Parameterize C by
x(t) = 2 cos(t) ⇒ dx/dt = -2 sin(t)
y(t) = 2 sin(t) ⇒ dy/dx = 2 cos(t)
with -π/2 ≤ t ≤ π/2. Then the line element is
ds = √((dx/dt)² + (dy/dt)²) dt = 2 dt
and the line integral is
[tex]\displaystyle \int_C xy^4 \, ds = \int_{-\frac\pi2}^{\frac\pi2} 2\cos(t) \cdot (2\sin(t))^4 \cdot (2 \, dt) = 64 \int_{-\frac\pi2}^{\frac\pi2} \cos(t) \sin^4(t) \, dt[/tex]
Substitute u = sin(t) and du = cos(t) dt. Then
[tex]\displaystyle \int_C xy^4 \, ds = 64 \int_{-1}^1 u^4 \, du = \frac{64}5 (1^5 - (-1)^5) = \boxed{\frac{128}5}[/tex]
What is the potential energy of a rock that weighs 5 kg and sits on top of a 10- meter high hill?.
Answer:
490 Joule
Explanation:
Solution:
Given,
Mass (m) = 5 kgAcceleration due to gravity= 9.8 m/sHeight (h)= 10 mHere,
Potential Energy (P.E.)= mgh
=5×9.8×10
= 490 Joule
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.
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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.
The distribution of number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and standard deviation 7. Volunteers in the top 20 percent of hours worked will receive a certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 ?.
Explanation:
Using the normal distribution, it is found that the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is closest to:
B 0.123
In a normal distribution with mean \muμ and standard deviation \sigmaσ , the z-score of a measure X is given by:
Z = \frac{X - \mu}{\sigma}Z=σX−μ
It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
The mean is of 80, hence \mu = 80μ=80 .
The standard deviation is of 7, hence \sigma = 7σ=7 .
The minimum value is the 80th percentile, which means that it is X_mXm when Z has a p-value of 0.8.
The probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is P(X_m < X < 90)P(Xm<X<90) , which is the p-value of Z when X = 90 subtracted by the p-value of Z when X = X_mX=Xm , hence the p-value of Z when X = 90 subtracted by 0.8.
Z = \frac{X - \mu}{\sigma}Z=σX−μ
Z = \frac{90 - 80}{7}Z=790−80
Z = 1.43Z=1.43
Z = 1.43Z=1.43 has a p-value of 0.9236.
0.9236 - 0.8 = 0.1236, hence closest to 0.123, option B.
Using the normal distribution, it is found that the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is closest to:
Letter B
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}\\Z=\sigma X - \mu[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. In this problem:
The mean is of 80, hence [tex]\mu = 80[/tex]. The standard deviation is of 7, hence [tex]\sigma = 7[/tex]. The minimum value is the 80th percentile, which means that it is [tex]X_m[/tex] when Z has a p-value of 0.8.The probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90, which is the p-value of Z when X = 90 subtracted by the p-value of Z when X = X_mX=Xm , hence the p-value of Z when X = 90 subtracted by 0.8.
[tex]Z = \frac{X - \mu}{\sigma}\\Z=\sigma X - \mu\\Z = \frac{90 - 80}{7}\\Z=790 - 80\\Z = 1.43Z=1.43[/tex]
Has a p-value of 0.9236.
[tex]0.9236 - 0.8 = 0.1236[/tex]
Hence closest to 0.123.
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A certain wire stretches 0. 90 cm when outward forces with magnitude f are applied to each end. The same forces are applied to a wire of the same material but with three times the diameter and three times the length. The second wire stretches:.
Answer:
A certain wire stretches 0. 90 cm when outward forces with magnitude f are applied to each end. The same forces are applied to a wire of the same material but with three times the diameter and three times the length. The second wire stretches:
Explanation:
How does the author unfold the details of the text painter of light.
The author unfolds the details of the "Painter of Light" text when presenting Kinkade's life chronology.
We can arrive at this answer because:
"Painter of Light" is a text with a chronological structure, which presents a series of events that occurred in a timeline.In this text, this kind of structure is used for Kinkade's life chronology, showing the most important events in his life and how that made him relevant to introduce to readers.It is important to point out that textual structure is the way a text is organized to present information to the reader.
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Answer: The answer is A
Explanation:
Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1. 50 more than the cost of a one loaf of bread. What is the combined cost of one loaf of bread and one package of cheese?.
Answer:
Bitlog
Explanation:
iklog
Based on the diagram, can point d be the centroid of triangle acf? explain. Yes, point d is the point of intersection of segments drawn from all three vertices. Yes, de is three-quarters of the length of the full segment. No, de should be longer than ad. No, the ratio between ad and de is 3:1.
Answer:
A is the correct answer
Explanation:
EDGE
A centroid in a triangle, is the point where all the medians meet.
now a peculiar thing about the centroid is that, it cuts all medians in a 2:1 ratio. So, if that's true, then the median AE, is being cut in two segments AD and DE and AD : DE are on a 2 : 1 ratio.
What is centroid?In a triangle, the centroid is the point of intersection of the three medians, which are line segments joining each vertex to the midpoint of the opposite side.
The centroid divides each median into two segments, with the distance from the centroid to the vertex being twice the distance from the centroid to the midpoint of the opposite side.
