PLEASE!!! HELP NEEDED!!!

Given the following equation, x^4 - x^3 - 3x - 2. Use synthetic division to test the following 3 points and show which one is a root. Must show synthetic division for all 3 of the following test points. Test these 3 possible root points also called possible zeros using synthetic division: (x,y) = (-1, 0) (-3, 0) (2, 0).

PLEASE SHOW YOUR WORK!!!

Answer:

Step-by-step explanation:

A function maps an x-value to a single y-value. The graph of the parabola on the left does that.

The table on the right maps -1 to both 10 and 20, so does not meet the definition of a function.

Answer:

A.Cause and effect

Step-by-step explanation:

Answer:

-61

Step-by-step explanation:

Probability can be a natural number, from O to infinity. In fact, how can you represent a -61 probability? it's impossible, at maximum you can have a null probability, that is 0

Answer:

1. 6x+15y-12

2. 25

3. 5(11x-5)

Step-by-step explanation:

1. We have the expression [tex]3(2x+5y-4)[/tex] we have to distribute number 3 to simplify the expression:

[tex]3(2x+5y-4)=\\3.(2x)+3.(5y)-3.(4)=\\=6x+15y-12[/tex]

Then the correct answer is the first choice: 6x+15y-12

2. We have to find the value of the expression when c=4, we have

[tex]f(c)=4c + 3c -2c + 5[/tex]

Then when c=4:

[tex]f(4)=4.(4) + 3.(4) -2.(4)+ 5\\f(4)=16+12-8+5\\f(4)=28-3\\f(4)=25[/tex]

Then the correct answer is the first choice: 25

3. We have to factor the expression 55x-25,

we can see that (5).11=55 and (5).5=25, then the common factor in this expression is number 5,

[tex]55x-25=\\(5).11x-(5).5=\\=5(11x-5)[/tex]

Then the correct answer is the first choice: 5(11x-5)

Answer:

  x = 0

Step-by-step explanation:

You know the answer to this because you know the identity element for addition is 0: 5 + 0 = 5.

__

Or, you can make use of the addition property of equality and add -5 to both sides of the equation:

  5 - 5 + x = 5 - 5

  x = 0 . . . . . . . . . . simplify

Answer:x=0

Step-by-step explanation:

Answer:

  A.  {(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

Step-by-step explanation:

A function has no repeated values of the independent variable. Only choice A meets that requirement.

___

B: (-9, 12) and (-9, 8) both have -9 as a first value; not a function.

C: (8, -2) and (8, -10) both have 8 as a first value; not a function.

D: (-2, 0) and (-2, 3) both have -2 as a first value; not a function.

Answer:

A.

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

Step-by-step explanation:

In mathematics, a function [tex]f[/tex] is a relationship between a given set [tex]x[/tex] (domain) and another set of elements [tex]y=f(x)[/tex] (range) so that each element x in the domain corresponds to a single element [tex]f(x)[/tex] of the range. This can be expressed as:

[tex]f:x \rightarrow y\\\\a \rightarrow f(a)\\\\Where\hspace{3}a\hspace{3}is\hspace{3}an\hspace{3}arbitrary\hspace{3}constant[/tex]

So according to that, the only set that satisfies the definition of a function is:

A.

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

This is because:

In B.

-9 is the first element in more than one ordered pair in this set.

In C.

8 is the first element in more than one ordered pair in this set.

In D.

-2 is the first element in more than one ordered pair in this set.

Answer: Ok, there are two types of variables, the independent and the dependents.

a dependent variable is one that changes in response to the independent variable.

In an experiment, yo usually have control over the independent variable, it may be the temperature on an oven, the intensity of an x-ray cannon, the time you let something heat under the sun, etc.

and the dependent variable will response to the independent variables in some way, so if you can observe how it changes you can understand te relationship between them, that is the goal of the experiment.

So it's true, yo want to know how the response variable "responds" to the treatment you apply.

