The dimensions of the cylinder that has the maximum volume can be
found be finding the maximum value of the volume function.
[tex]\mathrm{The \ \underline{height \ of \ the \ cylinder \ of \ maximum \ volume \ is \ \dfrac{8}{\sqrt{3} }}}[/tex][tex]\mathrm{The \ \underline{radius \ of \ the \ cylinder \ of \ maximum \ volume \ is \ \dfrac{8 \cdot \sqrt{6} }{3}}}[/tex]Reasons:
The known parameter of the hemisphere are;
The radius of the hemisphere = 8
Required;
The radius and height of the maximum volume of the inscribed cylinder.
Solution:
Let h represent the height of the cylinder, and let r represent the radius of
the cylinder, we have;
r² + h² = 8²
Therefore;
r² = 8² - h² = 64 - h²
r² = 64 - h²
The volume of the cylinder, V = π·r²·h = π·(64 - h²)·h
V(h) = π·(64·h - h³)
At the maximum volume, we have;
[tex]\dfrac{dV(h)}{dh} = \dfrac{d}{dh} \left(\pi \cdot \left(64 \cdot h - h^3 \right) \right) = \pi \cdot \left(64 - 3 \cdot h^2 \right) = 0[/tex]
64 - 3·h² = 0
64 = 3·h²
[tex]h =\sqrt{\dfrac{64}{3} } = \dfrac{8}{\sqrt{3} }[/tex]
[tex]\underline{\mathrm{The \ height \ of \ the \ cylinder, \ h} = \dfrac{8}{\sqrt{3} }}[/tex]
[tex]r^2 = 64 - \dfrac{64}{3} = \dfrac{128}{3}[/tex]
[tex]r =\sqrt{\dfrac{128}{3}} = \dfrac{8 \cdot \sqrt{6} }{3}[/tex]
[tex]\underline{\mathrm{The \ radius \ of \ the \ cylinder, \ } r = \dfrac{8 \cdot \sqrt{6} }{3}}[/tex]
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White shapes and black shapes.
Answer:
9/32
Explanation:
Hopefully it’s relevant to the question.
If and cx = 5 units, what is dz? 2 units 3 units 4 units 5 units.
Based on the calculations, the magnitude of side DZ is equal to 4 units.
How to calculate the magnitude of DZ?From the diagram, we can deduce that CD is parallel to XZ and as such, triangle XYZ is similar to Triangle YCD. Thus, the ratio of their corresponding side lengths are equal.
By applying the similarity condition, we have:
XY/CY = ZY/YD
(XC + CY)/CY = (DZ + DY)/DY
Substituting the given parameters into the formula, we have;
(5 + 25)/25 = (DZ + 20)/20
30/25 = (DZ + 20)/20
600 = 25DZ + 500
25DZ = 600 - 500
25DZ = 100
DZ = 100/25
DZ = 4 units.
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Which of the following is not a characteristic of all plants?.
In the interior of the earth can be classified as primordial and radiogenic heat brainly.
The Core is in the interior of the earth can be classified as primordial and radiogenic heat
Water melts at 0°c. A student observes a liquid that melts at 10ºc. Which conclusion can the student reasonably draw?.
Expain 5 factors that can slow down
the growth of democracy in Nigeria
Answer:
hmm I think is Salam or lukira
hjjttttyfdgrefffffffff
Shawn and Dorian rented bikes from two different rental shops. The prices in dollars, y, of renting bikes from the two different shops for x hours is shown. Shop Shawn used: y = 10 3. 5x Shop Dorian used: y = 6x If Shawn and Dorian each rented bikes for the same number of hours and each paid the same price, how much did each pay for the rental? $.
Answer:
They both rented the bikes for 4 hours and paid $24.
Explanation:
What is the best choice for the equation of the line of best fit shown? Note that this estimate would be a strong prediction since it is an interpolation (between data points) and the graph shows fairly strong negative correlation.
Answer: b. Y= -1.5x + 23
Explanation: got it right on edge
Answer:
first one is y= -1.5x+23
second one is 11
Explanation:
Which of the following is not a traditional food found in Uruguay?.
Answer:
Gnocchi is not a traditional food found in Uruguay.
Explanation:
Emily, an 11-year-old girl, wants to sign-up for a fashion newsletter and sweepstakes. In order to do so, the website wants to know emily's name, address, phone number, and email address. Which of the following is correct?.
