Find the volumes of the solids whose bases are bounded by the circle x^2 + y^2 = 9, with the indicated cross sections taken perpendicular to the x-axis.
a) Squares

Answers

Answer 1

x ^2 + y ^2 = 9   =>   y = y(x) = ± √(9 - x ^2)

Each cross section would be a square with side length equal to the vertical distance between the upper and lower semicircles defined by y(x), which is

√(9 - x ^2) - (- √(9 - x ^2)) = 2 √(9 - x ^2)

The area of each square section is the square of this length,

(2 √(9 - x ^2)) = 4 (9 - x ^2) = 36 - 4x ^2

We get the whole solid for -3 ≤ x ≤ 3, so integrating gives a volume of

[tex]\displaystyle\int_{-3}^3(36-4x^2)\,\mathrm dx=\boxed{144}[/tex]


Related Questions

Select the FALSE statement regarding the relationship between sampling error and sample size. a.) As a sample size decreases, the standard deviation increases. b.) An estimate becomes more accurate as you increase the sample size. c.) You can resolve poor data collection by increasing the sample size. d.) Increasing the sample size will decrease the sampling error.

Answers

Answer:

Option C

Step-by-step explanation:

The standard deviation of any sample is inversely proportional to the size of the sample. Thus, as the sample size increases, the standard deviation reduces or vice versa. Thus, option A is in correct

As the sample size increases, the confidence in estimate also increases Hence, option B is also incorrect

Option D is true to its words , hence it is also a wrong choice for this question

Hence, option C is correct

Answer:

You can resolve poor data collection by increasing the sample size

Step-by-step explanation:

What is 103% of 127?

Answers

Answer:

130.81

Step-by-step explanation:

127 ⋅ ( 103/ 100 ) =130.81

Find the number of sides of a regular polygon if the sum of the interior angles of the
polygon is 7020

Answers

Answer:

n = 6

Step-by-step explanation:

Given the following data;

Sum of interior angles, S = 720°

Mathematically, the sum of the interior angles in a regular polygon is given by the formula;

S = 180(n - 2)

Where;

n is the number of sides.

S is the sim of the interior angles

720 = 180(n - 2)

720 = 180n - 360

180n = 720 + 360

180n = 1080

n = 6

The 8 red markers in a package account for 4% of all markers in the package. How many markers are in the package?

Answers

Answer:

192 markers

Step-by-step explanation:

if 8 = 4% then 2=1%

so we can assume there are 200markers in the package.

8-200= 192 markers

How many degrees Fahrenheit is -20°C?

Answers

answer:

-4°f

step-by-step explanation:

(-20°c × 9/5) + 32

= -4°f

good luck :)

i hope this helps

brainliest would be highly appreciated

have a nice day!

How much INTEREST would you earn investing $5000 that earns 7% simple annual interest for 3 years?

Answers

Answer:

$1,125.26

Step-by-step explanation:

Start of Year 1 5000.00

Start of Year 2 5350.00

Start of Year 3 5724.50

Start of Year 4 6125.26


2. Celesta used to spend 90 minutes a day on the phone. Now she spends
60 minutes a day. What is the PERCENT DECREASE? *

Answers

Answer:

33%

Step-by-step explanation:

sorry my bad i did percentage increase.

The identity (x2 + y2) = (x2 - y2) + (2xy)? can be used to generate Pythagorean triples. What
Pythagorean triple could be generated using x=8 and y=3

Answers

Answer: 5329, 3025, 2304

Step-by-step explanation:

I just did the test

Pythagorean triple generated is 5329

What is Pythagorean triple?

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written, and a well-known example is. If is a Pythagorean triple, then so is for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime

We have,

([tex]x^{2}[/tex]+[tex]y^{2}[/tex] )=( [tex]x^{2}[/tex]-[tex]y^{2}[/tex]) + [tex]2xy[/tex]

Using Points,

x =8, y=3

According to the questions

Taking square in both sides

[tex](x^{2} + y^{2}) ^{2}[/tex] = [tex](x^{2} - y^{2} ) ^{2}[/tex] + [tex](2xy)^{2}[/tex]

when, x = 8, and  y = 3

[tex](8^{2} + 3^{2} )^{2}[/tex] = [tex](8^{2} - 3^{2}) ^{2}[/tex]  + [tex](2.8.3)^{2}[/tex]

               = 3025 + 2304

               = 5329

Hence ,Pythagorean triple is 5329

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A hat contains 3 blue and 5 black tickets.

