Determine whether the following statements are true and give an explanation or counterexample. If f is not one-to-one on the interval [a, b], then the are of the surface generated when the graph of f on [a, b] is revolved about the x-axis is not defined.

Answers

Answer 1

Answer:

Step-by-step explanation:

The missing equation is:

[tex]S = \int ^b_a 2 \pi f(y) \sqrt{1 + f' (y)^2 } \ dy[/tex]

Suppose f = nonnegative function whose first derivative is within (a,b) and it is continuous, Then the area of the surface generated is revolved about the x-axis:

The area of the surface revolution is:

[tex]S = \int ^b_a 2 \pi f(x) \sqrt{1 + f' (x)^2 } \ dx[/tex]

So; if  [tex]x = g(y)[/tex] for [tex]y \ \varepsilon \ [c,d][/tex]

Then; substituting a with c and b with d; f(x) also with g(y) and dx with dy;

Then;

[tex]S = \int ^d_c 2 \pi g(y) \sqrt{1 + g' (y)^2 } \ dy[/tex]

SInce;

[tex]g(y) \ne f(y)[/tex]; Then the statement is false.

Provided that the semicircle [tex]y = \sqrt{1-x^2}[/tex] isn't on [tex][-1,1][/tex] interval.

Then, the solid generated by the revolution about the x-axis is a sphere.

However, the surface is well defined and the statement is false.


Related Questions

9/10 times 1/5 PLS HURRY I ONLY HAVE 2 MINUTS

Answers

0.18 or as a fraction: 9/50
0.18 or 9/50. it depends which one your asking for.

Plz helpppp!!!!! Much love

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Answer:

B.

Step-by-step explanation:

Classify by degree of polynomial:
3x3 - 6x

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Answer:

3x(x2−2)

Step-by-step explanation:

7283
+3124
----------​

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Answer:

10407

Step-by-step explanation:

There are more than one answer help me and I give brainilest

Answers

Answer:

Equivalent to a), b), and d). It is NOT equivalent to c).

Step-by-step explanation:

6m + 12 is also equivalent to a) 3(2m+4) because when you distribute, it's 6m + 12. It is also equivalent to b) 3m + 8 + 4 + 3m because if you add them together, you get 6m + 12. It is not equivalent to c) but is do d) 4m + 2(m + 6) cause you use the distributive property then add. I hope this helped and please mark brainliest!

Natalie earned a grade of 72% on her multiple choice history final that had a total of 200 problems. How many problems on the final exam did Natalie get wrong?

Answers

Answer:56

Step-by-step explanation:

72% of 200= 144

200-143=56

Two sides of a right triangle measure 2 units and 4
units.

What is the area of the square that shares a side with the third side of the triangle?
units^2
2
squared

Answers

Hey there!

The answer is √20 or approximately 4.47

We can use the Pythagoreon Theorem, which is [tex]a^2 +b^2=c^2[/tex]. [tex]a[/tex] and [tex]b[/tex] are the names of the two sides, and [tex]c[/tex] is the name of the hypotenuse leg, or the longest side. We will plug the numbers into the formula, and solve:

[tex]2^2+4^2=c^2\\4+16=c^2\\20=c^2\\4.47...=c[/tex]

Have a terrifcly amazing day!

Simplify -3a + 5b - c given a = 2, b = -1 and c= 10

Answers

Answer:

-21

Step-by-step explanation:

-3a + 5b - c

-3(2)+5(-1)-(10)=-21

Complementary angles

Find the value of x in each right angle.

