How do you do this question?

How Do You Do This Question?

Answers

Answer 1

Answer:

1) ∫₀¹ 2π x (x − x²) dx

4) ∫₀¹ π ((√y)² − y²) dy

Step-by-step explanation:

The solid formed is a hollow, upside down cone.  We can either use washer method or shell method to find the volume.

If we use washer method, the thickness of the washers is dy.  The outside radius is R = x₂ = √y, and the inside radius is r = x₁ = y.

Therefore, the volume of each washer is:

dV = π (R² − r²) t

dV = π ((√y)² − y²) dy

The total volume is the sum of all washers from y=0 to y=1.

V = ∫ dV

V = ∫₀¹ π ((√y)² − y²) dy

If we use shell method, the thickness of each shell is dx.  The radius of each shell is r = x.  The height of each shell is h = y₂ − y₁ = x − x².

Therefore, the volume of each shell is:

dV = 2π r h t

dV = 2π x (x − x²) dx

The total volume is the sum of all shells from x=0 to x=1.

V = ∫ dV

V = ∫₀¹ 2π x (x − x²) dx


Related Questions

There are 38 cars parked in the parking structure the parking structure is nor full to. Capacity there are 13 parking spaces that are empty what is the ratio of available parking spaces to parked cars

Answers

Answer: Decide which of the two given prices is the better deal and explain why. You can fill a 12 gallon tank of gas for $42.47 or buy gas for $3.60/gallon.

Step-by-step explanation:

A 3-column table has 3 rows. Column 1 is labeled Item with entries bread, peanut butter, jelly. Column 2 is labeled Quantity with entries 25 loaves, 2,400 ounces, 2,400 ounces. Column 3 is labeled unit price with entries 1 dollar and 95 cents per loaf, 16 cents per ounce, 8 cents per ounce. The table shows the quantity and unit prices for the items Camillo bought. Total cost for bread: ...? Total cost for peanut butter: .....? Total cost for jelly: ....? If he would have spent $986.50 without better-buy unit prices, how much money did he save?

Answers

Answer:

Bread total: 48.75

Penute butter: 384

Jelly: 192

He would have saved 361.75

Step-by-step explanation:

986.50- 48.75- 394-192= 361.75

Solve 6 sec^2x-1= 7.

Answers

x=4

2x-1=7
Move the constant to the right - 2x=7+1
Calculate - 2x=8
Divide both sides - x=4

If elephant grass grows 3 2/5 inches a day, how many inches will it grow in 7 days?

Answers

Step-by-step explanation:

do 3 2/5 times by 7 to get ur answer

Pablo's retirement party will cost $8 if he invites 4 guests. If there are 6 guests, how
will Pablo's retirement party cost? Solve using unit rates.

Answers

Answer:

$12

Step-by-step explanation:

Step 1:

$8 : 4 = x : 6

Step 2:

4x = 48

Answer:

x = 12

Hope This Helps :)

If QR = 18, RS = x -11, and QS = 2x - 11, what is QS?

Answers

Answer:

QS =25

Step-by-step explanation:

QR + RS = QS

18 + (x-11) =2x-11

7 +x =2x -11

18=x

Plug in x

2(18) -11

36-11

QS=25

18 + (18-11) = 2(18)- 11

18+ 7 = 36 -11

25= 25

True

Answer:

QS=QR+RS

2x-11= 18+x-11

2x-x= 18

x= 18

QS=2*18-11

=36-11

=25

) One weekend, there were 98 pizzas ordered for the sophomore dorm. That weekend 19 customers ordered their pizza with just pepperoni, 16 customers ordered their pizza with just sausage, 20 ordered theirs with just onions, 15 ordered theirs with pepperoni and sausage, 9 ordered theirs with sausage and onions, 17 ordered theirs with pepperoni and onions, and 2 ordered theirs with all three items. How many customers ordered their pizza with pepperoni or sausage (or both)

Answers

Answer:

19+16+15=50 pizzas

Step-by-step explanation:

-3/2+3/7 The denominator needs to be the same

Answers

Answer:

Step-by-step explanation:

To make the denominator same, find Lease common denominator of 2 and 7

LCD of 2 and 7 = 2*7 = 14

[tex]\frac{-3}{2}+\frac{3}{7}=\frac{-3*7}{2*7}+\frac{3*2}{7*2}\\\\\\=\frac{-21}{14}+\frac{6}{14}\\\\\\=\frac{-21+6}{14}\\\\\\=\frac{-15}{14}\\\\\\=-1\frac{1}{14}[/tex]

Answer:

-15/14

Step-by-step explanation:

Find the Least Common Denominator (LCD) for the two fractions, so the operation can be performed. The LCD is constructed from the factors the fractions have, making sure that all factors they need are included.

