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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Related Questions

Help me please, I don't get it. Please & thank you, xoxo !

Answers

Sorry I accidentally touched it

Explain how magnesium is produced at the negative electrode from molten magnesium chloride

Answers

Answer:

being cation it migerates to cathode to be reduced to elemental magnesium

Explanation:

Mg+2. +2e -----------Mg

Describe the physical properties of Copper (Cu) based on what you know about metals, nonmetals, and metalloids

Answers

Answer:

Copper is reddish brown color

Its density is 8.93 g cm-3

highly malleable at ordinary temp, but is brittle near its melting point

god conductor of heat and electricity

Explanation:

una pieza de hierro de 25cm3 tiene una masa de 195g cual es su densidad?

Answers

Answer:

Pretend you are a TV producer. Think of ideas for new TV shows. Your objective is to create ideas that will be successful, regardless of whether this is quality programming or not. Think of an idea of a copy. Explain the basics of what this show will be like and what show it is copying. Explain why you feel this show will be popular. Think of an idea of a spin-off. Explain the basics of what this show will be like and what show it is spinning off from. Explain why you feel this show will be popular. Think of an idea for a TV show that falls into one of the genre categories listed in the genre chart. Describe the basics of the show and how it falls under the genre’s expectations for characters, plots, and aesthetics. Explain why you feel this show will be popular.

How to calculate work done with change in volume and pressure.

Answers

[tex]W = \displaystyle \int dW = \displaystyle \int^{V_2}_{V_1} p ~dV = p(V_2 - V_1) = p \Delta V[/tex]

Write the balanced chemical equation for the reaction
of solid carbon with oxygen gas to form carbon monoxide gas.

Answers

Answer:

2C +O2 - CO

Explanation:

mark me brainliest

The balanced chemical equation for the reaction of solid carbon with oxygen gas to form carbon monoxide gas is  2 C + O₂[tex]\rightarrow[/tex] 2 CO.

What is chemical equation?

Chemical equation is a symbolic representation of a chemical reaction which is written in the form of symbols and chemical formulas.The reactants are present on the left hand side while the products are present on the right hand side.

A plus sign is present between reactants and products if they are more than one in any case and an arrow is present pointing towards the product side which indicates the direction of the reaction .There are coefficients present next to the chemical symbols and formulas .

The first chemical equation was put forth by Jean Beguin in 1615.By making use of chemical equations the direction of reaction ,state of reactants and products can be stated. In the chemical equations even the temperature to be maintained and catalyst can be mentioned.

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1. Which of the following statements pertaining to the ionic solids represented below are true?
(0)
1.
Both structure are ductile.
II. Structure (1) has a higher melting point than structure (ii)
III. Both structures conduct electricity in the solid state.
IV. Both structures conduct electricity in the liquid state.

Answers

Answer:

B

Explanation:

so A is nosense C and D the question is saying the stament for a being repersentation of solid not whether eletric or not

Explain why photosynthesis is essential for living plants and animals.​

Answers

The main reason why photosynthesis is essential for living and animals because photosynthesis allows plants to make glucose, which is need to make energy and cellular structures. Photosynthesis is also the main source of food on earth. It release oxygen which is an important element for survivals

What is the agent that causes frost wedging?

Answers

Answer:

Freeze wedging is caused by the repeated freeze-thaw. Frost wedging occurs as the result of 9% expansion of water when it is converted to ice. Cracks filled with water are forced further apart when it freezes.

Please help me no links
if good answer you get brainliest

Answers

The crystals will not be oxidised since it will be underground

Answer:

plutonic rocks are formed when magma cools and solidifies underground This shows us if the rock is plutonic or volcanic. When magma cools underground, it cools super slow and when lava cools above ground, it cools faster. When magma and lava cool, mineral crystals start to form in the molten rock.

Explanation:

i hope this is correct

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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Does chlorine have a smaller ionic radius than soium.

Answers

Answer:

sodium atoms are much larger than chlorine atoms but in case of sodium ions they are much smaller thqn chlorine ions

Calculate the molecular mass of the element

They give:H=1,AI=27,S=32,0=16,Cu=64,P=31,Mg=24,N=14,Na=23

Answers

Answer:

Mg (NO3)2

24 + 2×(14+ 3×16)

24+2×(14+48)

24+2×(62)

24+ 124

=148g

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:

welp it would be this option : Move the decimal in 85 TWO places to the right to decrease the value.

Explanation:

Answer:

Option A

Explanation:

Moving the decimal point 2 places to the right will give you 8500 cm=85m

the atomic number of RE is 75. the atomic mass of one of its isotopes is 186. how many neutrons are in an atom of this isotopes

Answers

Answer:

111

Explanation:

Answer:

I believe Rhenium has 111 neutrons in the atoms isotopes.

