DETAILS SESSCALCET2 13.7.501 XP. MY NOTES PRACTICE ANOTH Evaluate the surface integral F.cs for the given vector field F and the oriented surface S. In other words, find the flux of Facross S. For closed surfaces, use the positive (outward) orientation F(x, y, 2) - y9k S is the boundary of the region enclosed by the cylinder * +22.1 and the planes y = 0 and x + y = 8

Answers

Answer 1

The flux of F across S is 1/4.

The given vector field F is

F(x,y,z) = (x, -y, 0).

The surface S is the boundary of the region enclosed by the cylinder * +22.1 and the planes

y = 0

and

x + y = 8.

For closed surfaces, we use the positive (outward) orientation.

Here, the value of z is 2.

We are supposed to evaluate the surface integral F.cs for the given vector field F and the oriented surface S.

In other words, we need to find the flux of F across S.

To evaluate the surface integral, we first need to find a unit normal vector n to the surface S, and then we need to find the dot product of F and n over the surface S.

The outward unit normal vector to the surface S is given by the cross product of the gradient of the function

g(x,y,z) = y:

grad g(x,y,z)

= (-∂g/∂x, -∂g/∂y, 1)

= (0, -1, 1).

Therefore,

n = (0, -1, 1)/√2

is the unit normal vector to the surface S.Over the surface S, we have

x² + y² = 22.1

and

0 ≤ y ≤ 8 - x.

Using the parameterization

x = r cos θ,

y = r sin θ,

z = z we have:

r = √(22.1)sin θ

and

0 ≤ θ ≤ π.

Hence, we have:

x = √(22.1)sin θ cos θ,

y = r sin θ = √(22.1)sin²θ,

z = 8 - x - y = 8 - √(22.1)sin θ (cos θ + sin θ).

Therefore,

F(x,y,z) = (x, -y, 0)

= (√(22.1)sin θ cos θ,

-√(22.1)sin²θ, 0).

We also have

n = (0, -1, 1)/√2 = (0, -√2/2, √2/2).

Hence,

F . n = [√(22.1)sin θ cos θ](0) + [-√(22.1)sin²θ](-√2/2) + (0)(√2/2)

= √(22.1)sin²θ/√2.

Using the formula for the flux integral, we have:

Flux of F across

S = ∫∫S F . n dS

= ∫₀²π ∫₀√(22.1) sin θ [(√(22.1)sin²θ/√2) dθ dr

= (1/2) ∫₀²π [∫₀√(22.1)sin θ (√(22.1)sin²θ) dr] dθ

= (1/2) ∫₀²π (√(22.1)sin³θ) dθ

= -[(1/4) cos 4θ]₀²π

= 1/4.

Therefore, the flux of F across S is 1/4.

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Related Questions

I need this today
pls help

I need this today pls help

Answers

Answer:

5. radius= TD

inscribed angle =RQS

diameter =TA

6. radius=SY

secant=TU

Tangent=S

A function is defined by f (x) = 6 x + 1.5. What is f(2.5)?

Answers

Step-by-step explanation:

6×(2.5)+1.5

15+1.5

16.5

or

f(x)= 6x+1.5

f(2.5)= 6(2.5)+15

f(2.5)=16.5

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the mathcounts international airport had 738,114 departures in 2001. if these were distributed uniformly throughout each 24-hour period, what is the mean number of seconds between each departure time? express your answer to the nearest whole number.

Answers

The MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.

For given question,

In 2001 there were 738,114 departures.

As we can see, 2001 was not a leap year.

So, the number of days in 2001 = 365

We find the number of departures per day in 2001.

738,114 / 365 = 2,022.23

So, approximately 2,022 departures per day.

Now we find the number of departures in an hour.

2,022 / 24 = 84.25

This means, approximately 84 departures per hour

We know that, 1 hour = 3,600 seconds

Now we find the mean number of seconds between departure time.

3,600 / 84 = 42.8

                  ≈ 43 seconds

Therefore, the MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.

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I need help with this. It's due tommorow

I need help with this. It's due tommorow

Answers

The total amount of cheese used in all the recipes is 29 3/4 cups.

Given is line plot we need to find the amount of cheese used in all the recipe,

so, 3 1/2 cups are used for one time, 3 3/4 used for 6 times and 4 cups are used for 1.

So,

3 1/4 + 3 3/4 × 6 + 4

= 13/4 + 15/4 × 6 + 4

= (13 + 90 + 16) / 4

= 119 / 4

= 29 3/4

Hence, the total amount of cheese used in all the recipes is 29 3/4 cups.

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Helppp!!!! please!!!

Helppp!!!! please!!!

Answers

Answer:

A) 120 ft^2

Step-by-step explanation:

The total surface area is the sum of the areas of the 4 congruent triangular sides and the area of the square base.

