Find the volume of the solid generated by revolving the region
bounded by the graphs of the equations about the x-axis.
y = e^-3x
y = 0
x = 0
x= 7

Answers

Answer 1

The volume of the solid generated is π(e^-42 - 1).

The given graphs are y = e^-3x, y = 0, x = 0, and x = 7.

These are the three boundaries: y = 0, y = e^-3x, and x = 7.

The fourth boundary is the x-axis.

When the region formed is rotated around the x-axis, a solid is produced.

The formula for calculating the volume of the solid produced when a region is rotated about the x-axis is given by:

V = ∫ab π(f(x))^2dx

Where a and b are the limits of integration, and f(x) is the equation of the curve.

When we substitute the given values of the integral, we get:

V = ∫07 π(e^-3x)^2dx

V = π∫07 e^-6xdx

Using u-substitution, let:

u = -6x; du = -6dx

When x = 0, u = -6(0) = 0

When x = 7, u = -6(7) = -42

So:

V = π∫0^-42 e^udu

= π[e^u]0^-42

= π(e^-42 - e^0)

Therefore, the volume of the solid generated is π(e^-42 - 1).

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Related Questions

AY
X
1 2 3 4 5
RA
-5 -4 -3 -1
-2
4. Select the correct slope for the graph pictured above.
0 (zero)
undefined
0 1

AYX1 2 3 4 5RA-5 -4 -3 -1-24. Select the correct slope for the graph pictured above.0 (zero)undefined0

Answers

Answer:

slope is undefined

Step-by-step explanation:

The slope of a vertical line parallel to the y- axis is undefined

An electric frying pan was on sale for 20 percent off. The sale price was $36. What was the original price?

Answers

Answer: $45

Step-by-step explanation:

Let the original price be x.

Since there was a discount of 20%, it means the person bought the frying pan at (100% - 20%) = 80% of the original price. This can then be formed into an equation as:

80% × x = $36

0.8 × x = $36

0.8x = $36

x = $36/0.8

x = $45

The original price was $45

Which video game should i get? Hollow knight, cup head, or untitled goose game?
LEt ME know.

Answers

Answer:

I think hollow knight sounds good I've played cup head before and it's so boring but I think u should get hollow knight.

A circular lawn has an area of 1138 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle? Round your answer to one decimal place and use π = 3.14 π = 3.14

Answers

Answer:

\(r = 19.0\ ft\)

Step-by-step explanation:

Given

\(Area = 1138ft^2\)

\(\pi = 3.14\)

Required

Determine the radius of the circle

The area is calculated using;

\(Area = \pi r^2\)

Substitute for Area and π

\(1138 = 3.14 * r^2\)

Make r the subject

\(r^2 = \frac{1138}{3.14}\)

\(r^2 = 362.420382166\)

\(r = \sqrt{362.420382166}\)

\(r = 19.0373417831\)

\(r = 19.0\ ft\) --- Approximated

If a normal sighted woman whose father was color-blind marries a color-blind man, what is the probability that they will have a colorblind child?

Answers

The probability of them having a color-blind child is 50%.

Color blindness is a sex-linked genetic disorder that is passed down from parents to their children. The gene for color blindness is located on the X chromosome, which means that males are more likely to be affected than females, as they only have one X chromosome.

If a normal-sighted woman whose father was color-blind marries a color-blind man, we can assume that the woman is a carrier of the color-blindness gene on one of her X chromosomes, but does not express the trait herself. The man, being color-blind, has the color-blindness gene on his only X chromosome.

In this scenario, the probability of them having a color-blind son is 50%, as the son will inherit the color-blindness gene from his mother and the affected X chromosome from his father. The probability of them having a color-blind daughter is also 50%, as the daughter will inherit the color-blindness gene from her mother and the affected X chromosome from her father. However, the daughter will be a carrier like her mother and will not express the trait.

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What is mass if force is 45 N and acceleration is 39 m/s/s?

Answers

Answer:

The answer is 1.15 kg

Step-by-step explanation:

To find the mass of an object given it's acceleration and the force acting on it we use the formula

\(mass = \frac{force}{acceleration} \\ \)

From the question

force = 45 N

acceleration = 39 m/s²

We have

\(force = \frac{45}{39} = \frac{15}{13} \\ = 1.153846...\)

We have the final answer as

1.15 kg

Hope this helps you

A certain star is 2.4 x 102 light years from the Earth. One light year is about 5.9 x 1012 miles. How far
from the earth (in miles) is the star?
TL
miles from Farth

Answers

The distance of the earth from the star is; 1.416 x 10¹⁵ miles

What are exponents?

