the formula of the are for the triangle, which is b*h*1/2

So we know that the height and bass of the triangle is the same as the rectangle's legnth and width.

Meaning that we can replace b*h with 13.5.

So plug that into the quation.

13.5*1/h= Area of ACE

6.75= Area of ACE

hence, 6.75 is your answer

The area of the triangle ACE is; 6.75 square units.

According to the question; a triangle is inscribed in a rectangle with each vertex of the triangle lieing on a side of or at a vertex of the rectangle.

In essence, to find the number of square units in the area of shaded triangle ACE,

We have to divide the area of the rectangle by 2.

Therefore, the area of the triangle ACE is;

6.75 square units.

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Answer:

i think c which is 14

Answer:

Step-by-step explanation:

A ratio is used in scale drawings of maps and buildings.  

That is:

The scale of a drawing = Drawing Length : Actual Length

A scale is usually expressed in one of two ways:

-using units as in 1 cm to 1 km

-without explicitly mentioning units as in 1 : 100,000.

A scale of 1 : 100,000 means that the real distance is 100,000 times the length of 1 unit on the map or drawing.

In your case, where the room has a length of 7m and 1cm on the diagram:

1 cm to 7m = 1cm : 7m

                  = 1cm : 700cm

                  = 1 : 700

Answer:

A) 11(0.65)+c=10

Step-by-step explanation:

Step 1: Calculate the price of 11 oranges at $0.65 each.

11 × 0.65 = $7.15

Step 2: Consider the constraint: if Maribel only has a $10 bill, we have to deduct $7.15 from $10 to find our answer:

$10.00 - $7.15 = $2.85

Step 3: Write an equation based on our solution:

C = 10-0.65x ; Where:  

* 10- indicates that we start with $10, and subtract from there.
* C is the amount of change per purchase.
* X is the number of oranges a customer buys.

Answers:

1. The customer receives $2.85 in change.
2. Given a case where a customer pays with one 10-dollar bill, their purchase amount can be calculated with C = 10-0.65x

I hope this helped! Have a great day.

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Answer:

A. 16 to 20 is equivalent to ratio 32:40

The smallest number of coins you could have had before finding the bag of 53 coins is 371. which is more than 200.

There are seven bags, so there are 7x coins in total:

7x = T.

Since the number of coins in each bag must be an integer, (T + 53) must be a multiple of 8. We know that T = 7x, so we can write this as follows:

(7x + 53) ≡ 0

(mod 8)This means that 7x ≡ 3 (mod 8).

The solutions to this congruence are

x ≡ 3, 11 (mod 8).

Since x is a positive integer, we take

x = 11

(the other possibility, x = 3,

leads to a smaller value for T).

Therefore, T = 7x = 77, and the total number of coins after the bag of 53 coins is found is

T + 53 = 130.

After redistributing the coins into eight equal bags, each bag contains 16 coins.

Therefore, the number of coins you had initially was

7x = 77,

so the smallest number of coins you could have had before finding the bag of 53 coins is

77 - 53 = 24.

After redistributing the coins, you had

8 × 16 = 128 coins left,

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\(Perimeter = \\ 9v - 7 + v + 10 + 9v - 7 + v + 10 \\ = 9v - v + 9v + v - 7 + 10 - 7 + 10 \\ = 8v + 10v - 17 - 17 \\ = 18v - 34\)

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Answer: I got it :)

The equation that represents the number of haircuts she needs to do is 10.5x = 168.

Step-by-step explanation:

Given, The Hair Care Salon charges a stylist $30 per day to rent a station at the salon, Rhonda, a stylist makes $10.50 on each haircut.

Therefore, She needs to earn $138 + $30 to make a profit of $138 and let

'x' be the number of haircuts.

Therefore, the equation that equation that represents this situation is.

10.50x = 138 + 30.

10.5x = 168.

Answer:

2

Step-by-step explanation:

Answer:

D. 12 by 12 inches

Step-by-step explanation:

36*36= 1296

100*44= 4400

50*22= 1100

none of these answers equal 144 except for 12*12

hope this helps <3

Answer:

176•74

Step-by-step explanation:

area of circle is πr^2

π=3•142

r=7•5

3•142×7•5×7•5

=176•737

176•74

An equation of the form y = mx + b represents a linear relationship between two variables, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.

To determine whether the equation shows a proportional relationship or some other relationship, you need to analyze the value of the slope, m. If m is a constant value, then the equation represents a proportional relationship between x and y. In a proportional relationship, as the value of x increases or decreases, the value of y changes proportionally, such that the ratio of y to x remains constant.

On the other hand, if m is not a constant value, then the equation represents a non-proportional relationship between x and y. In a non-proportional relationship, the ratio of y to x changes as x changes. This means that the relationship between x and y is more complex and cannot be described by a simple proportionality constant.

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Answer:

The length of the curtain is 10.625 feet

Step-by-step explanation:

The length of the curtain to cover one side of the room depends on the shape of the room

Given a room shape of a square, we have;

Perimeter = 4 × Side length of the room

Length of the curtain = Side length of the room

Therefore;

Perimeter = 4 × Length of the curtain

42.5 feet = 4 × Length of the curtain

Length of the curtain = (42.5 feet)/4 = 10.625 feet

The length of the curtain = 10.625 feet.

The angle of rotation about the origin that maps (4, -2) to (2, 4) is 180, the correct option is B.

The difference in the coordinate is the change in the sign of the x and y

values.

The coordinate of a point (x, y) following a 180° rotation about the origin

is the point (-x, -y).

Given;

The coordinate of the point C on the preimage = (4, -2)

The coordinate of the point C' on the image = (2, 4)

Here,

angle=180

Therefore, by transformation the angle of rotation will be 180.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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The number of potatoes peeled by Tom was 36 potatoes after peeling a pile of 64 potatoes

An equation is an expression that shows the relationship between two or more variables and numbers.

Let t represent the time after Tom joined.

number of potatoes peeled by Ben = 2(5 minutes) + 2t = 2t + 10

number of potatoes peeled by Tom = 4t

Since they are 64 potatoes, hence:

2t + 10 + 4t = 64

t = 9 minutes

number of potatoes peeled by Tom = 4(9) = 36 potatoes

The number of potatoes peeled by Tom was 36 potatoes after peeling a pile of 64 potatoes

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Answer:

-5 because it is negative

Step-by-step explanation: