Let D = D(R), where Þ(u, v) = (u², u + v) and
R = [1, 8] × [0, 6].
Calculate
y dA.
Note: It is not necessary to describe D.
Joyda
=

Let D = D(R), Where (u, V) = (u, U + V) AndR = [1, 8] [0, 6].Calculatey DA.Note: It Is Not Necessary

Answers

Answer 1

The region [tex]D[/tex] is essentially parameterized in three dimensions by

[tex]\Phi(u,v) = (u^2, u+v, 0)[/tex]

with [tex]1\le u\le8[/tex] and [tex]0\le v\le6[/tex].

The normal vector to [tex]D[/tex] is

[tex]\vec n = \dfrac{\partial\Phi}{\partial u} \times \dfrac{\partial\Phi}{\partial v} = (0,0,2u)[/tex]

with norm [tex]\|\vec n\| = 2u[/tex].

Then the surface integral is

[tex]\displaystyle \iint_D y \, dA = 2 \int_0^6 \int_1^8 (u+v)u \, du \, dv \\\\ = 2 \int_0^6 \left(\frac{1022}3 + 63 v\right) \, dv = \boxed{3178}[/tex]


Related Questions

What division problem does this area model represent?

Answers

Answer:

2,160 ÷ 36 = 60

Step-by-step explanation:

The division problem that this area model represents is,

2,160 ÷ 36 = 60

23.4571 to the nearest 10

Answers

23.4571 to the nearest 10

asnwer: 23.5

Can someone solve this eq (integration)


I did it but the answer I got is different to what my textbook says

Answers

Answer:

I hope you can help

find the midpoint of the line segment between the points (11, -5) and (-3, -7)

Answers

Answer:

(4, -6)

Step-by-step explanation:

(x1+x2)/2 + (y1+y2)/2 = midpoint

(11+-3)/2 = 8/2 = 4.     x = 4

(-5 + -7)/2 = -12/2.      y = -6

4, -6 is the midpoint

give brainliest please! hope this helps :)

a puppy weighs 1 pound. what does the puppy weigh after 4 weeks​

Answers

i think it would be around 7 lbs
(i could be wrong but i think this is about right)

the mean of the data set is 18. what number is missing? 21,11,_,27,22,13,16

Answers

The missing number given the mean of the data set is 16.

What is the missing number?

Mean is the average of a data set. It is determined by adding all the numbers in the data set and dividing the sum by the numbers in the data set.

Missing number = (mean x total number in the data set) - sum of numbers in the data set

(18 x 7) - ( 21 + 11 + 27 + 22 + 13 + 16)

126 - 110

= 16

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Solve the system of equations
−5x−3y=−28 and x+2y=0 by combining the equations

Answers

Answer: (8, -4)

Step-by-step explanation:

-5x - 3y = -28
  x + 2y = 0

1. Multiply both sides of the bottom system by 5 to cancel the x out

   5(x+2y=0)

   5x + 10y = 0

2. rewrite

   -5x - 3y = -28

    5x + 10y = 0

3. add

   0x + 7y = -28

4. divide by 7

   7y = -28

5. y = -4

6. plug in -4 for y in one of the original equations

   x + 2(-4) = 0

7. simplify

   x = 8

9. solution is

   (8, -4)

(07.03 MC)

Victoria used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:


Color of
Marble Number of
Times Rolled
Blue
18
Green
20
Yellow
12


Heads Tails
20 30


Using Victoria's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
48 over 50
38 over 50
540 over 2500
360 over 2500

Answers

The probability of pulling a blue marble and the coin landing tails up is 360/2500

How to determine the probability?

The tables of values are given as:

Color     Times

Blue        18

Green     20

Yellow    12

Heads    Tails

20          30

The probability of obtaining a blue marble is:

P(Blue) = 18/50

The probability of landing tails up is:

P(Tail) = 20/50

The required probability is:

P = P(Blue) * P(Tail)

This gives

P = 18/50 * 20/50

Evaluate the product

P = 360/2500

Hence, the probability of pulling a blue marble and the coin landing tails up is 360/2500

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13. Figure QRSP is a rectangle.
Q.
100°
What is the measure of angle RPS?
A. 40 degrees
C. 80 degrees
B. 50 degrees]

Answers

Answer:

b 50 degrees bavaggagshdd

which expresstion is equivalent to 22 - 3

Answers

Answer:

48-29

Step-by-step explanation:

22-3=19, so put on that makes 19.

Answer:

19 + 3(19 + 22) - 22(3 * 7) + 1

MEAN, MEDIAN AND MODE OF GROUPED DATA

Answers

See the attached files!!!!

Question 4 of 10
If ƒ(x) = 3(x+5) +−, what is f(a+2)?