Answer:
Emily must have permission from her parents in order to furnish the information to the website.
Explanation:
She's underaged
How do you embody the burger king® brand values of dreaming big, meritocracy, and authenticity?.
Burger King's brand values are vital in dictating the company's brand message, meritocracy, and personality.
The brand values of Burger King include dreaming big, meritocracy, and authenticity. They're placed at the core of the brand and dictate the message of the company.
The brand values are vital in shaping the decision-making processes. The brand values of dreaming big, meritocracy, and authenticity are can be applied in the life of an individual as it helps in one's development.
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What increases the frequency of adaptive mutations.
Answer:
What increases the frequency of adaptive mutations? = hitch-hiking.
Explanation:
the mutator allele increases in frequency by hitch-hiking, thus facilitating the appearance of a second adaptive mutation
A sound with more vibrations per second sounds higher than a sound with fewer vibrations per second. Lesson 4. 05 Question 8 options: True False.
Answer:
true
Explanation:
because
An automated packaging systems is responsible for packing boxes.
An automated packaging machine is a device mostly found in industrialised environment used to package and seal fast moving consumable goods.
The products could be packaged in sachets or in boxes depending on the type of packaging needed
The various types of packaging are listed bellow
Primary PackagingSecondary PackagingPrimary Package: These are package that are used to enclose the product directly, if the product is edible, the primary package is mostly food safe i.e when it comes in contact with product it does not have any form of harmful effect to the final consumer
Secondary Package: These are packages that are use to enclose are large amount of products are are enclose in a primary package, they are usually in boxes
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The following is a chemical reaction for _______ with ozone. Reaction 1: C l O B r O right-arrow C l B r O 2. Reaction 2: C l O 3 right-arrow C l O O 2. Reaction 3: B r O 3 right-arrow B r O O 2. A. Chlorofluorocarbons b. Halons c. UV radiation d. None of the above.
Answer:
B
Explanation:
The ozone is being broken up in the second and third, which indicates halons. Halons destroy ozone and extinguish fires.
Answer:
B
Explanation:
How does groundwater become polluted? a. Pollutants mixed with water pass through permeable layers above the aquifer. B. Factories dump their waste directly into aquifers. C. Refuse infiltrates the water table when garbage is dumped. D. All of the above Please select the best answer from the choices provided A B C D.
Answer:
A
Explanation:
Pollutants mixed with water pass through permeable layers above the aquifer.
What is Groundwater?
Water that is found underground in saturated regions beneath the surface of the earth is known as groundwater. The water table is the term for the saturated zone's upper surface.
Contrary to popular perception, underground rivers are not created by groundwater. Similar to how water fills a sponge, it fills the pores and cracks in subterranean materials like sand, gravel, and other rock.
Rock materials are referred to as aquifers if groundwater flows naturally out of them or if it can be pumped out of them. One of the most significant natural resources for the country is groundwater, which is found in aquifers beneath the Earth's surface.
Therefore, Pollutants mixed with water pass through permeable layers above the aquifer.
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Which of the following would not be considered a characteristic of communism.
What is the difference of the volumes of the two oblique pyramids, both of which have square bases? Round the volumes to the nearest tenth of a centimeter. 2 oblique pyramids with square bases are shown. Pyramid A is a base edge length of 2. 6 centimeters and a height of 2 centimeters. Pyramid B has a base edge length of 2 centimeters and a height of 2. 5 centimeters. 0. 7 cm3 1. 2 cm3 1. 8 cm3 2. 3 cm3.
Answer:
What brought an end to efforts during the late thirteenth century to form an alliance of European states and the il-khanate of Persia aimed at crushing Islamic forces in the eastern Mediterranean
Explanation:
The elevation of mt everest is 29028 feet.
A vector makes an angle, θ, with the horizontal. The horizontal and vertical components of the vector will be equal in magnitude if θ is.
A vector has horizontal and vertical components.
The value of [tex]\mathbf{\theta }[/tex] is 45 degrees, when the horizontal and vertical components are equal
Let the magnitude of the vector be H.
