Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2
Answers
This question is incomplete, the complete question is;
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y; about the y-axis
Answer:
V = π (512/15)
Step-by-step explanation:
Given that;
region of rotation
y² = 2x, x = 2y
Region is rotated about y-axis as shown in the image
for the point of intersection,
y²/2 = 2y
y² - 4y = 0
y(y-4) = 0
∴ y = 0, y = 4
so the region lies in 0 ≤ y ≤ 4
Now cross section area of washer is
A(y) = π(outer radius)² = π(inner radius)²
A(y) = π(2y)² - π(y²/2)²
A(y) = π(4y²) - π(y⁴/4)
A(y) = π(4y² - (y⁴/4))
now volume of the solid of revolution is
V = ⁴∫₀ A(y) dy
V = ⁴∫₀ π(4y² - (y⁴/4))dy
V = π {4⁴∫₀ y² - 1/4⁴∫₀y⁴ dy }
V = π { 4/3 [y³]₀⁴ - 1/20 [y⁵]₀⁴ }
V = π { 4/3 [4]₀⁴ - 1/20 [4]₀⁴ }
V = π { 4/3 [64]₀⁴ - 1/20 [1024]₀⁴ }
V = π { 256/3 - 1024/20 }
V = π { (5120 - 3072) / 60 }
V = π (512/15)
Related Questions
two - way frequency tables
Answers
Answer: Two-way frequency tables are especially important because they are often used to analyze survey results. Two-way frequency tables are also called contingency tables. Two-way frequency tables are a visual representation of the possible relationships between two sets of categorical data.
Step-by-step explanation:
What is the equation of the line that passes through the point (-3,0) and has a
slope of 4/3
Answers
Answer:
y = 4/3x +4
Step-by-step explanation:
Mikayla bought a bag of 84 pieces of candy and she wants to divide them up evenly and place into bags but doesn’t won’t more than 20 bags list the possible ways she can fill the bag
Answers
Answer:
[tex]1.073\times 10^{19}\ \text{ways}[/tex]
Step-by-step explanation:
It is given that,
Total no of candy are 84
She want to divide the candy up evenly and place into bags but doesn’t won’t more than 20 bags.
We need to find the possible ways she can fill the bag. It mean that this problem is based on the concept of combination.
[tex]^{84}C_{20}=\dfrac{84!}{20!(84-20)!}\\\\=\dfrac{84!}{20!64!}\\\\=1.073\times 10^\\{19}[/tex]
There are [tex]1.073\times 10^{19}\ \text{ways}[/tex].
Cole is making decorated jellybean bags for a party. Each bag contains 5 pounds of jellybeans. If Cole has purchased 1,000 pounds of jellybeans, then how many party bags can make?
А. 833 party bags
B. 166 party bags
C. 1,200 party bags
D. 6.000 party bags
Answers
Answer:
The correct answer would be 200, but in your case 166 is the closest
Step-by-step explanation:
divide 1000 by 5
The total number of bags needed are 200 bags.
We have Cole who has purchased 1,000 pounds of jellybeans. Each bag contains 5 pounds of jellybeans.
We have to determine how many party bags can make 1,000 pounds of jellybeans.
If you need a total of 'x' number of toffees and each packet contains 'y' toffees, then how many packets will be needed?The total number of packets(n) required will be -
[tex]$n=\frac{x}{y}[/tex]
According to the question, we have -
Amount of jelly beans in a bag - 5 pounds.
Amount of jelly beans needed - 1000 pounds.
Assume that the number of bags needed are n. Then -
n = [tex]\frac{1000}{5}[/tex] = 200 Bags.
Hence, The total number of bags needed are 200 bags.
To solve more questions on Quantity estimation, visit the link below-
https://brainly.com/question/22407520
#SPJ2
Round to the nearest cent.
5. $406.439
Answers
Answer:
406.4
Step-by-step explanation:
When rounding you only look at the number you're rounding and the one before it. In this case it would be the 4 and 3 after the decimal since we're rounding to the nearest cent. If the numbers before the one you're rounding are 0-4 then you leave the number the same. If the numbers are between 5-9 then you add one to the number. Since the number before 4 is between 0-4 you leave it as 4. But if it was between 5-9 then you'd change the 4 to 5.
How many different five-card hands can be dealt from a standard deck of fifty-two cards?