Answers

[tex]f(x) = 3(x+5)\\\\f(a+2) = 3(a+2 +5) \\\\~~~~~~~~~~~~=3(a+7)\\\\~~~~~~~~~~~~=3a+21[/tex]

Samples of size n = 60 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the mean is taken for each sample. What is the distribution of the sample means?

Answers

The distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).

How is the sample explained?

Calculating the sample mean is as simple as adding up the number of items in a sample set and then dividing that sum by the number of items in the sample set.

Here, the distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).

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Simplify the following
(3a 2b ×2a 6b)

Answers

Answer:

3a 2b ×2a 6b = 72a²b² = 72× (ab)²

Step-by-step explanation:

3a 2b ×2a 6b = (3 × 2)×(a × b) × (2 × 6)×(a × b)   [commutative property]

                      = (6×ab) × (12×ab)  [associative property]

                      = (6×12) × (ab×ab)  [commutative + associative]

                      = (72) × (ab)²

                      = 72× (ab)²

                      = 72a²b²  [exponent property]

The measure of an exterior angle of a regular polygon is 45º. How many sides does the polygon have?

Answers

Answer:The answer is 8 sides

Step-by-step explanation:

Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the
following is true.
P(-C≤Z≤c)=0.9715
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Answers

Using the normal distribution, considering it's symmetry, it is found that the value of C is of 2.19.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The standard normal distribution has mean and standard deviation given, respectively, by:

[tex]\mu = 0, \sigma = 1[/tex].

Hence, considering the symmetry of the normal distribution, the value of c is Z with a p-value of (1 + 0.9715)/2 = 0.98575, hence c = Z = 2.19.

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4(x-5)-(6x + 1)= 2x -19

Answers

Answer:

Step-by-step explanation:

Comment

I take it you want the value for x.

Solution

4(x-5)-(6x + 1)= 2x -19                       Remove the Brackets.

4x - 20 - 6x - 1 = 2x - 19                   Combine like terms

-2x - 21 = 2x - 19                              Add 2x to both sides

-2x-21+2x = 2x + 2x - 19                  Combine

-21 = 4x - 19                                     Add 19 to both sides

-21+19 = 4x -19 + 19                          Combine like terms

-2 = 4x                                              Divide by 4

-2/4 = x

x = - 1/2

Answer: x = - 1/2

or x = -0.5

( PLEASE HELP WILL MARK BRAINLIEST PLEZ ) Calculate the area of a triangle with a base of 6 cm and a height of 12 cm. Draw and label the triangle.

Answers

Base=B=6cmHeight=H=12cm

Area

1/2BH1/2(6)(12)3(12)36cm²

Step-by-step explanation:

Base=6cm

Height=12cm

So,

1/2BH

= 1/2×6×12

= (3×12)

= 36 cm²

_________________________________

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Seven increased by the product of six and the number is 19

Answers

The number is that was multiplied by 6 is 2.

What is the number?

The equation that can be derived from the question is :

7 + (6a) = 19

Where a is the unknown number that 6 was multiplied with

Given the above equation, in order to determine the value of a, take the following steps:

Combine similar terms: 6a = 19 - 7

Subtract similar terms: 6a = 12

Divide both sides by 6: a = 12 / 6

a = 2

Here is the complete question:

Seven increased by the product of six and the number is 19. What is the number?

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6 x (3+2) divided by 10

Answers

It is letter c 10x r t

Nala wants to find out if the quadrilateral shown is a rectangle. Nala's plan: • Find the slopes of all four sides. • See if there are two pairs of equal slopes. • See if there are two pairs of slopes that are negative reciprocals. Will her plan work? Why or why not?

Answers

Checking if the two pairs of slopes are negative reciprocal will help he determine if the lines are perpendicular to each other. Therefore her plan will work.

Proof for a quadrilateral

A quadrilateral are shapes with 4 sides. A rectangle is a quadrilateral with 2 parallel sides.

According to Nala's plan to find out if the quadrilateral shown is a rectangle, she can do the following;

See if there are two pairs of equal slopesSee if there are two pairs of slopes that are negative reciprocal

Checking if the two pairs of slopes are negative reciprocal will help he determine if the lines are perpendicular to each other.  

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There are 10000 people living in a certain city. Suppose that the rate of population growth in the city is proportional to the number of inhabitants. Suppose that 10% of the original amount increase in 30 years, how much will the population in the city after 60 years?​

Answers

Answer:

.............30000.............