In our case, for the first fraction, the factor 2 is needed, and for the second fraction, the factor 7 is needed. Then the LCD is: 2 * 7 = 14

So now, let's write both denominators with the same LCD, by finding the appropriate equivalent fractions:

- 3 /2 = - (3*7) / (2*7) = -21 / 14

3 / 7 = (3*2) / (7*2) = 6 / 14

Therefore the combining can now be performed and renders:

- (21/ 14) + (6/ 14) = - (15/14)

The result is then the fraction : -15/14

Fraction Operation pls help

Answers

61/45 or 1 16/45 or 1.35

what is 4(1/2+3/4)+(-2)

Answers

Answer:

3

Step-by-step explanation:

4(1/2+3/4)+(-2)

4 x 5/4 - 2

5 - 2

3

i hope this helps :)

Answer:

your answer is 3

Step-by-step explanation:

Is 9.4 rational or irrational :p, please help

Answers

Answer:

i think its rational.  

Step-by-step explanation:

Maggie's brother is 8 years younger than twice her age. The sum of their ages is 25.
How old is Maggie?
Maggie is
years old.

Answers

Answer:

the sum is 25 not 24?

Step-by-step explanation:

Please help!!!!!!!!!!!

Answers

Answer:

with what?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Vertical angles are always congruent or equal

first when vertical angles are both 90 degrees , then vertical angles are supplementary and vertical

Simplify. 24/36 divided by 9/27

Answers

The answer for that would be 2

Graph the image of the given triangle under a dilation with a scale factor of –4 and center of dilation (0,0).

Answers

Step-by-step explanation:

Hey there!

The coordinates of a triangle are;

A (1,2)B (1,-2)C (-2,-2)Scale factor = -4 and centre at (0,0)

Now, We have;

P(x,y)----------- P'(kx, ky)

Keep formula;

A(1,2)---------- A'(-4×1 ,-4×2)

= A'(-4, -8)

B(1,-2)------------- B'(-4,8)

C(-2,-2)-------------C'(8,8)

[ The A' should be kept in (-4,-8). There was no place in this graph so, i kept it just below -7. Please while plotting remember to keep it on "-8".]

Hope it helps..

Choose the best description of the following number 18

Answers

Answer:

4.243

step by step explanation:

9.63 repeating as a mixed number

Answers

Answer:

9 and 7/11

Step-by-step explanation:

i hope this helps

The sum of two numbers is seventy-two. Twice one of them equals ten times the other. What are the numbers? Please Help MEE It would be Amazing

Answers

Let's create a system of equations to solve this.

x + y = 72

2x = 10y

Let's solve this equation for x

2x = 10y

Divide both sides by 2

x = 5y

Plug 5y into our first equation to solve for y

5y + y = 72

Combine like terms

6y = 72

Divide by 6

y = 12

x = 5y = 5(12) = 60

solve for x). -1/3x < -6 . Enter the solution to the inequality ​

Answers

Answer

x≥18

Step-by-step explanation:

What is 9.1% of 80? Round to the nearest hundredth (if necessary).

Answers

Answer:

7.28

Step-by-step explanation:

Answer: 7.28

Step-by-step explanation:

Which coordinate pair represents the reflection of (-4,6)

Answers

The answer is C because when it reflects the 4 stays negative and the 6 because negative because it reflected on the negative side

Hope this helped! :))

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 61 type I ovens has a mean repair cost of $79.60, with a standard deviation of $23.47. A sample of 45 type II ovens has a mean repair cost of $75.25, with a standard deviation of $15.07. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens.Step 3 of 4 : Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Answers

The question is missing some parts. Here is the complete question.

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost in type II ovens. A samplle of 61 type I ovens has a mean repair cost of $79.60, with a standard deviation of $23.47. A sample of 45 type II ovens has a mean repair cost of $75.25, with standar deviation of $15.07. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let [tex]\mu_{1}[/tex] be the true mean repair cost for type I ovens and [tex]\mu_{2}[/tex] be the true mean repair cost for type II ovens.

Step 1 of 4: State null and alternative hypothesis for the test.

Step 2 of 4: Compute the value of test statistics. Round your answer to 2 decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to 3 decimal places.

