A cube with volume 8 $\text{cm}^3$ is cut in half by a plane which contains two edges of the cube. What is the area of the rectangle formed by the intersection of the plane and cube? express your answer in simplest radical form.

Answers

Answer 1

The area of the rectangle formed by the intersection of the plane and cube is [tex]4\sqrt{2}cm^2[/tex]

The diagram of the cube and the cutting plane is shown in the figure.

Since the cube has a volume of [tex]8cm^3[/tex], the sides are [tex]2cm[/tex] each.

From the diagram, the red rectangle is the rectangle formed from the intersection of the plane and the cube. It has an area given by

[tex]A_R=\text{side of cube}\times \text{diagonal}=2d[/tex]

and, using Pythagoras' theorem,

[tex]d=\sqrt{2^2+2^2}\\d=\sqrt{8}=2\sqrt{2}\text{ cm}[/tex]

Substituting the value of [tex]d[/tex] into the formula for [tex]A_R[/tex]

[tex]A_R=2\times d\\=2\times 2\sqrt{2}\\=4\sqrt{2}[/tex]

The area of the rectangle formed by the intersection of the plane and cube is [tex]4\sqrt{2}cm^2[/tex]

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A Cube With Volume 8 $\text{cm}^3$ Is Cut In Half By A Plane Which Contains Two Edges Of The Cube. What
Answer 2

Answer:

4 square root of 2cm

Explanation:

cool stuff


Related Questions

Which of the following is not a benefit of warm up exercise.

Answers

Among the given option only one is not a benefit associated to good warm-up, and it is A:Decreases the temperature of your muscles
A warm up can be regarded as activities involving a gradual increase in intensity when when one is engaging in physical activity.
These warming up activities could be;
joint mobility exercise.
Jumping jacks.
Walking jacks.
stretching
It is important that the body is warm ups before a physical activities brings about Increases metabolic rate and with this, oxygen will be delivered to the muscles more quickly.
Also, injury can be prevented, because of elasticity in muscles.
Therefore, A is right

So just don't get overwhelmed and you'll make it out.

Answers

the answer you have stated is in fact correct, “you will make it out sometimes”

You can have ice cream you finish your dinner.

Answers

"You can have ice cream while you finish your dinner" does not make sense in context, as ice cream is usually reserved for dessert.

Write your own lyrics in english using the music/rhythm of your favorite song.

Answers

Fall into sea
Another way to go, peacefully
Take your time
The money holder says get in line
Forget the colored stars in your mind

Back, back and fourth doubled as a curse, you’re falling short
Both, both are wrong
Excessive as it is, it’s way to long
Push your way through, you’re too strong

I’ve got something to say
Tied in your macramé tears
Fighting off evil things space is what love can bring, now

Persistent like a dog, locked up in your demagogue, go
Play it off like a joke, locked up in gentle strokes, no

Too and forth i make mistakes
Remember about this place, i know
We never know what to say, i know.

Do you ever wish your dreams could come true?

Dream of things that won't make you boo.

Dreams can come real,

just make sure you make them feel.

If it's a nightmare make sure you hide up the back stairs,

and if it's a good dream make sure you make it seen.

So I really wish dreams were real,

that way I could start to feel.

Explanation: Sorry it isn't that good I did the best I could. It's also rrrreeeealllllllyyyyy short sooo.......

Scientists discover a new organism. The organism is autotrophic, with membrane-bound organelles. To which of these kingdoms does this organism most likely belong?.

Answers

Protista, would be the answer

Which of the following people worked with government in the 1960s to get laws passed to help noncitizens and farm workers? Huey Newton Bobby Seale Stokely Carmichael Dolores Huerta.

Answers

Government often makes laws that aim for the betterment of its people. Cesar Chavez worked with government in the 1960s to get laws passed to help noncitizens and farm workers.

Cesar was known to be a man who use nonviolent means as used by Mahatma Gandhi and Martin Luther King Jr. in all his works.

He was known to be the founder of the National Farm Workers Association (later the United Farm Workers of America)

He won a lot of significant victories so as the pay and improve working conditions for farm workers is improve in the late 1960s and 1970s

See full question below

Which of the following people worked with government in the 1960s to get laws passed to help noncitizens and farm workers?