Answer: 0.9962

Step-by-step explanation:

Given : According to a 2009 Reader's Digest article, people throw away approximately 10% of what they buy at the grocery store.

i.e. the proportion of the people throw away what they buy at the grocery store [tex]p=0.10[/tex]

Test statistic for population proportion : -

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

For [tex]\hat{p}=0.02[/tex]

[tex]z=\dfrac{0.02-0.1}{\sqrt{\dfrac{0.1(1-0.1)}{100}}}\approx-2.67[/tex]

Now by using the standard normal distribution table , the probability that the sample proportion exceeds 0.02 will be :

[tex]P(p>0.02)=P(z>-2.67)=1-P(z<-2.67)=1-0.0037925\\\\=0.9962075\approx0.9962[/tex]

Hence, the probability that the sample proportion exceeds 0.02 =0.9962

From a statistical point of view, considering a normal sampling distribution with the known population proportion (10% or 0.10), the probability that the sample proportion of grocery shoppers throwing away groceries exceeds 0.02 or 2% is almost certain (0.996). This is calculated considering the Z-score for 0.02 using standard deviation calculated using the Central Limit Theorem.

This question is about the calculation of probability in relation to sampling distributions. In this case, we want to find out the probability that the sample proportion (the percentage of people who throw away groceries) exceeds 0.02 or 2%. Since the proportion of people who throw away groceries in the population (according to the Reader’s Digest article) is 10% or 0.10, the probability that the sample proportion exceeds 0.02 is basically 1, because 0.02 is significantly less than 0.10.

However, to apply this concept accurately, we need to consider the distribution for the sample proportion, which is approximately normal with a mean equal to the population proportion (0.10) and a standard deviation calculated as sqrt[(0.10*(1-0.10))/100] = 0.03, according to the Central Limit Theorem. Given this, the Z-score for 0.02 was calculated using Z = (sample proportion - population proportion)/standard deviation = (0.02-0.10)/0.03 = -2.67.

Looking up this Z-score in a standard normal table or using a probability calculator shows that the probability of getting a score this extreme or more (Z <= -2.67) is close to 0.004. Therefore, the probability that the sample proportion exceeds 0.02, in other words that Z > -2.67, is 1 - 0.004 = 0.996. So, it is almost certain (with a probability of 0.996) that the sample proportion will exceed 0.02.

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Answer:

The answer to your question is : 80 minutes

Step-by-step explanation:

Data

Mark = 120 minutes

Alexis = 240 minutes

Together = ??

We need to write an equation, we consider that in 1 minute, Mark loads 1/120 and Alexis 1/240. Then the equation is:

                   1 = x/120 + x/240             1 = truck uploaded ;   x = time in minutes

   Solve it     1 = (2x + x) /240

           240 = 3x

             x = 240/3

             x = 80 minutes              

The Mark and Alexis work together will take to load all of the packages is 80 minutes.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Mark can load a truck with packages = 120 minutes

Mark's rate of work = [tex]\frac{1}{120}[/tex]

Alexis can load a truck with packages = 240 minutes

Alexis's rate of work = [tex]\frac{1}{240}[/tex]

Rate of work together by Mark and Alexis is

⇒ [tex]\frac{1}{120}+\frac{1}{240}[/tex]

⇒ [tex]\frac{2}{240}+\frac{1}{240}[/tex]

⇒ [tex]\frac{3}{240}[/tex]

⇒ [tex]\frac{1}{80}[/tex]

Thus Mark and Alexis work together will take to load all of the packages is [tex]\frac{1}{\frac{1}{80} }[/tex]

⇒ [tex]80[/tex]

Hence we can conclude that the Mark and Alexis work together will take to load all of the packages is 80 minutes.

Learn more about word problems here

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Answer:

11,36 pounds

Step-by-step explanation:

Trayvon's weight on earth= 142 pounds

Trayvon's weight on Saturn= (0,92)*Trayvon's weight on earth=

(0,92)*142=130,64 pounds

The difference between Trayvon's weight on earth and Saturn:

Trayvon's weight on earth- Trayvon's weight on Saturn

142-130,64=11,36 pounds.

The student should watch for 32.135 on the dial pressure gauge when inflating the tire since the specified tire pressure is 32 27/200 psi.

