Find the volume of the solid generated by revolving the region r bounded by y=e^-2x, y=0, x=0, x=ln9

Answer:

16π m²

Step-by-step explanation:

area of circle = πr²

area = π × (4 m)²

area = 16π m²

By analyzing and understanding the graph of the absolute value function, we find that the function evaluated at the x-value equal to 1 is equal to the y-value equal to 3.

In this problem we find the representation of an absolute value function, where the horizontal axis corresponds to the values of the domain, whereas the vertical axis is for the values of the range. In that picture we must look up for the y-value associated with a given x-value.  

Then, we proceed to evaluate the absolute value function at x = 1. In accordance with the graph, the y-value , that is, from the vertical axis, associated with the x-value, that is, from the horizontal axis, equal to 1 is equal to a value of 3.

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Explanation:

To find the inverse, we swap x and y, then solve for y.

y = 2x-3

x = 2y-3

x+3 = 2y

2y = x+3

y = (x+3)/2

y = x/2 + 3/2

y = (1/2)x + 3/2

This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.

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Another approach:

Since we're given a list of multiple choice answers, we can rule out the non-answers.

Plug x = 0 into the first equation of choice A. It leads to y = 2

That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.

This allows us to rule out choice A. Choices B and C are similar stories.

Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.

Answer:

Step-by-step explanation:

Algorithm for deriving the formula of the inverse function

Step 1. In the formula for the original function, replace the notation of the argument and the value:

Step 2. From the resulting formula, express y(x).

Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.

[tex]\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no[/tex]

[tex]y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes[/tex]

Using linear functions, we have that:

a. For 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.

b. For any number of games, the cost at alley B will be less.

A linear function is modeled by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence they are given as follows:

The cost for A will be less when:

A(x) < B(x).

Hence:

4x + 7.5 < 4.5x + 5

-0.5x < -2.5

0.5x > 2.5

x > 2.5/0.5

x > 5.

Hence for 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.

For item b, with the increase of $0.5 per game, we have that:

A(x) = 4.5x + 7.5.

Then the costs per game will be the same, while alley B has the lower intercept, meaning that for any number of games, the cost at alley B will be less.

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Answer:

when you =0.8=4/5

4x + 8(4/5)=40

4x=40-32/5

4×=(200-32)/5

x=168/20

Step-by-step explanation:

4x+8y=40, when y=0.8

4x+8(0.8)=40

4x+6.4=40

4x=40-6.4

4x=33.6

x=33.6/4

x=8.4

f(x) + k will shift the graph up k units.

For example, the notation f(x) + 5 will shift the curve up by 5

If k is negative, then the curve shifts down that amount

-------------------------

f(x-h) shifts the graph to the right h units

Example: f(x-2) shifts to the right 2 units

Another example: f(x+7) shifts left 7 units. In this case, h = -7

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y = -f(x) is a reflection over the x axis

This is because we're multiplying each y coordinate by -1

A point like (1,2) reflects to (1,-2)

The length of the segment CA is 7.

Length of the segment

Basically, length of the line segment is fixed, which is the distance between two fixed points.

The length here can be measured by metric units such as centimeters (cm), millimeters (mm) or by conventional units like feet or inches.

Given,

A is lies between C and T.

Then the values of CT = 25 and AT = 18.

Now we have to find the length of the segment CA.

Consider the point C, A and T are in straight line.

Then A lies between C and T.

So, it is the center point between C and T.

Here we have the length of total line that is

=> CT = 25.

And the length of AT, that is

=> AT = 18.

Then we need to find the length of the segment CA,

By subtracting the length of AT from the total length CT,

That is,

=> CA = CT - AT

Apply the values,

=> CA = 25 - 18

=> CA = 7.

Therefore, the length of the segment CA is 7.

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Answer:

B and D

Step-by-step explanation:

The percentage change is 2.1%

The Yankees won 95 games in 2010

They also won 97 games in 2011

Therefore the percentage change can be calculated as follows

= 97 - 95/97 × 100

= 2/97 × 100

= 0.021 × 100

= 2.1

Hence the percentage change is 2.1%

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Answer:

Yep,

Step-by-step explanation:

First the expression is in this way:

x+4=10

Now shift the 4 ro RHS, then it will become as follows:

x=10-4

Now 10-4 is 6

Therefore, x=6

Answer: p = 4s

Step-by-step explanation:

     The perimeter is the measurement around a shape's sides. In other words, if a square has four sides, we will add up all the sides to find the perimeter.

      Since a square's sides are all congruent, we can multiply the length of one side (s) by 4 to find the total perimeter (p). This becomes:

      p = 4s

quotient = the answer to a division problem

To divide by a fraction, multiply by the reciprocal of the fraction

reciprocal of a fraction = the numerator and denominator are reversed

First, convert "three and two thirds" into an improper fraction:

[tex]3\dfrac{2}{3}[/tex]

⇒ Multiply the whole number by the denominator and add the numerator:

[tex]\dfrac{11}{3}[/tex]

Now, we want to divide this number by three fifths:

[tex]\dfrac{11}{3}\div\dfrac{3}{5}[/tex]

⇒ Dividing by a fraction is the same as multiplying by its reciprocal:

[tex]= \dfrac{11}{3}\times\dfrac{5}{3}\\\\=\dfrac{55}{9}[/tex]

[tex]\dfrac{55}{9}[/tex]

theannswer wold be 100 .33 .87

(rand() % 6) + 1 is the expression randomly rolls one dice, directly yielding one of those values.

