Mathematics, 02.07.2021 01:00 alexmoy45p8yd7v

Please Help NO LINKS Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
9
,
about the
y
-axis.

V
=

Answers: 1

Show answers

Answers

Answer from: ari313

$\displaystyle V = \frac{6561 \pi}{2}$

General Formulas and Concepts:

Algebra I

FunctionsFunction NotationGraphing

Calculus

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Shell Method: $\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx$

[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volume

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 9

Step 2: Identify

Find other information from graph.

See attachment.

Bounds of Integration: [0, 9]

Step 3: Find Volume

Substitute in variables [Shell Method]: $\displaystyle V = 2\pi \int\limits^9_0 {x(x^2)} \, dx$ [Integrand] Multiply: $\displaystyle V = 2\pi \int\limits^9_0 {x^3} \, dx$ [Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^9_0$ Evaluate [Integration Rule - FTC 1]: $\displaystyle V = 2\pi \bigg( \frac{6561}{4} \bigg)$ Multiply: $\displaystyle V = \frac{6561 \pi}{2}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

Please Help NO LINKS

Use cylindrical shells to find the volume of the solid obtained by rotating th

Answer from: Quest

answer: 2 multiplied by x =24

step-by-step explanation:

Answer from: Quest

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:00, vanessadaniellet21

Analyze the data sets below. data set a 25,25,25,26,26,26,27,28,28,29,30,31 ,31,32,33,33,34,35,35,35 data set b 25,25,25,26,26,26,26,27,27,27,27,28 ,28,29,29,30,31,31,32,34 which of the following statement are true? select all that apply. a. data set a is relatively symmetric and data set b is skewed left. b. the means of the data sets are within 3 units from eachother. c. the data sets have the same standard deviation. d. the mean of data set a is 27.95 and the mean of data set b is 30. e. the data set b has a higher standard deviation than data set a. f. the mean and median of data set a are close in value.

Answers: 3

continue

Mathematics, 21.06.2019 21:00, gavinarcheroz2jxq

Ireally need subtract and simplify.(-y^2 – 4y - 8) – (-4y^2 – 6y + 3)show your work, ! i will mark you brainliest but you have to show your work.

Answers: 1

continue

Mathematics, 21.06.2019 22:00, kashbaby

Aschool had an election where the candidates received votes in the ratio 1: 2: 3. if the winning candidate received 210 votes, how many total people voted in the election?

Answers: 1

continue

Mathematics, 21.06.2019 22:30, carleenespriu

Opposite angles in a parrellelogram are

Answers: 1

continue

You know the right answer?

Please Help NO LINKS Use cylindrical shells to find the volume of the solid obtained by rotating th...