Use cylindrical shells to find the volume of the solid generated when the region
R under y = x2 over the interval (0,2) revolved about the line y = -1

Use Cylindrical Shells To Find The Volume Of The Solid Generated When The RegionR Under Y = X2 Over The

Answers

Answer 1

Answer:

[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Terms/CoefficientsExpandingFunctionsFunction NotationGraphingExponential Rule [Root Rewrite]:                                                                     [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]

Calculus

Integrals

Definite IntegralsArea under the curve

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

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

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

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

Shell Method:

[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

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

Step-by-step explanation:

Step 1: Define

Identify

Graph of region

y = x²

x = 2

y = 4

Axis of Revolution: y = -1

Step 2: Sort

We are revolving around a horizontal line.

[Function] Rewrite in terms of y:                                                                      x = √y[Graph] Identify bounds of integration:                                                           [0, 4]

Step 3: Find Volume Pt. 1

[Shell Method] Find distance of radius x:                                                       [tex]x = y + 1[/tex][Shell Method] Find circumference variable f(x) [Area]:                                 [tex]\displaystyle f(x) = 2 - \sqrt{y}[/tex][Shell Method] Substitute in variables:                                                           [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - \sqrt{y})} \, dy[/tex][Integral] Rewrite integrand [Exponential Rule - Root Rewrite]:                    [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - y^\bigg{\frac{1}{2}})} \, dy[/tex][Integral] Expand integrand:                                                                            [tex]\displaystyle V = 2\pi \int\limits^4_0 {(-y^\bigg{\frac{3}{2}} + 2y - y^\bigg{\frac{1}{2}} + 2)} \, dy[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]:                        [tex]\displaystyle V = 2\pi \bigg( \frac{-2y^\bigg{\frac{5}{2}}}{5} + y^2 - \frac{2y^\bigg{\frac{3}{2}}}{3} + 2y \bigg) \bigg| \limits^4_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:              [tex]\displaystyle V = 2\pi (\frac{88}{15})[/tex]Multiply:                                                                                                             [tex]\displaystyle V = \frac{176 \pi}{15}[/tex]

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

Unit: Applications of Integration

Book: College Calculus 10e


Related Questions

You are a 60 year old male. You want $1,000,000.00 in term life insurance. It will cost you $13.22 per $1,000.
Calculate the annual premium.
A $11,220.00
B $12,220.00
C $13,220.00
D $14,220.00

Answers

Answer:

C $13,220

Step-by-step explanation:

PLEASE HELP ME PLEASE

Answers

Answer:

Ok so these triangle are the same with equivalent angles

so we can add up the angles 80+26=106

now we subtract from 180

180-106=74

so the measure of angle b is 74

Hope This Helps!!!

Give two examples of subtraction of fractions ( between 0-1) with different denominators.
SHOW ALL STEPS

Answers

Answer:

3/4-1/2=1/4 4/5-3/15

Step-by-step explanation:

3/4-1/2

=3/4-2/4

=1/4

4/5-3/15

=4/5-1/5

=3/5

ok i think you guys can do it​

Answers

[tex] {64}^{ \frac{2}{3} } \div {27}^{ \frac{5}{3} } \times 54 \\ = > \: {({2}^{3} )}^{ \frac{2}{3} } \div ({{3}^{3}})^{ \frac{5}{3} } \times 54 \\ = > \: {2}^{2} \div {3}^{5} \times 54 \\ = > \: 4 \div 243 \times 54 \\ = > \: 4 \div 13122 \\ = > \: \frac{4}{13122} \\ = > \: \frac{2}{6561} [/tex]

Hope it helps!!!!!!!!!!

((64)^1/3)^2 / ((27)^1/3)^5 x 54
= 4^2 / 3^5 x 54
= 16 x 54 / 243 [= 16 x (2 x 27) / (9 x 27)]
= 32/9

Please show process!!!!
THANK YOU!
Will mark brainylist

Answers

Answer: 103 degrees

Step-by-step explanation:

51 + 26 = 77

A triangle adds up to 180 degrees

180 - 77 = 103

= 103 degrees

How do I make people brainliest

Answers

Answer:

you have to wait until two people answer then you click their answer to make them brainliest

Step-by-step explanation:

i dont know

blah blah blah blah blah blah blah blah blah blah blah blah

Evaluate for x=2 and y=3: x^2y^-3/x^-1y

Answers

Answer:

8/81

Step-by-step explanation:

It's most efficient to simplify the quotient algebraically before inserting the values of the variables x and y.  

The given expression reduces to x³ / y^4.

Substituting 2 for x and 3 for y, we get:

 (2)³           8

--------- = ---------- (Agrees with first given possible answer)

 (3)^4         81

What is the longest side of a right angled triangle called?

Answers

Answer:

The hypotenuse

1-0.4^n>=0.99 howwwwwwwwwwwwwwwwwwwwwwwwww

Answers

Answer:

n>=6

Step-by-step explanation:

1-0.4ⁿ>=0.99

1-0.99>=0.4ⁿ

0.4ⁿ<=0.01

Apply log10:

Log10(0.4ⁿ)<=log10(0.01)

n×log10(0.4)<=log10(0.01)=-2

Because log10(0.4)=-0.39794 is negative we get:

n>=5.028.

Since n is integer, we have n>=6

Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
X +3 SO
X-220
y

Answers

Answer:

Step-by-step explanation:

X+3 SO = Cymath can't further simplify this.

Please try another operation.

X-220= Cymath can't further simplify this.

Please try another operation.

y= AsymptotesFind the vertical, horizontal and slant asymptotes.

"Asymptotes y=x^2/(x+8)"

"Asymptotes y=1/x"

DifferentiateFind the derivative.

"Differentiate cos(x)^4"

"Differentiate x^5/y for x"

DomainFind the domain of a function.

"Domain y=2/x"

"Domain y=sqrt(x-3)"

You work for a parts manufacturing company and are tasked with exploring the wear lifetime of a certain bearing. You gather data on oil viscosity used and load. You see the regression output given below.
Predictor Coef Stdev t-ratio P
Constant -147.973 41.972 -3.53 0.004181
viscosity 6.262 0.474 13.21 <0.0001
load 0.298 0.04 7.43 <0.0001

s = 13.507 R² = 95.73% R² (adj = 95.02%

Analysis of Variance

Source DF SS MS F
Regression 2 49131.93 24565.96 134.65
Error 12 2189.38 182.45
Total 14 51321.3

Required:
What is the correct conclusion about the regression slopes based solely on the F-test

Answers

Answer:

We reject the Null and conclude that There is significant evidence that the slope values are greater than 0.

Step-by-step explanation:

Based on the ANOVA output given :

The F critical value can be obtained thus ;

F(df regression, df error)

Using an α-value of 0.01

F(2, 12) at α = 0.01 is 6.927

The F statistic as obtained from the ANOVA table = 134.65

Since, F statistic > F critical we reject the Null and conclude that slope values are significantly > 0

Similarly,

Using the Pvalue :

The Pvalue of the slope are extremely small :

Viscosity <0.0001

Load <0.0001

At α = 0.01, 0.025

The Pvalue < α ; The null will be rejected.

Recall the creative calligraphy case we discussed in class. Suppose you have received a rush order of 55 invitations that have to be created in the next (four hour) work session. What is the most time You (i.e. not Susie) can spend writing on the card and envelope for each invitation and still fill the order

Answers

Answer:

About 4 minutes and 3 seconds

Step-by-step explanation:

If I have 55 invitations to be created in four hours.

4 hours × 60 =240 minutes

240/55= 4.36 minutes

So if I spend 4 minutes and 3 seconds on an invitation, I should be able to fill the order.

Which describes the transformations applied in the figure above?
1. A clockwise rotation of 180 degrees about the origin.

2. A counterclockwise rotation of 270 degrees about the origin.

3. A counterclockwise rotation of 90 degrees about the origin.

4. A clockwise rotation of 270 degrees about the origin.

Answers

Answer:

2. A counterclockwise rotation of 270 degrees about the origin.

Step-by-step explanation:

Point A before the transformation:

Before the transformation, point A was at (-2,2).

After the transformation, point A' is (2,2).

Point B:

Before the transformation, point B was at (-6,-3)

After the transformation, point B' is (-3,6).

Transformation rule:

From the transformations of points A and B, we get that the transformation rule is (x,y) -> (y,-x), which is a counterclockwise rotation of 270 degrees about the origin., and the correct answer is given by option 2.

When randomly selecting​ adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) ​represent? Is P(M|B) the same as P(B|M)​?

Answers

Answer:

See explanation

Step-by-step explanation:

Given

[tex]M \to[/tex] randomly selecting a male

[tex]B \to[/tex] randomly selecting someone with blue eyes

Solving (a): Interpret P(M|B)

The above implies conditional probability

The interpretation is: the probability of selecting a male provided that a person with blue eyes has been selected

Solving (b): is (a) the same as P(B|M)

No, they are not the same.

The interpretation of P(B|M) is: the probability of selecting a person with blue eyes provided that a male has been selected

For the inequality 4x2>y−3, where is the graph shaded and is the curve solid or dotted?

Answers

Answer:

Dotted Curve

Shaded Area includes the Origin.

Step-by-step explanation:

I am assuming that you mean 4x² > y-3.

Since the inequality sign is greater than, the line would be dotted. The curve would be solid if the inequality was an 'X or equal to' sign.

----------------------------------

4(0)² > 0 - 3

0 > -3

Since the given statement is true, the origin is a solution and we would shade below the curve.

----------------------------------

See the graph attached.

Hope this helps.

$2900 at 13% for 30 years. i need simple interest and compounding interest

Answers

Answer:

Step-by-step explanation:

simple:

2900(1+.13*30)=14210

Compounding

[tex]2900(1+.13)^{30}=113436.1041[/tex]

Answer:

113436.1041

Step-by-step explanation:

2900 ( 1 +0.13 ) ^ 30

Formula : amount ( 1 + percentage ) ^ years

PLEASE ANSWER ILL MARK !!

Answers

Step-by-step explanation:

a) Use sine law:

[tex]\dfrac{g}{\sin 60} = \dfrac{17\:m}{\sin 49}[/tex]

Solving for g,

[tex]g = \left(\dfrac{\sin 60}{\sin 49}\right)(17\:m)=19.5\:m[/tex]

b) Use the cosine law here:

[tex]q^2 = (11\:\text{cm})^2 + (16\:\text{cm})^2 \\ - 2(11\:\text{cm})(16\:\text{cm})\cos 29[/tex]

Solving for q,

[tex]q = 8.3\:\text{cm}[/tex]


Which of the following is equivalent to
5v13^3

Answers

Answer:

13⅗ is the answer of your quest

The answer is D. The last one.

13 3/5.

How's The online class?

Answers

Answer:

weak

Step-by-step explanation:

i dont be having fun at all

Ehhhhh it’s okay I guess

please simplify this one. I need answers fast as possible .(chapter name : surds )​

Answers

[tex] \sqrt[5]{32} \times 2 \sqrt[3]{81} \\ = {32}^{ \frac{1}{5} } \times 2 {(81)}^{ \frac{1}{3} } \\ = ({{2}^{5}})^{ \frac{1}{5} } \times {2({3}^{3})}^{ \frac{1}{3} } \\ = {2}^{1} \times 2({3}^{1}) \\ = 2 \times 2 \times 3 \\ = 4 \times 3 \\ = 12[/tex]

This is the answer.

Hope it helps!!

5xsr(32) x 2xcr(81)
= 5xsr(4x4x2) x 2xcr(3x3x3x3)
= 5 x 4 x (2)^1/2 x 2 x 3 x (3)^1/3
= 5 x 4 x 2 x 3 x (2^3)^1/6 x (3^2)^1/6
= 120 x (8)^1/6 x (9)^1/6
= 120 x (72)^1/6

If a student answered 77 exam questions correctly out of 100, what fraction
and what percentage of questions did the student answer incorrectly?
Choose two answers.
A. 0.77%
B.
20
100
IC
23
100
I D. 23%
O E. 77%
OF
77
100

Answers

Answer: 23%

Step-by-step explanation: 77 + 23 is 100

Answer:

77 out of 100

Step-by-step explanation:

For a fraction, it would look like 77/100,

and for percentage, 77%.

The waiting time for a fire department to get called to a house fire is exponentially distributed with an average wait time of 14 minutes. Given that it has already taken 11 minutes, what is the probability that the wait time will be more than an additional 16 minutes?

Answers

Answer:

0.319 = 31.9% probability that the wait time will be more than an additional 16 minutes

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: It has already taken 11 minutes.

Event B: It will take 16 more minutes.

Exponentially distributed with an average wait time of 14 minutes.

This means that [tex]m = 14, \mu = \frac{1}{14}[/tex]

Probability of the waiting time being of at least 11 minutes:

[tex]P(A) = P(X > 11) = e^{-\frac{11}{14}} = 0.4558[/tex]

Probability of the waiting time being of at least 11 minutes, and more than an additional 16 minutes:

More than 11 + 16 = 27 minutes. So

[tex]P(A \cap B) = P(X > 27) = e^{-\frac{27}{14}} = 0.1454[/tex]

What is the probability that the wait time will be more than an additional 16 minutes?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1454}{0.4558} = 0.319[/tex]

0.319 = 31.9% probability that the wait time will be more than an additional 16 minutes

