Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = 9 − x2 R: square with vertices (0, 0), (2, 0), (0, 2), (2, 2)

Answers

Answer 1

Answer:

The area of the surface over R is [tex]\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]

Step-by-step explanation:

From this study,

The surface area of f(x,y) is expressed by:

[tex]A = \iint_R \sqrt{1 +f^2_x+f^2_y}} \ dA[/tex]

where

[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 2[/tex]

Given that:

f(x,y) = 9 - x²

Thus, [tex]f_x = -2x[/tex] and   [tex]f_y = 0[/tex]

However, the area becomes:

[tex]A = \iint_R \sqrt{1+(-2x)^2+0^2} \ dxdy[/tex]

[tex]A = \iint_R \sqrt{1+4x^2} \ dxdy[/tex]

From above, replacing x with [tex]\dfrac{1}{2} \ tan \ u[/tex]

then [tex]dx = \dfrac{1}{2} sec^2 \ udu[/tex]

[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint \sqrt{1 + 4u^2 } \ sec^2 \ udu[/tex]

[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint sec^2 \ udu[/tex]

[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} ( \sqrt{4x^2 + 1x} + \dfrac{1}{2} In \sqrt{4x^2 + 1}+2x)[/tex]

Hence;

[tex]\mathsf{A = \int \limits ^2_0 \begin {bmatrix} \dfrac{1}{2}(\sqrt{4x^2 +1 x}+ \dfrac{1}{2} In ( \sqrt{4x^2+1}+2x \end {bmatrix}^2_0 \ dy}[/tex]

[tex]\mathbf{A = 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]

Therefore, the area of the surface over R is [tex]\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]


Related Questions

Question 14 Multiple Choice Worth 1 points)
(02.05 LC)
+
The amount $4.50 is 6% of what price?
O $10.50
O $13.30
O $27.00
O $75.00

Answers

Answer:

.27

Step-by-step explanation:

4.5*6/100

=.27

Answer:

$27.00

I stayed up all night studying for this test and I got the question right haha

a tourist information center is between a bus station and a train station when mapped on a grid, the tourist information center is located at (1,4) and the bus is located at (-3,7) the train station is located at point

Answers

Answer:

dfd

Step-by-step explanation:


In a survey of 18 college students, it was found that 11 were taking an
English class, 6 were taking a math class, and 4 were taking both
English and math. How many students were taking a math class only?
A.7
B.11
C.2
D.5

Answers

Answer:

C.)2

Step-by-step explanation:

6-4=2

Answer:

I am choosing C ok it close to correct

2 lines intersect. Where the 2 lines intersect, 4 angles are created. Labeled clockwise, from uppercase right: angle 1 (3 x minus 1) degrees, angle 2 is blank, angle 3 (2 x + 9) degrees, and angle 4 is blank. What are the numerical measures of each angle in the diagram? ∠1 and ∠3 measure degrees. ∠2 and ∠4 measure degrees.

Answers

Answer:angle 1 and 3 measure 29 degrees.

angle 2 and 4 measure 151 degrees.

Step-by-step explanation:

Answer:

29 and 151

Step-by-step explanation:

Marco sorted these solid figures into two groups. What is true about the groups?
Group 1
Group 2
All figures in Group 2 appear to have at
least one triangular face.
<) All figures in Group 1 are rectangular
prisms
)) All figures in Group 2 are triangular
prisms
1) All figures in Group 1 appear to have at
least one square face,

Answers

Answer:

All figures in Group 1 appear to have at

least one square face

Step-by-step explanation:

Let us examine each statement and see whether they are true or not.

The first statement is not true. Only one of the figures (square pyramid) has at least one triangular face. It has 4 triangular faces, actually.

The second statement is not true. Only one of the figures is a rectangular prism. The remaining two are triangular pyramid and triangular prism respectively.

The third statement is not true also. Only 1 figure is a triangular prism.

The fourth statement is correct. In group 1, all the figures has at least one square face.

how many minutes (min ) are in 2 hours?

Answers

Answer:

120

Step-by-step explanation:

1 hour = 60 minutes

2 hours = 2* 60 = 120 minutes

point a is at (-7,-9) and point b is at (6,3) what is the midpoint of line segment AB

Answers

Answer:

(-1/2,-3)

Step-by-step explanation:

(-7,-9) =x1, y1

(6,3) = x2, y2

now,

Mid point= x1+x2 /2 , y1+y2 /2

= -7+6 /2, -9+3 /2

= (-1/2 , -3)

Factor 5x 4 - 30x 2 - 135. 5(x2 + 9)(x2 - 3) 5(x - 3)(x + 3)(x2 - 3) 5(x - 3)(x + 3)(x2 + 3)

Answers

Answer:

Step-by-step explanation:

[tex]5x^{4} -30x^{2} -135[/tex]

We need to pull out 5 to make the rest easier to factor.

[tex]5(x^{4} -6x^{2} -27)[/tex]

Now we can factor.

Consider all combinations of how to get 27.

1 x 27

3 x 9

And that's it before you end up just switching the place i.e. 9 x 3 and 27 x 1

This makes it easy to see that 3 and 9 are our best choice because 9 - 3 is 6 which is our middle term in the equation.