Explanation:

If a 435.767 g sample of bottled water contains 2.797 x 10-3 g of lead, what is the concentration of lead in the bottled water, in units of parts per million (ppm)

Answers

Answer:6.42 ppm

Explanation:ppm = (g soluto/g soluzione) ×1000000

4. If the speed of an object increases, its kinetic energy
stays the same
decreases
increases

Answers

Answer:

I think the answer is increases

Two chemical reactions are shown:
A. Ca(OH)2 - CaO + H2O
B. 4K + O2 + 2K20
Which statement is true?

A. Both are synthesis reactions
B. Both are decomposition reactions
C. A is a synthesis reaction, and B is a decomposition reaction
D. A is a decomposition reaction, and B is a synthesis reaction

Answers

Answer: A is a decomposition reaction, and B is a synthesis reaction

Explanation: the first equation shows the reactant breaking up into 2 parts aka decomposition and equation 2 shows the reaction being combined into one part, aka synthesis. hope that helps!

Answer:

Answer d

Explanation:

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
2
first shell is the same.
3
third shell is lower
4
third shell is the same.

Answers

Answer:

First shell is lower

Explanation:

The electron has to absorb energy to excite and go to higher energy levels/ shells and should release energy to go to lower energy levels/ shells. This means higher the shell , more energy is required and vice versa

What is q in chemistry.

Answers

Answer:

The reaction quotient!

Explanation:

hope this helped :D

HURRY for a BRAINLIST

Answers

Answer:

B  

Explanation:

Answer:

answers

B

Explanation:

Explicaciónexplicacaca

(i will give brainliest)


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

Complete the sentence.

Atoms form chemical bonds to satisfy the ______
rule and to become _______

Answers

The first one is octet and the second one is stable

What is the wave length of an electromagnetic radiation ,having a frequency of 5.2 x 10^12 Hz? Note: c= 3.00 x 10^8 m/s

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

c is the speed of the wave

f is the frequency

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

2. How many of valence electrons do the elements in column 4 have? Are these elements very reactive?
Explain your answer.

Answers

Answer:

4

Explanation:

Elements in group 14 have 4 valence electrons. Meaning that to achieve a stable octet they need to either gain or lose 4 electrons in total.

cobalt iii percarbonate as a formula

Answers

Answer:

Co2(CO3)3

Hope this helps!!

an atom of ordinary hydrogen consists of an electron and a

Answers

Answer: hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force.

Explanation:

An atom of ordinary hydrogen consists of one electron and one proton and zero neutrons.

What is a hydrogen atom?

Hydrogen is a chemical element placed at the top of group 1 in the periodic table and is represented by the chemical symbol H and atomic number 1.

A hydrogen atom is the lightest atom of the element in the whole periodic table. Hydrogen exists as a gas of diatomic molecules having the formula H₂ at standard conditions. Hydrogen gas is tasteless, colorless, odorless, non-toxic, and highly combustible.

Hydrogen is constituting roughly 75% of all normal matter and is the most abundant chemical substance in the universe. Most of the hydrogen element on Earth exists in forms like water and organic compounds.  Each atom of hydrogen (¹H) has one proton, one electron, and no neutrons.

Hydrogen element is nonmetallic and easily forms a single covalent bond with most nonmetallic elements, forming compounds like water.

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5) When rain falls to the earth, it just doesn't sit there. Instead, the rain water starts moving. Some of the precipitation seeps into the ground to replenishing groundwater. However, most of
it flows downhill as runoff. Runoff is important in filling rivers and lakes, but it also changes the landscape by erosion and can be a powerful mover. Flowing water is a powerful force,
capable of moving boulders and carving out canyons. Runoff has an impact on streams and rivers, but it also has an impact on the ocean system. What can you infer about the impact of
runoff on Ocean life? Choose ALL that apply.
A) Runoff drops a lot of sediment in the ocean, decreasing salinity.
B) Runoff builds up the coastline, depositing sediment, disrupting habitats of marine wildlife.
Runoff can lead to overgrowth of algae that can cause oxygen deprivation and create a dead zone.
D) Runoff carries pollutants into the ocean, causing illness and death of vulnerable marine populations.
) Runoff can carry bacteria, viruses and other pathogens from pet and livestock waste that can harm shellfish and other marine organisms.

Answers

Answer: Rain evaporates and this same process happens over and over again.

Explanation:

Distinguish between the first, second, and third ionization energies of an atom. b. How do the values of successive ionization energies compare

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 :)

C2H4NH Lewis structure

Answers

if it’s just C2H4 it’ll be
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