Parameterize S in cylindrical coordinates by the vector function
r(u, v) = (x(u, v), y(u, v), z(u, v))
with
x(u, v) = u cos(v)
y(u, v) = u sin(v)
z(u, v) = 36 - u²
with 0 ≤ u ≤ 3 and 0 ≤ v ≤ 2π. Take the normal vector to S to be
[tex]\vec n = \dfrac{\partial r}{\partial u} \times \dfrac{\partial r}{\partial v} = (2u^2\cos(v),2u^2\sin(v),u)[/tex]
so that the surface element is
[tex]dS = \|\vec n\| \, du\,dv = u \sqrt{1+4u^2}\, du\, dv[/tex]
Then the surface integral is
[tex]\displaystyle \iint_S y^2\,ds = \int_0^{2\pi} \int_0^3 u\sqrt{1+4u^2} \, du\, dv[/tex]
[tex]\displaystyle \iint_S y^2\,ds = 2\pi \int_0^3 u\sqrt{1+4u^2} \, du[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac{2\pi}8 \int_0^3 8u\sqrt{1+4u^2} \, du[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac\pi4 \int_0^3 \sqrt{1+4u^2} \, d(1+4u^2)[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac\pi4 \cdot \frac23(1+4u^2)^{\frac32} \bigg|_0^3 = \boxed{\frac\pi6 \left(37^{\frac32}-1\right)}[/tex]
We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of +/-0. 06 at 95% confidence?.
Using the appropriate sample size formula, the minimum number of samples required is 267
Using the relation :
N = [(Z² × pq) / e²] e = Error Margin = 0.06² = 0.0036p = 0.5 q = 1 - 0.5 = 0.5 Zcritical at 95% = 1.96Substituting the values into the equation :
N = [(1.96² × (0.5 × 0.5)) / 0.0036]
N = (0.9604 / 0.0036)
N = 266.777
N = 267
Hence, the minimum number of samples required is 267
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Un camión traslada 12 vehículos. Algunos son autos y otros son camionetas. Cada auto tiene una masa de 2 toneladas y cada camioneta de 3 toneladas. En total, el camión lleva una carga de 33 toneladas.
Encontrando y resolviendo un sistema de ecuaciones, veremos que hay 9 camionetas y 3 autos.
Sabemos que hay 12 vehículos en el camión.
Definamos:
a = número de autosc = número de camionetas.tal que a + c = 12
La masa total será:
a*2 ton + c*3 ton
Y sabemos que el camión lleva 33 toneladas, entonces tenemos:
a*2 ton + c*3 ton = 33 ton
Así encontramos el sistema de ecuaciones:
a + c = 12
a*2 ton + c*3 ton = 33 ton
Para resolverlo, primero aislamos una de las variables en una de las ecuaciones, aislemos a en la primera:
a = 12 - c
Ahora reemplazamos esto en la otra:
(12 - c)*2 ton + c*3 ton = 33 ton
24 ton + c*1 ton = 33 ton
c*1 ton = 9 ton.
c = 9
Es decir, hay 9 camionetas.
Entonces los 3 vehículos restantes son autos.
Hay 9 camionetas y 3 autos.
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What detail of the myth is suggested in the poem but not in the painting? What connection between the painting's landscape and the myth does this detail convey?.
The myth shows the moment when the sun melts the wings of Icarus, while the painting does not present this moment. This detail shows that nature contributes to the death of Icarus.
We can arrive at this answer because:
The painting shows only the death of Icarus, showing the moment when he fell into the water and drowned.The purpose of the painting is to show how the universe and all other human beings remained indifferent to Icarus' death.Although the myth also features the death of Icarus, it sets out in more detail.The myth shows why Icarus wanted to use the waxwings and why these wings melted.The myth focuses on nature's action on the death of Icarus, while the painting reinforces the universe's indifference to this death.
This question is about “Landscape of the Fall of Icarus.”
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Answer:
B & C
Explanation:
Y E S
A charged capacitor is connected to an ideal inductor. At time t = 0, the charge on the capacitor is equal to 6. 00 μc. At time t = 2. 00 ms the charge on the capacitor is zero for the first time. What is the amplitude of the current at that same instant?.
