Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y2=x,x=2yy 2 =x,x=2y; about the y-axis
Answers
Answer:
Step-by-step explanation:
From the first image attached below, we will see the sketch of the curve x = y² & x = 2y
In the picture connected underneath, the concealed locale(shaded region) is bounded by the given curves. Now, we discover the marks of the crossing point of the curves. These curves will cross, when:
[tex]y^2 =2 y \\ \\ or y^2 -2y = 0 \\ \\ y(y-2) = 0 \\ \\ y = 0 \ \ or \ \ y = 2[/tex]
Thus, the shaded region fall within the interval 0 ≤ y ≤ 2
Now, from the subsequent picture appended we sketch the solid acquired by turning the concealed region about the y-axis.
For the cross-sectional area of the washer:
[tex]A (y) = \pi (outer \ radius)^2 - \pi ( inner \ radius )^2 \\ \\ A(y) = \pi (2y^)2- \pi (y^)^2 \\ \\ A(y) = 4 \pi y^2 - \pi y^4 \\ \\ A(y) = \pi( 4 y^2 -y^4)[/tex]
Finally, the volume of (solid) is:
[tex]V = \int^2_0 A(y) \ dy \\ \\ V = \int^2_0 \pi (4y^2 -y^4) \ dy \\ \\ V = \pi \int^2_0 (4y^2 -y^4) \ dy \\ \\ V = \pi \Big[\dfrac{4}{3}y^3 - \dfrac{y^5}{5} \big ] ^2_0 \\ \\ V = \pi \Big [ \dfrac{4}{3}(2)^3-\dfrac{2^3}{5} \Big ] \\ \\ V = \dfrac{64}{15}\pi \\ \\ V = (4.27 ) \pi[/tex]
Related Questions
Solve 4ax + 5ax = 6 ax + 9 for x. Assume a = 0.
Answers
Step-by-step explanation:
4ax + 5ax = 6 ax + 9
If a=0
Then
0+0≠0+9
so x is undefined
If the value of 'a' is zero. Then the solution of the equation will be not defined.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The equation is given below.
4ax + 5ax = 6ax + 9
Simplify the equation for x, then the equation is given as,
4ax + 5ax = 6ax + 9
4ax + 5ax - 6ax = 9
3ax = 9
x = 3 / a
If the value of 'a' is zero. Then the solution of the equation will be
x = 3 / 0
x = not defined
If the value of 'a' is zero. Then the solution of the equation will be not defined.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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can somebody help me?
Answers
Which table represents an exponential function?
X
0
1
2
3
4
у
5
13
21
29
37
Х
0
1
2
3
4
у
0
22
44
66
88
X
0
1
2
3
4
у
2
4
8
16
32
0
1
2
3
4
у
5
6
7
8
9
Answers
The exponential function from the table is given by y = 2(2)ˣ
What is an exponential function?
An exponential function is in the form:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
At x = 0, y = 2, hence a = 2
At x = 1, y = 4, hence:
4 = 2b¹
b = 2
The exponential function is given by:
y = 2(2)ˣ
The exponential function from the table is given by y = 2(2)ˣ
Find out more on exponential function at: https://brainly.com/question/12940982
Scale factor from A to B is 4:5.
Help
Answers
Answer:
24
Step-by-step explanation:
4/5 = x/30, then (4×30)/5 =24
The missing value is 24.
We have,
From the figure,
We can write an expression as:
4:5 = x : 30
This can be written as,
4/5 = x/30
Now,
Cross multiply.
x = 4 x 30 / 5
x = 4 x 6
x = 24
Thus,
The missing value is 24.
Learn more about expressions here:
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what is the remainder
Answers
I am down help please
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Answer:
180 degrees
Step-by-step explanation:
angle 1 = 90 degrees
angle 4 = angle 1 because they are vertical angles
360 - 90 - 90 = 180 degrees
z=-5x(x-20) solve for x
Answers
Step-by-step explanation:
there is no solution
How to covert feet into miles
Answers
If an item is marked 15% off to a sale price of $12.75 ,What is the price of the item before the discount
Answers
Answer:
$85
Step-by-step explanation:
Divide 15% by $12.75
Change 15% into a decimal by multiplying it by 100
$12.75/0.15= $85
Mrs. Hilt has 6 boxes of markers. Each box has 19 markers in it. If she sold each maker for $0.75, how much money would Mrs. Hilt earn?
