(1 point) Let S be the part of the plane 3c + 4y + z = 3 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F = 3i+ 4j + 1k across the surface S.

Answers

Answer 1

The flux of the vector field F across the surface S is -9/2.

To use Stokes' theorem to find the flux of the vector field F across the surface S, we need to first find the curl of F.

curl F = (d/dx)1 - (d/dy)4 + (d/dz)3 = -4i - 3j + k

Next, we need to find a curve C that bounds the surface S. Since S lies in the first octant and is oriented upward, we can choose the curve C to be the boundary of the portion of the plane 3x + 4y + z = 3 that also lies in the first octant and is oriented counterclockwise when viewed from above. This curve consists of three line segments:

C1: x = 0, y = 0, z = 3/4
C2: x = 3/4, y = 0, z = 0
C3: x = 0, y = 3/4, z = 0

Using Stokes' theorem, the flux of F across S is equal to the line integral of the curl of F along the curve C:

flux = ∫∫S curl F · dS = ∫C curl F · dr

We can compute this line integral by breaking it up into three parts, one for each segment of the curve C:

∫C1 curl F · dr + ∫C2 curl F · dr + ∫C3 curl F · dr

For the first segment, we have dr = (0, 0, -3/4) and curl F = (-4, -3, 1), so

∫C1 curl F · dr = (-4)(0) + (-3)(0) + (1)(-3/4) = -3/4

For the second segment, we have dr = (3/4, 0, 0) and curl F = (-4, -3, 1), so

∫C2 curl F · dr = (-4)(3/4) + (-3)(0) + (1)(0) = -3

For the third segment, we have dr = (0, 3/4, 0) and curl F = (-4, -3, 1), so

∫C3 curl F · dr = (-4)(0) + (-3)(3/4) + (1)(0) = -9/4

Adding up these three line integrals, we get

flux = ∫C curl F · dr = ∫C1 curl F · dr + ∫C2 curl F · dr + ∫C3 curl F · dr = (-3/4) + (-3) + (-9/4) = -9/2

Therefore, the flux of the vector field F across the surface S is -9/2.

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Related Questions

What is the multiplicative rate of change for the exponential function f(x)= 3 (2/3)^-x
A. 0.4
B. 2.5
C. 0.6
D. 1.5

Answers

Answer:

C basta Yan ang sagot HAHAHA dko mapicturan solution ko e

Step-by-step explanation:

ano ba yan arte nyo sabing yan ang sagot e

Answer:

c 0.6

Step-by-step explanation:

lol

The demand for good X has been estimated by Qxd=12-3Px + 3Py. Suppose that good X sells at $2 per unit and good Y sells for $1 per unit. Calculate the own price elasticity. Multiple Choice -0.2 -0.67

Answers

Therefore, the own price elasticity of good X is approximately -0.67.(rounded to 2 decimal places)

To calculate the own price elasticity of good X, we need to use the formula:

Own Price Elasticity = (% change in quantity demanded) / (% change in price)

Given that the price of good X is $2 per unit, we can substitute the price (Px) into the demand equation:

Qxd = 12 - 3Px + 3Py

Substituting Px = $2 and Py = $1 into the equation, we get:

Qxd = 12 - 3(2) + 3(1)

= 12 - 6 + 3

= 9

Now, let's calculate the quantity demanded when the price changes by a small amount, let's say $0.10. We can substitute Px = $2.10 into the demand equation:

Qxd' = 12 - 3(2.10) + 3(1)

= 12 - 6.30 + 3

= 8.70

Using these values, we can calculate the percentage change in quantity demanded and the percentage change in price:

% change in quantity demanded = (Qxd' - Qxd) / Qxd * 100

= (8.70 - 9) / 9 * 100

= -0.30 / 9 * 100

= -3.33% (rounded to 2 decimal places)

% change in price = (Px' - Px) / Px * 100

= (2.10 - 2) / 2 * 100

= 0.10 / 2 * 100

= 5%

Now, let's calculate the own price elasticity using the formula:

Own Price Elasticity = (% change in quantity demanded) / (% change inprice)

= -3.33% / 5%

= -0.67 (rounded to 2 decimal places)

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CAN SOMEONE HELP AND EXPLAIN THIS TRIGONOMETRY PROBLEM

CAN SOMEONE HELP AND EXPLAIN THIS TRIGONOMETRY PROBLEM

Answers

Step-by-step explanation:

Hey there!

Simply work with it.

As it is a Right angled triangle, taking angle 40° as a reference angle. Then,

Length of board = hypotenuse = 15 feet.