Let M be the midpoint of side AB, N be the midpoint of side AC, and P be the midpoint of side BC. Then, we have:
CD = 2DP
CE = 2DN
We are also given that DE = 15. Since D is the centroid, we have:
AD = BD = CD/3
AE = CE/3
DC + DP = PC
CE + DN = NE
AD + AE = DE
Using these relationships, we can find CD and CE:
CD = 2DP = 2(PC - DC) = 2((AD + DP) - (AD/3)) = 2(2AD/3) = 4AD/3
CE = 2DN = 2(NE - CE) = 2((AE + DN) - (AE/3)) = 2(2AE/3) = 4AE/3
To find AD and AE, we can use the fact that AD + AE = DE and AD = BD:
AD + BD = DE
AD + (2AD/3) = 15
5AD/3 = 15
AD = 9
AE = DE - AD = 15 - 9 = 6
Substituting these values into the equations for CD and CE, we get:
CD = 4AD/3 = 4(9)/3 = 12
CE = 4AE/3 = 4(6)/3 = 8
Therefore, CD = 12 and CE = 8.
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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)
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.
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:
Solve for n. 11(n – 1) + 35 = 3n n = –6 n = –3 n = 3 n = 6.
Answer:
[tex]n = - 3[/tex]
is answer
A retailer is able to track which products draw the most attention from its customers through the use of 5g-enabled motion sensors placed around the store. With this knowledge, the retailer can supply the proper amount of products to meet customer demand.
There is a wide spread of 5g technology. The technology that combines with 5G capabilities and used in the monitoring of the shopping trends is the Internet of Things.
The Internet of things is known to explain real or physical objects that are found along with sensors, processing ability, software, and other technologies.
They act by connecting and exchanging data with other devices and systems through the Internet or other communications networks.
The examples of Internet of Things are:
Connected appliances. Smart home security systems. Wearable health monitors etc.See full question below
A retailer is able to track which products draw the most attention from its customers through the use of 5G-enabled motion sensors placed around the store. With this knowledge, the retailer can supply the proper amount of products to meet customer demand.
Which technology combines with 5G capabilities to allow the monitoring of shopping trends in this way?
platooning
network slicing
internet of things
beamforming
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How many differences can you spot candy house.
Answer:
There no image to reference lol. Can't help you
Explanation:
Which description from "sugihara" best indicates that several hours have passed?.
Answer:
its A
Explanation:
hope this helps, pls lmk if its wrong
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]
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.
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bài bánh trôi nước được viết theo phương thức biểu đạt nào? Nếu thể thơ của bài thơ giải
Answer:
I dont understand what you are saying
Crane chose to present this account in a short story form. Which of the following is an aspect of "the open boat" that would be most difficult to convey in a painting depicting the same scene?.
The Open Boat is a popular book that was written by Stephen Crane. The aspect of "the open boat" that is most difficult to convey Thereafter was that 'there was something strange in his voice'.
Crane in his book want the readers to connect deeply with the specific characters in the book and feel their different struggle as they work had in hand to reach the shore alive.
He showed his readers how nature can be powerful and the experience gotten increasing people's ignorant views of the world around them.
See full question below
Crane chose to present this account in a short story form. Which of the following is an aspect of "The Open Boat” that would be most difficult to convey in a painting depicting the same scene?
answer choices
a. These waves were of the hue of slate, save for the tops, which were of foaming white.
b. These waves were most wrongfully and barbarously abrupt and tall.
c. His sleeves were rolled over his fat forearms, and the two flaps of his unbuttoned vest dangled as he bent to bail out the boat.
d. Thereafter there was something strange in his voice.
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My primary group brainly.
Answer:
???
Explanation:
Write and answer the following in your answer sheet.
If a unit price label has a unit price of 21. 5 cents per pound, how much is the total price for an 8 pound package? a. $0. 37 b. $1. 72 c. $2. 69 d. $17. 20.
Answer:
b $1.72
Explanation:
21.5 cents for 1 pound
p for 8 pounds
p = 8 * 21.5
= 172 cents
= $172 / 100
= $1.72
do you think the earth is round or flat
Answer:
cube
Explanation:
Given three consecutive integers, if the sum of the first and third integers is increased by 8, the result is 5 less than triple the second integer. Find the three consecutive integers. *
Answer:
The three consecutive integers are 12, 13 & 14
Explanation:
Let the three consecutive integers be x, x + 1, x + 2
According to the question,
If sum of the first and third integers is increased by 8, the result is 5 less than triple the second integer.
[tex] \therefore [/tex] x + x + 2 + 8 = (x + 1) × 3 - 5
2x + 10 = 3x + 3 - 5
2x + 10 = 3x - 2
10 + 2 = 3x - 2x
x = 12
So, The three consecutive integers are 12, 13 & 14
An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $6750 with a population standard deviation of $265. A sample of randomly selected 30 days reveals a daily mean revenue of $6280. If you were to test the null hypothesis that the daily mean revenue was $6750, which test would you use?.
Based on the given value of sample size and the population standard deviation, the required test for the null hypothesis is the Z test of population mean.
The Z test of population is used to test the null hypothesis of a Normal distribution. Since, the sample size is large (>30) and the variance of the population is known, the most appropriate test of hypothesis to use is the Z test of population mean.Learn more : https://brainly.com/question/25576166
What is the vertex form of the equation? y = – x 2 + 12 x – 4.
Answer:
(6,32)
Explanation:
Which of the following is a way to buy stocks.
Answer:
Through Hiring a Stockbroker
Answer:
Online through a brokerage Web site
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
Which of the following is not a benefit of warm up exercise.
who likes food should tell me
Explanation:
Whooo doesn't like food