Step 4 of 4: Make the decision for the hypothesis test. (Reject or fail to reject Null Hypothesis)

Answer and Step-by-step explanation:

First, state null and alternative hypothesis:

[tex]H_{0}: \mu_{1}=\mu_{2}[/tex]

[tex]H_{a}: \mu_{1}>\mu_{2}[/tex]

Use z-statistics:

[tex]z = \frac{x_{1}-x_{2}}{y}[/tex]

where x₁ and x₂ are the means and:

[tex]y=\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}} }[/tex]

Calculating value of test stattistic:

[tex]y=\sqrt{\frac{(23.47)^{2}}{61}+\frac{75.25^{2}}{45} }[/tex]

[tex]y = \sqrt{9.030+5.046}[/tex]

[tex]y = \sqrt{14.076}[/tex]

y = 3.752

[tex]z = \frac{79.6-75.25}{3.752}[/tex]

z = 1.16

The test statistics is z = 1.16

The decision rule for rejecting null hypothesis is: [tex]\alpha[/tex] ≤ test statistics

Using z-score table, it is possible to determine p-value, which is:

p-value = 0.877

Comparing p-value with level of significance (α = 0.05):

0.877 > 0.05

Therefore, we fail to reject the null hypothesis.

In Seattle, WA, it is said to rain 66% of the time. Since there are 365 days in a year, approximately how many days is it expected To rain? ​

Answers

365days is 100%
xdays is 66%

66x365 =24090
24090/100= 240,9
it’s expected to rain approximately 241 days

In a year with 365 days, it should rain for about 240 of those days for the given condition.

What is the percentage?

It is the ratio of two integers expressed as a decimal fraction of a whole number. It is a statistic for contrasting two sets of data, and the % sign is used to describe it as a percentage. Percentages are often and creatively used. For instance, a lot of data is published as percentages in the media, including bank interest rates, retail discounts, and inflation rates.

It is supposed to rain 66% of the time in Seattle, Washington. Considering that there are 365 days in a year,

Suppose the number of days is it expected to rain obtained be x,

x=66% of 365

x=66/100 × 365

x=240,9 ≈ 240

Thus, it should rain for about 240 days.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ2

what is the slope of the line ?

Answers

Answer:

The slope is -1.

Answer:

-1

Step-by-step explanation:

To solve follow the formula Y1-Y2 over X1-X2, pick two points like (0,2) and (1,1) then plug them in.

2-1 over 0-1 which equals -1/1

You have a part-time job. You earn $7.75 per hour. If you work 20 hours
each week, what is your straight-time pay for each week?

A. $140
B. $145
C. $148
D. $150
E. $152
F. $155

Answers

Answer:

F. $155

Step-by-step explanation:

For this problem we simply need to multiply the base hourly pay by the amount of hours worked to find the straight-time pay for each week.

$7.75 * 20 = $155

Thus, your weekly pay will be $155.

Cheers.

F 155 earned per hour if you worked

Find the percent change. State whether it is an increase or decrease. Round to the nearest tenth of a percent. From 50 to 42

Answers

Answer:

16% decrease

Step-by-step explanation:

A car rental business charges a daily fee along with a one-time fixed charge to refuel the car when it is returned. The equation the business uses to calculate the total rental cost, c is c=15d+24c = 15 d + 24, where d represents the number of rental days. What is the daily increase in the total cost of the rental?

Answers

Answer:

$15

Step-by-step explanation:

Since we are given the actual equation, which is c = 15d + 24 (it is repeated in the question twice) we can see that the independent variable would be the number of days that the car is rented. Therefore we can simply plug in a value for this to calculate c. So below we can see the total cost for 1 day rent (d = 1 ) and 2 days rented (d = 2)

c = 15(1) + 24 = 39

c = 15(2) + 24 = 54

Now we can simply subtract these two values and to see the daily increase

54-39 = 15

Therefore we can see that the total price will increase by $15 for each day that it is rented.

Inez says you can plot 4/5 on a number line, but Jeremiah says you cannot. Who is correct?

Answers

Inez is correct, 4/5 is a real number

Answer:

Inez is correct.

Step-by-step explanation:

You can plot any real number on a number line.

9-6=3, 6+3=9, 3+6=9 what is the missing fact family?

Answers

Answer:

9-3=6

Step-by-step explanation:

An addition/subtraction fact family has 2 addition equations and 2 subtraction ones.

The question already states both addition ones, but only one subtraction

The subtraction one stated is 9-6=3

The opposite is 9-3=6

Hope this helps :-)

.48 covert to fraction

Answers

Answer:

12/25

Step-by-step explanation:

answer: 12/25 48%
explanation: Since there are 2 digits in 48, the very last digit is the "100th" decimal place. So we can just say that . 48 is the same as 48/100. terms by dividing both the numerator and denominator by 4.
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