To find: height of ladder = perpendicular.

Now,

Taking sin ratio,

\( \sin = \frac{p}{h} \)

\(sin \: 40 = \frac{p}{15} \)

or, as in per the given sin value is 0.6428

so,

\(0.6428 = \frac{p}{15} \)

or, 15 × 0.6428 = p

or, p = height of ladder = 9.642.

Therefore, p = height of ladder = 10 feet. { rounding off we get 10 feet as answer}.

Hope it helps...

20 The rectangle ABCD represents a park.
B
Not to scale
40m
A
D
60m
The lines show all the paths in the park.
The circular path is in the centre of the rectangle and has a diameter of 10m.
Calculate the shortest distance from A to C across the park, using only the paths shown.

Answers

Answer: 33

Step-by-step explanation:

What is the value of x in |-6|= x? Select one: a. 6 and -6 O b. 6 a co d. 6​

Answers

Answer:

X=6

Step-by-step explanation:

Can everybody that sees this subscribe to my YT Channel its : KingEli322     I'm trying to get to 1,000 subs before January 1, 2021 Plz and thankyou

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SOMEONE HELP ME PLEASE

SOMEONE HELP ME PLEASE

Answers

I NEED HELP TOOOO LIKE ASAPPPP IM IN SUMMER SCIOL LOL
Answer: 1/36
First roll 1/6 chance of getting 1. Second chance 1/6 chance of getting 1. Multiply the two.

What are 2 equivalent fractions for 2/3 1/2 4/5 ∝

Answers

The equivalent fractions of the following given fractions are as follows:

2/3 = 4/6 and 8/12

8/121/2 = 2/4 and 4/8

4/84/5 = 8/10 and 16/20

What are equivalent fractions?

Equivalent fractions is defined as the fractions that can represent the same fractions when simplified to the least fraction.

The method that can be used to find equivalent fractions is through multiplying the numerator and the denominator with the same whole number.

To find the equivalent fraction of 2/3, 1/2 and 4/5 multiple through with 2 and 4. That is;

2/3 = 2×2/3×2 = 4/6 and 2×4/3×4= 8/12

1/2 = 1× 2/2×2 = 2/4 and 1×4/2×4 = 4/8

4/5 = 4×2/5×2 = 8/10 and 4×4/4×5 = 16/20

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Sandra saves 9% of her salary for retirement. this year her salary was $3,000 more than in the previous year, and she saved $4,050. what was her salary in the previous year?

Answers

Answer:

She earned $42,000 in the previous year

Step-by-step explanation:

9% can be rewritten as 0.09

0.09x is 4050

divide both sides by 0.09

0.09x becomes x

4050 becomes 45,000

then we subtract 3,000 from 45,000 to find the previous years salary

My entire life I have noted the sun rises every morning and sets every evening. I am concluding that the sun will rise tomorrow morning and set tomorrow evening. Make an argument as to why this can be inductive or deductive reasoning and include details that indicate your knowledge of the topic.

Answers

The argument that the sun will rise tomorrow morning and set tomorrow evening is based on inductive reasoning, using past observations of consistent sunrise and sunset patterns to predict future occurrences.

1. The observation: Throughout your entire life, you have consistently noticed that the sun rises every morning and sets every evening. This is an observation based on personal experience.

2. Inductive reasoning: Based on this observation, you make an inference or prediction about the future. You reason that since the sun has always risen in the morning and set in the evening in the past, it is likely to continue doing so in the future.

3. Pattern and consistency: The assumption is that natural phenomena, such as the rising and setting of the sun, follow a pattern or regularity. This assumption is based on the principle of uniformity of nature, which suggests that the future will resemble the past in terms of natural occurrences.

4. The limitations of inductive reasoning: While inductive reasoning provides a useful way to make predictions based on past observations, it is not foolproof. There is always a small possibility that something unexpected could happen, such as a rare astronomical event or an external factor that alters the pattern. However, based on the available evidence and the consistency of the observed pattern, the prediction that the sun will rise tomorrow morning and set tomorrow evening is highly probable.

In summary, the argument relies on inductive reasoning, using the past consistent observation of the sun's rising and setting to predict that it will continue to do so in the future. While this reasoning is not infallible, it is a reasonable and practical way to make predictions based on observed patterns in nature.

