(q9) Find the volume of the solid obtained by rotating the region enclosed by the curves
and y = x2 about the y-axis.

Answers

Answer 1

The volume of the solid obtained by rotating the region enclosed by the curves [tex]y=\sqrt{x^3}[/tex] and [tex]y = x^2[/tex] about the y-axis is [tex]\pi/14[/tex] . option B

To determine the solid's volume after rotating the area bounded by curves

[tex]y = \sqrt{x^3}[/tex] and [tex]y = x^2[/tex]

We can apply the cylindrical shell approach to the y-axis.

First, let's locate the spots where the two curves intersect:

[tex]\sqrt{x^3} = x^2[/tex]

Squaring both sides:

[tex]x^3 = x^4[/tex]

Rearranging:

[tex]x^4 - x^3 = 0[/tex]

Factorizing [tex]x^3(x - 1) = 0[/tex]

Therefore, the locations of intersection are x = 0 and x = 1.

The integral for the solid's volume must then be set up using cylindrical shells. The following formula determines the volume of a cylindrical shell:

V is equal to 2[a, b] x * h(x). dx where a and b are the integration limits, x is the shell's radius, and h(x) is the height of the shell.

The radius of the shell in this instance is x, while the height of the shell is the ratio of the two curves: [tex]h(x) = \sqrt{x^3} - x^2.[/tex]

Since those are the locations of intersection, the range of integration's bounds is 0 to 1.

The integral then becomes:

∫[tex]V = 2\pi [0, 1] x * (\sqrt{x^3} - x^2) dx[/tex]

We can simplify the formula inside the integral in order to evaluate it:

V = 2π ∫[0, 1] (x^(5/2) - x^3) dx

We can integrate each word by applying the power rule for integration as follows:

[tex]V = 2\pi [(2/7)x^{(7/2)} - (1/4)x^{4}] |[0, 1][/tex]

Calculating the limits of the definite integral:

[tex]V = 2\pi [(2/7)(1^{(7/2))} - (1/4)(1^{4)}] - 2\pi [(2/7)(0^{(7/2})) - (1/4)(0^{4)}][/tex]

Simplifying further:

V = 2π [(2/7) - (1/4)]

V = 2π (8/28 - 7/28)

V = 2π/28

Simplifying the fraction:

V = π/14 ,Therefore, the correct answer is option B.

For more question on volume visit:

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Related Questions

Help please !! need it adap

Answers

Answer:

m < Q = 40°

m < M = 60°

Step-by-step explanation:

1.) All angles in every triangle altogether equal 180°

From the 4 measurements, you can tell angle Q and S are equal in order to make all angles equal 180 and those angles to be equal (below)

180 - 100 = 80

80/2 = 40

2.) This is an isoceles (all angles and sides are equal) There are three angles (divide 180 by 3)

180/3 = 60

A wheel with radius 1 foot makes 1 revolution in 4 seconds. What is the linear velocity, in feet per second, of a point on the edge of the wheel? 4π 8π

Answers

Answer:

[tex]v=\dfrac{\pi}{2}\ ft/s[/tex]

Step-by-step explanation:

Given that,

A wheel with radius 1 foot makes 1 revolution in 4 seconds

We need to find the linera velocity of a point on the edge of the wheel. We know that, the linear velcity is given by :

[tex]v=r\omega[/tex]

Where

[tex]\omega[/tex] is angular velcocity,[tex]\omega=2\pi\ rad[/tex]

[tex]\omega=\dfrac{1}{4}\times 2\pi\\\\=0.5\pi\ rad/s[/tex]

[tex]v=1\times 0.5\pi\\\\v=\dfrac{\pi}{2}\ ft/s[/tex]

So, the linear velocity of the wheel is equal to [tex]\dfrac{\pi}{2}\ ft/s[/tex].

Answer:

pi/2

Step-by-step explanation:

Got it right on EG

Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation?

{–22, 14}
{–14, 22}
{–10, 2}
{–2, 10}

Answers

Answer:

The answer is D. (-2,10)

Step-by-step explanation:

Answer:

The Answer is D. -2, 10 :P

Step-by-step explanation:

The person above is correct as well! Hope this helps :)

Containers that have different shapes can not have the same volume.
True
False

Answers

Answer:

true

Step-by-step explanation:

rjdkejdkdkekewnensjwkw

Stella was out at a restaurant for dinner when the bill came. Her dinner came to $10. She wanted to leave a 25% tip. How much was her meal plus the tip, before tax, in dollars and cents?