The student's question involves converting a fraction to a decimal. The situation deals with the air pressure in a tire being 32 27/200 pounds per square inch (psi). To express this as a decimal, we perform the division operation of 27 divided by 200 which equals 0.135. This means the air pressure should be 32.135 psi on the dial pressure gauge.

For example, if a tire gauge reads 34 psi, this represents the pressure inside the tire without considering the atmospheric pressure. However, the absolute pressure within the tire will be gauge pressure plus atmospheric pressure. Therefore, if you're reading the gauge, you should aim for it to display 32.135 psi as it is in this context that we're discussing tire pressure.

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Answer:

  y = (5/2)x + 6

Step-by-step explanation:

The given line has a slope (coefficient of x) of -2/5. The perpendicular line will have a slope that is the negative reciprocal of this:

  -1/(-2/5) = 5/2

Since you are given a point you want the line to go through, the point-slope form of the equation of the line is useful. That form for slope m and point (h, k) is ...

  y = m(x -h) +k

For your slope m=5/2 and point (h, k) = (-2, 1), the equation of the line is ...

  y = 5/2(x +2) +1

  y = 5/2x +6 . . . . . eliminate parentheses

Answer:

21.6

Step-by-step explanation:

9.2+0.5+6+5.9=21.6 Because it is looking for the TOTAL amount you add the numbers.

Answer: 21.6 inches

Step-by-step explanation:

Given : Last winter, Michigan had these snow fall totals (in inches) over a one month period: 9.2, 0.5, 6, and 5.9.

Then, By suing the addition operation.

The total amount of snow during the month will be (Sum of all the amount of snow fall ) :-

9.2+0.5+6+5.9 = 21.6 inches

Therefore, the  total amount of snow during the month= 21.6 inches

Answer: a) Yes, there is enough fance

b) 58.1° and 47.9°

c) The city will not approve, because 1/3 of the area is just 2220.5ft²

Step-by-step explanation:

a) using law of cosines: x is the side we do not know.

x² = 126² + 110² - 2.126.110.cos74°

x² = 20335.3

x = 142.6 ft

So 150 > 142.6, there is enough fance

b) using law of sine:

sin 74/ 142.6 = sinα/126 = sinβ/110

sin 74/ 142.6 = sinα/126

0.006741 = sinα/126

sinα = 0.849

α = sin⁻¹(0.849)

α = 58.1°

sin 74/ 142.6 = sinβ/110

sin 74/ 142.6 = sinβ/110

0.006741 = sinβ/110

sinβ = 0.741

β = sin⁻¹(0.741)

β = 47.9°

Checking: 74+58.1+47.9 = 180° ok

c) Using Heron A² = p(p-a)(p-b)(p-c)

p = a+b+c/2

p=126+110+142.6/2

p=189.3

A² = 189.3(189.3-126)(189.3-110)(189.3-142.6)

A = 6661.5 ft²

1/3 A = 2220.5

So 2300 >  2220.5. The area you want to build is bigger than the area available.

The city will not approve

Answer:

16 in × 20 in

Step-by-step explanation:

Area of picture= length by width

                         =4*6=24 in²

Area of frame=Length by width

                      =16*20=320 in²

% of the picture in the frame will be

                        (24/320) * 100% =7.5%

     2. Finding the % of the picture that can fit in 18 × 24 frame

Area of picture=24 in²

Area of frame =Length by width

                       =18*24=432 in²

% of the picture in the frame will be;

                        (24/432)*100%=5.6%

The frame 16 by 20 in will keep 7.5% of the original picture

The frame 18 by 24 in will keep 5.6% of the original picture

Hence you should use the frame  of 16 by 20 in because it will keep more of the original picture.

Answer:

The guy wire lenght is 500 ft.

Step-by-step explanation:

The Pythagorean Theorem says the sum of the squares two adyacent sides is equal to the square of the opposite side.

Applied in this example, we can rephrase it as:

The sum of the square of the pylon height with the square of the distance from the guy wire tip to the pylon is Equal to the  square of the Guy wire lenght.