Small objects (polyhedrons) used as playing pieces for dice games and other gambling-related activities. The cube, the most popular type of die, has one to six tiny dots on each side (spots). The spots are positioned in the following traditional patterns: 1 and 6, 2 and 5, 3 and 4, so that spots on opposite sides always sum up to 7. The poker and crown and anchor dice, as well as many other types of dice with 4, 5, 7, 8, 10, 12, 16, and 20 sides, are examples of dice with different configurations of spots or other face designs. The majority of the time, dice are employed to generate a random outcome (usually a number or a mixture of numbers), and the mathematical probabilities depend on the physical characteristics and quantity of dice thrown.

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[tex]- 4 - 9 = - 13[/tex]

Answer:

x = -5

Step-by-step explanation:

add 14 to both sides:

x = -19 + 14

x = -5

Answer:

Step-by-step explanation: Well €550 Euros is equal to $547.42 US dollars in currency. But since this is approximately, (D) should be correct.

The required histogram is attached as a picture.

Given the information on how many pages each of the 20 pupils read throughout the summer.

163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431

With frequency on the y axis and class on the x axis.

we observe the histogram and make out that:

class 160 - 220 has the highest frequency of 6 students whereas

400 - 460 has the least with 2 students.

The classes between them range as follows:

220 - 280 has 5 students

280 - 340 has 4 students

340 - 400 has 3 students.

Hence the required histogram is created .

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Answer: Click on this: a=13.6cm,b=9.5cm and c=2.6cm for the triangle show it has a step by step way

Step-by-step explanation:

Answer: Original value: 0.076952

Value (with 3 decimal places): 0.077

Step-by-step explanation: hope this helps

Answer:

let's assume that Sandra's regular hourly rate is x dollars per hour then she is paid 1.5x per hour for the overtime and we have 40x + (48 - 40) *1.5x = 442

Step-by-step explanation:

Step-by-step explanation:

[tex] = \frac{ {2}^{4} }{ {2}^{7} } [/tex]

[tex] = {2}^{4 - 7} [/tex]

[tex] = {2}^{ - 3} [/tex]

[tex] = \frac{1}{ {2}^{3} } [/tex]

[tex] = \frac{1}{2 \times 2 \times 2} [/tex]

[tex] = \frac{1}{8} [/tex]

The answer is not 8, but 1/8.

Answer:

a

Step-by-step explanation:

the unknown value is n then 3 less than this value is

n - 3

Answer:

answer is C

because other equations normally n>3 but C equation normally is n<3

so answer is C

For 6 hours the temperature is held steady

Solution :

Line Graph:

A line graph—also known as a line plot or a line chart—is a graph that uses lines to connect individual data points. A line graph displays quantitative values over a specified time interval. In finance, line graphs are commonly used to depict the historical price action of an asset or security.

Line graphs can be compared with other visualizations of data including bar charts, pie charts, and (in trading) candlestick charts, among others

Temperature Rose:

It is the increase over ambient temperature of the winding due to energizing and loading

stayed steady:

A steady situation continues or develops gradually without any interruptions and is not likely to change quickly.

Temperature fall :

Temperature drop (T1−T2) is a direct indication of energy extracted. For a given resource, it is dependent on T2 which is in turn dependent on the minimum temperature of the process Ti.

There, we can see that the temperature between 12 noon to 6 pm is not changed much.

therefore we can say that for 6 hours the temperature is holding steady.

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The statement is sometimes true.

Points that are located along a single or shared straight line are referred to as collinear points. If two or more points on a line are situated either close to or far from one another, they are said to be collinear in Euclidean geometry.

Three points are automatically coplanar if they are collinear.

What was just said is sometimes true.

This is because three points along a line are typically recognized to be collinear, however it is not always the case.

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The conditional operator creates a compound statement that sets up a condition for something to be true. Therefore, if the condition is met, the statement is true. The parts of the conditional statements are two, the first simple statement in a conditional is called the antecedent  and the second simple statement is called the consequent. So, for two statements A (antecedent) and B (consequent) we will have that:

A → B that means: If A then B

In this problem:

A:  A number is even.

B: The number is divisible by 2.

Thus:

A → B: If a number is even, then the number is divisible by 2.

So, the conclusion of this conditional statement is the consequent, that is,  the number is divisible by 2.

Accordingly, the right answer is D. The number is divisible by 2.

the complete question is

What is the conclusion of the following conditional? A number is divisible by 2 if even.

A. The sum of the digits of the number is divisible by 2.

B. If a number is even, then the number is divisible by 2.

C. The number is even.

D. The number is divisible by 2.

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Answer:

It is the same as subtracting 6.

Step-by-step explanation:

1 + (-6) = 5

1 - 6 = 5

Answer:

6 trust me

Step-by-step explanation:

Answer:

The answer is option C

Step-by-step explanation:

The roots of the quadratic equations are x= 6 or x= -4

X-6=0 or x+ 4=0

⇒(x-6)(x+4)

F(x)=(x-6)(x+4)

Answer:

Perpendicular lines.