39. What is the value of x?

Answers

Answer:

x = 15

Step-by-step explanation:

the sum of the exterior angles of a polygon = 360°

sum the 5 exterior angles and equate to 360

5x + 3 + 4x + 8 + 5x + 5 + 6x - 1 + 3x = 360 , that is

23x + 15 = 360 ( subtract 15 from both sides )

23x = 345 ( divide both sides by 23 )

x = 15

a group of 20 students in four adults are going on a field trip to the museum What is the ratio of students to adults complete the statement.

Answers

Answer:

5:1

Step-by-step explanation:

Originally the ratio is 20:4

but then it is simplified to 10:2

then 5:1

please help me Im almost done​

Answers

Answer:

[tex]\mathsf {x = 76}[/tex]

Step-by-step explanation:

The given pair of angles lie on a line, hence they are classified as linear angles. They possess the property by which their sum is equal to 180°.

[tex]\textsf {Solving :}[/tex]

[tex]\implies \mathsf {x + 17 + 87 = 180}[/tex]

[tex]\implies \mathsf {x + 104 = 180}[/tex]

[tex]\implies \mathsf {x = 180 - 104}[/tex]

[tex]\implies \mathsf {x = 76}[/tex]

13 × (11 + 11) - (4 × 17) - 6 = X​

Answers

Answer: 212

Step-by-step explanation:

13 * 22 - 68 - 6 = X

286 - 68 - 6 = X

286 - 74 = X

X = 212

If a hot air balloon pilot inflates the balloon at an average wind speed of about 5 miles per hour with an altitude of 35,000 feet, how fast will the radius of the balloon increase as it goes up higher and higher performing certain tricks? Using the differentiation formula applicable for this situation, estimate the speed of inflation and the speed of landing. Will this be able to help the pilot still perform other tricks before making a colorful landing? Give at least two comprehensible reasons and explain your answer.​

Answers

700 is not to 100%sure

The speed of landing is 15.69 ft/sec.

What is differentiation ?

"Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.    

The three basic derivatives (D) are: (1) for algebraic functions, D(xn) = nxn − 1, in which n is any real number; (2) for trigonometric functions, D(sin x) = cos x and D(cos x) = −sin x; and (3) for exponential functions, D(ex) = ex."

Let the length of the rope = r

Height of the balloon = h

we are given dr/dt = 15ft/sec

at any time t we know:

[tex]r = 125 + 15*t[/tex]

By the Pythagoras theorem we know:

[tex]h^2 + 125^2 = r^2[/tex]

We have to find dh/dt at time t = 20 sec

[tex]d/dh(h^2 + 125^2) = d/dt(r^2)[/tex]

By chain rule:

[tex]d/dh(h^2 + 125^2)*dh/dt\\ = d/dr(r^2)*dr/dt\\2h*dh/dt = 2r* dr/dt\\h*dh/dt = r*dr/dt\\dh/dt = (r/h)*dr/dt[/tex]

[tex]= [(125 + 15*20)/(425^2 - 125^2)^1/2]*15[/tex]--------------------- at time t = 2

=15.69 ft/sec

Hence dh/dt = 15.69 ft/sec

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A bicycle company is designing women's bicycle frames The frames can accommodate any woman taller than 54.5 inches. Given that the heights of adult American women are normally distributed, with a mean of 65 inches and a standard deviation of 3.5 inches, what percentage of American women CANNOT use the bicycles designed by this company?​

Answers

Using the normal distribution, it is found that 0.13% of American women CANNOT use the bicycles designed by this company.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 65, \sigma = 3.5[/tex]

The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{54.5 - 65}{3.5}[/tex]

Z = -3

Z = -3 has a p-value of 0.0013.

0.0013 = 0.13% of American women CANNOT use the bicycles designed by this company.

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The area of Louisiana is approximately 4 x
104 square miles. The area of the United
States is approximately 225 times greater
than the area of Louisiana. What is the
approximate area of the United States?

Answers

Answer:

93,600

Step-by-step explanation:

4x104= 416

416x225 = 93,600

how to find the length of sides using pythagorean theorem​

Answers

Answer:

Pythagorean theorem is mainly used for finding the length of the third side of a right angled triangle if the lengths of other two sides are known.

For this, it is more useful if the theorem is stated in terms of the length of the sides of the triangle.

Consider a right angled triangle with sides of lengths p,b and h, where p,b and h are the lengths of perpendicular,base and hypotenuse respectively.

Draw squares on each of these sides.These squares have areas p²,b² and h².

For any right angled triangle with sides of length p,b and h;

[tex] \: \: \: \: \: \: \: {h}^{2} = {p}^{2} + {b}^{2} ....................(i)[/tex]

[tex] \therefore \: h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]

From (i); p²=h²-b²

[tex] \therefore \: p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]

Similarly,

[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]

Step-by-step explanation:

[tex] \blue{ \frak{seolle_{aphr.odite} }}[/tex]

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