a) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
xy = 2, x = 0, y = 2, y = 4
b) Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = x3, y = 8, x = 0; about x = 9

Answers

Answer 1

(a) See the attached sketch. Each shell will have a radius y chosen from the interval [2, 4], a height of x = 2/y, and thickness ∆y. For infinitely many shells, we have ∆y converging to 0, and each super-thin shell contributes an infinitesimal volume of

2π (radius)² (height) = 4πy

Then the volume of the solid is obtained by integrating over [2, 4]:

[tex]\displaystyle 4\pi \int_2^4 y\,\mathrm dy = 2\pi y^2\bigg|_{y=2}^{y=4} = 2\pi (4^2-2^2) = \boxed{24\pi}[/tex]

(b) See the other attached sketch. (The text is a bit cluttered, but hopefully you'll understand what is drawn.) Each shell has a radius 9 - x (this is the distance between a given x value in the orange shaded region to the axis of revolution) and a height of 8 - x ³ (and this is the distance between the line y = 8 and the curve y = x ³). Then each shell has a volume of

2π (9 - x)² (8 - x ³) = 2π (648 - 144x + 8x ² - 81x ³ + 18x ⁴ - x ⁵)

so that the overall volume of the solid would be

[tex]\displaystyle 2\pi \int_0^2 (648-144x+8x^2-81x^3+18x^4-x^5)\,\mathrm dx = \boxed{\frac{24296\pi}{15}}[/tex]

I leave the details of integrating to you.

A) Use The Method Of Cylindrical Shells To Find The Volume Of The Solid Obtained By Rotating The Region
A) Use The Method Of Cylindrical Shells To Find The Volume Of The Solid Obtained By Rotating The Region

Related Questions

Liam's monthly bank statement showed the following deposits and withdrawals:
$32.35, -−$114.95, $63.09, $98.79, -−$79.41
If Liam's balance in the account was $62.45 at the beginning of the month, what was the account balance at the end of the month?

Answers

Answer:

I think it's $62.32?

Step-by-step explanation:

1. $62.45 USD subtracted by ($114.95 + $79.41) = -131.91 USD

2. $-131.91 + ($32.35 + $63.09 + $98.79) = $62.32

Joe reads 24 chapters of a book in 8 hours. What is his rate chapters per hour?

Answers

24 chapters in 8 hours = 3 chapters per hour

24 : 8 = 3

Answer:

3

Step-by-step explanation:

The rate formula is to divide the length by the time.

In this, 24 chapters is the length and 8 hours is the time.

Divide:

24/8 = 3

So, the speed is 3 chapters per hour

Hope this helped.

Hytgvvuccuchccucucuvff hxhxhxhxu u uh

Answers

Answer:

Angle 6 = 120 (corresponding angles)

Correct^^^^^^^^^^^^^^^^^^%




Select two ratios that are equivalent to 27: 9.
Choose 2 answers:

Answers

Answer:

1. 9:3

2. 3:1

Step-by-step explanation:

Hope it really helps you

I need help please!!!
Worth 10 points will give brainliest if correct!​

Answers

Answer:

the x coordinate is 1 and the y coordinite is 5

help me plss im timed :(

Answers

Answer:

-138u+56

Step-by-step explanation:

(-8×-10u)+(-8×6u)+(-8×-7)-10u

-80u+(-48u)+56-10u

-80u-48u-10u+56

-138u+56

Answer:

22u + 56

Step-by-step explanation:

https://mathsolver.microsoft.com/en/solve-problem/-8%20%60left(%20-10u%2B6u-7%20%20%60right)%20%20-10u

Maths f(x) type of question please help

Answers

Since 1 < x < 5, adding each side by a, where a is negative, gives

a > ax > 5a

and adding b to each side gives

a + b > ax + b > 5a + b

or

5a + b < ax + b < a + b

Since 7 < f(x) < 23, it follows that

5a + b = 7

a + b = 23

Solve for a by eliminating b :

(5a + b) - (a + b) = 7 - 23

4a = -16

a = -4

Solve for b :

-4 + b = 23

b = 27

[IMAGE ATTACHED]
I don’t understand this please help.

Answers

Answer:

9

Step-by-step explanation:

1. You would make these to equations equal to each other because there are parellel(they have the same angel)

2. EQUAL these 2 equations together to find r.

3. SOLVING for r

7r - 5 = 6r + 4

r = 9

How do you do this. Please give a full answer and explain why.

Answers

Law of Exponent

[tex] \displaystyle \large{ {a}^{ - n} = \frac{1}{ {a}^{n} } }[/tex]

Compare the terms.

[tex] \displaystyle \large{ {a}^{ - n} = {( - 2)}^{ - 3} }[/tex]

Therefore, a = -2 and n = 3. From the law of exponent above, we receive:

[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ {( - 2)}^{ 3} } }[/tex]

Exponent Def. (For cubic)

[tex] \displaystyle \large{ {a}^{3} = a \times a \times a }[/tex]

Factor (-2)^3 out.

[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{( - 2) \times ( - 2) \times ( - 2)}}[/tex]

(-2) • (-2) = 4 | Negative × Negative = Positive.

[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{4 \times ( - 2)}}[/tex]

4 • (-2) = -8 | Negative Multiply Positive = Negative.

[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ - 8}}[/tex]

If either denominator or numerator is in negative, it is the best to write in the middle or between numerator and denominators.

Hence,

[tex] \displaystyle \large \boxed{ {( - 2)}^{ - 3} = - \frac{1}{ 8}}[/tex]

The answer is - 1 / 8

Find the slope and y-intercept of the following line.
- 10 - x= -5
BER
Find the slope of the line. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The slope of the line is
(Simplify your answer. Type an integer or a fraction.)
B. The slope of the line is undefined.
(Answer quickly)

Answers

Answer:

The Slope of the line is undefined

Step-by-step explanation:

Complete the table of values.

Answers

(0,-7)
(3,0)
(-3, -14)

find the relative error of the number 8.6 if both of it's digits are correct​

Answers

HOPE THIS HELPS YOU...PLEASE MARK ME AS BRAINILIST......

Answer:

if the X number is rounded up to N decimal place then EA=12(10-N)

10⁴ has how many zeros?​

Answers

Answer:

4 zeros

Step-by-step explanation:

10·10·10·10=10000

Answer:

10,000.

Step-by-step explanation:

10 to the power of 4 = 10 x 10 x 10 x 10 = 10,000. hope this helps

what is the solution to 2x+3= -7

Answers

2x + 3 = -7

2x = -7 - 3

2x = -10

x = -10/2

Answer:

Step-by-step explanation:

2x +  3 = -7

2x = -10

x = -5

I need help on this problem!

g(h+2/3)=1 for h

Answers

Answer:

[tex]g(h + \frac{2}{3} ) = 1 \\ \\ gh + \frac{2}{3} g = 1 \\ \\ gh = 1 - \frac{2}{3} g \\ \\ h = (1 - \frac{2}{3} g ) \div g \\ \\ h = (1 - \frac{2}{3} g ) \times \frac{1}{g} \\ \\ h = \frac{1}{g} - \frac{2}{3} [/tex]

I hope I helped you^_^

x – Зу +8x47+ 15 – 4у

Answers

Answer:

X-7y+391

Step-by-step explanation:

First multiply

8x47=376

Now group those that are the same together

X-3y -4y+376 +15

X-7y+391

Answer:

x - 7y + 391

Step-by-step explanation:

[tex]x - 3y + 8 \times 47 + 15 - 4y[/tex]

[tex]x - 3y + 376 + 15 - 4y[/tex]

[tex] - 3y - 4y = (- 3 - 4)y = - 7y[/tex]

[tex]x - 7y + 376 + 15[/tex]

[tex] = x - 7y + 391[/tex]

Find the amplitude of f(x) = 8 sin(6x + 4) – 3.

Answers

9514 1404 393

Answer:

  8

Step-by-step explanation:

The amplitude is the coefficient of the sine function: 8.

Answer:

8

Step-by-step explanation:

Amplitude is the onehalf of highest value minus the lowest value

since sine function has maximum 1 and minimum -1, then the highest value of f(x) is 8(1) - 3 = 5 and the minimum value is 8(-1)-3 = -11.

Therefore the amplitude is (1/2) ( 5 +11) = 8.

2____+2_____=5_____
what are the nouns

Answers

Answer:

nous hkgjgjdoyufslhddigxupfFuDdyYofzufzplud

Number 2? I’m so confused..

Answers

Answer:

answer is 4. each square is 0.5

Step-by-step explanation:

Determine if each term is synonymous to SLOPE.

Answers

Answer:

A to C and B to D

Step-by-step explanation:

Thats how it works dude/Bro

Error Analysis jeremy incorrectly says that 2 1/8 is the same as 2.18 Convert 2 1/8 to a decimal correctly. Then explain ​'s likely error.

Answers

Answer:

1 divided by 8 = 0.125 let's replace the 0 with a 2 since 2 is the whole number = 2.125 is correct

Step-by-step explanation:

Jeremy has mistaken 2 1/8 as 2.18 probably because he thought 1/8 was 0.18

The correct decimal value is 2.13.

We have Jeremy who incorrectly said that [tex]2\frac{1}{8}[/tex] is the same as 2.18.

We have Convert [tex]2\frac{1}{8}[/tex] to a decimal correctly.

How will you convert the mixed fraction -  [tex]5\frac{2}{3}[/tex] to normal fraction?

The method to convert the mixed fraction to normal fraction is -

[tex]5\frac{2}{3}\\[/tex] = [tex]\frac{3\times 5 +2}{3} = \frac{17}{3}[/tex]

According to question, we have -

Mixed fraction = [tex]2\frac{1}{8}=\frac{17}{8}[/tex] = 2.125 = 2.13

Hence, the correct decimal value is 2.13.

To solve more questions on Error analysis, visit the link below -

https://brainly.com/question/11152559

#SPJ2

Plsssssssssssssssssssss help me fast

Answers

Answer:

The answer is 95cm2

Step-by-step explanation:

A=b×h

=19×5

= 95 cm2

please mark me the brainliest

Area of a parallelogram=base×height
Area=19×5=95cm²

Hope my answer helped u :)

Please help review this explain why its wrong and tell me whats right pls

Answers

The answer would be 0, -1,-5,-7

Answer:

for 1st one B is corret

for 2nd one D is correct

Step-by-step explanation:

Arrange the following integers in ascending order, putting the smallest first. Look at the negative numbers first. The smallest negative number is -35, then -2. Then look at the positive numbers.

Simplify 6^9/6^3

20 characters :/

Answers

Answer:

=46,656

Step-by-step explanation:

=6^9                               =6^3

=10,077,696                   =216

          =10,077,696 / 216

        =46,656

Solve this problem and show the steps please because I’m so confused

Answers

Answer:

= 77

Step-by-step explanation:

{3 × [tex]2^{2}[/tex] - 3} -2 × 11

Solve the brackets first

{ 3 × 4  - 3} -2 × 11

{12 - 3 }  -2 × 11

9  -2 × 11

9  -22

= -13

Answer:

-13

Step-by-step explanation:

Solve in the bracket first

(3*4 -3) -2 * 11

(12 - 3) -22

9 - 22

-13 is the final answer

write a decimal equivalent to the fraction
[tex]-\frac{7}{10}[/tex]

Answers

9514 1404 393

Answer:

  -0.7

Step-by-step explanation:

7 goes in the tenths place. That's what seven tenths means. Of course, the decimal number has the same negative sign.

  -0.7

A rectangle has sides measuring (4x + 5) units and (3x + 10) units.

Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)

Part B: What are the degree and classification of the expression obtained in Part A? (3 points)

Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

Answers

Answer:

PART A :

AREA OF RECTANGLE = LENGTH × BREADTH

A = (4x + 5) (3x + 10)

A = 12(x^2) + 55x + 50

PART B: The above is a trinomial with the second degree. Trinomial because it has 3 terms and second degree because the variable(x) is squared.

PART C : Closure under addition and multiplication. Look at the signs.

Find the value of 9 ÷ 2/5​

Answers

Answer:

22(½)

Step-by-step explanation:

9 ÷ 2/5

9 × 5/2

45/2

22(½)

Answer:

Hello!

9 ÷ 2/5 = 9 × 5/2 = 45/2

Order the following decimals from least to greatest (separated by
commas).
0.33 0.83 0.2 0.57 0.5

Answers

Answer:

0.2, 0.33, 0.5, 0.57, 0.83

0.2 ,0.33, 0.5,0.58,0.83

f(x)=x2

g(x)=x−3

Find the composition of the two functions and show your process:

f(g(x))

Answers

Answer:

x²-6x+9

Step-by-step explanation:

f(x) = x²

g(x) = x-3

f(g(x)) = (x-3)²

=(x-3) (x-3)

= x²-3x-3x+9

= x²-6x+9

Answer:

[tex]f(x) = {x}^{2} \\ g(x) = x - 3 \\ f(g(x) = f(x - 3) = {(x - 3)}^{2} \\ = {x}^{2} - 2 \times x \times 3 + {3}^{2} \\ = {x}^{2} - 6x + 9 \\ thank \: you[/tex]

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