Answer:
6.000000üc po
Explanation:
tes times i divede mo po at i plas mo po
Based on the graph, what conclusion can be drawn about trade between the United States and China? The United States has a trade surplus with China. China’s economy is declining, which has harmed trade. The United States has a trade deficit with China. China’s economy is improving, which has helped trade.
The conclusion that can be drawn is that the United states has a trade deficit with China.
What is a trade deficit?This trade deficit is known to often takes place only when the value of a country's imports is said to be more than the value of their exports in terms of physical goods and services.
Note a trade deficit implies that a country such as United States is buying more goods and services than they are actually selling and as such, the conclusion that can be drawn from the graph is that the United states has a trade deficit with China.
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Answer:
The United states has a trade deficit with China.
Explanation:
Its correct
A current of 15 amps flows through a circuit with a resistance of 0. 10 ohms. What is the voltage?.
Answer: I=U/R
U=I*R U=0.10*15=1.5
Explanation:
Use the drop-down menus to complete the statements below to answer this question: can you determine whether a system of linear equations has a solution just by looking at the graph of the equations?.
Answer:
The coordinates of a point satisfies the equation of a line if the point lies on the line
If a single point satisfies the equations of two lines, the point is on both lines, so the lines will intersect at that point.
This means that each point where the two lines touch is a solution to the system of equations
This means that if you substitute the x and y values of the point for x and y in the equations, both equations will be true
Explanation:
Answer:
on the line
on both lines, intersect
intersect, solution
true
Explanation:
I did it on Imagine Math.
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?.
Answer:
(1,1) is the answer you're looking for.
who likes food should tell me
Explanation:
Whooo doesn't like food
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?.
Answer:
0°C
Explanation:
water always freezes at 0 degrees
The answer is mashed potatoes.
Answer: what did he sayyy
Explanation:
Which of the following best describes the uses of private land?.
Private property is a legal designation for the ownership of property by non-governmental legal entities.Private property is distinguishable from public property, which is owned by a state entity, and from collective or cooperative property, which is owned by a group of non-governmental entities. The distinction between private and personal property varies depending on political philosophy, with socialist perspectives making a hard distinction between the two,while others blend the two together.[better source needed] As a legal concept, private property is defined and enforced by a country's political system.
Earth is slightly closer to the sun in december than it is in june. The force of gravity of the sun on earth in december compared to june is —.
The Earth is known as a spherical body. The force of gravity of the Sun on Earth in June compared to December is slightly smaller.
Earth is simply known to slightly closer to the Sun on one side of its orbit than on the other side.Kepler's second law states that as a planet moves round the Sun, it sweeps out equal areas in equal times.
All the planets do moves around the Sun in nearly the same plane. The Sun is found to be slightly off-center from the middle of each planet's orbit.
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Brainly. Com answers.
Answer:
what is this
Explanation:
tell right questions
I often relate to the following groups early childhood brainly.
Which substances are necessary for the synthesis of most materials in an organism.
Enzymes
Explanation:
are substances necessary for the synthesis of most materials in an organism.
I hope this is an option???
Marianna is working on improving her communication skills. To be a good listener she should.
You enter a room 2 dogs 4 horses.
(2+4=6) supercalifragilisticexpialidocious
As a result of mitosis, each of the two new cells produced from the parent cell during cytokinesis.
Answer and Explanation: As a result of mitosis, each of the two new cells produced from the original cell during cytokinesis have the same chromosomal constitution as the parental nucleus. Cytokinesis is the actual division of the cytoplasm that results in two daughter cells that are diploid. Mitosis is a type of division that occurs during growth in somatic cells through replication of chromosomes and their subsequent redistribution.
If you have a cb radio, you can turn to channel ___________ and request police assistance.
Based on radio analysis, if you have a CB radio, you can turn to channel Nine (9) and request police assistance.
What is CB Radio?CB Radio is the acronym for Citizen band radio. It is divided into 40 channels.
Each CB radio has channel frequencies between 26.965 to 27.405 MHz.
To request police assistance on CB Radio, one must tune to Channel 9. Channel 9 is designated for Emergency communication, and it has a frequency of 27.065 MHz.