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

We are given that 1 light year ≈ 5.9 x  10¹² miles

so: the Coefficients for the problem are mathematically given a

Coefficients =2.4 x 5.9

Coefficients = 14.16

For Exponents;

Exponents=   10² x 10¹² = 10⁽²⁺¹²⁾

Exponents =10¹⁴

In conclusion, we put them together once again to produce a scientific notation;

14.16 x 10¹⁴

1.416 x 10¹⁵ miles

The distance of the earth from the star is; 1.416 x 10¹⁵ miles

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Help I will give crown and brainiest

Help I will give crown and brainiest

Answers

Answer:

quad then hex then oct then non

Step-by-step explanation:

URGENT PLEASEE



A pharmacist put 10.6 ounces of vitamin pills into a bottle. She put 0.053 ounce of vitamin pills in each bottle. How many bottles did the pharmacist use for these vitamin pills?

Answers

Answer:

200 bottles

Step-by-step explanation:

This is a unit rate problem, which requires simple division

\(\frac{10.6}{0.053} = 200\)

If A = 5 1/2-2 3/4 (five and one half minus two and three fourths). what is A?​

Answers

Answer:

the answer to this question is 11/4 or 2 3/4

integer operations
11. -60
12. 10
13. -9
14. 14
15. 37

Answers

Answer:

\(11. - 60 = - 49 \\ 12.10 = 12.1 \\ 13. - 9 = 4 \\ 14.14 = \frac{707}{50} \\ 15.37 = \frac{1537}{100} \)

HELP!! Solve this logarithmic equation for the value of the variable. Be sure to check for extraneous solutions. Thanks!!

HELP!! Solve this logarithmic equation for the value of the variable. Be sure to check for extraneous

Answers

The solution to the equation log₄(x) + log₄(x + 6) = 2 is x = 2.

Using the property logₐ(b) + logₐ(c) = logₐ(cb), we can rewrite the equation as:

log₄(x(x + 6)) = 2

Next, we can use the property logₐ(b) = c is equivalent to \(a^c=b\), to rewrite the equation in exponential form:

4² = x(x + 6)

16 = x² + 6x

x² + 6x - 16 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.

In this case, we'll use factoring:

(x + 8)(x - 2) = 0

Setting each factor equal to zero:

x + 8 = 0 --> x = -8

x - 2 = 0 --> x = 2

Therefore, the solution to the equation log₄(x) + log₄(x + 6) = 2 is x = 2.

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Arianna is working two summer jobs, making $6 per hour walking dogs and making $10 per hour tutoring. In a given week, she can work at most 11 total hours and must earn at least $80.

Answers

Step-by-step explanation:

x = number hours dog walking

y = number hours tutoring

x + y <= 11

6x + 10y >= 80

the solution is the common area below the first line and above the second line.

the first line is above the second line (due to the y-intercept of 11 vs. 8) until the crossing point.

for the crossing point we use the regular equations :

from the first we get

x = 11 - y

using this in the second

6×(11 - y) + 10y = 80

66 - 6y + 10y = 80

4y = 14

y = 14/4 = 7/2 = 3.5

x = 11 - y = 11 - 3.5 = 7.5

so, she has to do at least 3.5 hours tutoring (and then 7.5 hours dog walking) for the minimum of $80 earning, all the way up to the maximum of 11 hours tutoring (and 0 dog walking) for $110 earning.

Y = 2x + 3 find f(0)

Answers

If \(y=2x+1\) then that means \(f(x)=2x+3\) and when you plug in \(x=0\) you get \(f(0)=2\cdot0+3=\boxed{3}\).

Hope this helps :)

Answer:

3

Step-by-step explanation:

y=2x+3

f(x)=2x+3

f(0)=2(0)+3=0+3=3

Solve the system of equations by graphing
y = 6
y = 3x - 3

Answers

Answer: x=3, See the graph below

Step-by-step explanation:

SINCE THE QUESTION ASK FOR GRAPHING

See the graph below

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

I AM ALSO GOING TO SHOW A SECOND WAY WITHOUT GRAPH FOR EXTRA

Given

y=6

y=3x-3

Use substitution (Substituting the value of y)

3x-3=6

Add 3 on both sides

3x-3+3=6+3

3x=9

Divide 3 on both sides

3x/3=9/3

x=3

Hope this helps!! :)

Please let me know if you have any questions

 Solve the system of equations by graphingy = 6y = 3x - 3

Answer:

Step-by-step explanation:

 Solve the system of equations by graphingy = 6y = 3x - 3

Solve the system using the substitution method. -3x – 4y
= 2 x = y - 3

Answers

Answer:

y= −5/4x

heart if it helped!

What number does A represent in the recipe?

What number does A represent in the recipe?
What number does A represent in the recipe?