You and a friend were invited to a
party. You both were asked to bring
pizzas and chips. Your friend brought
three pizzas and four bags of chips
and spent $48.05. You brought five
pizzas and two bags of chips and
spent $67.25. What is the cost of
each? Answer should be in (Pizza, Chips)

Answers

Answer:

Pizza = 12.35

Chips = 2.75

Step-by-step explanation:

Let :

Pizza = x

chips = y

3x + 4y = 48.05 - - - (1)

5x + 2y = 67.25 - - - (2)

Multiply (1) by 5 and (2) by 3

15x + 20y = 240.25

15x + 6y = 201.75

Subtract :

20y - 6y = 240.25 - 201.75

14y = 38.50

y = 38.50/ 14

y = 2.75

Put y = 2.75 in (1)

3x + 4(2.75) = 48.05

3x + 11 = 48.05

3x = 48.05 - 11

3x = 37.05

x = 37.05 / 3

x = 12.35

Pizza = 12.35

Chips = 2.75

The principal P is borrowed at a simple interest rate are for a period of time T. Find the loans future value A, or the total amount due at time T

Answers

Answer:

The total amount due after five years is $57,000.

Step-by-step explanation:

Recall that simple interest is given by the formula:

[tex]\displaystyle A=P(1+rt)[/tex]

Where A is the final amount, P is the principal amount, r is the rate, and t is the time (in years).

Since we are investing a principal amount of $38,000 at a rate of 10.0% for five years, P = 38000, r = 0.1, and t = 5. Substitute:

[tex]\displaystyle A=38000(1+(0.1)(5))[/tex]

Evaluate. Hence:

[tex]\displaystyle A=\$ 57,000[/tex]

The total amount due after five years is $57,000.

Ralph bought a computer monitor with an area of 384 square inches. The length of the monitor is six times the quantity of five less than half its width.

Answers

Answer:

eh width = 103.5 inches

Step-by-step explanation:

x = width

Length = (x/2 - 5 )*6

so 384=x+3x-30

414=4x

x=414/4=103.5 inches

Need help putting the answer in

Answers

Step-by-step explanation:

We can rewrite the given equation as

[tex]x^2 + \frac{1}{5}x - \frac{12}{25} = (x + \frac{4}{5})(x - \frac{3}{5})[/tex]

As a check, let's multiply out the factors:

[tex](x + \frac{4}{5})(x - \frac{3}{5}) = x^2 - \frac{3}{5}x + \frac{4}{5}x - \frac{12}{25}[/tex]

[tex]= x^2 + \frac{1}{5}x - \frac{12}{25}[/tex]

and this is our original equation.

An 8-oz bottle of hair spray costs $4.46. Find the unit price in cents per ounce

Answers

Answer:

55.75 cents per ounce

Step-by-step explanation:

Take the cost and divide by the number of ounces

We want cents per ounce so change dollars to cents

446 / 8

55.75 cents per ounce

X+ 1
If g(x)=
X-2 and h(x) = 4 – x, what is the value of (g•)(-3)?
ola Mo Nional
15
2
18

Answers

It’s 2 because I said so and I also just took the test

Identify the level of measurement (nominal, ordinal, or interval-ratio) of each of the following variables: (1) How satisfied a person is with his or her employment benefits, measured as very satisfied, somewhat satisfied, neither satisfied nor dissatisfied, somewhat dissatisfied, or very dissatisfied. (2) The number of times someone has shoplifted in her or his life. (3) The number of times someone has voted in a public election measured as 0-1 times, 2-3 times, or 4 or more times. (4) The type of attomey a criminal defendant has attrial, measured as privately retained or publicly funded.

Answers

Solution :

Nominal variable

A nominal variable is defined as a variable which is used to [tex]\text{nam}e \text{ or label or categorize some particular attributes }[/tex]  which are being measured.

An ordinal variable is the one in which the order matters, but the difference between any two orders does not matter.

In interval ratio variable is defined as the variable where the difference between any two values is meaningful.

The level of measurement  for each of the following are :

1) Variables that are categorized in categories so that it is ordinal data.

2) Data scaled with the two categories her or his,  so it is a nominal data.

3) Number of votes categorized in the intervals so it is Interval type data.

4) nominal data.

3. Tell whether each statement is true or false Explain how you know a) LCM (7, 18) - LCM (14.18) b) LCM (5,8) - LCM (10,8) c) The GCF of any two prime numbers is 1 and the number itself.​

Answers

Step-by-step explanation:

ok for a. the both are 126

and for b. the both are 30

for c. i believe its true

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