Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x^8, y = 1; about y = 3

Answer:

The answer is "\(x(\frac{250}{3}-x)\)"

Step-by-step explanation:

Both points are similar that's why the solution is:

\(\to \frac{6x+6y=500}{6}\\\\\to x+y=\frac{250}{3}\\\\\to y= \frac{250}{3}-x \\\\\to Area= xy\\\\ \to Area= x(\frac{250}{3}-x)\)

Answer:

y=-3/2x+1

Step-by-step explanation:

NOTE: Doing graphs by hand is a lot easier, it saves a lot more time as well.

Step 1: plot your 2 known points.

Step 2: draw a line that goes between both points

Step 3: find the distance of the points in RISE/RUN format.

-9/6. The slope is negative because the line goes down to the right.

Step 4: find your y-intercept.

1.

Step 5: simplify your equation

-9/6 = -3/2

Answer:

-1/2

Step-by-step explanation:

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

a. 170

b. −25

c. -25

d. 75√3 (Decimal: 129.903811)

The area of the figure given after dividing it to known figures is 58 mm².

Given a figure.

We have to find the area of the figure.

The given figure can be divided in to two rectangles by drawing a horizontal line where the length is increased.

Then we get two rectangles of dimensions,

Length = 6 mm and width = 5 mm

Length = 7 mm and width = 4 mm

Area of the figure = Total area of the two rectangles.

Area of a rectangle = length × width

Area of the figure = (6 × 5) + (7 × 4)

                              = 30 + 28

                              = 58 mm²

Hence the area is 58 mm².

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Answer:

<stv=153

Step-by-step explanation:

stu+stv=180 (being a straight angle)

3b +15b+18=180

18b=180-18

b=162/18

b=9

now

<stv=15b+18

=15 × 9 +18

=135+18

=153

<stv=153°

Answer:

it's between BCF/DCA and BCF/BCA

Yes, irrational numbers such as π are included in the domain of the function f(x) = 7.

The domain of a function is the set of all possible input values (x) for which the function is defined. In the case of the function f(x) = 7, the output value (y) is always equal to 7, regardless of the input value.

Since every real number, including irrational numbers like π, can be an input value for f(x) = 7, the domain of this function is the set of all real numbers, which includes both rational and irrational numbers. Therefore, π is included in the domain of the function f(x) = 7.

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The expression that represents the sum of the arithmetic series that has a first term of -12, a common difference of +7 and a number of terms of 5 is the option with the following;

An arithmetic series one that consists of the sum of an arithmetic sequence, such that each term of the series is obtained from the previous term by the addition or subtraction of a constant.

The series in the question is; -12 + (-5) + 2 + 9 + 16

The series in therefore a series of an arithmetic sequence

The equation of the series when the first term is -12 can therefore be presented as follows;

-12 + 7·k

Where;

-12 is the first term, 7 is the common difference, n is the number of terms, and k = n - 1

The above values for the terms of the series is obtained by using values of k that range from k = 0 to k = 4

The expression that represents the series is therefore the option;

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Answer:

A is the Answer

Step-by-step explanation:

Since the population is being split up into 2 divisions out of 5,000.

This means District X and Y must add up 5000.

\(x + y = 5000\)

District X and Y must differ no more than 500 people.

So this means that X and Y total people difference cannot be over 500 people. So the equation for this is

\(x - y \leqslant 500\)

A shows this so A is the answer.

Answer:

No

Step-by-step explanation:

The only consecutive integers that satisfy the Pythagorean theorem are 3, 4, and 5.

___

4^2 ≠ 2^2 + 3^2

16 ≠ 4 + 9 . . . . . . . an attempt at applying the Pythagorean theorem to the given numbers fails.

If the price of gasoline is $3.119/gal, then is its price in cents per liter is $68.54 cents/ Liter.

Dimensional Analysis:

The process of performing dimensional analysis is to obtain specific quantities with desired units. With this, we must also be familiar with the construction of the conversion factors needed to find answers to such questions. As we know, a conversion factor can be expressed as a ratio of two parameters with equal values.

We know according to unit:

On converting to galloon

41€ = 41€×(1L/1.3€)× (1qt/1L)× (1gal/4qt)

      = (10/1.3)gal

      = 8 gallons,

Now,

We convert the given measurement into the desired unit. For this issue, we have implemented the following identities:

100 cents = 1 dollars

1gal = 4.55 liter.

and construct appropriate conversion factors. We proceed with the solution.

$3.119/gal to cents/ liter

$3.119/gal = $3.119/gal × 100 cents/$1 × 1 gal/4.55 Liter

                 = $ 68.54cents/ Liter.

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Answer:19

Step-by-step explanation:

The number of each type of vehicle they can buy is: a) Vans: 160, b) Small trucks: 80, c) Large trucks: 70

Let's denote the number of vans as V, the number of small trucks as S, and the number of large trucks as L. From the given information, we can establish the following equations: V + S + L = 310 (The total number of vehicles is 310), V = 2S (Twice as many vans as small trucks). Now, let's calculate the cost equation based on the cost of each vehicle type: Cost of vans: 45,000 * V, Cost of small trucks: 40,000 * S, Cost of large trucks: 80,000 * L. Since the total cost is $16 million, we have: 45,000V + 40,000S + 80,000L = 16,000,000

Now, we can solve the system of equations: V + S + L = 310 (1), V = 2S (2)

45,000V + 40,000S + 80,000L = 16,000,000 (3). Substituting equation (2) into equation (1), we get: 2S + S + L = 310, 3S + L = 310. Now, we can substitute the value of V from equation (2) into equation (3): 45,000(2S) +