Huey Newton

Bobby Seale

Cesar Chavez

Dolores Huerta

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Answer:

Explanation:

Dolores huerta

According to the table, what is the total distance the hiker walked? 4 km 6 km 10 km 20 km.

Answers

Answer: 20 km

Explanation:

6 + 4 + 6 + 4 = 20

A current of 15 amps flows through a circuit with a resistance of 0. 10 ohms. What is the voltage?.

Answers

Answer: I=U/R

U=I*R U=0.10*15=1.5

Explanation:

It is affected by the structure of the bones and muscles surrounding the joint.

Answers

Answer:

um... ok

Explanation:

Hydrochloric acid (HCl) is combined with cesium hydroxide (CsOH) in a neutralization reaction. Which ions will combine to form a salt? Check all that apply. H H3O Cl- Cs OH-.

Answers

Answer:

Hydrochloric acid (HCl) is combined with cesium hydroxide (CsOH) in a neutralization reaction. Which ions will combine to form a salt? Check all that apply. H H3O Cl- Cs O

Explanation:

whatttttttttttttttttttt

Answer:

Its C and D, (CI- and Cs+)

Explanation:

Which sentence best concludes the paragraph? It is important to understand historical causes as the English language continues to develop. Many people wonder why international communication is so difficult. I can’t wait to see how the English language develops in the future.

Answers

Answer: ( Answer A) It is important to understand historical causes as the English language continues to develop

Explanation: because I just took the assignment

The sentence that best concludes the paragraph is that it is important to understand historical causes as the English language continues to develop. Thus, the correct option for this question is A.

What do you mean by Paragraph?

A Paragraph may be defined as a collection of sentences that significantly represents some thoughts and ideas to the reader or audience. It is a brief piece of writing that all relate closely to the topic sentence.

According to the context of this question, it is consequential in order to understand the causes and influence of the English language which continues to develop till now. It is the significance of the English language.

Therefore, it is important to understand historical causes as the English language continues to develop is the sentence that best concludes the paragraph. Thus, the correct option for this question is A.

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The heat required to change 1 gram of a solid at its normal melting point.

Answers

By definition, the heat required to change 1 gram of a solid at its normal melting point is called heat of fusion.

Latent heat is defined as the energy required by a quantity of substance to change state.

When this change consists of changing from a solid to a liquid phase, it is called heat of fusion and when the change occurs from a liquid to a gaseous state, it is called heat of vaporization.

Fusion is the process by which a solid becomes a liquid phase. In this case, the temperature remains constant throughout the time that the solid turns into a liquid.

This occurs because in the solid phase the molecules are held together forming a rigid crystalline structure, in such a way that the substance has a defined shape and volume. As heat is supplied, the energies of the solid's particles gradually increase. After a certain time, this energy becomes so great that some of the particles exceed the force that kept them in their fixed positions.

In this way, the greatest separation between the particles is associated with the liquid phase.

Thus, the energy absorbed by the substance is used to separate the molecules more than in the solid phase, so that the temperature does not increase during the change of state.

In summary, it is called "heat of fusion", the energy required to change 1 gram of substance from a solid state to a liquid state, without changing its temperature.

In others words, the heat required to change 1 gram of a solid at its normal melting point is called heat of fusion.

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Which of the following is a difference between phase i and phase ii of meiosis?(1 point).

Answers

AnswerHowever, Meiosis I begins with one diploid parent cell and ends with two haploid daughter cells, halving the number of chromosomes in each cell. Meiosis II starts with two haploid parent cells and ends with four haploid daughter cells, maintaining the number of chromosomes in each cell.:

Explanation:

Which of the following is not a function of the female reproductive system.

Answers

Answer:

The option A, releasing fimbria to for fertilization is not a function of the female reproductive system.

A student uses the apparatus to determine the concentration of a solution of hydrofluoric acid. Which component will the student put in the burette?.

Answers

Answer: Titrant

Explanation: make me brainlets

What does it mean to be ‘other oriented’?

Answers

Answer:

Putting others needs before your own

Answer:

thinking, caring and acting in accordance with the interests of others is a common relational style

Explanation:

egd

1) What is The Full form Of WWW ?
2)What Is The full form of 3 Cs ?