Answers
Answer:
85.50
Step-by-step explanation:
6 times 19 = 114 markers then times .75= 85.50
Please help and show work
Answers
Answer:
0.75x
Step-by-step explanation:
Theres not much to show. It says that you buy x bags of chips for $0.75. So how I got 0.75x is because you have to multiply 0.75 x times to get your answer,but here they just want you to write an equation with out solving it.
There are 12 cupcakes. 3⁄4 of them have pink icing.
1⁄3 of the cupcakes with pink icing have sprinkles. How many of the cupcakes have pink icing and sprinkles?
Answers
Answer:
3 of them should have sprinkles.
Step-by-step explanation:
PLEASE HELP ILL MARK BRAINLY FOR CORRECT ANSWER
Answers
Answer:
120 minutes
Step-by-step explanation:
12 x 10 = 120
10 x 12 = 120
15 x 8 = 120
You will put the muffins in 10 times and you will put the cookies in 12 times then you will put the scones in 8 times. If you have different numbers, you can first start out with one number and times all of the numbers by that one number. For example I picked 5 to start out with:
12 x 5 = 60 minutes 10 x 5 = 50 minutes 15 x 5 = 75 minutes.
Then I did 12 x 6 = 72 minutes, 10 x 6 = 60 minutes, 15 x 6 = 90 minutes
Since I still don't have the numbers to add up to the same answer, I went to timing them by 7:
12 x 7 = 84 minutes, 10 x 7 = 70 minutes, 15 x 7 = 105 minutes
They are still not the same answer so lets try 8:
12 x 8 = 96 minutes, 10 x 8 = 80 minutes, 15 x 8 = 120 minutes.
Since I don't want to go farther than 120 minutes, I will keep trying different numbers for the other ones besides 15.
12 x 9 = 108 minutes, 10 x 9 = 90 minutes
12 x 10 = 120 minutes, 10 x 10 = 100 minutes
Now we will focus on getting 10 to 120 because we got 12 to 120.
10 x 11 = 110 minutes
10 x 12 = 120 minutes
To sum all of this, it took 8 trips to get 15 minutes to 120 minutes, 10 trips to get 12 minutes to 120 minutes, and 12 trips to get 10 minutes to 120 minutes.
One more way to think about this is:
10, 12, and 15 can go into 120 evenly.
[tex]12\sqrt{120} = 10[/tex]
[tex]10\sqrt{120} = 12\\15\sqrt{120} = 8[/tex]
First person to answer this gets BRAINLIEST!
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Answer:
7 square miles
Step-by-step explanation:
Answer:
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Step-by-step explanation:
the triangle looks like a triangle but then the reason why I said I think it's the on the right is because the acute angle makes it look like a trapezoid but then on the other side it has a right angle but I think its the right side.
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Second gap is 10
You know that 28 strawberries make 4 smoothies, so you also know that 7 strawberries makes 1, you find this out by dividing 28 by 4.
You then need to do 7 x 3 which is 21, and 70 / 7 which is 10.
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Answer:
Step-by-step explanation:
Greater than (<)
together, ben and kyle have 43 fishing lures. Kyle,(K), has 15 more lures than ben, (B). which statements are correct for this situation
Answers
Answer:
k + b = 43
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Answer:
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Given a and b are numbers, and a + b = 180, which
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a = 180 - 6
a - 180 = b
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a = 90 and b = 90
Answers
Also, 360 = 2a + 2b is correct
How can you write and solve an addition or subtraction equation?
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0.06%
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6%
40%
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Answer:
is there an image where i can see?
Step-by-step explanation:
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Answer:
3 x 10 = 30 man-days per house
Answer:
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Step-by-step explanation:
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True or False: Slope is always rise over run.
Answers
Answer:
The formula for slope is sometimes referred to as "rise over run", because the fraction onsists of the "rise" (being the change in y, going up or down) divided by the "run" (being the change in x, going from left to the right).
Step-by-step explanation:
Answer:
Good sir/madam, in a fraction, it is always rise over run.