​If one ticket is chosen at random from the hat, what is the probability that it is blue?

I WILL GIVE BRAINLIST ANSWER

Answers

Answer:

the answer is 3/8

Step-by-step explanation:

Which choices describe a Subscript n Baseline = 4 (0.9) Superscript n? Check all that apply.

S1 = 4
S2 = 6.84
S3 = 10.156

The sequence diverges.

Answers

Answer:

b and d

Step-by-step explanation:

edge 2021

If the first term (a) is 4 and the common ratio (r) is 0.9, then the sequence diverges. Then the correct option is D.

What is a geometric sequence?

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

a, ar, ar², ar³, ...

The sequence is given below.

[tex]\rm a_n = 4 (0.9)^n[/tex]

Then the sum of the sequence will be given as

The first term (a) is 4. And the common ratio (r) is 0.9.

Then we get

[tex]\rm S_n = \dfrac{a (1 - r ^n)}{ (1 - r)}\\\\\rm S_n = \dfrac{4 (1 - 0.9 ^n)}{ (1 - 0.9)}\\\\\rm S_n = \dfrac{4 (1 - 0.9 ^n)}{0.1}\\\\\rm S_n = 40 (1 - 0.9^n)[/tex]

For n = 1, we have

S₁ = 40 (1 - 0.9)

S₁ = 40 x 0.1

S₁ = 4

For n = 2, we have

S₂ = 40 (1 - 0.9²)

S₂ = 40 x 0.19

S₂ = 7.6

For n = 3, we have

S₃ = 40 (1 - 0.9³)

S₃ = 40 x 0.271

S₃ = 10.84

If the common ratio is less than one then the sequence will diverge.

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Pls help 10 ptsss
NO LINKS

Answers

Answer:

0,15/ 5,20/ 10,25/ 15,30/ 25,35

Step-by-step explanation:

the additional hours is x and total hours is y.

What number is halfway between 0.36 and 0.48 on a number line?

Answers

Answer:

0.42

Step-by-step explanation:

they are both multiples of 0.06

think of it like 6 x 6= 36 and 6 x 8 = 48

6 x 7 = 42 would be halfway

Answer:

0.42

Step-by-step explanation:

To find the half, add da numbers and divide by 2. So 0.36 and 0.48 added together is 0.84. That divided by 2 is 0.42.

What is the mean?
-4 -3 0 -4 -3 0

Answers

Answer:

−4−(3)(0)−4−(3)(0)

=−8

Answer:

-2 and 1/3

Step-by-step explanation:

-4+-3+0+-4+-3+0 = -14

6 numbers

-14/6 = -2 1/3

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

A)2 1/4
B)-9 1/4
C)-2 1/4
D)-8 2/3

Answers

Answer:

-9 1/4

Step-by-step explanation:

-5 3/4 - 3 1/2

Get a common denominator

-5 3/4  - 3 1/2 *2/2

-5 3/4  - 3 2/4

-8  5/4

Rewritng

-8 4/4 - 1/4

-9 1/4

The radius of a circle is 6.1 millimeters. What is the circle's area?

Answers

[tex]area = \pi \times {r}^{2} \\ area = 3.142 \times {6.1}^{2} \\ area = 3.142 \times 37.21 \\ area = 116.91 {mm}^{2} [/tex]

Find the midpoint of the line segment with endpoints (3,-5) and (7.9).​

Answers

Answer:

x midpoint 5

y midpoint 2

(5,2)

What is a hand drawn picture or design of a 3D object

Answers

Answer:

hello

Step-by-step explanation:

i think it is modelling

hope it helps

have a nice day

I am pretty sure it's modeling!

Number 26 (PlSss Help I really need help on this) I’ll give 15 points!!!!!!

Answers

[tex]\mathcal\pink{The \: answer \: is }[/tex]

only one window has height that is a whole number of centimeters

[tex]\mathcal{HOPE \: IT \: HELPS}[/tex]

[tex]\huge\pink{mark \: as \: brainliest}[/tex]

What is the volume of an 8-inch by 4-inch by 44-inch rectangular box?​

Answers

Answer:

1408

Step-by-step explanation:

Answer:

1,408 cm³.