So now we have:

[tex]5(x^{2} -9)(x^{2} +3)[/tex]

We can break down [tex]x^{2} -9[/tex] even further because it's a perfect square.

(x - 3)(x + 3)

Our final factor is

5(x - 3)(x + 3)[tex](x^{2} +3)[/tex]

Which phrase should be inserted in the line to make a true statement? 2/3 is _____ 8/12 A. Is greater than B. Less than C. Cannot be compared.D.is equal to (HELP I NEED THIS HURRYY PLSSSS)

Answers

Answer:

the answer is equal because 8/12=2/3 so 2/3=8/12 (2/3)

Step-by-step explanation:

I bought three pencils costing 18 cents each. how much change did I get from $1​

Answers

Answer:

15 pencils

Step-by-step explanation:

18c/3

x/1

cross multiply then divide

Answer:

46 cents

Step-by-step explanation:

18 x 3 = 54

100 - 54 = 46

What degree is the polynomial function shown on the graph? A) third B) fourth C) fifth D) sixth

Answers

uhh where is the graph?

Answer:

Step-by-step explanation:

Question 3 Write each fraction as an equivalent fraction with the denominator 30. Then write the
original fractions in descending order
1/15, 5/6 , 7/10, 1/2

Answers

Answer: 5/6, 7/10, 1/2, 1/15

Step-by-step explanation:

5/6=25/30, 7/10=21/30, 1/2=15/30, 1/15=2/30

jim's bookshelf has 24 inches remain in. each of his notebooks is 3/4 inches wide. how many notebooks will fit in the remaining space

Answers

Answer:

32 notebooks will fit.

Step-by-step explanation:

Write the name of the
period that has the
digits 913.

Answers

the answer is the thousands group . its the way they word the problem that complicates it . 913,256 256 being the ones group 913 being the thousands group . so the name of the period with 913 , is the thousands group .
It’s kinda in between, but I’ll say the thousands since it’s rlly close.

One sample has a mean of M=7.2 and a second sample has a mean of M=12.8. The two sample are combined into a single set of scores. a. What is the mean for the combined set if both the samples have n=5? b. What is the mean for the combined set if the first sample has n=5 and the second sample had n=35?

Answers

Answer:

a. M = 50

b. M = 242

Step-by-step explanation:

mean =  [tex]\frac{sum of scores}{number of samples}[/tex]

⇒ sum of scores = mean x number of samples

Let the mean be represented by M, and the number of samples be represented by n,

sum of scores = M x n

a. When n = 5 for both samples,

The first sample's sum of scores = M x n

                                     = 7.2 x 5

                                     = 36

The second sample's sum of scores = M x n

                                     = 12.8 x 5

                                     = 64

The mean for the sum of scores of the combined set = [tex]\frac{36 + 64}{2}[/tex]

                                     = 50

When both samples have n = 5, the mean of the combined set is 50.

b. When the first sample has n = 5, the sum of scores = 36.

If n = 35 for the second sample, the sum of scores = M x n

                                                          = 12.8 x 35

                                                          = 448

The mean for the sum of scores of the combined set = [tex]\frac{36 + 448}{2}[/tex]

                                                    = 242

10/r - 7 - 6b if r = 5 and b = -6

Answers

Steps to solve:

10/r - 7 - 6b when r = 5 and b = -6

~Substitute

10/5 - 7 - 6(6)

~Simplify

5 - 7 + 36

~Subtract

-2 + 36

~Add

34

Best of Luck!

If your exponent on your power 10 is positive, is your number larger or smaller than 10?

Answers

Answer:

See below.

Step-by-step explanation:

The number maybe less than 10, equal to 10, or larger than 10.

Examples:

A.

exponent: 1/2

10^(1/2) = sqrt(10)           (less than 10)

B.

exponent: 1

10^1 = 10                  (equal to 10)

C.

exponent: 2

10^2 = 10 * 10 = 100          (larger than 10)

Simplify the expression: 7 + 24 / 6 * 10 *

Answers

Hi the answer is 47

Here is the step by step process

7+24/6*10

PEMDAS states that you do multiplication first but it matters if division or multiplication is first in the equation.

So based on the equation you would do division first.

You will have

7+4*10

Next you do multiplication

7+40

Your final answer is 47

Hope this helps! Have a great day!! :)

Answer:

47

Step-by-step explanation:

Since we are following PEMDAS and doing the problem left to right, first you would divide 24/6 which is 4 and then multiply by 10 which is 40. Then add the remaining 7 and your answer is 47. Simple.

What is the value of the digit 5 in the number 4.105

Answers

Answer:

thousanths place

Step-by-step explanation:

Answer:

4.105

5-hundredths place if I’m correct

104 percent of 102 is what

Answers

Answer:

106.08

Step-by-step explanation:

Answer:

106.08 percent

solve system

a = 5 - 2b; a +2b = 6

Answers

Answer:

This System has no solutions.

What number should be added to 78to get a sum of 97

Answers

THE ANSWER TO THAT PROBLEM IS SIMPLY 175

Answer:

19

Step-by-step explanation:

All you need to do is subtract 78 from 97 to find the "remainder." Or you can also add until you get to 97.

