Assignment 9: Problem 6 with Previous Problem Problem List Next Problem (1 point) Calculate the circulation, SC F dř, in two ways, directly and using Stokes' Theorem. The vector field F = 2y1 – 2aj and C is the boundary of S, the part of the surface z = 9-22 - y above the ry-plane, oriented upward. Note that is a circle in the ry-plane. Find a F(t) that parameterizes this curve. F(t) =

Answers

Answer 1

We get:F = 2(a sin(θ))i - 2aj

The problem involves calculating the circulation of a vector field F along a closed curve C in two ways: directly, and using Stokes' Theorem. The vector field F and the curve C are given, and we need to find a parameterization of the curve C in order to perform the calculations. To find a parameterization of the curve C, we are given that it lies in the r-y plane and is a circle. Therefore, we can parameterize C using polar coordinates, with r = a and θ ranging from 0 to 2π, where a is the radius of the circle. Specifically, we can use the parametric equations:x = a cos(θ)y = a sin(θ)z = 9 - 2x - ySubstituting these equations into the vector field F, we get:F = 2(a sin(θ))i - 2ajUsing this parametrization and the definition of circulation, we can calculate the circulation of F along C directly. Alternatively, we can use Stokes' Theorem to calculate the circulation by finding the curl of F and evaluating its surface integral over the surface S bounded by C.

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Related Questions

A model for the population P(t) in a suburb of a large city is given by the intial value problem
dP/dt = P(10^-1 - 10^-7P), P(0) = 7000;
where t is measured in months. What is the limiting value of the population?

Answers

The limiting value of the population is 10^(-6).

To find the limiting value of the population, we need to analyze the behavior of the population model as time (t) approaches infinity. In this case, the limiting value represents the maximum population that the suburb can sustain in the long run.

We can start by setting up the differential equation dP/dt = P(10^(-1) - 10^(-7)P) and solving it for equilibrium points, where the population growth rate is zero.

At equilibrium, dP/dt = 0, so we have P(10^(-1) - 10^(-7)P) = 0.

This equation gives us two possible solutions: P = 0 or 10^(-1) - 10^(-7)P = 0.

Solving the second equation for P, we get 10^(-1) - 10^(-7)P = 0, which leads to P = 10^(-6).

Now, we need to determine whether these equilibrium points are stable or not. To do that, we can analyze the sign of the derivative dP/dt around each equilibrium point.

For P = 0, dP/dt = P(10^(-1) - 10^(-7)P) = 0, indicating that the population remains constant at zero. This is an unstable equilibrium.

For P = 10^(-6), dP/dt = P(10^(-1) - 10^(-7)P) < 0, meaning that the population decreases over time and approaches the equilibrium point of P = 10^(-6). This is a stable equilibrium.

Given that the initial population P(0) = 7000, which is larger than the limiting value of P = 10^(-6), the limiting value of the population in the long run is 10^(-6).

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Suppose that y varies directly with x and inversely with z, and y = 6 when x = 8 and z = 4. Write the equation that models the relationship. Then find y when x = 2 and z = 3

Answers

Answer:

y=18

Step-by-step explanation:

explanation is in the attachment above

Suppose that y varies directly with x and inversely with z, and y = 6 when x = 8 and z = 4. Write the

5. What is "Data Triangulation" in general? Give 2 real-world examples.

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Data triangulation is a research method that involves using multiple data sources or methods to gather and analyze information, enhancing the validity and comprehensiveness of findings.

Data triangulation is a research method that involves using multiple sources or methods to gather and analyze data on a particular topic or research question. By combining different data sources, researchers aim to enhance the validity, reliability, and comprehensiveness of their findings.

Two real-world examples of data triangulation are:

Qualitative-Quantitative Triangulation in Market Research: In market research, qualitative methods like focus groups or interviews can be combined with quantitative methods like surveys or sales data analysis. By triangulating these data sources, researchers can gain a deeper understanding of consumer preferences, behaviors, and market trends, combining the richness of qualitative insights with the statistical power of quantitative data.Methodological Triangulation in Educational Research: In educational research, methodological triangulation can be employed by using multiple research methods to investigate a learning phenomenon. For example, a researcher may use classroom observations, interviews with teachers, and student performance data to gain a comprehensive understanding of a teaching strategy's effectiveness. By triangulating these data sources, the researcher can capture a more complete picture of the learning environment and draw robust conclusions.