Step-by-step explanation:

To find the volume of a rectangular prism, or in this case, a rectangular box, multiply the length, width, and height.

[tex]4*8*44=1,408 in^3.[/tex]

Therefore, the volume of the rectangular box is 1,408 cm³.

H
45
G
8
F
3
Ε
Find
cos FHE.

Answers

Answer:

no sé pero lo nesesito porfavor

Answer:

Its B. 4/5

Step-by-step explanation:

on edge 2020 :)

Mr. Matthews gives each of his 32 students 15 minutes to
present a book report to the class. How many minutes
will it take for all of his students to present their reports?

Answers

Answer:

480 minutes or 8 hours

Step-by-step explanation:

1 student = 15 minutes

32 students = x

x= 32 students *15 minutes

x=  480 minutes

480 minutes it takes for all of his students to present their reports.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total Students= 32

Each student can take = 15 minutes.

So, time taken by 32 students

= 32 x 15

= 480 minutes.

Hence, students take 480 minutes to complete the report.

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Which one is greater?
1.74 × 0.84
OR
1.79 × 0.69
- NO LINKS DOCS OR FILES ETC

Answers

Answer:

1.75 * 0.84

Step-by-step explanation:

1.74 * 0.84 = 1.4616

1.79 * 0.69 = 1.2351

Answer:

1.74 x 0.84 is greater

Step-by-step explanation:

1.74 x 0.84 = 1.4616

while

1.79 x 0.69 = 1.23509

What is the coefficient in the following expression?
5a– 7

Answers

5 is the Coefficient
the coefficient is 5

Find the value that makes the proportion true

5/6= ?/180

Answers

Answer:

D, or 150

Step-by-step explanation:

We can see that we have to multiply 6 by 30 to get 180. So, if we multiply the denominator by this and we want an equal fraction, we can multiply 5 by 30 to get [tex]5\cdot30=150[/tex].

Answer/Step-by-step explanation:

I think its "D. 150"!

-Hope this helped, Comment if you have any other questions!

Beth has a box containing music CDs. Each CD contains songs from only one of these three genres: pop (P), hip-hop (H), and rock (R). She picks one CD from the box, replaces it, and then picks another CD. The sample space for this event is listed.

P-P H-P R-P
P-H H-H R-H
P-R R-R


What is the missing term for this compound event? What is the sample size?

A.
The missing term is H-P, and the sample size is 9.
B.
The missing term is H-R, and the sample size is 9.
C.
The missing term is H-P, and the sample size is 3.
D.
The missing term is H-R, and the sample size is 3.

Answers

Answer:

B). The missing term is H-R, and the sample size is 9.

Step-by-step explanation:

Compound event is characterized as the likelihood of occurring two autonomous events at least one or more than one probable outcome.

As per the details provided, 'the term that is omitted in the given event of the compound would be (H-R) and the size of the sample would be 9(' including this missing one. The eight combination possibilities of the CDs have already been provided and thus, the last one would be 'H-R'(hip-hop and rock music CDs). This is why the total number of possibilities turns 9. Thus, option B is the correct answer.

Answer:  the answer is B :)

Step-by-step explanation:

Find the surface area of the cone. Round answer to the nearest tenth.*

Answers

Answer:

628.319 rounded= 628.3

Step-by-step

Find the perimeter X(-2,1) Y(4,3) Z(5,-1)

Answers

Answer:

17.728

Step-by-step explanation:

In the figure to the right, what is the measure of angle DAC ?

I’m not going to show answer Options because I don’t want anyone to put something random

Don’t put links cs I’m not going to press it <3

Answers

Answer:

47 degrees

Step-by-step explanation:

i am super smart

A rectangular prism with a length of 5 centimeters, width of 4 centimeters, and height of 3 centimeters.
What is the volume of the prism?
20 cm3
36 cm3
47 cm3
60 cm3

Answers

Answer:

60 cm3 is the volume of the prism

Step-by-step explanation:

Because the formula for volume is length * width * height!

please mark the brainliest!

Answer:

60

Step-by-step explanation:

Elena and Diego each wrote an equation to represent the diagram. Elena wrote 35+w+41=180. Diego wrote 35+w=180.which equation do you agree with? You can assume that angles that look like right angles and indeed right angles

Answers

Answer:

Step-by-step explanation:

i need to see the diagram, to help you

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