TA = 4 * area of triangle + area of square

TA = 4 * bh/2 + s^2

TA = 4 * 6 ft * 7 ft/2 + (6 ft)^2

TA = 84 ft^2 + 36 ft^2

TA = 120 ft^2

Answer:

A) 120 ft^2

Step-by-step explanation:

Para repartir en partes iguales 5 alfajores entre 3 niñas y niños,sin que sobre nada,ana dibujo todos los alfajores y "corto" cada uno en 3 partes igualdad. Despues,indico que le corresponde 1/3 de cada alfajor para cada niña y niño recibe 5 pedacitos de 1/3 de alfajor,es décir 5/3. Departing 7 alfajore entre 4 niñas y niños de manera que todos reciban lo mismo y no quede nada sin repartir

Answers

Answer:

Para compartir 7 alfajores entre 4 niños y niñas para que no quede nada, a cada niño y niña se les debe dar 7/4 alfajores

Step-by-step explanation:

Al compartir 5 alfajores, entre 3 niños y niñas, los alfajores se cortan en tres partes cada uno de manera que cada niño y niña recibe 5/3 piezas de alfajore

Luego, la pregunta es, ¿cómo se pueden compartir 7 alfajores entre 4 niñas y niños sin que quede nada?

Por el proceso de compartir ejemplos, obtenemos;

Cada alfajores debe dividirse en el número total de niños y niñas, que son cuatro piezas cada uno.

El número total de 1/4 piezas = 7 × 4 = 28 piezas de 1/4 alfajores

Cada niño y niña recibe 7 de las piezas de 1/4 alfajores

El número total de alfajores, n, compartidos entre los cuatro niños y niñas viene dado por la expresión;

n = 7 (1/4 alfajores) × 4 = 28 piezas de 1/4 alfajores

Por lo tanto, para compartir 7 alfajores entre 4 niños y niñas para que no quede nada, cada niño y niña debe recibir 7/4 alfajores.

Which of these is not a variable term found in the binomial expansion of (a + b)8? (ignore coefficients. ) a7b a3b5 ab6 b8.

Answers

ab⁶ is not a variable term found in the binomial expansion of \((a + b)^{8}\)as this is because, the powers must sum up to 8

What is binomial expansion?

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

The Binomial Expansion of \((a+b)^8\) is -

\((a + b)^8 = a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a3^b^5 + 28a^2b^6 + 8ab^7 + b^8.\)

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Answer:

9

C

D

Step-by-step explanation:

If measure angle 7 , recall that alternate interior angles have equal measures. Thus , the measures of angle is 65 degree. What is the measure of angle 9 degree?

Answers

Answer:

Angle 9 = 65°

Step-by-step explanation:

Given:

Angle 7 = 65°

Angle 7 is alternate to Angle 9

Find:

Angle 9

Computation:

We know that

alternate interior angles are equal and angle 7 is alternate to angle 9

So,

Angle 7 = Angle 9

So,

Angle 9 = 65°

if 8 adult smartphone users are randomly selcted, find the probabailty that exactly 6 of them use their

Answers

The probability that exactly 6 of the 8 adult smartphone users will use their smartphones is 0.004419921875.

How to find probability?

If 8 adult smartphone users are randomly selected, the probability that exactly 6 of them use their smartphones is calculated as follows:

P(6) = C(8,6) × (0.75)^6 × (0.25)^2P(6) = 28 × 0.1779785 × 0.0625P(6) = 0.3125P(6) = 0.004419921875

The probability that exactly 6 of the 8 adult smartphone users will use their smartphones is 0.004419921875.

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Ellie took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.50 plus $5 per mile. The total fare was $76.50, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.

Answers

Answer:

15 miles

Step-by-step explanation:

5 = price per mile   x= number of miles   1.5 = pick-up fee   76.5 = total  

5x + 1.5 = 76.5

5x = 76.5 - 1.5

5x = 75

x =75/ 5

x = 15

which fraction represents 35%

Answers

Answer:

7/20

Step-by-step explanation:

Answer:7/10

Step-by-step explanation:

Here is the way that I think is the simplest method of changing a percentage a fraction. This percentage has two digits in it, so put it over a 1 and two zeros and then simplify. 35/100 is simplified to 7/20.

Examine the equation.

–2(–x + 9) = 2(x – 9)

2x – 18 = 2x – 18

This equation has .

Answers

Answer:

B

Step-by-step explanation:

I took the Assignment

Examine the equation.2(x + 9) = 2(x 9)2x 18 = 2x 18This equation has .

Answer:

b

Step-by-step explanation:

a local bbq restaurants offers 2 side dishes with a lunch plate. there are 7 side dishes. how many choices of side dishes does a customer have? note: there is no requirement that the customer chooses different side dishes (i.e. he or she can choose say baked beans twice as their side dish).