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Select the correct answer. jessica has 12.7 moles of a compound for an experiment. how many particles of the compound does she have? a. 2.11 Ã— 1023 b. 4.74 Ã— 1023 c. 7.65 Ã— 1023 d. 4.74 Ã— 1024 e. 7.65 Ã— 1024

Answers

The 12.7 moles of a compound contain 7.65 x 10 24 particles.

Avogadro's number is the number of units, which could be atoms, particles, electrons, molecules, or even ions, per mole of a substance. The value of Avogadro's number is 6.02214076 x 10 23.

To answer this question, we will multiply the given moles of the compound to Avogadro's number, which will have a unit of particles/mol.

Number of particles of given compound = number of moles * Avogadro's number in particles/mol = 12.7 moles * 6.02214076 x 10 23 particles/moles

Number of particles of given compound = 7.65 x 10 24 particles

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How do u solve 3/8+1/8-2/7+1/4

Answers

Answer:

13/28

Step-by-step explanation:

using pemdas we can determine that the equation is directly solves from left to right

first

we have

3/8 + 1/8

which is 4/8

you can simplify this to 1/2

then you have 1/2 - 2/7

you must make them have the same numerator

you can multiple 1/2 by 7/7 and 2/7 by 2/2

7/14 - 4/14 = 3/14

now you must add 3/14 and 1/4

but you to make them have the same numerator

so you multiply 3/14 by 2/2 and 1/4 by 7/7

6/28 + 7/28 = 13/28

that is your final answer

Please help!!! WILL MARK U THE BRAINLIEST OR WHATEVER ITS CALLED

Answers

Answer:

584

Step-by-step explanation:

Hope this helps

584 ok?? I am just guessing

Here is Diya's work writing the expression 6 - 2x + 5 + 4x with fewer terms. Describe the mistake that Diya made.

Diya's Work
6- 2x + 5 + 4x
4x +
9x
13x Write an expression equivalent to 6 - 2x + 5 + 4x that has two terms.

Answers

Answer:

Below.

Step-by-step explanation:

This is the correct solution:

6 - 2x + 5 + 4x

= -2x + 4x + 6 + 5

= 2x + 11.

It looks like they added unlike terms together (4x + 5) to give 9x (incorrect) then added the 4x to give 13x.

An angle measures eleven more than four times a number. Its compliment is
two more than three times the number. What is the measure of each angle?

Answers

Answer:

35 and 55 degrees

Step-by-step explanation:

Let's use n for the number

Angle 1 = 4n+11

Angle 2 = 3n+2

Since it states that these angles are complimentary, they add up to 90 degrees

So we can write an equation using what is given.

Angle 1 + Angle 2 = 90

4n+11+3n+2 = 90

Combine like terms

7n+13 = 90

Subtract 13 from each side

7n = 77

n = 11

Now we plug eleven in for n and solve for the measure of each angle.

Angle 1 = 4(11)+11

Angle 1 = 44+11

Angle 1 = 55

Angle 2 = 3(11)+2

Angle 2 = 33+2

Angle 2 = 35

A hospital has to be patrolled by security guards 24 hours a day. Seven security guards are ordered to split each day’s guard duty equally. How long will each security guard spend on guard duty in one day? Record your answer in hours rounded to the nearest tenth.

Answers

Answer:

3 hours

Step-by-step explanation:

24/7 = 3.42 hours and rounded that will be 3 hours

on weekends a movie ticket costs $10.50. form an inequality and solve it to find the maximum umber of tickets kate can buy with $205

Answers

Answer:

kate can buy 20 tickets

Step-by-step explanation:

hope this helps

i am not sure about the answer

Answer:
10.50x ≤ 205
The maximum number of tickets, x, would be 19.
Step-by-step explanation:
Given,
The cost of one ticket = $ 10.50,
The cost of x tickets = 10.50x dollars,
Since, the total cost can not exceed $ 205,
⇒ 10.50x ≤ 205
∵ 10.50 > 0 thus, when we multiply both sides by 1/10.50 the inequality sign will not change,
⇒ x ≤ ≈ 19.52
Hence, the maximum number of tickets would be 19.

there are 4 people i steven's family there shoe size is 6,8,10 and 10 find the range.modal and the median

Answers

Answer:

Below

Step-by-step explanation:

6, 8, 10, 10

Mode = 10

Median = 9

range is 4 because 10-6=4

What is the hcf of 124

Answers

Answer:

Step-by-step explanation:

You're answr is 2
have a great day

Solve the following formula for the specified variable.