Answers

Bill $10
Tip at 25% is $2.50
Total before tax is $12.50

Answer:

12.50

Step-by-step explanation:

Simple stain consists of
A. complex of dyes
B. one dye
C. two
D. all are correct

Answers

all are correct so D

andrew, who is about 120 cm tall, notices that when he stands at the bottom of his garden, which is 20 meters away from his house, his dad, who is 180 cm tall, looks as big as the house when he is about 2.5 meters away. How high is the house ?

Answers

Answer: http://gestyy.com/eyLImX

Step-by-step explanation: go here

Joe bought four books at a bookstore. Here are their prices (in dollars). 7.34, 11, 13.2, 5.3 What is the total amount Joe paid at the bookstore?

Answers

Answer:

36.84

Step-by-step explanation:

just add them it is all really just basic addition nothing more to it

What is the product of 3.8X102 and 6.4X106 expressed in scientific notation?

Answers

Answer:

24.32x10^8

Step-by-step explanation:

3.8x10^2 and 6.4x10^6

Put in expression.

(3.8x10^2)+(6.4x10^6)

Remover parenthesis.

3.8x10^2+6.4x10^6

Rearrange so like terms are together.

(3.8x6.4)+(10^2x10^6)

Then combine like terms.

24.32x10^8

So that's the answer.

---

hope it helps

please answer i will give crown :D

Answers

Answer:

0.24

Step-by-step explanation:

1.679-1.439

Please help soon! Im timed!

Answers

Answer:

5 times a number and 7 : last option

8 more than the product of 7 : second option

5 less than the quotient of 8 ..... : first option

twice the difference of 8 and a number : thrid option

Step-by-step explanation:

Common sense

help me plssssssssssss☺☺☺☺

Answers

Answer:

1. supplementary angles

2. vertically opposite angles

3. corresponding angles

4. alternate interior angles

5. alternate exterior angles

6. corresponding angles

7. corresponding angles

8. alternate exterior angles

hope this helps

good day mate

Carlos bikes 2 1/2 miles in 1/4 hours. At that rate, how many miles would he bike in 1 hour?

Answers

Answer:

Step-by-step explanation:

since it’s 1/4 1 out of the four is 2.5 so just multiply by four

Jim qualifies for $0 down payment but makes a $2,500 down payment on his car purchases anyway. Will this payment help or hurt him

Answers

Answer:

help him

Step-by-step explanation:

Paying a $2,500 down payment on an automobile would normally benefit Jim. He reduces the total amount of the loan for the vehicle he will need to take out by making a down payment, which reduces the cost of his monthly payments and the amount of interest he will have to pay over the life of the loan. Furthermore, having a down payment increases his chances of getting approved for a loan or receiving a cheaper interest rate.

What is Down payment?

A down payment is an upfront cash payment made when purchasing a significant ticket item like a car or a house. The down payment is often a proportion of the total cost of ownership and is made in order to lower the amount of financing required. Lower monthly payments or a shorter loan term are sometimes the outcome of a higher down payment.

A down payment is an initial up-front payment in part for the purchase of a large item or service, such as a car or a house. It is normally paid in cash or in the form of an equivalent at the time the transaction is completed. The balance of the payment is then financed by a loan of some kind.

Therefore, paying a $2,500 down payment on an automobile would normally benefit Jim.

Learn more about Down payment, here:

https://brainly.com/question/29397199

Step-by-step explanation:

where is x in the question

A door to a playhouse is 50 inches tall. Which of the following is another measure equal to the height?
A- 4ft 2in,
B-4ft 1in.
C-4ft 1/2in
D-5ft

Answers

Answer:

4 ft 2 in.

Step-by-step explanation:

A door to a playhouse is 50 inches tall

we know that

1 in---------------> is 0.0833333 ft

50 in-------------> 50*0.0833333---------> 4.167 ft

4.167 ft----------> [4 ft+0.167 ft]

remember that

1 in---------------> is 0.0833333 ft

X in----------------> 0.167 ft

X=0.167/0.0833333----------> X=2 in

4.167 ft----------> [4 ft+0.167 ft]--------> [4 ft+2 in]

Help me please! Its really complicated

Answers

1. 4.5 cm

2. 25.13 inches

3. 78.54 cm

4. 13 cm. 6.5 +6.5

Radius is half the diameter

Step-by-step explanation:

1) Radius = Half of Diameter

[tex]r = \frac{1}{2} d \\ r = \frac{1}{2} \times 9 \\ = 4.5cm[/tex]

2) Given r = 4 in.