So, the horizontal (h) and the vertical components (v) of the vector would be:
[tex]\mathbf{v = Hcos(\theta)}[/tex] --- vertical
[tex]\mathbf{h = Hsin(\theta)}[/tex]
Equate both expressions
[tex]\mathbf{h = v}[/tex]
Substitute values for h and v
[tex]\mathbf{Hcos(\theta) = Hsin(\theta)}[/tex]
Divide both sides by H
[tex]\mathbf{cos(\theta) = sin(\theta)}[/tex]
When [tex]\mathbf{cos(\theta) = sin(\alpha)}[/tex], then
[tex]\mathbf{\theta + \alpha = 90^o}[/tex]
So, we have:
[tex]\mathbf{\theta + \theta = 90^o}[/tex]
[tex]\mathbf{2\theta = 90^o}[/tex]
Divide both sides by 2
[tex]\mathbf{\theta = 45^o}[/tex]
Hence, the value of [tex]\mathbf{\theta }[/tex] is 45 degrees
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y = 4(x - 2)(x + 4)
In the quadratic equation above, a is a nonzero
constant. The graph of the equation in the xy-plane
is a parabola with vertex (c,d). Which of the
following is equal to d ?
A) -90
//
B) -8a
©) -5a
D) -2a
Answer-A
Explanation:
Most individuals and businesses are likely to find their judicial interactions in _____.
Answer:
State courts
Explanation:
If the weight of an object on earth is 245 n, what must be the mass of the object?.
Answer:
128
Explanation:
A city's population is represented by the function P=25,000(1. 0095)t , where t is time in years. How could the function be rewritten to identify the daily growth rate of the population? What is the approximate daily growth rate? Drag and drop the choices into the boxes to correctly complete the table. If a value does not match, do not drag it to the table. Function Daily growth rate.
Answer:
The yearly growth rate is 0.95%. For the daily growth rate, change t, to t/365/
Explanation:
A conclusion that can be drawn from the outcome of flight 93 on september 11, 2001, is that.
Answer:
Flight 93 was the plane that was hijacked and caused 9/11
Explanation:
Answer:
A edge 2021
Explanation:
the plane hit the dirt due to the passengers fighting for control
Pick one of the body parts shown in Sammi's model. How would a disease or injury to this organ affect the process modeled? How would it affect the body as a whole?.
Answer:
The heart, the heart is what makes every moving part working inside our body even though the brain is the one who tells them or gives them signals to work. the heart is what keeps them alive and if the heart takes any kind of negative damage the would not take care of everything it's supposed to. If the heart starts to fail it will effect the blood suply to all your body parts and blood is what carries the oxygen throughout your body and without getting the proper blood or oxygen supply to those certain body parts will have an effect like you couldn't keep warm or cool off, fight infections, or get rid of our own waste products. Without enough blood, we'd weaken and die.
Explanation: That's my answer
The body part that can be picked in the given model is heart. Any injury can affect the bloop supply throughout the body.
What is circulatory system?Blood vessels in the circulatory system transport blood away from and towards the heart. Arteries transport blood away from the heart, while veins transport blood back to the heart.
The heart in the body is analogous to a car's engine in that it pumps oxygen carrying blood cells into all organs, and without these oxygen carrying blood cells, the entire body will stop functioning.
An injury or disease to the heart will have a negative impact on the rate of blood distribution to all parts of the body, which will have a negative impact on the overall wellbeing of the body and will also have a negative impact on the process being modeled.
Thus, the heart is the body part shown here.
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Which letter shows the type of wave that can be seen by humans.
Brea and colin do business as dig excavators. In acting on the firm’s behalf, brea makes an honest error in underestimating the cost of a certain project. In this situation, to her firm, brea is liable for a breach of the duty of.
People often breach duty as a result of some factors. In this situation, to her firm, Brea is liable for one of the choices of breach of the duty.
There are times, the court will say that a breach of duty of care is due to the existence of certain factors. When an individual is injured, the defendant is said to have breached the duty of care.
Breach of duty often takes place when an individual's conduct fails to meet an applicable standard of care.
As the error was due to a honest mistake, she will be ask to make appropriate corrections.
See full question below
Brea and Colin do business as Dig Excavators. In acting on the firm's behalf, Brea makes an honest error in underestimating the cost of a certain project. In this situation, to her firm, Brea is liable for a breach of the duty of
Loyalty.
accounting
care.
none of the choices.
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Difference between point to point and continuous path control system.
Answer:
Continuous path control system is continuous operation that perform by tool.The program used in continuous path control system is more complex .
Explanation: