Find the area of the surface. The part of the surface z = xy that lies within the cylinder x^2 + y^2 = 9

Answers

Answer 1

Answer:

The area of surface is [tex]\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]

Step-by-step explanation:

Given that,

The equation of cylinder is

[tex]x^2+y^2=9[/tex]

The part of the surface z = xy

The coordinates is,

[tex]z_{x}=y[/tex]

[tex]z_{y}=x[/tex]

We need to calculate the value of ds

Using formula of ds

[tex]ds=\sqrt{1+z_{x}^2+z_{y}^2}dA[/tex]

Put the value in to the formula

[tex]ds=\sqrt{1+y^2+x^2}dA[/tex]....(I)

We know that.

The polar coordinates,

[tex]x=r\cos\theta[/tex]

[tex]y=r\sin\theta[/tex]

The general equation of cylinder is

[tex]x^2+y^2=r^2[/tex]

compare from given equation

[tex]x^2+y^2=3^2[/tex]

0<=θ<=2π, 0<=r<=3

Area element in polar coordinates is,

[tex]dA=r dr d\theta[/tex]

Put the value of dA in equation (I)

[tex]ds=\sqrt{1+r^2}r dr d\theta[/tex]....(II)

We need to calculate the area of surface

Using equation (II)

[tex]s=\int_{0}^{2\pi}\int_{0}^{3}\sqrt{1+r^2}r dr d\theta[/tex]

[tex]s=\int_{0}^{2\pi}\dfrac{1}{3}((1+r^2)^{\frac{3}{2}})_{0}^{3}d\theta[/tex]

[tex]s=\int_{0}^{2\pi}\dfrac{1}{3}((1+3^2)^{\frac{3}{2}}-(1+0^2)^{\frac{3}{2}})d\theta[/tex]

[tex]s=(\dfrac{1}{3}((10)^{\frac{3}{2}}-1)\theta)_{0}^{2\pi}[/tex]

[tex]s=\dfrac{1}{3}(10^{\frac{3}{2}}-1)(2\pi-0)[/tex]

[tex]s=\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]

Hence, The area of surface is [tex]\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]


Related Questions

On Monday a team of street sweepers cleaned 4 city blocks. Tuesday, the team cleaned 2 1/6 times as many blocks as on Monday. How many city blocks did the street sweepers clean on Tuesday?

Answers

1/5 is the answer :0000

There will be twelve and a half city blocks of the street sweepers clean on Tuesday.

What is a fraction?

The numerator, which is found at the top of the fraction number, and the denominator, which is located at the bottom, are its two component components.

It is given that, four city blocks were cleaned by a crew of street sweepers on Monday. The crew cleaned 2 1/6 as many blocks on Tuesday as they did on Monday.

Suppose the number of city blocks the street sweepers cleaned on Tuesday will be x,

x = 4 +  2 1/6 × 4

x=4+13/6×4

x=12.6≈ 12 1/2

Thus, the street sweepers will clean twelve and a half city blocks on Tuesday.

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The product of 2 and the sum of a number and 8 is equivalent to 16.
Which equation models this sentence?

Answers

x = some unknown number

x+8 = sum of the number and 8

2(x+8) = product of 2 and the sum of a number and 8

2(x+8) = 16 is the final answer

HEEEEEEEEEEEEEEEELLLLLLLLLLLLLP :(

Answers

1 2/5 for mixed number and 7/5 one fraction I think

What is the value of the expression below?
x/3+6=12

Answers

Answer:

x=108

Step-by-step explanation:

x/3+6=12        [tex]\frac{x}{3+6}=12[/tex]

1) 3+6=9

2) multiply both sides by 9

     9x/9=12*9   [tex]\frac{9x}{9}=12*9[/tex]

3) Simplify

     9x/9=x    [tex]\frac{9x}{9}=x[/tex] (9 cancels out)

     12*9=108

      x=108

Given 4 c + 5 not-equals 0 and c is a real number, what is the multiplicative inverse of 4 c + 5 not-equals 0

Answers

Answer:

1 / 4c+5

Step-by-step explanation:

Given :

4c + 5 ≠ 0

c is a real number.

Find the multiplicative inverse of equation ?

The multiplicative inverse of a number is reciprocal of number

Let

x = a number

The multiplicative inverse = 1/x

Let 4c + 5 ≠ 0 be a number x

Then, the multiplicative inverse of x = 1/x

x = 4c + 5

1/x = 1 / 4c+5

Therefore, the multiplicative inverse of 4c + 5 = 1 / 4c+5

Answer:

yes what he said

Step-by-step explanation:

on edge

What is the value of x that satisfies the equation 4/3=x+10/15

Answers

Answer:

4/3=x+10/15

x=4/3 - 10/15

x=4/3 - 2/3

x=4-2/3

x=2/3

X=23 will be your answer for this

Suppose P(C) = 98%; P(D) = 88%; and P(C or D) = 33%.
Find P(C and D).
Can this really be a probability? If not, explain why not.

Answers

Answer:

[tex]P(C\ and\ D) = 153\%[/tex]

Step-by-step explanation:

Given

[tex]P(C) = 98\%[/tex]

[tex]P(D) = 88\%[/tex]

[tex]P(C\ or\ D) = 33\%.[/tex]

Required

[tex]P(C\ and\ D)[/tex]

In probability, the relationship between the given parameters and the required parameter is:

[tex]P(C\ and\ D) = P(C) + P(D) - P(C\ or\ D)[/tex]

Substitute values in the above formula

[tex]P(C\ and\ D) = 98\% + 88\% - 33\%[/tex]

[tex]P(C\ and\ D) = 153\%[/tex]

No, it can't be a probability

Because [tex]P(C\ and\ D) > 100\%[/tex]

Solve the equation: 2^2 − 9 + 10 = 0 Step by step

Answers

Step-by-step explanation:

2^2 − 9 + 10 = 0

4-9+10=0

4+1=0

5=0

False

Quadrilateral EFGH is a scaled copy of quadrilateral ABCD. Select ALL of the true statements.
A. Segment EF is twice as long as segment AB, True or False
B. Segment CD is twice as long as segment FG. True or False
C. The measure of angle HEF is twice the measure of angle DAB. True or False
D. The length of segment EH is 16 units. True or False
E. The measure of angle BCD is the same as the measure of angle GFE. True or False

Answers

Answer: b,e

Step-by-step explanation:

Which problem can be solved with the equation 1.75+(-1.75)=0?

Answers

Answer:

bank account one is the answer

Step-by-step explanation:

bank account one is the answer

Hope it helps

Pls mark as brainliest

Problem number 4 is solved by the equation 1.75 + (-1.75).

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

In problem number 4, the question is the number Sam deposited in the amount of $1.75 and then purchased a movie ticket for $1.75.

The account balance will be represented by the equation.

Account = 1.75 + (-1.75)

The actual account balance will become zero.

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If a container of liquid contains 40 oz of​ solution, what is the number of ounces of pure acid if the given solution contains the following acid​ concentrations? ​(a) 20​% ​(b) 15​% ​(c) 40​% ​(d) 60​%

Answers

Answer:

(d) 60% hope this helped

Given: f = {(0, 1), (2, 4), (4, 6), (6, 8)} and g = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)} Complete the ordered pair below for the function shown.
f(x)
-----
g(x)

(4,__)

6/7
1
7/6

Answers

Answer: Choice A.  6/7

=======================================================

Explanation:

The given ordered pair is (4, ___) so we have x = 4 here.

We will plug this into f(x) and g(x) to get

f(4) = 6

g(4) = 7

So we have [tex]\frac{f(4)}{g(4)} = \frac{6}{7}[/tex]

-----------

If you're curious where f(4) = 6 came from, all we're doing is looking through the set of points

f = {(0, 1), (2, 4), (4, 6), (6, 8)}

to see which has 4 listed first as the x coordinate. That point is (4,6) so x = 4 leads to y = 6, ie, f(x) = 6 when x = 4. A similar situation happens with g(x) as well.

36599 round to the nearest thousand 100,699 round to the nearest thousand

Answers

Answer:

36,599 rounded to the nearest thousand is 37,000

100,699 rounded to the nearest thousand is 101,000

hope this helps! best of luck <3

Answer:

37000

101000

Step-by-step explanation:

You pick a card at random 6,7,8,9. What is P (8)?

Answers

Answer:

1/4

Step-by-step explanation:

what is the reciprocal of 2 8/9

Answers

9/26

2 8/9 = 26/9

Reciprocal of 16/9 is 9/26


10 POINTS : What is the solution to the equation 3/5x-6=-1/6x+7, rounded to three decimal places?

Answers

Answer:

x = 16.957

Step-by-step explanation:

(3/5)x - 6 = (-1/6)x + 7

Add (1/6)x to both sides. Add 6 to both sides.

(3/5)x + (1/6)x = 7 + 6

(18/30)x + (5/30)x = 13

(23/30)x = 13

Multiply both sides by 30/23.

x = 13/1 * 30/23

x = 390/13

x = 16.957

anyone do the Algebra 2 unit 1 test on edg?

Answers

Step-by-step explanation:

no not me .. I'm doing math unit test

The solution to the equation 3x + 7 = 16 - 2x is x = 9/5.

Option A is the correct answer.

We have,

To solve the equation 3x + 7 = 16 - 2x for x, we need to isolate the variable x on one side of the equation.

Let's solve it step by step:

Start with the original equation:

3x + 7 = 16 - 2x

- Add 2x to both sides of the equation to get rid of the -2x on the right side: 3x + 2x + 7 = 16 - 2x + 2x

- Simplifying, we have: 5x + 7 = 16

- Next, subtract 7 from both sides of the equation to isolate the term with x: 5x + 7 - 7 = 16 - 7

- Simplifying, we have: 5x = 9

- Finally, divide both sides of the equation by 5 to solve for x: (5x)/5 = 9/5

- Simplifying, we have: x = 9/5

Therefore,

The solution to the equation 3x + 7 = 16 - 2x is x = 9/5.

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The complete question:

Solve the following equation for x: 3x + 7 = 16 - 2x

a) x = 9/5

b) x = 5

c) x = 4

d) x = 6

Which of the following inequalities is incorrect?
00>-2
6 >-12
-5<-8
0-7<-5

Answers

Step-by-step explanation:

First, is 0 greater than -2? Correct

Next, is 6 greater than -12? Correct

Is -7 less than -5? Correct

Finally, is -5 less than -8? NERP!!

So C. is incorrect. Or in this case, it is...

draw a flat shape that has no straight sides or angles

Answers

Answer:

try drawing a circle or an oval

Step-by-step explanation:

There are no edges or corners to a circle, ovals, or semicircles, making it a spherical form. Shapes may be categorized and sorted using these qualities as well as size.

What is a circle?

A group of points that are all at the same distance from a fixed point is how it is characterized (called the center of a circle).

Ovals, semicircles, circles, and other closed forms all lack straight lines. Having one curved edge and one straight edge, a semicircle is a closed form.

An oval is a circle that has been flattened such that it resembles an egg or an ellipse: a mirror with an oval shape; a face with an oval shape. Ellipsoidal comparison.

By dividing a circle into two equal halves along the diameter line, a semicircle is created. There is just one line of symmetry in the semicircle, and that is the reflection symmetry. A half-disk is another name for the semicircle.

Thus, the flat shape that has no straight will be ovals, semicircles, and circles.

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PLEASE HELP FAST
The city council budgeted $536 to buy new garbage cans. If each garbage can costs $67, how
many garbage cans will the city be able to buy?
garbage cans
Submit

Answers

Answer:8 garbage cans

Step-by-step explanation:

The budget is $536 and each garbage can is $67 so you need to divide $536 by $67 and the answer is 8.

A gardener fills a 2 1/2 cubic foot wheelbarrow 2/3 of the way without soil weight 75.25 pounds. What is the weight of the soil un wheelbarrow?​

Answers

Volume of wheelbarrow , V = 2 1/2 ft³ = 5/2 ft³.

Volume of soil in wheelbarrow , [tex]v = \dfrac{5}{3}\ ft^3[/tex] .

Mass of soil in wheelbarrow , m = 75.25 pounds.