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write an exponential expression showing organism B’d increase in population over the same 8 days

Answers

Answer:

the answer is 5^2

Step-by-step explanation:

Name the kind or kinds of symmetry the following figure has: point, line, plane, or none. (Select all that apply.)
(B)
point
plane
line
none

Answers

Answer:

Plane

Step-by-step explanation:

A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles. You randomly select a marble from the bag, record the color, and then put that marble back in the bag. If you were to do this 200 times, how many times would you expect to pull out a blue marble?

Answers

Answer:

70

Step-by-step explanation:

We have 7 blue marbles, and 20 total marbles. As a result, if we randomly chose one marble from the bag, the probability would be (number of favorable outcomes)/(number of total outcomes) = 7/20.

This means that for each 20 trials, we would expect to pull out a blue marble 7 times, as the probability does not change over time (because we put the marbles back, there are the same amount of each marble). Over 200 trials, we can simply make it out of 200 instead of 20. We can thus multiply 7/20 by 10/10 (10/10 is equal to 1, keeping the proportions equal) to get 70/200, so we can expect 70 blue marbles out of 200.

given a function f : a → b and subsets w, x ⊆ a, then f (w ∩ x) = f (w)∩ f (x) is false in general. produce a counterexample.

Answers

Therefore, f(w ∩ x) = {0} ≠ f(w) ∩ f(x), which shows that the statement f(w ∩ x) = f(w) ∩ f(x) is false in general.

Let's consider the function f: R -> R defined by f(x) = x^2 and the subsets w = {-1, 0} and x = {0, 1} of the domain R.

f(w) = {1, 0} and f(x) = {0, 1}, so f(w) ∩ f(x) = {0}.

On the other hand, w ∩ x = {0}, and f(w ∩ x) = f({0}) = {0}.

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Which of the following is equivalent to 16^3/4
O 6
O 8
O 12
O 64

Answers

Answer:

the answer is 8

Answer:

Answer is 8

Step-by-step explanation:

Which of the following is equivalent to 16^3/4O 6O 8O 12O 64

(X-3)^2-49 into standard form

Answers

Answer: (x-10) • (x+4)

Convert the angle 0=180° to radians

Convert the angle 0=180 to radians

Answers

Answer:

\(\pi radians\)

its a Geometry question that i don't understand

its a Geometry question that i don't understand

Answers

The two triangles in the figure are similar by the AA (Angle-Angle) similarity theorem, indicating that they have the same shape but may differ in size.

a. The two triangles in the figure are similar because they have the same shape, but may differ in size. More specifically, they are similar by the AA (Angle-Angle) similarity theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

In the given figure, we can see that:

Angle A in triangle ABC is congruent to angle D in triangle DEF.

Angle C in triangle ABC is congruent to angle F in triangle DEF.

Therefore, by the AA similarity theorem, we can conclude that the two triangles ABC and DEF are similar.

b. We can write a similarity statement for the two similar triangles as:

Triangle ABC is similar to triangle DEF, written as ΔABC ~ ΔDEF.

Note that this similarity statement indicates that the two triangles have the same shape, but may differ in size. Also, the order of the vertices is important and should be listed in the same order for both triangles.

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Please answer this thanks

Please answer this thanks

Answers

Answer: down below

Step-by-step explanation:

1. How many hay bales did the farmer sell?

To do that, you need to divide the weight of a hay bale by the total weight of the hay bales that the farmer sold.

That will be 24,300 / 75 = 324 bales

2. Divide the new number (26,700) by the same number 75.

26,700 / 75 = 356 hay bales

Subtract the bales from last year to the bales from this year:

356 bales - 324 bales = 32 bales

what is the theoretical probability of rolling a 1 or a 2 on the 6-sided die? answer as a fraction

Answers

Answer:

1/3

Step-by-step explanation:

as 1/6 for a one and 1/6 for a 2 and 1/6 + 1/6 is 2/6 or 1/3

please someone help me with this problem

please someone help me with this problem

Answers

from the question we know
18*11+5*18 = 288.

Total tickets, 11 adult tickets and 18 kids tickets: $288

Total tickets, a adult tickets and k kids tickets:
$(18a+5k)

A scale model of a building has a height of 1/5 meter. The scale of the model is 1 cm = 0.5m. What is the height of the building?

Answers

Answer:

2000 meters

Step-by-step explanation:

first you have to convert the meters into centimeters so then 1cm=100 cm

1/5 meter=20 cm

20*100=2000

2000 centimeters or 20 meters

hope this helps

brainliest?

1. A population of insects is very dynamic, depending on many variables. A simple model for a particular species of insect is found to be as given. 3- 12 +16 PO) 15 - 2+1 What happens to this population in the long run, i.e. will it die out (extinction), boom (grow indefinitely), or settle into an equilibrium (stability)? Justify your claim with the appropriate mathematics. If the result is equilibrium, then give the value of the stable population.

Answers

Therefore, the insect population will remain stable, neither increasing nor decreasing and the estimated  stable population is 2.

Given the equation:3-12+16 PO) 15-2+1

In order to determine the stability of a population of insects, we must first calculate the equilibrium value of PO.

A population's equilibrium is defined as the point at which the population remains stable over time, indicating that the population is neither declining nor growing indefinitely.

Stable population equilibrium is defined as follows:

Let P* be the equilibrium value of the population.

This implies that:P* = 15 - 2 + 1 / 3 - 12 + 16

This simplifies to:P* = 14/7 or 2

Therefore, the equilibrium value of the insect population is 2. If the population is greater than 2, it will decrease. If it is less than 2, it will increase.

In this case, the population of insects will settle into an equilibrium state.

The value of the stable population is 2.

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By how much could the largest sample observation be decreased without affecting the value of the median?

Answers

Using the median concept, the largest sample observation could be decreased until it is equal to the median without affecting the value of the median.

What is the median of a data-set?

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

From it, we get that the median is the middle value and is not influenced by outliers, hence the largest sample observation could be decreased until it is equal to the median without affecting the value of the median.

If it is decreased by to a value lower than the median, the middle value would change than the median would be affected.

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if medain of 10, 20, x+5,x+10,50,60 is 35 then find x

Answers

Answer:

X = 27

Step-by-step explanation:

10, 20, 32, 37, 50, 60

First things first, take off 10, 20, 50, and 60.

Now, you remain with 32 and 37. Now from here it is simple.

Average of 32 and 37 = 34.83

Round 34.83 to 35

32 averaging 37 (Rounding Terms) ≈ 35

So X is 27

A cylinder has a height of 14 millimeters. Its volume is 17,584 cubic millimeters. What is the radius of the cylinder?

Use ​ ≈ 3.14 and round your answer to the nearest hundredth.
help me

Answers

Answer:

V = πr2h (Volume of a cylinder is the area of a circle times its height). V = 8167.14. π = 3.14. h = 9.

Step-by-step explanation:

The distance between two lines measured along a perpendicular line to the line is always the same.

Answers

Answer:

the same

Step-by-step explanation:

perprendicular lines never touch

When writing equations for lines of best fit, will all answers be different, especially since you’re going to be doing your own line of fit and choosing two points on the line?

Answers

Finding a line equation that can roughly represent the data is your goal. the best-fit line or regression line.

what is equation ?

A mathematical equation is a formula that connects two statements using the equal sign (=) to signify equivalence.  For instance, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematically, the connection between two phrases on either side of a letter is stated. The symbol doubles as the sole variable most of the time. for illustration, 2x - 4 = 2.

given

Perfect or exact lines are not present in real-world data sets.

Your task is to identify a line equation that can roughly reflect the data. The regression line or line of best fit is what we refer to as here.

You might draw a line by eye from the graph, choose some random integers, and do this.

Finding a line equation that can roughly represent the data is your goal. the best-fit line or regression line.

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Choose the multiplicative inverse of 5/3

Answers

Answer: I think that would be 5x3

Step-by-step explanation:

Find the height of a cylinder of volume 200cm^3 and radius 4

Answers

Answer:

3.98 cm

Step-by-step explanation:

V= πr²h

V= 200 cm³, r= 4 cm, h=?

h= V/(πr²)= 200/(3.14*4²)= 3.98 cm

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 18%. You would like to be 95% confident that your estimate is within 4.5% of the true population proportion. How large of a sample size is required?

Answers

Therefore, a sample size of at least 602 is required to estimate the population proportion with a 95% confidence level and an error tolerance of 4.5%.

To determine the required sample size to estimate a population proportion, we can use the formula:

\(n = (Z^2 * p * (1-p)) / E^2\)

Where:

n = required sample size

Z = Z-value corresponding to the desired confidence level (in this case, for a 95% confidence level, Z ≈ 1.96)

p = estimated population proportion

E = maximum error tolerance

In this case, the estimated population proportion (p) is 0.18 (18%) and the maximum error tolerance (E) is 0.045 (4.5% expressed as a decimal).

Substituting these values into the formula, we get:

n =\((1.96^2 * 0.18 * (1-0.18)) / 0.045^2\)

n ≈ 601.692

Since the sample size must be a whole number, we round up to the nearest whole number:

n = 602

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