I cannot get this wrong

Answers

Answer:

The value of x = 28°

Step-by-step explanation:

Explanation:-

Complementary angles:-

Two angles are called Complementary angles when their measures add to 90 degrees

         ∠A + ∠B = 90°

     (x+40)° + 22° = 90°

        x + 62° = 90°

        x = 90 - 62

        x = 28°

harriet is 2 years less than a thirnd of her brothers ace. Harriet is 3 years ols. How old is her brother?​ please help right now

Answers

Answer:

her brother is 15 years old

Step-by-step explanation:

let 'b' = her brother's age

Harriet is 3 years old but Harriet is also '1/3b - 2'

3 = 1/3b - 2

5 = 1/3b

b = 5(3) or 15

Write and solve the inequality.
Nine less than the product of a number n and is no more than 95.
Fill in the boxes,

Answers

box 1: 1/4

first arrow: - (less than)

second arrow: < (less than or equal to if that's an option, that means there would be a line underneath <)

box 2: 1/4

third arrow: same as second arrow

last arrow: =

box 3: 104 ÷ 1/4 = 416

message if you dont understand

hope this helped

The inequality shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥  

The inequality that represents the given statement is

(1/4)n ≤ 95 + 9

The number n is n ≤ 416.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥  

We have,

Nine less than the product of a number n and 1/4 is no more than 95.

Let the number be n.

Now,

No more than means,

We have less than, greater than, and equal to.

We can use less than and equal to.

The inequality can be written as,

1/4 x n - 9 ≤ 95

(1/4)n - 9 ≤ 95

Add 9 on both sides.

(1/4)n ≤ 95 + 9

(1/4)n ≤ 104

Multiply 4 on both sides.

n ≤ 416

Thus,

The inequality that represents the given statement is

(1/4)n ≤ 95 + 9

The number n is n ≤ 416.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ2

Charlotte used a calculator to subtract.
She copied her answers from the display, but her teacher said her answers were wrong! Tell how Charlotte got each wrong answer.
1. 204.59 – 23.67 = 0.92

2. 936.4 – 15.85 = 77.79

3. 56.3 – 27.04 = 19.26

Answers

Answer:

Step-by-step explanation:

1.  She omitted the 0 from the minuend, entering 24.59 instead of 204.59

2. She misplaced the decimal point of the minuend, entering 93.64 instead of 936.4

3. She typed 4 instead of 5 in the minuend, entering 46.3 instead of 56.3

Out of numbers: 5, 7, 21, 25, 28, 35, 42, 56, 75, and 80, choose those which are multiples of 4 or 7

Answers

Answer:

Multiples of 4= 28

Multiples of 7= 7,21,28,35,42

Step-by-step explanation:

I hope this helps, and have a great day! :)

Please help!!! Will give brainliest

Answers

Answer:

option C

Step-by-step explanation:

option C is the correct answer of this question.

plz mark my answer as brainlist plzzzz vote me.

hope this will be helpful to you.

Read the picture carefully...there can be more than ONE ANSWER

Answers

Answer:

D

Step-by-step explanation:

Please please help me in the question someone

Answers

Answer:

perimeter is  34 cm

Step-by-step explanation:

Notice you need to find the value of two sides whose measure is not given. The first one is horizontal and 10 cm - 4 cm = 6 cm in length

The second one is vertical with a measure of 7 cm - 4 cm = 3 cm

Then, the addition of all sides going clockwise becomes:

7 + 10 + 4 + 6 + 3 + 4 = 34 cm

A group of college students believes that herbal tea has remarkable restorative powers. To test its theory, the group makes weekly visits to a local nursing home, visiting with residents, talking with them, and serving them herbal tea. After several months, many of the residents are more cheerful and healthy.

1. The lurking variable in this experiment is

a. visits of the college students.
b. the fact that this is a local nursing home.
c. herbal tea.
d. the emotional state of the residents.

2. The explanatory variable in this experiment is

a. visits of the college students.
b. herbal tea.
c. the emotional state of the residents.
d. the fact that this is a local nursing home.

3. Which of the following may be correctly concluded from this study?

a. The results of the study are not convincing because only a local nursing home was used and only for a few months.
b. Herbal tea does improve one's emotional state, at least for the residents of nursing homes.
c. There is some evidence that herbal tea may improve one's emotional state. The results would be completely convincing if a scientist had conducted the study rather than a group of college students.
d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.

Answers

Answer:

1. a. visits of the college students.

2. b. herbal tea.

3. d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.