Answers
Answer:
2598960 ways
Step-by-step explanation:
Given
Standard Deck = 52
Five-card hands
Required
Determine the number of ways
To solve this question, we make use of combination formula
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]
Where n = 52 and r = 5
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex] becomes
[tex]^{52}C_5 = \frac{52!}{(52-5)!5!}[/tex]
[tex]^{52}C_5 = \frac{52!}{47!5!}[/tex]
[tex]^{52}C_5 = \frac{52 * 51 * 50 * 49 * 48 * 47!}{47! * 5 * 4 * 3 * 2 * 1}[/tex]
[tex]^{52}C_5 = \frac{52 * 51 * 50 * 49 * 48}{5 * 4 * 3 * 2 * 1}[/tex]
[tex]^{52}C_5 = \frac{311875200}{120}[/tex]
[tex]^{52}C_5 = 2598960[/tex]
Hence, there are 2598960 ways
What number is 1/10 of 10?
Answers
Answer:
Hey there!
1/10 of 10 is 1.
Your answer is 1.
Hope this helps :)
Answer:
1
Step-by-step explanation:
Simplify the following:
10/10
Hint: | Divide 10 by 10.
10/10 = (10×1)/10 = 1:
Answer: 1
Which size would you see on the box for a new television whose screen measures 32 inches wide by 18 inches high?
Answers
Answer:
37
Step-by-step explanation:
The calculation of size for a new television is shown below:-
With the help of Pythagoras theorem
[tex]h^2 = b^2 + p^2[/tex]
where
h indicates hypotenuse which is the diagonal length
b indicates the base which is the length of the horizontal side
p indicates perpendicular which is the TV length of the vertical side.
[tex]h^2 = \sqrt{b^2 + p^2}[/tex]
now, we will put the values into the above formula
[tex]= \sqrt{32^2 + 18^2} \\\\ = \sqrt{1024 + 324} \\\\ = \sqrt{1348}[/tex]
Which gives result
= 36.7
or
= 37
Write an equation to find the missing angle in the triangle. Remember all the angles of a triangle add up to 180 degrees. The full question is in the picture.
Answers
Because the other angle is a right angle which is always 90. So, if you take the sum of the numbers you have and subtract that from 180 (because all triangles equal 180) you will get the missing angle.
Evaluate k + np2
if k = 0.5, n = –3, and p = –2.
Answers
Answer:
12.5
Step-by-step explanation:
0.5+(-3)×(-2)×2
=0.5+12
=12.5
Value of equation, k + np² is -11.5
Given that;Value of equation = k + np²
And
k = 0.5
n = -3
p = -2
Find:Value of equation
Computation:Value of equation = k + np²
And
k = 0.5
n = -3
p = -2
So,⇒ k + np²
⇒ 0.5 + (-3)(-2)²
⇒ 0.5 + (-3)(4)
⇒ 0.5 - 12
⇒ -11.5
Value of equation, k + np² is -11.5
Learn more:https://brainly.com/question/14431182?referrer=searchResults
The Distribution of Sample Means expresses the way in which sample means taken from a population and of a given sample size are distributed around the population mean.
a. True
b. False
Answers
Answer:
a. True
Step-by-step explanation:
This is because, since the sample mean equals the population means, the distribution of the sample means about the sample size would also be the distribution of the sample size distributed about the population mean.
This usually results in a normally distributed population for a sample size greater than 30.
So, if the sample size is greater than 30, the population mean and sample mean would have the same value and distribution.
How many thousands of blue crayons are in 327,412
Answers
Answer:327412000
Step-by-step explanation:
using any
combination of quarters, dimes, nickles,
pennies how many way
can you make
50 cents?
Answers
Answer:
49
Step-by-step explanation:
2 quarters
1 quarter, 2 dimes, 1 nickel
1 quarter, 1 dime, 3 nickels
1 quarter, 5 nickels
5 dimes
4 dimes, 2 nickels
3 dimes, 4 nickels
2 dimes, 6 nickels
1 dime, 8 nickels
10 nickels
10 ways without pennies. Pennies can be substituted for any quarter, dime, or nickel, so ...
8 ways to have 5 pennies
7 ways to have 10 pennies
6 ways to have 15 pennies
5 ways to have 20 pennies
4 ways to have 25 pennies
3 ways to have 30 pennies
2 ways to have 35 pennies
2 ways to have 40 pennies
1 way to have 45 pennies
1 way to have 50 pennies
For an additional 39 ways with pennies.
