Mathematics College

Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

y = 3 − 3x^2, y = 0

Answers

Answer 1

Answer: [tex]9.6\pi[/tex]

Step-by-step explanation:

Given

Curve is [tex]y=3-3x^2[/tex]

boundary is y=0 i.e.

[tex]\Rightarrow 0=3-3x^2\\\Rightarrow x^2=1\\\Rightarrow x=\pm 1[/tex]

The volume of solid generated when rotated about the x-axis is

[tex]\Rightarrow V=\int_a^b\pi y^2dx[/tex]

Putting values we get

[tex]\Rightarrow V=\int_{-1}^{1}\pi (3-3x^2)^2dx\\\\\Rightarrow V=\int_{-1}^{1}\pi(9+9x^4-18x^2)dx\\\\\Rightarrow V=\pi \left [ \frac{9x^5}{5} - 6 x^3 + 9 x\right ]_{-1}^{1}\\\\\Rightarrow V=9.6\pi[/tex]

Related Questions

m(x)=x(x+6)
p(x)=x(x+3)²-9

Show that m(x) and p(x) are equivalent

Answers

Answer:

m=x+6

Step-by-step explanation:

Let's solve for m.

mx=x(x+6)

Step 1: Divide both sides by x.

2x/x=    x²+6x/x

m=x+6

Hope this helps :)

PLS BRAINLIEST

rename 8/100 i need help somebody​

Answers

Answer:

0.08

Step-by-step explanation:

8/100ths is the fraction way of writing 0.08 which is the same amount just written in decimal form

Answer:

rename 8/ 100

Step-by-step explanation:

8% or 0.08 in decimal and percentage form.

IN A CRISIS RN SO COULD SOMEONE PLEASE HELP ME?

Answers

Answer:

D

Step-by-step explanation:

Answer:Use math Papa

Step-by-step explanation:

The sum of two numbers is 102. One number is 2 times theother number. Find the two numbers.

Answers

Answer:

2x + x is the equation

The number(s) is 34

Step-by-step explanation:

2x + x = 102

3x = 102

divide by 3

x = 34

Hope this helped! Have a nice day! Plz mark as brainliest!!!

-XxDeathshotxX

Answer:

34 and 68

Step-by-step explanation:

102/3=34

34(2)=68

68+34=102

Type in the correct value for m... (Only the numerical answer)
369 + m = 908

Answers

Answer

M = 539

Expo nation

1 + 8(9k – 8) step-by-step answer.

Answers

Answer:

no se entiende bien porque

can you help me understand this question​

Answers

Answer:

Which one?

Step-by-step explanation:

If twice a number, added to 3 is divided by the number plus 4 ,the result is seven fourths. Find the number

Answers

Answer:

The number is 16

Step-by-step explanation:

I NEED HELP ASAP PLEASE I'll give brainliest to whoever answers.

Answers

Answer:

the first one is 36

Step-by-step explanation:

Answer:

#4 - 36

#5 - 2

Step-by-step explanation:

For the first question, #4, I believe you have to just find what both those numbers go into, that's 36, so the 36th customer will get both.

For the second question, #5, all you need to know is how many time 2/3 can go into 2 2/3, then that is your answer. So 2/3 only goes in twice, it almost makes it to three but that doesn;t matter you don't have enough raisins to make it there she can only make two batches with the raisins she has.

Make sure to label - if you're supposed to!

Hope this helps! :)

In the right triangle shown, mZA = 45° and AB = 12. How long is BC?

Answers

Answer:

I think BC is 45°÷2 Or 12÷2

Step-by-step explanation:

so the answer is 15° or 6

What does 15+5= 18 +

Answers

Answer:

2

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

which expression is equivalent to - iz q(-60r + 24q) – 8r(5q + r)?
A 2q2 - 35gr + 8r?
B-2q2 - 45gr + 8r2
© 292-45gr - 8r2
D-2q2 - 35gr - 8r2

Answers

Answer:b

Step-by-step explanation:

Draw a Picture:
Four towns are located along a
straight highway. Abacus is 50
miles west of Barometer. Deka is 30
miles east of Barometer. Calculus is
10 miles west of Deka. How far is it
from Abacus to Calculus?

Answers

Answer: 30 miles

I am right.

7/10 - ___ + 3/2 = 6/5. I want to know the blank and how you did it so I can solve it on my own! Thank you!