97 - 78 = 19

78 + 19 = 97.

Simplify: (5x2 - 3x - 4)(3x - 7) A. 15x3 - 44x2 + 9x - 28 B. 15x3 - 44x2 + 9x + 28 C. 15x3 + 26x2 - 33x - 28 D. 15x3 - 26x2 - 33x + 28

Answers

Answer:

A. 15x^3 -44x^2 +9x +28

Step-by-step explanation:

(5x^2 -3x -4)(3x - 7)

first, distribute by multiplying the terms in each parenthesis with each other:

(5x^2 * 3x) - (3x * 3x) - (4 * 3x) - (5x^2 * 7) + (3x * 7) + (4 * 7)

simplify:

15x^3 -35x^2 -9x^2 +21x -12x +28

Now combine like terms:

15x^3 -44x^2 +9x +28

need a answer for all of them

Answers

(fill the answers in left from right in each line)

1. -20, -5, 10

2. -16, 0, 16, 32

3. -8, -6, -3

4. 0, 6, 18, 24

5. -12, 0, 16
1. -20 -5 10 for question 1

Suppose a charity event serves a prix fixe dinner that consists of one from each category: (1) soup or salad (not both), (2) appetizer, (3) entree, (4) dessert, and (5) beverage. The restaurant is offering five kinds of soup, three kinds of salad, four kinds of appetizers, six entrees, five desserts, and four beverages. How many different prix fixe dinners are possible

Answers

Answer:

3840

Step-by-step explanation:

Using the fundamental counting principle

The restaurant is offering five kinds of soup, three kinds of salad, four kinds of appetizers, six entrees, five desserts, and four beverages.

There are 5 independent events happening (5 prixe dinners)

(1) soup or salad (not both)

We have five kinds of soup, three kinds of salad

soup or salad (not both), = 5 + 3

= 8

(2) appetizer = 4

(3) entrees = 6

(4) dessert = 5

(5) Beverage = 4

Hence,

8 × 4 × 6 × 5 × 4

= 3840

The number of different prix fixe dinners are possible is 3840

a company's budget increase from 29 million to 133 million over a period of 10 years. growing by the same percent each year. What was the annual percent increase? Express your answer as a common fraction

Answers

I think it’s 1217 but I’m not sure

The temperature in Miami, Florida is 22 degrees warmer than three times the temperature in Bangor, Maine. The temperature in Miami is 82 degrees. Write an equation to determine the temperature in Bangor.

Answers

Answer:

See Explanation

Step-by-step explanation:

Let the temperatures of Miami and Bangor be M and B degrees respectively.

According to the given information:

M = 3B + 22... (required equation)

Plug M = 82

82 = 3B + 22

82 - 22 = 3B

60 = 3B

B = 60/3

B = 20 degrees

Thus, the temperature in Bangor is 20 degrees.

The required temperature in Bangor is 52 degrees and the required equation is 82 = 3B + - 22.

Given that,
The temperature in Miami, Florida is 22 degrees warmer than three times the temperature in Bangor, Maine.
The temperature in Miami is 82 degrees.
An equation to determine the temperature in Bangor is to be determined.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the temperature in Bangor be B
The temperature in Miami is 82 degrees.
The temperature in Miami, Florida is 22 degrees warmer than three times the temperature in Bangor. Implies,

82 = 3B + - 22
3B = 82 + 22
3B = 104
B = 52 degrees

Thus, the required temperature in Bangor is 52 degrees.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Find Cos N 73 48 E 55

Answers

Answer:

1. cos73 is 0.29

2. cos48 is 0.67

3. cos55 is 0.57

These are the answers for cos. Hope this helps!

You want to get an idea of how much your children will benefit from the education system in a state. Which column of numbers will you use for your analysis? Why?

Answers

use the Per-Pupil Expenditure column to compare how much each state spends on average for each student. Total expenditure for the state can be misleading. A state with a high number of students could have a high overall expenditure, even if it doesn't spend very much on each student. I'm more concerned about how much the state is likely to spend on each of my children, not how much they spend overall.

Step-by-step explanation:

Answer:

I'd use the Per-Pupil Expenditure column to compare how much each state spends on average for each student. Total expenditure for the state can be misleading. A state with a high number of students could have a high overall expenditure, even if it doesn't spend very much on each student. I'm more concerned about how much the state is likely to spend on each of my children, not how much they spend overall.

-PLATO

Which point on the graph could represent the ratio of 2 white flowers for every 3 pink flowers that will be in one row of Molly’s garden?

Answers

Answer: It’s B

Step-by-step explanation:

I just did the quiz

Answer:

The answer would be B

Step-by-step explanation:

take a look at your question.

If you look at the x axis you can see that it is 12 but c is also that.

Now take a look at the y axis, you can see that the letter B is connected to 18.

If you remember your previous problems you would remember that that was an answer (12, 18). But for those who do not remember you can multiply 2x6(which you got your 12 from) and 3x6 ( which is where the 18 is from)

So there for you are left with the answer B.

Let me know if this helped!!! :))))

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