Answers

The number of choice out of 7 that consumer have are 42.

What is permutation?

The term permutation alludes to a numerical computation of the quantity of ways a specific set can be sorted out. Set forth plainly, a change is a word that depicts the quantity of ways things can be requested or organized. With stages, the request for the course of action matters.

According to given data:

Number of choices of side dishes does a customer have,

total dishes(n)=7 , r = 2

ⁿP₂

⁷P₂

7×6 = 42

Thus required number of ways are 42.

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Need help please can you answer it how the question is telling you

Need help please can you answer it how the question is telling you

Answers

Answer:

243 m³

Step-by-step explanation:

The volume of a rectangular pyramid is given by:

\(V = \frac13lwh\)

Where

l = length = 9m

w = width = 9m

h = height = 9m

so the volume is 1/3*9*9*9 = 243 m³

Answer:

243

Step-by-step explanation:

The formula for the volume of a square-based pyramid is

\(V=\frac{lwh}{3}\)

\(l\) = length

\(w\) = width

\(h\) = height

\(V=\frac{9 \times 9 \times 9}{3}\)

\(V=\frac{729}{3}\)

\(V=243\)

The area is 243 cubic meters.

Last week, Akira spent 5 hours doing homework. Brendan did homework for 3/4 as many
hours as Akira did. How many hours did Brendan spend doing homework?
Write your answer as a fraction or as a whole or mixed number.
hours
Submit

Answers

Answer:

3 hours 45 minutes.

Step-by-step explanation: 5 hours is 300 minutes. 3/4 of 300 is 225 minutes. 225 minutes is 3 hours 45 minutes. BAM

Also brainly would be great

can someone please help me! ASAP!! ​

can someone please help me! ASAP!!

Answers

Answer:

5 to the power of 2

Step-by-step explanation:

What’s the answers to these

Whats the answers to these
Whats the answers to these

Answers

Evaluating the algebraic expressions for the values given, we have:

a. -7

b. -10.

How to Evaluate an Algebraic Expression?

To evaluate and algebraic expression, plug in the value of the variable given and solve accordingly.

a. Given the algebraic expression, xy + 5.

If x = 2, and y = -6, then substitute x = 2 and y = -6 to evaluate the algebraic expression:

xy + 5

(2)(-6) + 5 [substitution]

= -12 + 5

= -7

b. Given the algebraic expression, x/y - 12, if x = 22 and y = 11, then substitute x = 22 and y = 11 into the expression and evaluate:

x/y - 12

22/11 - 12 [substitution]

= 2 - 12

= -10.

Thus, the values of the expressions when evaluated for the given variables are:

a. -7

b. -10.

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Find a formula for the nth term of the arithmetic sequence:
First Term -2
Common Diff. 8
=?

Answers

Answer:

Tn=a+(n-1)d

Tn=-2+(n-1)8

Tn=-2+8n-8

Tn=8n-10

Find the distance between the points. (2,3) and (-3,-6)

Answers

Answer:

D = 10.3

Step-by-step explanation:

Distance Formula = √(x₂-x₁)² + (y₂-y₁)²

D = \(\sqrt{(-3-2)^2 + (-6-3)^2}\)

D = \(\sqrt{(-5)^2+(-9)^2}\)

D = \(\sqrt{25+81}\)

D = \(\sqrt{106}\)

D = 10.3

A roll of paper is L m long. N pieces each of length rm are cut off the roll. If the length of paper left is Pm, write a formula for P. Use your formula to find the length of paper left from a roll that was 20 m long after 10 pieces, each of length 1.5 m, are cut off. idor each of length asm. If the perimeter ​

Answers

Length of paper left is 5 m.

What is length?

Distance is measured by length. Length is a quantity having the dimension distance in the International System of Quantities. Most measuring systems use a base unit for length from which all other units are derived. The metre is the basic unit of length in the International System of Units (SI). The greatest extended dimension of a stationary item is typically believed to be its length. This is not always the case, as it may depend on the location of the item. Height, sometimes known as vertical length or vertical extent, and width, breadth, or depth are all words used to describe the length of a stationary object. When length is the longest dimension, width or breadth generally refer to the shorter one.

Length of paper left = 20-(1.5x10) = 20-15 = 5 m.

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What 7÷56+3 I'm boreeeddxxxxxxxxx

Answers

Answer:

The answer is 3.125.

Answer:

It's 3.125

Step-by-step explanation:

Hope this help lol

I NEED HELP ASAP! Please lol

Show work: Lana makes $42,000 and is getting monthly raises of $500. Jason makes
$60,000, with monthly raises of $200. How many months, x, will it take for Lana and
Jason to make the same salary? How much will it be?

Answers

Answer:

39 months later

Step-by-step explanation:

or it is very close to that

Sarah is paid $20 an hour at her new job. She wishes to graph her total pay y, as a function of the
number of hours, x. She wants to be sure her graph shows her pay for 10 and 20 hours of work.