Answers

Maybe try solving it like this is so easy I’m on 8th grade bro

Use right triangle DCB to find the trig values for angle D
​

Answers

Answer:

sin D= 35/37

cos D= 12/37

tan D= 35/12

Answer:

sinD= 35/37  

cosD= 12/37  

tanD= 35/12

Step-by-step explanation:

Checked the answer key. Got it correct on my lesson.

Consider the number line graph of x > 28. Which numbers are solutions for the inequality?
A)
0

B)
21

C)
28

D)
30

E)
45

Answers

Answer:

D and E

Step-by-step explanation:

X is any number GREATER THAN 28, but it is not greater than or equal to so it is not C. A and B are less than 28, so those cannot be answers. D and E are both larger than 28, therefore those are correct.

Answer:

D and E

Step-by-step explanation:

X is any number GREATER THAN 28, but it is not greater than or equal to so it is not C. A and B are less than 2

Step-by-step explanation:

Look at the picture before trying to solve.
solve 2x^2 - 6x = -8

Answers

2x^2 - 6x = 8

1. Divide the equation by 2
-> x^2-3x=4

2. Move the constant to the left
-> x^2 - 3x + 4 = 0

3. Use the quadratic formula
—> - - (3) +/- square root -(3)^2 - 4 x 1 x 4 divided by 2x1

4. Plug into the calculator

Answer: 3 +/- square root 7 divided by 2
(Essentially the last one)

2 (4y + 3 + y) hellppp

Answers

Answer:

10y + 6 hope this helps :)

Step-by-step explanation:

it’s just 2 times everything in the parentheses and the. add the like terms to ge

dimensions of a house are 300 feet by 125 feet . if 1 inch represent 50 feet what are the dimensions of the house on the drawing​

Answers

The house would be -1,304 inches

the probability that it will rain tomorrow is 0.85what is the probability that it will not rain tomorrow​

Answers

Answer:

.15

Step-by-step explanation:

Probability of Rain = x

Probabiliy of No Rain = y

Y=1-X

Y=1-0.85

Y=.15

Select all the figures that are shaded to represent 60% of the whole. Select all that apply. A. B. Ó ő OC. D. o ó​

Answers

Answer:   (b)

step by step:

Answer:

A, C, and E

Step-by-step explanation:

Could someone please help me on this question? I’m having a proper Brain fart right now ☹️

Answers

caravan total cost is = 7000 + 20% VAT = 7000 + 0,20*7000 = 7000 + 1400 = 8400

Ria pays deposit = 3000

8400 - 3000 = 5400

rest to pay for 6 months

5400/6 = 900

monthly payment is 900

Can some one tell me the answer

Answers

Answer:

x = 13°

Step-by-step explanation:

The total must be 180°.

105° + 62° = 167°

180° - 167°

13°

Answer:

the answer is 13

Step-by-step explanation:

half of 360 is 180 (it has to be this number in the end)

105+62-180=-13

to check: 105+62+13=180

A boat travels 187 miles in 10
hours (with a constant speed).
How far can it travel in 14 hours
(with the same speed)?

Answers

Answer:

grufhvdyfvgysgddgfvsygujsbchusb

Step-by-step explanation:

I need help please i will give brianleist

Answers

Answer:c is the right answer

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Find the missing lengths in the rectangular prism. Please help.

Answers

Answer:

vgggghujvgjjihgfdryujgfdfg

Answer:

s=10.92

r=11.467

Step-by-step explanation:

3²+10.5²=s²

9+110.25=s²

119.25=s²

√119.25=s

s=10.92

3.5²+10.92²=r²

12.25+119.25=r²

131.525=r²

√131.5=r

r=11.467

The solution of the equation 16 m + 16 = 32 is


1

3

6

12​

Answers

16(1)=16
16(1)+16
16+16=32

Answer:

1

Step-by-step explanation:

16m = 32-16

16m = 16

m = 16 ÷ 16

m = 1

Identify each statement that represents a statistical question. (hint: only two are non-statistical)
A. How many books a year does each student read?
B. How many cans did your school recycle last month?
C. How do the students get to school each day?
D. How many computers does the school have?
E. Do shoppers prefer paper or plastic bags?
F. How much do drivers spend on gasoline each week?
Please hurry

Answers

Answer: How do the students get to school each day?

Step-by-step explanation: I had this question too and I go to k12

A rectangular painting is bordered on all sides by a frame. Write an
expression to describe the area of the frame.
A. 6x + 4
B. 4x2 + 3
C. 5x + 3
D. 4x2 + 5x + 3

Answers

I think it is a 6x+4

The required area of the frame shown is 5x + 3. Option C is correct.

What is surface area?