Circumference of Circle =

[tex]2\pi \: r \\ = 2\pi(4) \\ = 8\pi \: cm[/tex]

3) Given r = 5 in.

Area of Circle =

[tex]\pi {r}^{2} \\ = \pi {5}^{2} \\ = 25\pi {cm}^{2} [/tex]

4)Diameter = 2x Radius

[tex]d = 2r \\ = 2 \times 6.5 \\ = 13cm[/tex]

Note for questions 2 and 3 I will leave answers in terms of pi as the question did not specify to leave the answer as what. You can use your calculator to evaluate them if needed.

1. Tiffany bought a phone for $350. If the value of the phone depreciates at a rate of 6%
per year, what would you pay for the phone after 3 years?

Answers

Answer:

Amount of phone after 3 year = $290.7 (Approx.)

Step-by-step explanation:

Given:

Amount of phone = $350

Depreciation rate = 6% = 0.06

Find:

Amount of phone after 3 year

Computation:

A = p[1-r]ⁿ

Amount of phone after 3 year = Amount of phone[1-Depreciation rate]ⁿ

Amount of phone after 3 year = 350[1-0.06]³

Amount of phone after 3 year = 350[0.94]³

Amount of phone after 3 year = 350[0.83054]

Amount of phone after 3 year = $290.7 (Approx.)

I need help on number 26

Answers

Answer:

The number of required shelves is 5

You have to find the HCF of 45, 105, and 75.

dolls= 9
footballs=21
small cars=15

40 POINTS !! 40 POINTS !!

PLEASE HELP , DONT SKIP !

NO LINKS OR FILES.

Answers

Answer:

36?

Step-by-step explanation:

split in two, triangle 6x6=36/2=18, rectangle 6x3=18, whole 18+18=36 your answer is 36

Answer:

it's 36 square feet

Step-by-step explanation:

Pls helppp i have a timer!!
(10 points)

Answers

Answer:

they are both corresponding angles (equal)

48=4x

48/4=x

12=x

Answer:

x = 12

Step-by-step explanation:

4x and 48 are corresponding angles and are congruent, then

4x = 48 ( divide both sides by 4 )

x = 12

There are 20 monkeys in a zoo. There are 4 times as many lions monkeys as lions. How many lions are there

Answers

It is 80 lions......

Jennie is standing 52 km away from the Volcano and the volcano is 2.4 km high. Assuming Makayla and the base of the volcano are at the same elevation above sea level, what is the angle of elevation from Makayla to the top of the volcan??

Answers

9514 1404 393

Answer:

2.64°

Step-by-step explanation:

The relevant trig relation is ...

Tan = Opposite/Adjacent

Here, the side of the right triangle in this geometry that is adjacent to the angle of elevation is the distance to the volcano: 52 km. The side opposite is the height of the volcano: 2.4 km. Then the angle α is found from ...

tan(α) = 2.4/52

α = arctan(2.4/52) ≈ 2.64°

The angle of elevation from Makayla's position is about 2.64°.

Answer:

Solution :-

Since Jennie is standing away so,

[tex] \sf \: \tan( \arctan) = \dfrac{2.4}{52} [/tex]

=> 2.64⁰

Simplify 8-9+8÷4
Please help thank you

Answers

Answer:

Step-by-step explanation:

The equation 8 - 9 + 8 / 4 is given.

When solving equations with multiple signs in them, we need to follow PEMDAS.

Which is an acronym for a series of equations you need to follow in order.

Parenthesis

Exponent

Multiply

Divide

Addition

Subtraction.

So look at the equation, 8 / 4 would be first since it is dividing.

8 / 4

8 - 9 + 2

Now when it comes down to the last two of PEMDAS (Addition and Subtraction), we can just solve left to right.

Therefore,

8 - 9

-1

-1 + 2

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(q9) Find the volume of the solid obtained by rotating the region enclosed by the curves and y = x2 about the y-axis.

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(q9) Find the volume of the solid obtained by rotating the region enclosed by the curves
and y = x2 about the y-axis.