So:

[tex]PylonHeight^{2}  + floordistance^{2} = GuyWireLength^{2} \\160.000 + 90.000 = GuyWireLength^{2} \\\\\sqrt{160.000 + 90.000} =GuyWireLength\\GuyWireLength= 500 ft[/tex]

Final answer:

The length of the guy wire needed for a suspension bridge is calculated using the Pythagorean Theorem. Given the square of the distance between the wire on the ground and the pylon is 90,000 feet, and the square of the pylon's height is 160,000 feet, the guy wire length is found to be 500 feet.

Explanation:

The length of the guy wire needed for a suspension bridge can be calculated using the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The given squares of the distance between the wire on the ground and the pylon on the ground is 90,000 feet (a2), and the square of the height of the pylon is 160,000 feet (b2). To find the length of the guy wire (c), we can add these two values and then take the square root:

a2 + b2 = c2
90,000 + 160,000 = c2
250,000 = c2
c = √250,000
c = 500 feet

Therefore, the length of the guy wire is 500 feet.

Answer:

see explanation

Step-by-step explanation:

Given

x + [tex]\frac{1}{2}[/tex] ≤ - 3 or x - 3 > - 2

Solve the left and right inequalities separately, that is

x + [tex]\frac{1}{2}[/tex] ≤ - 3 ( isolate x by subtracting [tex]\frac{1}{2}[/tex] from both sides )

x ≤ - 3 - [tex]\frac{1}{2}[/tex], that is

x ≤ - [tex]\frac{6}{2}[/tex] - [tex]\frac{1}{2}[/tex], thus

x ≤ - [tex]\frac{7}{2}[/tex]

OR

x - 3 > - 2 ( isolate x by adding 3 to both sides )

x > 1

Solution is

x ≤ - [tex]\frac{7}{2}[/tex] or x > 1

Answer:

  54 mph

Step-by-step explanation:

Let s represent the slower speed. The product of speed and time is distance, which did not change between the two trips. So, we have ...

  1.8(s +6) = 2(s)

  10.8 = 0.2s . . . . eliminate parentheses, subtract 1.8s

  54 = s . . . . . . . . divide by 0.2

Fran's average speed on Sunday was 54 miles per hour.

____

Her trip was 108 miles long.

To solve the problem, you can use the equation for speed which is distance divided by time. By substituting variables and solving the equation, you'll find that the average speed on Sunday was 54 mph when traffic was heavier.

To solve this, we need to use the formula for speed which is distance divided by time. Since the distance to her mother's house and back is the same for both trips, let's denote the distance as 'd'. We don't know the numerical distance, but we don't need to.

For Saturday, the formula is speed=d/1.8

For Sunday, the average speed is  d/2.

According to the problem, the average speed on Sunday was 6 mph slower than on Saturday. Therefore, the speed on Saturday minus 6 equals the speed on Sunday. So we have the equation: d/1.8 - 6 = d/2

To solve this equation, you first clear the fractions by multiplying each term by the common multiple of 2 and 1.8 which is 3.6. This gives us: 2d - 21.6 = 1.8d

Next, subtract 1.8d from 2d to get 0.2d = 21.6, then divide both sides by 0.2, yielding: d=108

Substitute d = 108 into the equation for Sunday to find the average speed: 108/2 = 54 mph. This is the answer, Fran's speed on Sunday was 54 mph when the traffic was heavier.

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Answer:

Jessica spent 10 months in Spain and 8 months in Colombia.

Step-by-step explanation:

Let x be the number of months Jessica lived in Spain, then she lived 18 - x months in Colombia.

She learned an average of 160 words per month when she lived in Spain, so she learned 160x words in Spain.

She learned an average of 200 words per month when she lived in Colombia, so she learned 200(18-x) words in Colombia.

In total, she learned a total of 3,200 new words, thus

[tex]160x+200(18-x)=3,200\\ \\160x+3,600-200x=3,200\\ \\160x-200x=3,200-3,600\\ \\-40x=-400\\ \\x=10[/tex]

Jessica spent 10 months in Spain and 8 months in Colombia.