B =1/2m(r + k) for r

Answers

Answer:

(2B/m) - k = r

Step-by-step explanation:

B =1/2m(r + k)

Multiply each side by 2

2B =m(r + k)

Divide each side by m

2B/m = m/m (r+k)

2B/m =(r+k)

Subtract k from each side

(2B/m) - k = r+k-k

(2B/m) - k = r

Four equal pipes are to be laid end to end under a street. If they were each three feet shorter, they would cover the exact length of the street. On the other hand, if they were each two feet longer, three pipes would be enough for that street. This situation can be expressed as:4(x−3)=3(x+2)What does the variable x represent? Select all that apply.Athe length of each pipeBthe length of the streetCthe length of the four pipesDthe length of four pipes minus 12 feetEone fourth of the length of the street plus three feet

Answers

the length of each pipe

help need plzzzzzzzzz

Answers

Answer:

The answer to the question provided is possibly 2.

Step-by-step explanation:

$ \: \: \: \: \: \: \: \: \: \: \: \: 3y + 77 = 2y + 79 \\ \frac{ - 2y \: \: \: \: \: \: = - 2y}{1y + 77 = 79} \\ \frac{ \: \: \: \: \: \: \: \: - 77 = - 77}{ \frac{1y}{1} = \frac{2}{1} } \\ \\ y = 2$

Please help me solve this question!

Answers

I hope you get right answer.

Pu in order answer show work I’ll give brainliest and 50 pnts

Answers

Answer:

1) no, it is not a right triangle. 3² + 4² ≠ 25²

2) no, it is not a right triangle. 38² + 77² ≠ 86²

3) no, it is not a right triangle. 10² + 36² ≠ 37²

4) yes, it is a right triangle. 30² + 40² = 50²

5) yes, it is a right triangle. 8² + 15² = 17²

6) yes, it is a right triangle. 18² + 24² = 30²

7) no, it is not a right triangle. 5.3² + 7.9² ≠ 8.1²

8) yes, it is a right triangle. 10² + 24² = 26²

What is the domain? I need help on this problem

Answers

The domain of the function $f(x) = \sqrt{\frac{1}{3}x + 2$ is (d) x ≥ -6

How to determine the domain of the function

From the question, we have the following parameters that can be used in our computation:

$f(x) = \sqrt{\frac{1}{3}x + 2$

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x ≥ -2

So, we have

x ≥ -6

Hence, the domain of the function is (d) x ≥ -6

Answers

Answer:

The answer would be B one solution

Hope this helps

1. you are fishing for trout and bass. gaming laws allow you to catch no more than 15 trout per day, no more than 10 bass per day, and no more than 20 total fish per day. can you catch 11 trout and 9 bass? why or why not?

Answers

toLet the number of trout = x

And the number of bass = y

gaming laws allow you to catch no more than 15 trout per day, no more than 10 basses per day.

So,

$\begin{gathered} x\le15 \\ y\le10 \end{gathered}$

And no more than 20 total fish per day

So,

$x+y\le20$

We will check if you can catch 11 trout and 9 bass

So, x = 11 and y = 9

So, 11 < 15

and 9 < 10

And (11+9) = 20

so, the answer of the question will be Yes

Because 11 trout and 9 basses are achieving the previous inequalitues.

Copy Central prints black and white or colored copies. Yesterday, they printed 9 black and white copies for every 5 colored copies. If they printed 200 color copies, then how many black and white copies were printed

Answers

Answer:

360

Step-by-step explanation:

ok sooo If 9 were black and white them there were 5 for colored so you do 200/5 so you can figure out what to multiple with the black and white. So 200/5 = 40 then you do 9 * 40 = 360. Sorry if this does not make sense.

the width of a rectangle is 2 less than twice its length. if the area of the rectangle is 143 cm 2 , what is the length of the diagonal?

Answers

The length of the diagonal of rectangle is 17.521 cm.

Diagonal of rectangle:

A diagonal of a rectangle is a line segment that connects two non-adjacent vertices. In the following rectangle, AC and BD are diagonals. We can see that AC and BD have the same length. A diagonal divides a rectangle into two right triangles. where the sides are equal to the sides and the hypotenuse of the rectangle. This hypotenuse is the diagonal. In the following rectangle, AC and BD are diagonals. AC and BD have the same length.