The surface area of any shape is the area of the shape that is faced or the surface area is the amount of area covering the exterior of a 3D shape.

Here,
The area of the picture is given as,
= 2x × x
= 2x²

The area of the whole painting with frame.

= (x + 1)(2x+ 3)
= 2x² + 5x + 3

The area of the frame is given as,
= area of picture with frame - an area of the picture,
= 2x² + 5x + 3 - 2x²
= 5x + 3

Thus, the required area of the frame shown is 5x + 3. Option C is correct.

Learn more about the surface area here: https://brainly.com/question/2835293

#SPJ2

Edward received a paycheck in the amount of $788. He is an appliance salesman and has a base salary of $200 a week. If he sells $10,000 in appliances, he gets 4% commission. If he sells more than $10,000 worth he receives 6% for the additional sales. What was the total of Greenberg’s sales this past week?​

Answers

Answer: The total is  $13,133.33

Step-by-step explanation:

We know that Edward's paycheck was $788

He has a base salary of $200, so the commission is:

$788 - $200 = $588

Now, we know that if he sells  $10,000, his commission is a 4%.

So let's suppose that he sold exactly $10,000

Then his commission is the 4% of $10,000, this is:

Commission = (4%/100%)*$10,000 = $400

This is not enough, so he sold more than $10,000 in this week.

There is:

$588 - $400 = $188 left.

We know that if sells more than $10,000, he gets a commission of the 6% for the extra sales.

Then let's suppose that the extra is N.

The extra $188 must be equal to the 6% of N, then we get:

$188 = (6%/100%)*N

$188 = 0.06*N

$188/0.06 = N

$3,133.33

This means that he sold $3,133.33 more than $10,000

Then, in total, he sold $10,000 +  $3,133.33 =  $13,133.33

Other Questions
Gail needs 9 yards of fabric for a quilt. How many different patterns of fabricdoes she need if she buys of a yard of each pattern?patterns How are electromagnets temporary?A.) They are only magnetic when an electric current runs through them.B.) They are only magnetic when a gravitational wave runs through them.C.) They are only magnetic when near a lodestone.D.) They are only magnetic for two weeks. What is the correct order of the events below:1. Organism breaks down sugar to release energy in its chemical bonds.2. Energy from the sun reaches Earth3. Radiant energy is converted into chemical energy What is this picture saying ? HELP WILL MARK BRAINLIST Why were Lewis and Clarks accomplishments so important for shaping the attitudes and expansion of the United States during the 1800s? SOMEONE HELP ME PLEASE !!!!Of the New Deal policies, which one had the biggest long-term impact on the American economy? f(-5) if f(x) = -2x + 8help Which equation shows the relationship between the volume, (V) of the prism and its height (h)? Goffman says that there are two institutions that oversee the journey children travel to adulthood explain and discuss the characteristics of these two institutions and what they offer. How much would it cost to purchase 7.5 lbs of walnuts? 3.5 Walnuts in Bulk It costs $3.45 to buy Alb of chopped walnuts. Explain or show your reasoning. What type of clothing can potentially inhibit patient care?A. Loose clothingB. ScrubsC. Colored clothingD. New clothing that has not been worn HELP PLSSSSSSSSS, this is due in two minutes, i need helpppppppp Quizizz help please brainiest GUARANTEED even if wrong What was the ultimate goal of the Nazis Final Solution? Which of the following is an example of what a poem might be written about. Select all that apply.A small childThe snowA flowerA person's life storyTUNEXT QUESTIONASK FOR HELPNo dodo What is the volume of the figure? 4,536 mm 3 3,402 mm 3 2,268 mm 3 1,134 mm 3 just put answer no explanation help needed, thanks ig :') Read this excerpt from The Great Fire.Schaffer's first signal went out at 9:30. Several minutes later, Schaffer realized his mistake and ordered Box 319 struck. This was still seven blocks away from the O'Learys', but close enough that firefighters could see the flames and alter their course. Unfortunately, Schaffer's young assistant, William J. Brown, stubbornly refused to strike Box 319, saying he was afraid it would confuse the situation. Brown was so stubborn about his decision that even after the fire he was able to write arrogantly in a letter that "I am still standing the watch that burned Chicago."What caused the fire engines to head toward the wrong location?The fire was too small for them to see.Several fires were burning at once.Schaffers assistant refused to correct the signal.Schaffer and his assistant struck multiple boxes. HELP!! WILL GIVE BRAINLY!! How are nitrogen bases held together in a double helix? A. carbon bondB. hydrogen bondC. covalent bond