130,000S + 80,000L = 16,000,000 (4). We can now solve the system of equations (3) and (4) to find the values of S and L. Solving equations (3) and (4) simultaneously, we get: 3S + L = 310 (3) 130,000S + 80,000L = 16,000,000 (4). Multiplying equation (3) by 80,000 and subtracting it from equation (4), we eliminate L: 130,000S + 80,000L - 80,000(3S + L) =  16,000,000 - 24,800,000 -110,000S = -8,800,000. Dividing both sides by -110,000, we find: S = 8,800,000 / 110,000, S = 80

Substituting the value of S back into equation (3), we find: 3(80) + L = 310

L = 310 - 240,L = 70. Now that we have the values of S and L, we can find the value of V using equation (2): V = 2S. V = 160. Therefore, the number of each type of vehicle they can buy is: a) Vans: 160, b) Small trucks: 80

c) Large trucks: 70.

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Answer: The slope would be negative 3/4, so -3/4.

The correct statement are:

Based on the given information, we can make the following conclusions:

A. The interquartile range for high school students is smaller than college students.

The statement is False

B. The mean for high school students is smaller than college students.

The statement is False because the mean of College is 25.28 and mean for High school is 30.4.

C. The range for high school students is larger than college students.

The statement is True .

D. The college median is equal to the high school median.

The statement is True because the median for both is 24..

E. The mean absolute deviation is larger for college students than high school students.

The statement is False.

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The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

C

Step-by-step explanation:

6.3/3 = 2.1

12.6/6 = 2.1

18.9/9 = 2.1

Answer:

Jun 25, 2018 — Reflection over the y -axis. Vertical stretch by a factor of two. Horizontal translation right two units. Vertical translation up two units. I hope this helps you .. ;]

Step-by-step explanation:

The distance between the points (a, b) and (c, d) is √((c - a)^2 + (d - b)^2). And the distance between the points (1, 2) and (7, 10) is 10 units.

The distance between two points (a, b) and (c, d) in a two-dimensional coordinate system can be calculated using the distance formula:

Distance = √((c - a)^2 + (d - b)^2)

In this case, we are given the points (1, 2) and (7, 10), and we need to find the distance between them.

Using the distance formula, we can calculate:

Distance = √((7 - 1)^2 + (10 - 2)^2)

        = √(6^2 + 8^2)

        = √(36 + 64)

        = √100

        = 10

Therefore, the distance between the points (1, 2) and (7, 10) is 10 units.

The distance formula is derived from the Pythagorean theorem. It calculates the length of the straight line between two points in a two-dimensional plane. The formula uses the differences between the x-coordinates (c - a) and the y-coordinates (d - b) of the two points and squares them. Then, it takes the square root of the sum of the squares to obtain the final distance.

In our case, we substitute the given coordinates into the formula and perform the calculations step by step. We subtract the x-coordinates and y-coordinates, square the differences, add them together, and finally take the square root of the sum. This gives us the distance between the two points.

The distance between (1, 2) and (7, 10) is found to be 10 units. This means that if we were to draw a straight line connecting these two points on a coordinate grid, the length of that line would be 10 units.

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The correct question is: The distance between the points (a, b) and (c, d) is ________. So the distance between (1, 2) and (7, 10) is __________.

Answer:

500 liters

Step-by-step explanation:

We want to find the total amount of water that was drained.

He drained 62.5 liters of water per minute and this went on for 8 minutes. The total amount of water drained is:

62.5 * 8 = 500 liters of water

Answer:

x=45

Step-by-step explanation:

We know that 2y+6 and 8y-102 are vertical angles to each other. This means that 2y+6=8y-102. \(6y=108\), which means that y=18. \(2\cdot(18)+6=36+6=42\). Since one line is a straight angle, it is 180 degrees we can do \(3x=180-45=135\), so x=45.

Answer:

y = 18

x = 46

measures of the angles:

8y - 102 = 42

2y + 6 = 42

3x = 138

Step-by-step explanation:

So first remember the verticle angles theorem, which states that, when two lines intersect there will be four angles formed; the angles that are opposite from each other will be congruent, that is,  they will have the same measure.

Using this we know that opposite angles have to be congruent:

so

(2y + 6) = (8y -102)

now there is an algebra equation that can be solved by inverse operations and simplifying

2y + 6 = 8y - 102

    +102      +102

2y + 108 = 8y

-2y             -2y

108 = 6y

/6        /6

18 = y

Also, remember that two adjacent angles that form a line will add up to 180,

so

3x + (2y + 6) = 180

*note: I could have also used (8y - 102) but I choose to use (2y + 6)

so now substitute in the value of y that was found

y = 18

3x + (2 * 18 + 6) = 180

simplify

3x + ( 36 + 6) = 180

3x + 42 = 180

now use inverse operations

3x + 42 = 180

     -42     -42

3x = 138

/3      /3

x = 46

Answer:

Rectangular Form. A function (or relation) written using (x, y) or (x, y, z) coordinates.

Step-by-step explanation:

??magic

Step-by-step explanation:

The slope of tghe line (m) = (y₂ - y₁) ÷ (x₂ - x₁)

                                          =  (- 6 -0) ÷ ( 0 - 7)

                                          =    ⁶/₇

We can now use the point-slope form to write the equation for this line:

y - y₁ = m(x - x₁) where (x₁ , y₁) = (7 , 0)

              y =  ⁶/₇ ( x  -  7 )

Answer:

y = 2x - 1

Step-by-step explanation:

Answer:

y=1x+0

Step-by-step explanation:

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