Answer:
6.7 km/h
Explanation:
Use stokes' theorem to evaluate s curl f · ds. F(x, y, z) = x2 sin(z)i + y2j + xyk, s is the part of the paraboloid z = 4 − x2 − y2 that lies above the xy-plane, oriented upward.
Stokes' theorem says that the surface integral of the curl of the vector field F across the surface S is equal to the line integral of F along the boundary of S.
In this case, the boundary is a circle in the x,y-plane with radius 2. (To see this, set z = 0 and rearrange the equation for the paraboloid as x² + y² = 4.)
Then
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_{\partial S} \vec F \cdot d\vec r[/tex]
where
[tex]\vec r = 2\cos(t) \,\vec\imath + 2\sin(t) \,\vec\jmath[/tex]
parameterizes the circular boundary of S with 0 ≤ t ≤ 2π. Then
[tex]d\vec r = \dfrac{d\vec r}{dt}\,\dt = (-2\sin(t)\,\vec\imath + 2\cos(t)\,\vec\jmath)\,dt[/tex]
and the integral becomes
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_{\partial S} \vec F \cdot d\vec r[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} \vec F(\vec r(t)) \cdot \frac{d\vec r}{dt}\,dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s \\= \int_0^{2\pi} ((2\cos(t))^2 \sin(0)\,\vec\imath + (2\sin(t))^2\,\vec\jmath + (2\cos(t))(2\sin(t))\,\vec k) \cdot(-2\sin(t)\,\vec\imath + 2\cos(t)\,\vec\jmath)\,dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} 8\sin^2(t)\cos(t) \, dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} 8\sin^2(t) \, d(\sin(t))[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \frac83 (\sin^3(2\pi)-\sin^3(0)) = \boxed{0}[/tex]
are there other universes?
Answer:
no
Explanation:
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
Do you think counselors are trustworthy.
Answer:
Yes.
Explanation:
I feel like they are because of the simple fact they cannot share your information, or anything you have said, with anyone because of confidentiality. The only way they can share anything is if you are going to hurt yourself or others, or if you give them verbal or written permission to do so.
A force acts on a particle that undergoes a displacement.
Answer:
An F Vector Force
Example:
The work done by the force on the particle is 1 J.
The angle between the force and the displacement is 81.87⁰.
The given parameters;
F = (4i - 3j)
displacement of the particle, s = (i + j)
The work done by the force on the particle is calculated as follows;
The angle between the force and the displacement is calculated as follows;
If 1=15 and 6=20 what is 3.
if 1 = 15 and 6=20 what is 3
=
25
Evaluate the line integral, where c is the given curve. C (x/y) ds, c: x = t3, y = t4, 1 ≤ t ≤ 4.
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 integralAccording 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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How can buddhism affect change on powerful countries that use war.
Buddhism is a religion that seeks to avoid conflict and harm, so other countries can learn from this.
The diagram shows 3 identical circles inside a rectangle.
Answer:
Explanation:
Diagram?
Which of the following is a way to buy stocks.
Answer:
Through Hiring a Stockbroker
Answer:
Online through a brokerage Web site
Explanation:
Write an outline the chosen reading text using your preferred format brainly.
I'll write a essay.
What is black? You may have already got an answer, but keep reading because your answer could also be incorrect. You might have the correct solution, but it might not be exactly right so you ought to take your time and keep reading this thoroughly.
You might think black is just defined as a color, but it isn't, just not the right properties to be defined as just a color. The definition of black goes deeper. Black isn't exactly defined as a color because it's the whole absence of light and shine, and also, color. Within the visible art world, black and white, sometimes are usually defined as distinct colors. This is different from the scenario of spectral colors in physics.
Black is really a color which ends up from missing or complete absorption of all visible/invisible light. It's a neutral color, without hue, like white and gray. It's often used symbolically or figuratively to represent darkness of the very darkest color because of the absence of or complete absorption of light; the other of white.
Well black represents darkness, evil, despair, and also the night/the abyss. It is the color accustomed to convey specifically/certain and jurisdiction, and when used because the opposite as white, it is a symbol of the eternal struggle between day and night, well-being and evil/hatred, and right and crime/wrong.
So in conclusion, black represents darkness, evil, and despair, it is a symbol of the eternal struggle between day and night, well-being and evil, between right and wrong. It is the color accustomed to convey specifically/certain and jurisdiction, and it is also the opposite of white. It is not just a color, it's more known as a distant color because it is without light and hue.
Carefully read sources a through d (listed below), including the introductory information for each source. Compose a thesis statement you might use for an essay in which you develop your position on the role, if any, that zoos should serve in the future. Then, select at least three pieces of evidence from the sources to support your position, briefly explaining how each piece of evidence might be used to develop your argument. Avoid merely summarizing the sources.
The above question wants to assess your writing ability, therefore it is not correct for me to write the thesis statement for you, but I will show you how to write it.
First, you should know that a thesis statement is a short, direct, and objective paragraph that shows your opinion or position on a particular issue.
This opinion must be substantiated by evidence taken from research sources, for this reason, you should read the sources that have been presented to you or research articles, essays, and publications on the subject.
