(q9) Find the volume of the solid obtained by rotating the region enclosed by the curves
and y = x2 about the y-axis.
Answers
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.
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Related Questions
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.
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hope it helps
Which of the quadratic equations below has solutions of x = 8 and x = -2?
F. x2 + 6x = 16
G. x2 + 6x = -16
H. x2 – 6x = 16
J. x2 – 6x = -16
Answers
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.
footballs=21
small cars=15
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
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
4) Is( 4,-5) a solution to
y +8 > -(x + 2)
Show your work
Please eplain
Answers
Step-by-step explanation:
[tex] - 5 + 8 > - (4 + 2) \\ 3 > - 6 \\it \: is \: true[/tex]
Answer:
yes
Step-by-step explanation:
There are 20 monkeys in a zoo. There are 4 times as many lions monkeys as lions. How many lions are there
Answers
Which are the points labeled to show the solution to the system of the equations?
Answers
Answer:
C
Step-by-step explanation:
It is where the two lines intersect, which is the answer
Answer: C
Step-by-step explanation: Point C is where the two lines intersect. This means there is a point where both x's share a value and both y's share a value.
please answer i will give crown :D
Answers
Answer:
0.24
Step-by-step explanation:
1.679-1.439
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.
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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
Find the value of x.
(a)
(10.7)" = 2
3x92x1 = 27*
(b)
Answers
Step-by-step explanation:
where is x in the question
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
Tip at 25% is $2.50
Total before tax is $12.50
Answer:
12.50
Step-by-step explanation:
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
so
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]
Carlos bikes 2 1/2 miles in 1/4 hours. At that rate, how many miles would he bike in 1 hour?
Answers
Answer:
10
Step-by-step explanation:
since it’s 1/4 1 out of the four is 2.5 so just multiply by four
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
The local street cart sells bacon egg and cheese sandwiches for $2.50, and soft drinks for $0.75. The street vendor made a total of $933 after selling a total of 747 sandwiches and soft drinks.
thanks:b
Answers
Answer:
Step-by-step explanation:
Containers that have different shapes can not have the same volume.
True
False
Answers
Answer:
true
Step-by-step explanation:
rjdkejdkdkekewnensjwkw
(ruu ule
(b) दिइएको समीकरणबाट झुकाव पत्ता लगाऊ ।
(Find the slope of the given equation): y-3 = 2x
Answers
Answer:
y-3 = 2x
2x-y+3=0 we have
slope
m =- coefficient of x/coefficient of y=-2/-3=2/3 is a slope..
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 :)
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
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
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.)
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.
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
Solve the system of equations by graphing
Answers
Answer:
Step-by-step explanation:
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:
Simple stain consists of
A. complex of dyes
B. one dye
C. two
D. all are correct
Answers
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]
So
[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
B
Step-by-step explanation:
Got it right on EG
Simplify 8-9+8÷4
Please help thank you
Answers
Answer:
1.
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
2
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
1