The probability of nobody winning in four rounds of a "nonconformity" game where players choose rock, paper, or scissors is [tex]\((\frac{1}{3})^4 = \frac{1}{81}\).[/tex]

To find the probability that nobody wins any of the 4 games, we need to consider under what conditions there is no winner in this game. There are two cases for no winner :

1. All three players choose the same symbol.

2. All three players choose different symbols.

Let's consider each case separately and calculate the probabilities.

Case 1: All three choose the same symbol

Each player has 3 choices (rock, paper, scissors).

For all three to choose the same symbol, the first player can choose any symbol, but the second and third must match.

Thus, there are 3 possible outcomes (RRR, PPP, SSS) out of a total of [tex]\(3 \times 3 \times 3 = 27\)[/tex] possible outcomes for each game.

Thus, the probability of this case is: [tex]\[\frac{3}{27} = \frac{1}{9}.\][/tex]

Case 2: All three choose different symbols

There are three possible different symbols (rock, paper, scissors). The possible outcomes for this case are RPS, RSP, PRS, PSR, SRP, SPR, giving a total of 6 distinct outcomes. Hence, the probability of this case is:

[tex]\[\frac{6}{27} = \frac{2}{9}.\][/tex]

Total Probability of No Winner

Combining the probabilities from Case 1 and Case 2, we get the total probability that there is no winner in a single game:

[tex]\[\frac{1}{9} + \frac{2}{9} = \frac{3}{9} = \frac{1}{3}.[/tex]

Since there are 4 games and each game is independent, the probability of no winner in any of the 4 games is: [tex]\[\left( \frac{1}{3} \right)^4 = \frac{1}{81}.\][/tex]

Thus, the probability that nobody wins any of the 4 games is[tex]\(\boxed{\frac{1}{81}}\).[/tex]

The complete question is : Mario, Yoshi, and Toadette play a game of "nonconformity": they each choose rock, paper, or scissors. If two of the three people choose the same symbol, and the third person chooses a different symbol, then the one who chose the different symbol wins. Otherwise, no one wins. If they play 4 rounds of this game, all choosing their symbols at random, what's the probability that nobody wins any of the 4 games? Express your answer as a common fraction.

Answer:

The volume of the ball with the drilled hole is:

[tex]\displaystyle\frac{8000\pi\sqrt{2}}{3}[/tex]

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

[tex]x^2+y^2=15^2\to y=\sqrt{225-x^2}[/tex]

Then we set the integral for the volume by using shell method:

[tex]\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx[/tex]

That can be solved by substitution:

[tex]u=225-x^2\to du=-2xdx[/tex]

The limits of integration also change:

For x=5: [tex]u=225-5^2=200[/tex]

For x=15: [tex]u=225-15^2=0[/tex]

So the integral becomes:

[tex]\displaystyle -\int_{200}^{0}\pi \sqrt{u}du[/tex]

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

[tex]\displaystyle \int_{0}^{200}\pi u^{1/2}du[/tex]

Then applying the basic rule we get:

[tex]\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}[/tex]

Since that is just half of the solid, we multiply by 2 to get the complete volume:

[tex]\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}[/tex]

[tex]=\displaystyle\frac{8000\pi\sqrt{2}}{3}[/tex]

To find the volume of the resulting solid, calculate the volume of the ball and subtract the volume of the hole. The volume of the resulting solid is (4/3)π(15)³ - 10πr².

To find the volume of the resulting solid, we need to calculate the volume of the ball and subtract the volume of the hole. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. So, the volume of the ball is V₁ = (4/3)π(15)³. The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is the height. The height of the cylinder formed by the hole is equal to the diameter of the ball, which is 2r. So, the volume of the hole is V₂ = π(5)²(2r) = 10πr².

Therefore, the volume of the resulting solid is V = V₁ - V₂ = (4/3)π(15)³ - 10πr².

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Answer:

11 pieces.

Step-by-step explanation:

We must divide 8 1/4 by 3/4

8 1/4 = 33/4

Dividing:

33/4 / 3/4

= 33/4 * 4/3

= 33/3

= 11.

Answer:

11 pieces.