Answers

Answer:

see image; 200; 400

Step-by-step explanation:

y=20x

graph

Sarah is paid $20 an hour at her new job. She wishes to graph her total pay y, as a function of thenumber

suppose researchers marked 800 turtles and later were able to trap a total of 300 individuals in that population, of which 200 were marked. what is the estimate for total population size?

Answers

Using Marked recapature formula for estimation on population size we get,

the estimate for total population size is 1200.

Marked recaputure Method :

first step is to capture and mark a sample of individuals. The assumption behind mark-recapture methods is that the proportion of marked individuals recaptured in the second sample represents the proportion of marked individuals in the population as a whole. In algebraic terms,

R/S = M/N

where R --> second time marked

S---> size of sample second time

N --> estimate population size

M ---> Marked in start point

We have given that ,

Total marked turtles by researchers (M) = 800

Second time total sample size (S) = 300

second time marked turtles(R) = 200

we have to find out estimate for total population size .

For this , Mark -Recapture method is very efficient to calculate estimate for total population size.

putting all known values in above formula we get, R/S = N/M

=> 200/300 = 800/N

=> 800× 300 = N× 200

=> N × 200 = 240000

=> N = 240000/200

=> N = 1200

so, the estimate for total population size is 1200.

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Oriah ate 5 out of 7 pieces of his pizza. What percentage of pizza is that? (can you solve this 2 ways?)

Answers

Answer;

71.43%

Explanation:

Given

Total pizza = 7 pizzas

Amount of pizza Oriah ate = 5 pizzas

percentage of the amount ate = Amount ate/Total pizza * 100

percentage of the amount ate = 5/7 * 100

percentage of the amount ate = 500/7

percentage of the amount ate = 71.43%

Hence the percentage Orian ate is 71.43%

What are 3 of the 6 essential principles in Jefferson's Inaugural Address ?

brainliest if u get it right

Answers

Step-by-step explanation:

above guy is right. i donot about this.sorry and thanks.

Samantha drives 4.2 miles each workday. How
far will Samantha drive after 18 workdays?

Answers

Answer:

75.6 miles

Step-by-step explanation:

Multiply 4.2 by 18

please help me please

please help me please

Answers

Answer:

Heres the answer Hope this helps!:)

please help me please

A sample is taken and the mean, median, and mode are all the same value. What is a correct conclusion the researcher could make here? A. The mean can be reported since the data is nearly symmetrical B. The researcher can be 100% sure that the actual population mean is the same as the sample mean C. A computational error must have been made because the mean, median, and mode cannot all be the same value D. A larger sample must be taken since the mean, median, and mode are only the same in smail data sets and small data sets may be inaccurate

Answers

If the mean, median, and mode of a sample are all the same value, it suggests that the data is likely symmetrical and the mode is the most frequent value.

it does not necessarily imply that the researcher can be 100% sure about the population mean or that a computational error has occurred. A larger sample size may not be required solely based on the equality of mean, median, and mode in small datasets.

Explanation:

The fact that the mean, median, and mode are all the same value in a sample indicates that the data is symmetrically distributed. This symmetry suggests that the data has a balanced distribution, where values are equally distributed on both sides of the central tendency. This information can be helpful in understanding the shape of the data distribution.

However, it is important to note that the equality of mean, median, and mode does not guarantee that the researcher can be 100% certain about the population mean. The sample mean provides an estimate of the population mean, but there is always a degree of uncertainty associated with it. To make a definitive conclusion about the population mean, additional statistical techniques, such as hypothesis testing and confidence intervals, would need to be employed.

Option C, stating that a computational error must have been made, is an incorrect conclusion to draw solely based on the equality of mean, median, and mode. It is possible for these measures to coincide in certain cases, particularly when the data is symmetrically distributed.

Option D, suggesting that a larger sample must be taken, is not necessarily warranted simply because the mean, median, and mode are the same in small datasets. The equality of these measures does not inherently indicate that the data is inaccurate or that a larger sample is required. The decision to increase the sample size should be based on other considerations, such as the desired level of precision or the need to generalize the findings to the population.

Therefore, option A is the most appropriate conclusion. It acknowledges the symmetrical nature of the data while recognizing that the mean can be reported but with an understanding of the associated uncertainty.

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it says to determine the scale factor and center of dilation that will carry ABCD onto A’B’C’D’ please help im stuck

it says to determine the scale factor and center of dilation that will carry ABCD onto ABCD please help

Answers

Answer:

3/2

Step-by-step explanation:

\(A'B'=6, AB=4\)

The scale factor is the ratio of the lengths of a pair of corresponding sides. (image to preimage).

Thus, the scale factor is \(6/4=3/2\).

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