2nd question is little confused .
plz Don't Spam .​

Answers

WWW is an abbreviation for World Wide Web ...

Corporation, Customer, Competitors (3C's) Model is a business model that focuses on the three key factors needed for success. This model was conceived by the famous business strategist, Kenichi Ohmae.

Answer:

• Full form of WWW :-

World Wide Web

WWW is an abbreviation for World Wide Web and it is commonly called the WEB. It is a system that is used to store documents and is accessed using URL(Uniform Resource Locator) which are accessible through Internet .

• The full form of 3 Cs :-

Corporation, Customer, Competitors

(3C's) Model is a business model that focuses on the three key factors needed for success. This model was conceived by the famous business strategist, Kenichi Ohmae.

Explanation:

Hope this helps you !!

What is the connotative meaning of the underlined word in the excerpt? a lavish event a humiliating sight an unexpected happening an entertaining performance.

Answers

Answer:

B) A humiliating sight

Explanation:

took the test on edge

Answer:

B

Explanation:

The first person was right

Evaluate the line integral, where c is the given curve. C (x/y) ds, c: x = t3, y = t4, 1 ≤ t ≤ 4.

Answers

We have

x = t³   ===>   dx/dt = 3t²

y = t⁴   ===>   dy/dt = 4t³

Then with the given parameteriztion, the line integral along C of x/y is

[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{t^3}{t^4} \sqrt{(3t^2)^2 + (4t^3)^2} \, dt[/tex]

[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac1t \sqrt{9t^4 + 16t^6} \, dt[/tex]

[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{\sqrt{t^4}}t \sqrt{9 + 16t^2} \, dt[/tex]

[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{t^2}t \sqrt{9 + 16t^2} \, dt[/tex]

[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 t \sqrt{9 + 16t^2} \, dt[/tex]

[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \int_1^4 32t \sqrt{9 + 16t^2} \, dt[/tex]

[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \int_1^4 \sqrt{9 + 16t^2} \, d\left(9+16t^2\right)[/tex]

[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \cdot \frac23 \left(9+16t^2\right)^{\frac32}\bigg|_1^4[/tex]

[tex]\displaystyle \int_C \frac xy \, ds = \frac1{48} \left(265^{\frac32} - 25^{\frac32}\right) = \boxed{\frac{265\sqrt{265}-125}{48}}[/tex]

The line integral will be "[tex]\frac{265\sqrt{265} - 125 }{48}[/tex]". To understand the calculation, check below.

Line integral

According to the question,

Curves, x = t³ or,

            [tex]\frac{dx}{dt}[/tex] = 3t²

             y = t⁴ or,

            [tex]\frac{dx}{dt}[/tex] = 4t³  

Now, the line integral along C will be:

→ [tex]\int\limits_C {\frac{x}{y} } \, ds[/tex] = [tex]\int\limits^4_1 {\frac{t^3}{t^4} }[/tex] √(3t²)² + (4t³)² dt

             = [tex]\int\limits^4_1 {\frac{1}{t} }[/tex] √9t⁴ + 16t⁶ dt

             = [tex]\int\limits^4_1 {\frac{t^4}{t} }[/tex] √9 + 16t² dt

             = [tex]\int\limits^4_1 {\frac{t^2}{t} }[/tex] √9 + 16t² dt

             = [tex]\int\limits^4_1[/tex] t√9 + 16t² dt

             = [tex]\frac{1}{32}[/tex] [tex]\int\limits^4_1[/tex] √9 + 16t² d (9 + 16t²)

             = [tex]\frac{1}{32}\times \frac{2}{3}[/tex] [tex](9+16t^2)^{\frac{3}{2} } |_1^4[/tex]

             = [tex]\frac{1}{48}[/tex] ([tex]265^{\frac{3}{2}} - 25^{\frac{3}{2}[/tex])

             = [tex]\frac{265 \sqrt{265 } -125 }{48}[/tex]

Thus the above approach is correct.

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Solve for x in the equation x^2-8x+41=0.

Answers

x^2-8x+41=0
x-8x+41=0
-7x+41=0
-7x=-41
x=41/7
Hope that helped :D

Which of the following theorems cannot be used to prove two lines are parallel?.