Displayed is the ordered data of body temperatures, in degrees Fahrenheit, for 65 healthy adult women: 96.4, 96.7, 96.8, 97.2, 97.2, 97.4, 97.6, 97.7, 97.7, 97.8, 97.8, 97.8, 97.9, 97.9, 97.9, 98.0, 98.0, 98.0, 98.0, 98.0, 98.1, 98.2, 98.2, 98.2, 98.2, 98.2, 98.2, 98.3, 98.3, 98.3, 98.4, 98.4, 98.4, 98.4, 98.4, 98.5, 98.6, 98.6, 98.6, 98.6, 98.7, 98.7, 98.7, 98.7, 98.7, 98.7, 98.8, 98.8, 98.8, 98.8, 98.8, 98.8, 98.8, 98.9, 99.0, 99.0, 99.1, 99.1, 99.2, 99.2, 99.3, 99.4, 99.9, 100.0, 100.8
Which value would need to be exceeded for a data point to be considered an outlier when using the 1.5 X IQ R rule?
a. 99,8
b. 100.0
c. 99.6
d. 100.8
Answers
Answer:
54932540-476715.jpeg
A study of stroke patients who survived 6 months after the stroke found that 6/45 men and 22/63 women lived in an institution (e.g., nursing home or assisted living facility). What is the risk difference of living in an institution between men and women (using men as the reference group)?
Data (1=males, 2 =females)
temp sex Heart rate
96.3 1 70
96.7 1 71
96.9 1 74
97 1 80
97.1 1 73
97.1 1 75
97.1 1 82
97.2 1 64
97.3 1 69
97.4 1 70
97.4 1 68
97.4 1 72
97.4 1 78
97.5 1 70
97.5 1 75
97.6 1 74
97.6 1 69
97.6 1 73
97.7 1 77
97.8 1 58
97.8 1 73
97.8 1 65
97.8 1 74
97.9 1 76
97.9 1 72
98 1 78
98 1 71
98 1 74
98 1 67
98 1 64
98 1 78
98.1 1 73
98.1 1 67
98.2 1 66
98.2 1 64
98.2 1 71
98.2 1 72
98.3 1 86
98.3 1 72
98.4 1 68
98.4 1 70
98.4 1 82
98.4 1 84
98.5 1 68
98.5 1 71
98.6 2 77
98.6 1 78
98.6 1 83
98.6 2 66
98.6 1 70
98.6 1 82
98.7 2 73
98.7 1 78
98.8 1 78
98.8 1 81
98.8 2 78
98.9 1 80
99 2 75
99 2 79
99 1 81
99.1 1 71
99.2 1 83
99.3 1 63
99.4 1 70
99.5 1 75
96.4 2 69
96.7 2 62
96.8 1 75
97.2 1 66
97.2 2 68
97.4 2 57
97.6 1 61
97.7 2 84
97.7 1 61
97.8 2 77
97.8 2 62
97.8 2 71
97.9 1 68
97.9 2 69
97.9 2 79
98 2 76
98 1 87
98 2 78
98 2 73
98 2 89
98.1 2 81
98.2 2 73
98.2 2 64
98.2 2 65
98.2 2 73
98.2 2 69
98.2 2 57
98.3 2 79
98.3 2 78
98.3 2 80
98.4 2 79
98.4 2 81
98.4 2 73
98.4 2 74
98.4 2 84
98.5 2 83
98.6 2 82
98.6 2 85
98.6 2 86
98.6 2 77
98.7 2 72
98.7 2 79
98.7 2 59
98.7 2 64
98.7 2 65
98.7 2 82
98.8 2 64
98.8 2 70
98.8 2 83
98.8 2 89
98.8 2 69
98.8 2 73
98.8 2 84
98.9 2 76
99 2 79
99 2 81
99.1 2 80
99.1 2 74
99.2 2 77
99.2 2 66
99.3 2 68
99.4 2 77
99.9 2 79
100 2 78
100.8 2 77
Step-by-step explanation:
At the zoo it is important to keep a good balance of male and
female animals. If 2 of the panda bears are female and there are
a total of 4 panda bears, what fraction of all the panda bears are
female?
Answers
Answer:
The answer is: 2/4
Step-by-step explanation:
There are a total of 4 panda bears, which makes 2 males and 2 females.
By making a fraction, you can say there are 2 panda bears, out of four.