The width of a rectangle is 4 less than twice its length

W = 2L - 2

Area of the rectangle is 161 cm2

LW = 143 cm²

L(2L- 4) = 143

2L² - 4L - 143 = 0

We can find L using the quadratic equation:

L = [-b ±√(b2-4ac)]/2a ,

a=2, b=-4, c = -143

⇒ L = [4 ±√((-4)2-4(2)(-143))]/2(2)

⇒ L = [4 ±√(1128)]/4

⇒ L = (4 ± 33.58)/4

⇒ L = 9.395 cm or L = -29.58 cm

Discarding the negative, the length is 9.395 cm

W = 2L- 2 = 18.79 - 4 = 14.79 cm

The rectangle is 9.395 cm by 14.79 cm

These will make up the lengths of the legs of a right triangle with the diagonal as hypotenuse

Using the Pythagorean theorem:

a²+ b² = c²

(9.395)² + (14.79)² = c²

88.266 + 218.744 = c²

307.01 = c²

c = √307.01

c = 17.521 cm

The diagonal is approximately 17.521 cm

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how to solve for examples of nonlevel annuities for which the payments for a pattern that is neither geometric nor arithmetic

Answers

The formula that is used to solve for examples of nonlevel annuities for which the payments for a pattern that is neither geometric nor arithmetic is explained below .

In order to solve for the present value or future value of a non-level annuity with payments that do not follow a geometric or arithmetic pattern, We use the formula for the present value or future value of an annuity that has varying payments:

⇒ PV = P₁/(1+r)¹ + P₂/(1+r)² + ... + Pₙ/(1+r)ⁿ

and

⇒ FV = P₁×(1+r)ⁿ⁻¹/(1+r)¹ + P₂×(1+r)ⁿ⁻²/(1+r)² + ... + Pₙ/(1+r)ⁿ

Where : PV = present value of the annuity

FV = future value of the annuity

P₁, P₂, ..., Pₙ = the payments for each period

r = the interest rate per period

n = the number of periods .

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What is the factored form of 2x2 + 20x + 50? (1 point) 2(x + 5)(x-4) 2(x - 5)(x + 4) 2(x + 5)2 2(x + 5)(x - 5)

Answers

Answer:

Hope it can help you.....Mark me as a brainlist...

What is the factored form of 2x2 + 20x + 50? (1 point) 2(x + 5)(x-4) 2(x - 5)(x + 4) 2(x + 5)2 2(x +

Someone help me please-

Answers

Answer:

Rectangle 11.59 sqft

Rectangle 36 sqft

Polygon 47.59 sqft

Step-by-step explanation:

13)There are 20 students in a class. 5 of
those students are women. What percent
are women?

Answers

Answer:25%

Step-by-step explanation: 20 in this situation is 100% and 5 is 1/4 of 20 witch is equal to 25%

answer: 25% are women
why?
because if you have 20 people divided 4 you get 5, so 100 divided 4 is 25

Find the area of the circle with a diameter of 12 m.
a 95.64 m2
b 112.27 m2
C 113.04 m2
d 210.36 m2

Answers

Answer:

113.04 is our answer

Step-by-step explanation:

When finding Area the formula to do so is

radius x radius x pi

Sense we arent given radius we have to find out whats the radius but we must remember radius is just half of the diameter so since we are given diameter we will just do diameter divided by 2 so 12 ÷ 2 = 6 now that we have are radius we square it thats just a fancy way of saying multiply by itself so 6 x 6 = 36 now we multiply 36 with 3.14 So

3.14 x 36 = 113.04 So c is our answer!

HELP ME AGAIN [GIVING BRAINLIEST TO BEST ANSWER]

Answers

Answer:

160 yards

Step-by-step explanation:

The answer would be 160 yards because you add 100 and 60. The reason you add these is because added together would equal the distance.

f is inversely proportional to √ g . When f = 10 , g = 121 Work out g when f = 11

Answers

Answer:

Hope the attached helps!

Step-by-step explanation:

f is inversely proportional to g . When f = 10 , g = 121 Work out g when f = 11

How many millimetres are there in 7.4 centimetres?

Answers

there are 74 millimeters

Answer:

Step-by-step explanaction

Formula=multiply the length value by 10

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