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
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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Answer:
4 square root of 2cm
Explanation:
cool stuff
Related Questions
What in the cinderella story suggests its origin, according to the author? why is her theory uncertain?.
Answers
Cinderalla is a very popular story. The suggestion of its origin, according to the author is that its origin could have been originated in Orient.
The theory is uncertain because Cinderella, as it is widely known among boys and girls, as a fairy tale, it has about 345 documented variants and many more versions that were not documented or recorded.
This can be referred too as inconsistency in its recording. The fact that Cinderella had small feet, was of some importance in the Orient that is ancient times.
Cinderella, The Legend is known too be of Protestant ethic as the moral principle in this fairy tale is that good fortune can be an advantage.
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How did buddhism influence east asian arts and crafts.
Answers
Adopting the Buddhist way of paying homage through art, Taoist art began being created and China developed its architectural culture.
A hoop of radius 1. 0 m is placed in the first quadrant of an xy-coordinate system with its rim touching both the x-axis and the y-axis. What are the coordinates of its center of gravity?.
Answers
Answer:
(1,1) is the answer you're looking for.
A spherical balloon is inflating with helium at a rate of. How fast is the balloon's radius increasing at the instant the radius is ft? how fast is the surface area increasing?.
Answers
Using implicit differentiation, and considering that the inflation rate is of 200 cubic feet per minute and the radius is of 5 feet, it is found that:
The radius is increasing at a rate of 0.6366 feet per minute.The surface area is changing at a rate of 80 feet squared per minute.The volume of an sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
For this problem:
Inflation rate of 200 cubic feet per minute, hence [tex]\frac{dV}{dt} = 200[/tex]Radius is of 5 feet, hence [tex]r = 5[/tex]Then:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]200 = 4\pi (5)^2\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt} = \frac{200}{100\pi}[/tex]
[tex]\frac{dr}{dt} = 0.6366[/tex]
The radius is increasing at a rate of 0.6366 feet per minute.
The surface area is:
[tex]S = 4\pi r^2[/tex]
Hence, the rate of change is:
[tex]\frac{dS}{dt} = 8\pi r\frac{dr}{dt}[/tex]
Hence:
[tex]\frac{dS}{dt} = 8\pi (5)(0.6366) = 80[/tex]
The surface area is changing at a rate of 80 feet squared per minute.
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Rami is graduating high school in the spring. He is interested in becoming a electrician. What are his options for learning this trade? select all that apply.
Answers
To be a licensed electrician requires deep knowledge of the field. Rami's options for learning this trade are;
He should applied degree at a two year college or He can study for a bachelor's degree at a four year collegeApprenticeship and trade schoolA licensed electrician job is not easy to obtain. It requires studying, years of being an apprentice or attending school, and years of work experience.
To be a licensed electrician, these steps should be followed:
Earn a high school diploma or Its equivalent. Try and attend a trade or vocational-technical school. Sign up as an electrician apprentice. Get licensed or certified.See full question blow
Rami is graduating high school in the spring. He is interested in becoming a electrician. What are his option learning this trade? Select all that apply.
applied degree at a two year college bachelor's degree at a four year college vocational training in the military apprenticeship and trade school going directly into the workplaceLearn more from
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Answer: 1) applied degree at a two year college
3) Vocational training in the military
4) apprenticeship and trade school
Explanation: did on edge :)
I often relate to the following groups early childhood brainly.
Answers
The lawmaking responsibility of the members of the house is to.
Answers
Answer:
The lawmaking responsibility of the members of the House is to 1) discuss pending bills with their constituents. 2) make sure their supporters approve of a bill. 3) propose, amend, and vote on bills and resolutions
Explanation:
The lawmaking responsibility of the members of the House is to
discuss pending bills with their constituents.
make sure their supporters approve of a bill.
propose, amend, and vote on bills and resolutions.
gather public support for their bills.
Write your own lyrics in english using the music/rhythm of your favorite song.
Answers
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.......
According to the table, what was the hiker’s average speed for the entire hike? 2. 0 km/h 5. 7 km/h 6. 7 km/h 10 km/h.