Step-by-step explanation:

In order to make this happen, you need to divide the total length of the wood by the length that he needs, so it would be 8 1/4 feet by 3/4 of foot:

[tex]\frac{8\frac{1}{4} }{\frac{3}{4} } =\frac{\frac{33}{4} }{\frac{3}{4} }\\\frac{4(33)}{(3)(4)} \\\frac{132}{12}=11[/tex]

So now we know that he will get 11 piecesof 3/4 of foot out of the 8 1/4 feet long piece of wood.

Changing [tex]x\mapsto -x[/tex] "inverts" the orientation of the x axis, so the graph of f(x) is transformed by reflecting it about the y axis.

The transformation f(-x) represents a reflection of function f(x) across the y-axis. Even functions are unchanged by this transformation, while odd functions are reversed.

The transformation f(-x) in mathematical terms represents a reflection of the function f(x) across the y-axis. For instance, if you have a function that plots as a certain curve when x is positive, applying function to f(-x) would result in the same curve but flipped horizontally across the y-axis. This is because replacing x with -x inverts the sign of every x-coordinates of the original points, causing a mirror image reflection over the y-axis. Thus, while the original function may say f(x) = x², f(-x) would also form a parabola, but it would be flipped across the y-axis.

For example, if f(x) = x³ for x > 0 which increases, f(-x) = -x³. As x values are now negative, the graph flips and for x > 0, f(-x) decreases.

Note that even functions like f(x) = x², which are symmetric about the y-axis, remain unchanged when transformed to f(-x), while odd functions like f(x) = x³, which are symmetric about the origin, are reversed when f(-x) is implemented.

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Answer:

A

Step-by-step explanation:

Let's first assume that the restriction doesn't hold.

So that way we can say that we can put ANY OF THE 9 DIGITS (1-9) on ANY OF THE 4 DIGIT COMBINATIONS.

Hence,

first digit can be any of 1 through 9

second digit can be any of 1 through 9

third digit can be any of 1 through 9

4th digit can be any of 1 through 9

So the total number of possibilities will be 9 * 9 * 9 * 9 = 6561

now, let's take into account the restriction. since all 4 digits cannot be the same, so we need to exclude:

1111

2222

3333

4444

5555

6666

7777

8888

9999

That's 9 numbers. So final count would be 6561 - 9 = 6552

Answer A is right.

The correct answer is a. 6552. There are 6561 total combinations for a 4-digit bike lock. After excluding 9 combinations where all digits are the same, 6552 combinations remain.

To determine the total number of possible combinations for a 4-digit bike lock with digits ranging from 1 to 9, we start with the total unrestricted possibilities. Each digit has 9 options (1 through 9), so we calculate:

However, the problem states that all 4 digits cannot be the same. This means we must subtract the 9 combinations where all four digits are identical (e.g., 1111, 2222, ..., 9999). Thus, we calculate:

The correct answer is a. 6552.

The volume of the solid generated by revolving the region bounded by ( y = [tex]\ln(x) \)[/tex], the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex] about the x-axis is given by the integral

[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]

Now, let's compute the volume step by step.

1. Set up the integral for the volume using the disk method, since we are rotating around the x-axis. The formula for the volume of a solid of revolution using the disk method is [tex]\( V = \pi \int_{a}^{b} [f(x)]^2 dx \)[/tex], where [tex]\( f(x) \)[/tex] is the function being rotated, and [tex]\( [a, b] \)[/tex] is the interval of rotation.

2. Since [tex]\( f(x) = \ln(x) \)[/tex] and we are rotating around the x-axis from [tex]\( x = 1 \)[/tex] to [tex]\( x = e^2 \)[/tex], our integral becomes

[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]

3. Solve the integral. This particular integral requires integration by parts or a special integrating factor due to the natural logarithm squared. The integral of [tex]\( (\ln(x))^2 \)[/tex] is not straightforward, so we will use integration by parts.

Let's solve the integral now.

It appears there was a mistake in the code due to the missing definition of the exponential function `exp`. Let me correct that and solve the integral again.

The volume of the solid generated by revolving the region bounded by [tex]\( y = \ln(x) \)[/tex], the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex] about the x-axis is approximately[tex]\( 40.14 \)[/tex]. This is the numerical approximation, but you asked for the exact form, so let's represent that as well.