Now, volume left , [tex]v'=\dfrac{5}{6}\ ft^3[/tex] .

Let, mass of  soil un wheelbarrow is x.

[tex]x=\dfrac{\dfrac{5}{6}\times 75.25}{\dfrac{5}{3}}\\\\x=37.625\ pounds[/tex]

Hence, this is the required solution.

which number can each term of the equation be multiplied by to eliminate the fractions before solving?
plzzz help

Answers

Answer:

12.

Step-by-step explanation:

Because 12 is the only number that comes in 2,3 as well as 4s table.

Which of the following is a trinomial with a constant term?
A. X²-6
B. 5x2 - 4 + x
C. 4x5 + 2x - 2x2
D. -3+4x4

Answers

Answer:

I'm going to say B

Is Nora or Sofia correct? Explain your reasoning.

Answers

Answer:

  Nora is correct

Step-by-step explanation:

Sophia used an appropriate method for computing the value of the repeating decimal fraction ...

  0.1212_12

Close examination of the given decimal fraction shows that it is non-repeating, so is an irrational number. It cannot be represented by the ratio of integers.

Nora is correct in saying Sophia made a mistake.

___

Sophia depended on 100x -x cancelling some part of the fraction, so the result was a finite decimal. For repeating 2-digit fractions, this works well:

  [tex]x=0.12\overline{12}\\100x=12.12\overline{12}\\100x-x=12.12\overline{12}-0.12\overline{12}=12\\x=12/99[/tex]

However, the decimal does not repeat, so this does not work:

  100x = 12.1121112

  100x -x = 12.1121112 -0.121121112 = 11.99099009900099... non-repeating

That is, the decimal part is not cancelled by Sophia's work, as we said above.

If someone is good in theoram please help me I need help with task 3,4,5

Answers

Answer:

C²= A²+B²

Step-by-step explanation:

A) 10²=( Base)² + 6²

(Base )²= 10² - 6²:

100-36

= 64

Base = √ 64

8

B) 17² = 8² + (Height)²

(Height) ² = 17²- 8²

= 289-64

= 225

Height = √225

= 15

C) 2.5² = Base ² + 1.5 ²

Base² = 2.5 ²- 1.5²

6.25- 2.25

= 4

Base = √4

= 2

D) 41² = Base²+ 40²

Base²= 41²- 40²

1681-1600

= 81

Base = √81

=9

E)26²=Base² +10²

Base² = 26²- 10²

676-100

= 576

Base= √576

= 24

F)25²= Base²+ 7²

Base² = 25²- 7²

625- 49

=576

Base= √576

= 24

What are the disadvantages of driverless cars? Check all that apply.​

Answers

Answer:

2 3 and 4

Step-by-step explanation:

Answer:

They cannot tell the difference between people and other objects. They will wait for crossing pedestrians even if signaled to keep driving.

Step-by-step explanation:

I need help with this geometry question​

Answers

Answer:

Angle [tex]AEC=80[/tex]°

Step-by-step explanation:

factor an expression:
(x²+x+1)²+3x(x²+x+1)-18x²​

Answers

Answer:

( x - 1 ) ^ 2 ( x ^ 2 + 7 x + 1 )

Step-by-step explanation:

Sorry about the spaces, thought it would make it look better!

Find the distance between the points E(3,7)and(6,5).find the exact distance between the two points ?

Answers

Step-by-step explanation:

Let the distance points E(3,7) and F(6,5)

Distance between EF = √[(x2-x1)²+(y2-y1)²]→Formula

Here, x1 = 3, y1 = 7

x2 = 6 , y2 = 5

Now,

Put all the values in distance formulae:

AB = √[(6-3)²+(5-7)²]

= √[(4)²+(2)²]

= √[(4*4)+(2*2)]

= √[16+4]

= √[20] = 2√5 Units.

Answer:- Hence, the distance between two points E(3,7) and F(6,5) is 2√5 Units.

Please help, I don't understand, please
5+(-5)

Answers

Answer: 0

Step-by-step explanation: To make this easier, ignore the addition sign (for this one, at least), so just do 5-5

Answer: 0

Step-by-step explanation:

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