Answers
Answer:
6.7 km/h
Explanation:
During the revolutionary war, how did the british convince slaves to run away from their owners and help the british war effort?.
Answers
Answer:
offered freedom
Explanation:
took the test
So just don't get overwhelmed and you'll make it out.
Answers
A consumer group is investigating the number of flights.
Answers
Which of the following devices is used in this experiment to separate the different wavelengths emitted by the light source?.
Answers
A spectrometer employs diffraction to divide light into a spectrum, which is a collection of wavelengths.
What different wavelengths emitted by the light source?A light source beam's wavelengths are spectrally isolated using monochromators. A monochromator separates poly chromatic light into a variety of distinct wavelengths.
The most common application of a spectrometer is to measure the wavelengths of electromagnetic radiation (light) that have interacted with a sample.
A sample may reflect, absorb, or transmit incident light; the way the incident light changes as it interacts with the sample is a characteristic of the sample.
When calculating the concentration of a colored solution, the wavelength of maximum absorbance is used because at this wavelength even a small change in concentration can result in a large change in light absorption.
Therefore, spectrometer devices are used in this experiment to separate the different wavelengths emitted by the light source.
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Solve for x in the equation x^2-8x+41=0.
Answers
x-8x+41=0
-7x+41=0
-7x=-41
x=41/7
Hope that helped :D
You enter a room 2 dogs 4 horses.
Answers
(2+4=6) supercalifragilisticexpialidocious
Andrei adds 50 ml of boiling water to 100 ml of tap water. If the 150 ml of water is then put into a freezer, at what temperature will the water freeze?.
Answers
Answer:
0°C
Explanation:
water always freezes at 0 degrees
What is the vertex form of the equation? y = – x 2 + 12 x – 4.
Answers
Answer:
(6,32)
Explanation:
are there other universes?
Answers
Answer:
no
Explanation:
An archer fish spies a meal of a grasshopper slader.
Answers
Answer:
sitting on a long slader of grass at the edge of the pond in which he is swimming.
Explanation:
sitting on a long stalk of grass at the edge of the pond in which he is swimming. If the fish is to bite him
Ryan invests a sum of money in a savings account with a fixed annual interest rate of 4. 31.
Answers
The amount of his initial investment is $8361
The complete question says:
Ryan invests a sum of money in a savings account with a fixed annual interest rate of 4.31% compounded 12 times per year. After 10 years, the balance reaches $12,855.94. What was the amount of the initial investment?
The initial investment is the amount required to start a particular project, and the amount of the initial investment can be calculated by using the compound interest formula:
[tex]\mathbf{A = P(1 + \dfrac{r}{n})^{nt}}[/tex]
where;
A = amountP = Principalr = interest rate n = number of months∴
[tex]\mathbf{12855.94 = P(1 + \dfrac{0.0431}{12})^{12 \times 10}}[/tex]
[tex]\mathbf{12855.94 = P(1 +0.003591666667)^{120}}[/tex]
[tex]\mathbf{12855.94 = P(1.53760)}[/tex]
[tex]\mathbf{P= \dfrac{12855.94}{(1.53760)} }[/tex]
P = $8361.043
P ≅ $8361
Therefore, we can conclude that the amount of the initial investment is $8361
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Where are my smart friends?? i had $3. 0. My mom gave $10. 0. My brother gave $30. 0. My aunt and uncle gave me $100. 0. I had another $7. 0. How much did i have?.
Answers
Answer: $150
Please mark me brainliest!
Explanation: 3 + 10 = 13
13 + 30 = 43
43 + 100 = 143
143 + 7 = $150
Successful entrepreneurs contribute to the economy by.
Answers
Answer:
B. Expanding markets.
Explanation:
Successful entrepreneurs contribute to the economy by expanding markets. The correct option is b.
What is an entrepreneur?Entrepreneurs are businesspeople that operate on a large scale by taking an original idea and turning it into reality by improving the lives of ordinary people through their goods or services.
A successful entrepreneur has the power to transform the world by reshaping the economy and developing novel goods, services, and market niches.
