Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. Y = 8x3, y = 0, x = 1; about x = 2.

Answers

Answer 1

The volume v of the solid obtained is 15.08

By using the cylindrical shell method to find the volume v of the solid which can be expressed by the formula;

V = 2πrh dr

Then, it is paramount to determine the radius and height of the shell.

From the given information;

The cylindrical shell formed by the rotation about the line x = 2Let consider the radius to be 2 - xThe circumference = 2π(2 - x)The height = 8x³

Then, the volume v of the solid can be estimated by using the cylindrical shell method as follows;

[tex]\mathbf{V = \int ^1_0 2 \pi (2-x) (8x^3) \ dx}[/tex]

Open brackets;

[tex]\mathbf{V = 2 \pi \int ^1_0 (16x^3 -8x^4) \ dx}[/tex]

Taking the integral form;

[tex]\mathbf{V = 2 \pi \Big [ \dfrac{16x^4}{4}-\dfrac{8x^5}{5} \Big]^1_0}[/tex]

Solving the terms in the bracket

[tex]\mathbf{V = 2 \pi \Big [ \dfrac{16(1)^4}{4}-\dfrac{8(1)^5}{5} -0\Big]}[/tex]

[tex]\mathbf{V = 2 \pi \Big [ 4-\dfrac{8}{5} \Big]}[/tex]

[tex]\mathbf{V = 2 \pi \Big [ \dfrac{20-8}{5} \Big]}[/tex]

[tex]\mathbf{V = 2 \pi \Big [ \dfrac{12}{5} \Big]}[/tex]

[tex]\mathbf{V = \dfrac{24\pi}{5}}[/tex]

[tex]\mathbf{V =15.08}[/tex]

Therefore, we can conclude that the volume v of the solid obtained is 15.08

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Answer:

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The following image shows what happens when the particles in a certain state occupy a space. What is the state of the substance that is occupying the space and how do you know?





A. The substance is a gas because the particles are spreading out to fill the space of the container.


B. The substance is a liquid because the particles inside are taking the shape of the container.


C. The substance is a mixture of a gas and a liquid because the particles are filling the space of the container.


D. The substance is a solid because the particles inside the box have a definite shape.

Answers

Answer:

A

Explanation:

The substance is a gas because the particles far randomly arranged and far apart from each other. This happens because when a substance is a gas, particles have weak attraction to each but a lot more kinetic energy which means the they move around all the time spreading out to fill the container. If it was a solid, then all the particles would be very close together and have a fixed position and if it was a liquid then the particles would be fairly close and moving around each other but as we can see in the diagram, all the particles are far apart confirming that it is a gas.

Answer:

the answer is A beacause the other person is right :)

Explanation:

please give them brainliest

For accurate answer i will mark you a brainlist:D

How will you convert 85 cm to 85 m, choose one of the following option:

( Remember there is a decimal in 85 after 5)

Question 12 options:

Move the decimal in 85 TWO places to the right to decrease the value.


Move the decimal in 85 THREE places to the right to increase the value.


Move the decimal in 85 TWO places to the Left to decrease the value.


Move the decimal in 85 THREE places to the Left to decrease the value.

Answers

Answer:

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Explanation:

Answer:

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Answers

Answer:

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Explanation:

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Answer:

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Answers

Answer:

[tex] \huge{5.77 \times {10}^{ - 5} m}[/tex]

Explanation:

The wavelength of a wave can be found by using the formula

[tex]\lambda = \frac{c}{f} \\[/tex]

where

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From the question we have

[tex] \lambda = \frac{3 \times {10}^{8} }{5.2 \times {10}^{ 12} } \\ \\ \\ \\ \large{ = 5.77 \times {10}^{ - 5} m}[/tex]

Hope this helps you

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Answer:

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Explanation:

Answer:

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Answer:

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Please help me no links
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Answer:

Mg (NO3)2

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Answer:

Answer d

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assume you are performing the calibration step of experiment 8 and you begin with 80 g of water at 20 oc and 80 g of water at 80 oc. after adding the two portions of water into your calorimeter setup and following the procedure outlined in the experiment, you determine the temperature of the mixed portions of water to be 45 oc. what is the heat capacity of the calorimeter?

Answers

The heat capacity of the calorimeter is 133.76 J°/C.

A calorimeter is an apparatus employed when estimating the amount of heat required in a chemical reaction.

For the given calorimetric function:

the heat lost by the hot water = to the heat gained by the cold water and the calorimeter.

These can be computed mathematically as:

[tex]\mathbf{m_wC_w\Delta \theta _w = m_cC_c\Delta \theta _c + C_{cal} \Delta_c}[/tex]

[tex]\mathbf{80 \ g\times 4.18 J/g^0 C \times (80-45)^0 \ C = 80 g \times 4.18\ J/g^0 \ \times (45- 20)^0 +C_{cal} \times (45- 20)^0 \ C}[/tex]

[tex]\mathbf{11704 \ J =8360 \ J+C_{cal} \times (25)^0 \ C}[/tex]

[tex]\mathbf{(11704 -8360) \ J= C_{cal} \times (25)^0 \ C}[/tex]

[tex]\mathbf{ C_{cal} = \dfrac{3344 \ J} { (25)^0 \ C}}[/tex]

[tex]\mathbf{ C_{cal} =133.76 \ J/^0 C}[/tex]

Therefore, the heat capacity of the calorimeter is 133.76 J°/C.

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(0)
1.
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Answers

Answer:

B

Explanation:

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Answers

Answer:

The third ionization energy is the energy it takes to remove an electron from a 2+ ion. (That means that the atom has already lost two electrons, you are now removing the third.) And 2nd ionization energy is higher than 1st ionization energy, 3rd is higher than 2nd, and so forth.

hope it is helpful :)

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Compared to the energy of an electron in the second shell of an atom of sulfur, the energy of an electron in the
1
first shell is lower
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Answers

Answer:

First shell is lower

Explanation:

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Answer:

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