Hence, in this case, it is concluded that the correct answer is "Channel 9."
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When making lemonade, 1 over 4 cup of sugar will make 5 glasses of lemonade. How many cups of sugar would be needed to make 22 glasses of lemonade?.
According to the table, what is the total distance the hiker walked? 4 km 6 km 10 km 20 km.
Answer: 20 km
Explanation:
6 + 4 + 6 + 4 = 20
do you think the earth is round or flat
Answer:
cube
Explanation:
Her nervousness had a profound.
Huh yes that would work out well I think it’s a great deal to get it done by the end of the
Which is a y-intercept of the graphed function? (–9, 0) (–3, 0) (0, –9) (0, –3).
Which of the following best describes the process of translation?.
Answer:
Translation is a universal process in biology where a protein formed of amino acids is made by using messenger Ribonucleic acid (mRNA) to dictate the order of amino acids. Following transcription (the conversion of DNA into mRNA) an mRNA strand leaves the nucleus and enters the cytoplasm via the nuclear pore.
Explanation:
Your welcome!
Translation is the conversion of genetic information from the language of nucleic acid to protein, hence option 6 is correct.
Ribosomes, which are huge complexes of proteins and RNA, catalyze the translation process. Ribosomes read the RNA transcript and translate it one amino acid at a time into a protein.
Peptide bonds are used to connect the amino acids to produce a polypeptide chain. Following that, the polypeptide chain folds into its ultimate shape, which determines its function.
Translation is the process through which an RNA transcript is converted into a protein. This procedure takes place in the cell's cytoplasm.
Thus, the option 6 is correct.
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The given question is incomplete, so the most probable complete question is,
Which of the following best describes the process of translation?
The addition of nucleotides to a DNA template the addition of nucleotides to an RNA template the conversion of genetic information from DNA nucleotides into RNA nucleotides o the conversion of genetic information from the language of proteins to the language of nucleic acids None of these the conversion of genetic information from the language of nucleic acids to the language of proteinsWhich statement about how mass media have changed over time is most accurate.
Answer:
statement 2
Explanation:
2 mass media changed over time is most accurate.
Determine the minimum mass of hydrogen gas required to produce 226 kj of heat.
By definition, the minimum mass of hydrogen gas required to produce 226 kJ of heat is 1.8697 grams.
The reaction is as follows:
2 H₂(g) + O₂(g) → 2 H₂O(g) ΔH = - 483.5 kJ
In this reaction, you can see that 2 moles of H₂ produces 483.5 kJ of heat. But you want to release 226 kJ of heat.
So you can apply the following rule of three: if 483.5 kJ is released by 2 moles of H₂, 226 kJ of heat is released by when moles of H₂?
[tex]amount of moles of H_{2} =\frac{226 kJx2 moles }{483.5 kJ}[/tex]
amount of moles of H₂= 0.93485 moles
Molar mass is the amount of mass that a substance contains in one mole. In this case, the molar mass of H₂ is 2 [tex]\frac{g}{mole}[/tex].
So, the mass containing 0.93485 moles is calculated as:
0.93485 moles× 2 [tex]\frac{g}{mole}[/tex]= 1.8697 grams
Finally, the minimum mass of hydrogen gas required to produce 226 kJ of heat is 1.8697 grams.
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https://brainly.com/question/9846800?referrer=searchResultshttps://brainly.com/question/24150635?referrer=searchResultsWhich range of the electromagnetic spectrum travels at the fastest speed.
Answer:
Photons travel in harmonic waves at the fastest speed possible in the universe: 186,282 miles per second (299,792,458 meters per second) in a vacuum, also known as the speed of light. The waves have certain characteristics, given as frequency, wavelength or energy.
Excessive smoking, substance abuse, and sleep disorders are all examples of ________ symptoms of stress.
Excessive smoking, substance abuse, and sleep disorders are considered to be behavioral symptoms of stress.
It should be noted that behavior-related stress symptoms include absence and turnover, changes in productivity, changes in eating habits, increased consumption of alcohol, and smoking.
In a case where an individual who doesn't usually drink alcohol or smokes before starts drinking alcohol, it's known as behavioral symptoms of stress. In such a situation, stress leads to a change of behavior.
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