Answers

Answer: Represent 6

Step-by-step explanation: Representa el 6 por que est en l lines de las letras que representan 6

Can someone please help me with this? I am not good at Algebra
Reward: 2 ppl answer 1s person gets a brainly, thanks on ur page, and a follow

Wrong Answers will get reported and so will nonsense

Can someone please help me with this? I am not good at AlgebraReward: 2 ppl answer 1s person gets a brainly,

Answers

the top option is correct 6x^2 + 5x -4/15

Find the Laplace transform where of the function f(t) =
{ t, 0 < t < {π + t π < t < 2π where f(t + 2 π) = f(t).

Answers

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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5 to 7 and please solve with equations thx

5 to 7 and please solve with equations thx

Answers

Answer:

See attached image

Step-by-step explanation:

The starting point for an e=inequality will have either an empty of filled-in circle.  When empty, it signifies that the exact point is NOT included.  If the inequality is x < 2, for example, the line would begin at 2, but marked with an empty circle.  If, however, the inequality is x =< 2, then the circle is filled in, signifying that the number 2 is included in the set.

5 to 7 and please solve with equations thx

A river flows at 2m/s. Juan’s boat can travel twice as fast down the river as it can go up the river. How fast can the boat go in still water?

Answers

Answer: 2m/s

Step-by-step explanation:

The boat goes twice as fast down the river, which means it goes twice as slow up the river.

Because the river flows at 2m/s, I think the answer is 2m/s

Which of the following will have a unit rate of 50 miles per hour

Which of the following will have a unit rate of 50 miles per hour

Answers

Answer:

Option J

Step-by-step explanation:

Given the following question:

In order to find the answer, we simply divide the miles by the hours to find the answer.

\(\frac{m}{h}\)

Option F:
\(210\div4=52.5\)
\(=52.5\)

Option G:
\(300\div5=60\)
\(=60\)

Option H:
\(250\div4=62.5\)
\(=62.5\)

Option J:
\(175\div3.5=50\)
\(=50\)

In order to have a unit rate of 50 miles per hour you will have to drive "175 miles in 3.5 hours" or option J.

Hope this helps.

Which of the following will have a unit rate of 50 miles per hour

J. 175 miles in 3.5 hours

SOLUTION:

Simply divide the Miles and Hours in each choices until you get the 50 miles per hour.

\(175 \div 3.5 = 50 \: miles\)

The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator.

The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator.

Answers

The length of side x in simplest radical form with a rational denominator is\(3\sqrt{4.5}\).

What is an isosceles triangle?

An isosceles triangle is a triangle with any two sides that are the same length and angles on opposite sides that are the same size.

The right triangle is isosceles, which indicates that its two legs are the same length. This length should be called "y".

Using the Pythagorean theorem, we know that:

\(y^{2}+y^{2}=9^{2}\)

Simplifying this equation:

\(2y^{2}=81\)

Dividing both sides by 2:

\(y^{2}\) = 40.5

Taking the square root of both sides:

y = \(\sqrt{40.5}\)

We can simplify this expression by factoring out a perfect square:

y = \(\sqrt{4.5*9}\)

y = \(3\sqrt{4.5}\)

Since we know that x has the same length as y, the length of x is also:

x = \(3\sqrt{4.5}\)

Therefore, the length of side x in simplest radical form with a rational denominator is\(3\sqrt{4.5}\).

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Assume you are flipping an unbiased coin and that the flipping process is entirely random. A psychic claims that he can sense the outcome of each flip. You put him to the test. You flip the coin 6 times and guess what

Answers

Given statement solution is :- If I were to assume the flipping process is entirely random and the coin is unbiased, the chances of correctly guessing the outcome of each flip would be 1 out of 2, or a 50% probability.

If I were to assume the flipping process is entirely random and the coin is unbiased, the chances of correctly guessing the outcome of each flip would be 1 out of 2, or a 50% probability. However, the psychic claims to have the ability to sense the outcome of each flip, which would suggest that he believes he can accurately predict the results.

To put the psychic to the test, you can proceed with flipping the coin six times and ask the psychic to guess the outcome of each flip. After the coin has been flipped, compare the psychic's guesses with the actual outcomes to evaluate the accuracy of their predictions.

Keep in mind that even if the psychic does make correct predictions, it does not necessarily prove their psychic abilities. Random chance can occasionally lead to a streak of correct guesses, even if there is no true psychic ability involved. To draw any meaningful conclusions, a larger sample size or repeated testing would be required.

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Select the lines that represent functions.

Select the lines that represent functions.