The exact form of the volume, without numerical approximation, is:

[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]

Now I will present the exact form of the integral result.

The exact form of the volume of the solid generated by revolving the region bounded by [tex]\( y = \ln(x) \),[/tex] the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex]about the x-axis is:

[tex]\[ V = \pi \left( -2 + 2e^2 \right) \][/tex]

This is the exact expression for the volume in terms of [tex]\( \pi \) and \( e \),[/tex] the base of the natural logarithm.

Answer:

(-3,-2), (-3,2) , (1,2) and (1,-2)

Step-by-step explanation:

Give the translation rule as; 3 units to the left and 2 units down, it means (-3,-2)

The given coordinates of the square are (0,0) and (4,4). You can plot the coordinates on a graph tool and determine the position of the other vertices

of the square as (0,4) and (4,0)

Applying the translation to each point

(0,0)⇒(-3,-2) = (-3,-2)

(0,4)⇒(-3,-2) = (-3,2)

(4,4)⇒ (-3,-2) = (1,2)

(4,0)⇒(-3,-2)= (1,-2)

The image of the vertices after transformation will be

(-3,-2), (-3,2) , (1,2) and (1,-2)

Answer:

  [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]

Step-by-step explanation:

The index of a radical is the denominator of a fractional exponent, and vice versa. If you think about the rules of exponents, you know this must be so.

For example, consider the cube root:

[tex]\sqrt[3]{x}\cdot \sqrt[3]{x}\cdot \sqrt[3]{x}=(\sqrt[3]{x})^3=x\\\\(x^{\frac{1}{3}})^3=x^{\frac{3}{3}}=x^1=x[/tex]

That is ...

[tex]\sqrt[3]{x}=x^{\frac{1}{3}} \quad\text{radical index = fraction denominator}[/tex]

Answer:

The answer to your question is below

Step-by-step explanation:

Equation 4x - 2y = 8 solve for y

First, pass 4x to the right side                -2y = -4x + 8

Pass -2 to the right side                             y = -4/-2 x  + 8 /-2

Simplify                                                        y = 2x -4 or    y = -4 + 2x

I can not see clearly the work of Charlize and Camille, but the one that has the answer shown above is correct.                                                                                    

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. It is convenient to start with point-slope form, then simplify the result to slope-intercept form. The two forms of the equation for a line are ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y = mx +b . . . . . . . . line with slope m and y-intercept b

The given lines are in slope-intercept form, so we can read the slope directly from the equation.

The slope of the parallel line will be the same as the slope of the given line: -4/5.

  point-slope form: y +5 = (-4/5)(x +3)

  slope-intercept form: y = (-4/5)x -37/5

__

2. The slope of the given line is 1/3. The slope of the perpendicular line is the negative reciprocal of that: -1/(1/3) = -3. Your lines are then ...

  point-slope form: y -1 = -3(x -4)

  slope-intercept form: y = -3x +13

Answer:

B 10% off sale, with a total price to pay of 756

Step-by-step explanation:

Retail price (Rp) = $800

Taxes (T) = 5%

Total price A (TA) = Rp - 75 + (Rp - 75) 5%

TA = 800 - 75 + (800-75) 5%

TA = 725 + 725 5%

725 5% = 725*5/100 = 36.25

TA= 725+36.25 = $761.25

Total price B (TB) = RP - RP 10% + (RP - RP 10%) 5%

TB = 800 - 800 10% + (800 - 800 10%) 5%

800 10% = 800*10/100 = 80

TB = 800 - 80 + (800 - 80) 5%

TB = 720 + 720 5%

720 5% = 720*5/100 = 36

TB = 720 + 36 = $756

store pays sales tax means Walden's family will not need pay for taxes

Total price C (TC) = RP - RP 5%

TC = 800 - 800 5%

800 5% = 800*5/100 = 40

TC = 800 - 40 = $760

Means that Walden's family will need pay just the retail price

TD = $800

The beast deal is from the store B

Answer:

the answer is b

Step-by-step explanation:

hoped this helped