After that, you can answer your question as follows:
Present your thesis statement, that is, present your opinion on the future role of zoos.Show information from the research sources that support your thesis statement.Explain how this information supports your opinion and shows it to be true.An example of a thesis statement would be: According to the reading, the function of zoos will become increasingly obsolete due to the growth of environmental awareness and animal rights.
More information:
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Jonathon works for a u. S. Company that doesn't produce goods domestically, but instead buys them from other countries and resells them in the united states. Jonathon's company illustrates the concept of.
Companies are known to have different areas at which they trade. Jonathon's company illustrates the concept of importing.
Importing by a firm simply means that a company/firm often buys goods outside the country and then resells them domestically.
Importing is don by bringing products or services into a country with the aim to sale that have been produce in another country.
Some U.S. companies are often engage in buying of products overseas and shipping them into the U.S. for sale, or as part of a product that is being assembled in the U.S.
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Which of the expressions below is equivalent to 4x^2/12x^2-4.
Answer:
(846_++=-06456 AND _089_)(
Explanation:
Which description from "sugihara" best indicates that several hours have passed?.
Answer:
its A
Explanation:
hope this helps, pls lmk if its wrong
What was the role of muslim religious leaders in africa.
Answer: In most cases, the Muslim religious leaders serve also as community leaders and have broad political influence; their visit will contribute to strengthening the diplomatic ties between Israel and Africa.
(i searched it. pls mark me brainliest)
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?.
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.
A similar problem is given at https://brainly.com/question/9543179
What does it mean to be ‘other oriented’?
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
do you think the earth is round or flat
Answer:
cube
Explanation:
Would you recommend dancing as an activity done at home.
Which substances are necessary for the synthesis and the breakdown of most materials in an organism?.
Enzymes
Explanation:
are the catalyst that require substrate for their function. Almost all the metabolic process in the body for synthesis of any substance requires enzymes.
I hope this is correct :)
How many differences can you spot candy house.
Answer:
There no image to reference lol. Can't help you
Explanation:
Which of the following theorems cannot be used to prove two lines are parallel?.
How are we supposed to answer this question without the theorems mentioned in the question????
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.
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]
Learn more about areas formed from cubes here: https://brainly.com/question/25636539
Answer:
4 square root of 2cm
Explanation:
cool stuff
Bills new porch is rectangular with an area of 50 square feet.
Considering the whole question, the perimeter of the porch is 30 feet.
This is because the whole question is, "Bill's new porch is rectangular, with an area of 50 square feet. if the length of the porch is two times the width, what is the perimeter of the porch?"
Therefore to find the perimeter of the porch, here is the step by step:
Given that the length of the porch is two times the width.
Hence, assume that the width = X
Also, assume that the length = 2X
The general formula here:
50 = X × 2X
X × 2X50 = 2x²
2x²X² = 50 ÷2
50 ÷2X² = 25
25X = √25
√25X = 5
Hence, width = 5 feet.
Given that length of the porch is two times the width = 5 × 2 => 10 feet
Therefore Perimeter of a rectangle = 2 (Length + Breadth)
Put all the values in the formula
Perimeter of the porch = 2 × (5 + 10)
= 2 × (15)
= 30 feet.
Hence, in this case, it is concluded that the correct answer is 30 feet.
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Francis has the standard plan offered by his employer and is making an office visit to an in-network doctor to treat his flu-like symptoms. How much would francis be asked to pay by the office manager in the doctor's office?.
There are different kinds of healthcare plans. Francis will not pay (Option one) if he be asked to pay by the office manager in the doctor's office.
There is a standard of minimum coverage that is applicable to employment based health plans.
A health plan must meets the minimum required value standard if;
a. It was designed to pay at least 60% of the total cost of medical services for a standard population.
b. Does the employer offer a health plan that meets the minimum value standard.
Francis is already covered in his his standard plan and therefore will not be expected to pay the money. But in cases of only some percentage of the plan is covered, then the individual can cover the rest expenses.
See full question below
Francis has the Standard Plan offered by his employer and is making an Office Visit to an in-network
doctor to treat his flu-like symptoms. How much would Francis be asked to pay by the office manager in
the doctor’s office?
a. $0
b. $15
C. $25
d $40
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Answer: C
Explanation:
A cell with 10 chromosomes undergoes mitosis.
Answer:
Yes every cell undergoes mitosis
List at least two facts you learned from your research that you could use when writing the opening statement. Remember to include information that is relevant to the main problem you are investigating.
Two facts that I learned during my research were narrowing down the research topic and setting appropriate goals.
When doing research, several aspects must be taken into account so that the research has good results and produces new knowledge. Here are two tips for proper research:
1. Limit the subject of the investigation: When conducting an investigation it is necessary to limit the subject so that it is easier to achieve an effective result. For example, time limits, a specific place, and more special aspects should be set to make the investigation more specialized.
2. Establish adequate objectives: When conducting an investigation it is necessary to establish objectives that can be achieved in the investigation. Highly ambitious goals can make research and information search difficult.
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Answer:
-The cost of college has risen faster than inflation for many years.
-The high price of student services and administration are two reasons for the rapid increase in cost.
Explanation:
good luck guys
A consumer group is investigating the number of flights.
Which of the following is not a benefit of warm up exercise.