Answers

Answer:

All of them except the squiggly one and the vertical one

Step-by-step explanation:

The rest are functions, two of them are lines, and the curved swoop is a parabola, which is also a function

Explanation

Function is a set of relation without same or repetitive domain. Because we are checking if the following graphs are function or not. It is easier to do line test.

How to check if the graphs are function.

Draw a vertical line.If the line passes or intercepts the graph only one point. The graph is function.If the line passes or intercepts the graph more than a point. The graph is not a function.

Overall, the graphs that are not function are the vertical line and the vertical curve graph.

AnswerA horizontal lineA line with slope or steepnessParabola aka curve graph (The graph is not a line. The question asks for lines which represent functions. I am not sure if they want all graphs that are function or just lines that are functions. A Parabola graph is also a function but not a line graph.)

Feel free to ask if you are confused.

The cost of a TV to Leons is $357. If Leons wants a 44% rate of markup on cost, determine the markup.

Answers

The markup on the TV for Leons is $156.84. This represents a 44% increase over the cost of $357. The selling price of the TV, including the markup, would be $513.84.

To determine the markup on the TV, we need to calculate 44% of the cost.

The cost of the TV is given as $357.

To find the markup, we multiply the cost by the markup rate:

Markup = 44% of $357 = (44/100) * $357 = $156.84

Therefore, the markup on the TV is $156.84.

The markup represents the additional amount added to the cost of the TV to cover expenses and generate a profit for the retailer. In this case, Leons is applying a 44% markup rate to the cost of $357.

The markup is typically expressed as a percentage of the cost. In this case, the markup amount of $156.84 is 44% of the cost.

It's important to note that the markup is not the same as the selling price. To determine the selling price, the markup is added to the cost:

Selling Price = Cost + Markup = $357 + $156.84 = $513.84

Therefore, the selling price of the TV, considering the 44% markup, would be $513.84.

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For which equation is g = 0 not the solution?

12 g = 0
3 g = 30
g + 8 = 8
9 g = 0

Answers

Answer:

3g = 30

Step-by-step explanation:

Well, lets check each one to see if any leaves g = 0

12g = 0      (Given)

÷12   ÷12    (Get "g" on its own)

g = 0          (0 ÷ 12 = 0)

We know it is not this one since g = 0

3g = 30    (Given)

÷3     ÷3    (Get "g" on its own)

g = 10       (30 ÷ 3 = 10)

This is our answer since g = 10 in this equation, and not g = 0 we know that this is our equation.

Just in case, I will do the other options just not as in-depth!

g + 8 = 8

   -8    -8

g = 0

9g = 0

÷9    ÷9

g = 0

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

I have no idea how to do this. I found the answer but now I have to explain it.

I have no idea how to do this. I found the answer but now I have to explain it.

Answers

Answer:

You have 3 + 2 + 2 which is the same as 7 on the other side.

Step-by-step explanation:

3 + 2 + 2 is 7

Answer:

x=2

Step-by-step explanation:

3+x+x=7

2x=4

x=2

Help please explain ​

Help please explain

Answers

Given:

\(\sin^{-1}\left(\dfrac{5}{8}\right)=A\)

To find:

The correct equivalent equation.

Solution:

We have,

\(\sin^{-1}\left(\dfrac{5}{8}\right)=A\)

Taking sin on both sides, we get

\(\sin \sin^{-1}\left(\dfrac{5}{8}\right)=\sin A\)

\(\dfrac{5}{8}=\sin A\)                      \([\because \sin (\sin^{-1}\theta )=\theta]\)

Interchanging the sides, we get

\(\sin A=\dfrac{5}{8}\)

Therefore, the correct option is 4.


Question 18
A wholesale grocery supplier shipped x2-pound blocks of cheese and y3-pound blocks of cheese to a caterer. The total weight of the cheese in the shipment was 44 pounds, and
the shipment consisted of 18 blocks of cheese. Which of the following systems of linear equations best represents this situation?
z+y=18
A
3z +2y=44
z+y=18
2x + 3y = 44
z+y=44
3z + 2y = 18
z+y=44
2z+3y=18
B
C
D
Imported (1)
The G

Answers

The system of linear equations that best represents the situation are:

z+y=18

3z +2y=44

What are the linear equations?

In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.

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The assistantshould explain that this difference in dosage is primarily because of the effect that aging has on which of the following pharmacokineticprocess Triangle XYZ is shown.Which triangle must be similar to triangle XYZ?Correct answer (1 point)A) A triangle with two angles that measure 45B) A triangle with angles that measure 40 and 60C) A scalene triangle with only one angle that measures 100D) An isosceles triangle with two angles that measure 40Give reasoning below, why your choice is correct. (2 points)Use formulas, definitions, or theorems in your reasoning.