Answers

How are we supposed to answer this question without the theorems mentioned in the question????

What amount of heat, in kj, would be involved in condensing 15. 8 g of ch₃oh? (∆hvap = 38. 0 kj/mol).

Answers

Considering the definition of enthalpy of vaporization, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is 18.8 kJ.

When a material changes phase from solid to liquid, or from liquid to gas, a certain amount of energy is involved in this phase change.

In case of phase change from liquid to gas, this amount of energy is known as enthalpy of vaporization (symbolized as ∆Hvap).

So, the enthalpy of vaporization is the amount of energy required to change a unit of mass (for example, moles or kg) of a substance from phase liquid to phase gas at constant temperature and pressure.

In this case, you know that enthalpy of vaporization is ∆Hvap = 38.0 kJ/mol.

On the other side, you want to vaporize 15.8 g of CH₃OH.  Then, being the molar mass of the compound 32 [tex]\frac{g}{mole}[/tex] (that is, the amount of mass contained in one mole), the number of moles to be vaporized is:

[tex]15.8 gramsx\frac{1 mole}{32 grams} =0.49375 moles[/tex]

Then, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is calculated taking into account the enthalpy of vaporization by:

0.49375 moles× 38.0 [tex]\frac{kJ}{mol}[/tex]= 18.76 kJ ≅ 18.8 kJ

Finally, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is 18.8 kJ.

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Which of the following is true of the capital requirement? check all that apply.

Answers

Answer:

Its intended goal is to protect the interests of those who hold equity in the bank.

The amount of capital required depends on the type of assets the bank holds.

Explanation:

edge!!

Tasha has mass 20 kg and wants to use a 4. 0-m board of mass 10 kg as a seesaw. Her friends are busy, so tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?.

Answers

Answer:

0.67 m

Explanation:

Mass of Tasha, m1 = 20 kg Mass of the board, m2 = 10 kg

0.67 m is correct for Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.

(Hope this helps can I pls have brainlist (crown)☺️)

Which of the following points lies on the line y = x ?.

Answers

Answer:

Where's the graph?

Explanation:

A taxi service charges a flat fee of $1. 25 and $0. 75 per mile. If Henri has $14. 00, which of the following shows the number of miles he can afford to ride in the taxi? m less-than-or-equal-to 17 m greater-than-or-equal-to 17 m less-than-or-equal-to 20. 3 m greater-than-or-equal-to 20. 3.

Answers

Answer:

Its less than or equal to 17

Explanation:

When you float an ice cube in water, you notice that 90% of it is submerged beneath the surface. Now suppose you put the same ice cube in a glass of some liquid whose density is less than that of water.

Answers

Answer:

option c

Explanation:

90% of the body is submerged in water.

Now it is immersed in an unknown liquid whose density is less than the density of water.

Buoyant force acting on the body depends on the volume immersed, density of liquid and gravity.

As the density of liquid is less than the density of water, so the buoyant force acting on the body by the unknown liquid is less than water. So it is submerged less than 90% in this liquid.

Which President's domestic policy included putting down the Whiskey Rebellion? Question 7 options: Andrew Jackson George Washington James Madison John Adams

Answers

Answer:

George Washington  

Explanation:

The square root of a number is between 8 and 9 which of these could be that number.

Answers

9

9 is a square root because when u multiply 3×3=9

Inspectors for a hospital chain with multiple locations randomly select some of their locations for a cleanliness check of their operating rooms. The inspectors check every operating room in the hospitals that were chosen. What type of sample is this?.

Answers

Considering the situation described in the question, the type of sample Inspector used is called Simple Random Sampling

What is Simple Random Sampling?

Simple Random Sampling is a random sampling technique in which participants are taken randomly from a given population.

How this situation is a Simple Random Sampling.

Here, the given population is the hospital chain with multiple locations; since the inspector only randomly selects some of their locations, this is a simple random sampling.

Type of Random Sampling Techniques

Simple Random SamplingCluster Random SamplingSystematic Random SamplingStratified Random Sampling

Hence, in this case, it is concluded that the correct answer is Simple Random Sampling

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