By opening up new markets, entrepreneurs help individuals become more prosperous and gain jobs because doing so creates a variety of opportunities for them. By seizing these chances, anyone can become wealthy and earn a living without relying on an entrepreneur.
Therefore, the correct option is b, expanding markets.
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The question is incomplete. Your most probably complete question is given below:
becoming wealthy.
expanding markets.
encouraging free trade.
creating business strategies.
Which statement about how mass media have changed over time is most accurate.
Answers
Answer:
statement 2
Explanation:
2 mass media changed over time is most accurate.
Which statement is accurate about Native Americans and the American Revolutionary War?.
Answers
Answer:
regardless of which side they chose, native americans would lose land due to the outcome of the war
Explanation:
k12 yes? good luck, hope this helps
Beth is listening to her friend melissa talk about a recent break-up. Beth wants to give an appropriate listening response to convey to melissa that she there for her friend and shares her point of view. Beth’s best listening response would be which of the following?.
Answers
Beth's best listening responses to convey to Melissa that she shares her view would be: supporting.
In communication, listening is very key which follows with a feedback to ensure what is being communicated is rightly decoded by the receiver of a message.
For feedbacks, many types of responses can be given. One of which is giving a listening response.
Types of listening responses include:
EmpathizingQuestioningParaphrasingEvaluatingSilent listeningEmpathizingSupporting.Supporting is a type of listening response whereby the listener shows solidarity with the speaker in a way that reflects the feelings about the speaker.
Therefore, Beth's best listening responses to convey to Melissa that she shares her view would be: supporting.Learn more about listening responses on:
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Jacob followed a recipe that requires 2 cups of water for ever 3 cups of flour. If he used 8 cups of flour, how many cups of water did he use?.
Answers
Answer:
I think he uses 5 1/2 cups of water.
Answer:
5 1/3
Explanation:
Between ant and grasshopper which would you choose to be why.
Answers
Answer:
ant
Explanation:
way more interesting, can carry objects way heavier than them and if they were to become human size they would pretty much rule the earth whereas a grasshopper is annoyinggggfg and if they were the size of humans we'd probably die of blood loss in the ears.
When it comes to the choice between an ant and a grasshopper, my choice would be an ant because:
Ants are really strong. Ants are farmers. Ants are very resilient as a species.Ants are known to be really strong such that they can carry things that are 50 times their body weight which allows them to carry a lot of food to their colonies.
Ants are also farmers in that they have been known to protect some other insects so that they can keep getting agricultural produce like honeydew.
Ants are also quite resilient in that they have been around for as long as dinosaurs which means they are some of the oldest species in the world.
In conclusion, ants are preferably to grasshoppers in my opinion.
Find out more about ants at https://brainly.com/question/5770298.
Which of the following team cups is played by only women?.
Answers
Answer:
softball.
Explanation:
I think this, because only the girls were allowed to join this. But you have to be specific, because i don't know the following team cups actually is. Hope this helps you though.
Which comparison between events in the passage would best support a claim that a significant theme of the passage is fulfillment?.
Answers
The comparison that illustrates the theme is Theodora's isolation from her family and her reading of the publisher's response regarding her manuscript.
The theme of a story simply means the central idea that's conveyed in a story. It illustrates what the author wants the readers to know in the story.
The comparison between events in the passage support a claim that a significant theme of the passage is fulfillment. This was illustrated as Theodora's isolation from her family and her reading of the publisher's response regarding her manuscript.
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Which of the following most directly contributed to the change over time depicted on the two maps?.
Answers
Locations are often shown on a map. The option that directly contributed to the change over time depicted on the two maps is the The building of canals and roads.
In 1800, U.S. citizens and immigrants to the country often traveled majorly by horseback or on the rivers.
As time went by, crude roads and canals were made. It was later on that railroads was made which was used to move people and goods with greater efficiency.Conclusively, A map is shows the visual representation of a location and the various part that is found in that specific location.
See full question below
Which of the following most directly
contributed to the change over time depicted on
the two maps?
(A) The construction of a national highway
system
(B) The establishment of different time zones
across the country
(C) The building of canals and roads
(D) The use of diesel engines
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