Step-by-step explanation:

1. The lurking variable in this experiment is - a. visits of the college students.

2. The explanatory variable in this experiment is - b. herbal tea

3. Which of the following may be correctly concluded from this study - d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.

There are 22 third-graders in Sally's town. If there are 4 more boys than girls, how many girls are there?

Answers

Answer:

22-4=18

Step-by-step explanation:

Answer:

9 girls

Step-by-step explanation:

First we know from the information there are 22 kids in total.

Next we know 11+11=22 so one number would be 2 more than the other.

So 13+9=22

Therefore, there is 9 girls in Sally's town.

Find the perimeter of a square with side lengths of 3x + 1. Use the distributive property to write an expression.

Answers

expression =
p= 4(3x+1)

PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.

Answers

Answer:

Step-by-step explanation:

y=x+69

Answer:

y=x+69

Step-by-step explanation:

5+69=74

6+69+75

etc.

You are saving money to buy a new video game. You already have $12, and each week you save another $5. Which expression can you use to represent the money you have after 'w' weeks?

Answers

Answer:yes 12 +5

Step-by-step explanation:Idrk

Answer:

12 + 5

Step-by-step explanation:

plz help
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Answers

Hi there!

[tex]\large\boxed{x < 2}[/tex]

[tex]\frac{4x + 6}{7} < 2[/tex]

Begin by multiplying both sides by 7:

[tex]4x + 6 < 2 * 7 \\\\4x + 6 < 14[/tex]

Subtract 6 from both sides to isolate for x:

[tex]4x + 6 - 6 < 14 - 6\\\\4x < 8[/tex]

Divide both sides by 4 to solve for x:

[tex]4x/4 < 8/4\\\\x < 2[/tex]

a) Dati cinci exemple de numere intregi mai mici ca zero.​

Answers

Answer:

Numerele întregi pozitive sunt toate numerele întregi mai mari decât zero: 1, 2, 3, 4, 5, .... Numere întregi negative sunt toate opusele acestor numere întregi: -1, -2, -3, -4, -5, .... Nu considerăm că zero este un număr pozitiv sau negativ. Pentru fiecare număr întreg pozitiv, există un număr întreg negativ, iar acești numere întregi se numesc opuse. De exemplu, -3 este opusul lui 3, -21 este opusul lui 21 și 8 este opusul lui -8. Dacă un număr întreg este mai mare decât zero, spunem că semnul său este pozitiv. Dacă un număr întreg este mai mic decât zero, spunem că semnul său este negativ.

Step-by-step explanation:

what is the equation for line b​

Answers

Answer:

y=1/2x+1

Step-by-step explanation:

you can literally do rise over run to get the answer

Which inequality is true for r = 20?

Answers

2r=40 i this this one is the correct

Hace 9 meses que no llueve cual es el número entero​

Answers

hnAnswer:

gjunn

Step-by-step explanation:

Answer:

en un menos de 9 meses

ya que es desmunusion es de 0

4x9? i have a math test on times

Answers

Answer:

the answer is 36

.......

Answer:

4x9? i have a math test on time

Step-by-step explanation:

Is 36

4+4+4+4+4+4+4+4+4= 36

HELP ME!!!!!!!!!!!!!!

Answers

Answer:

i wanna say it would be 1,735-3%y

There are 15 books on a shelf. 9 of these books are new. The rest of them are used.

Answers

Answer: 7

Step-by-step explanation:

15-9 =

9 10 11 12 13 14 15

1   2   3  4  5  6  7

7 books were used.

a
Solve. Add, subtract, multiply or divide.
Anosh collects feathers. His father started his collection by giving him 7
feathers. Since then he has collected 28 more feathers. How many feathers does
Anosh have?​

Answers

Answer:

Anosh has 35 feathers.

Step-by-step explanation:

Initially, he had 0 feathers.

His father started his collection by giving him 7 feathers.

After his father gave him, he has 7 feathers.

Since then he has collected 28 more feathers. How many feathers does Anosh have?​

So now, he has 7 + 28 = 35 feathers.

Anosh has 35 feathers.

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