There are a total of 10 +39 = 49 ways to make change for 50¢.
Joseph rides his bike for 30 miles in an hour going west
Answers
Answer:
is it acceleration or velocity?
Step-by-step explanation:
6(3-e) = 42
e =
what does e equal
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{e = - 4}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{6(3 - e) = 42}[/tex]
Distribute 6 through the parentheses
⇒[tex] \sf{18 - 6e = 42}[/tex]
Move 18 to right hand side and change it's sign
⇒[tex] \sf{ - 6e = 42 - 18}[/tex]
Subtract 18 from 42
⇒[tex] \sf{ - 6e = 24}[/tex]
Divide both sides of the equation by -6
⇒[tex] \sf{ \frac{ - 6e}{ - 6} = \frac{24}{ - 6} }[/tex]
Calculate
⇒[tex] \sf{e = - 4}[/tex]
Hope I helped!
Best regards!!
Let R unrestricted and R restricted be 0.4366 and 0.4149 respectively. The difference between the 9) unrestricted and the restricted model is that you have imposed two restrictions. There are 420 observations. The F-statistic in this case is:_______ A) 10.34 B) 4.61 C) 7.71 D) 8.01
Answers
Complete Question
Let R unrestricted and R restricted be 0.4366 and 0.4149 respectively. The difference between the 9) unrestricted and the restricted model is that you have imposed two restrictions. There are 420 observations. The F-statistic in this case is:_______
A) 10.34
B) 4.61
C) 7.71
D) 8.01
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The [tex]R^2_{unrestricted } = 0.4366[/tex]
The [tex]R^2_{restricted } = 0.4149[/tex]
The number of observation is n= 420
Generally the number of independent variables is k([tex]R^2_{unrestricted } , \ n \ \ and \ R^2_{restricted }[/tex]) = 3
Then the number of restriction is (i.e [tex]R^2_{unrestricted } \ and \ R^2_{restricted }[/tex]) is q = 2
Generally the F-statistics is mathematically represented as
[tex]F = \frac{\frac{R^2_{unrestricted } - R^2_{restricted}}{q} }{ \frac{(1- R^2_{unrestricted }) }{n-k-1} }[/tex]
substituting values
[tex]F = \frac{\frac{0.4366 -0.4149}{2} }{ \frac{(1-0.4366) }{420-3-1} }[/tex]
[tex]F = 8.01[/tex]
Since you have 15% off of $24.99, you should have found (on the previous Slide) that you will have to pay 85% of $24.99. Using this information, determine the cost of the shirt after applying the discount (and before taxes). After you input your answer, click 'Submit' to see if you are correct. Round to the nearest penny.
Answers
Answer: $21.24
Step-by-step explanation:
Well if you apply the discount you will have to pay 85% of the price which is already said .
So 85% of 24.99 will give you the cost of the shirt.
0.85 * 24.99 = 21.2415
TO the nearest penny will be 21.24
What is the mean of the following data values? 52, 70, 88, 15, 65 A. 58 B. 82 C. 62 D. 78
Answers
Answer:
A) 58
Step-by-step explanation:
Mean = Sum of all the data ÷ total number of data
[tex]=\frac{52+70+88+15+65}{5}\\\\\\=\frac{290}{5}\\\\\\= 58[/tex]
Starbucks reports net income for 2015 of $2,634.4 million. Its stockholders' equity is $5,605 million and $6,151 million for 2014 and 2015, respectively. a. Compute its return on equity for 2015. Round answer to one decimal place (ex: 0.2345 = 23.5%) Answer 44.8 % b. Starbucks repurchased over $1.4 billion of its common stock in 2015. Did this repurchase increase or decrease Starbucks’ ROE? ROE usually decreases since the repurchase of shares reduces the denominator (avg. stockholders' equity). ROE usually increases since the repurchase of shares reduces the denominator (avg. stockholders' equity). ROE usually increases since the repurchase of shares increases the denominator (avg. stockholders' equity). ROE usually decreases since the repurchase of shares increases the denominator (avg. stockholders' equity). c. If Starbucks had not repurchased common stock in 2015, what would ROE have been? Note: Round answer to one decimal place (example: 20.6%). Answer %
Answers
Answer:
A. 44.82%
B.
Option b. Return On Equity usually increases since the repurchase of shares reduces the denominator (avg. stockholders' equity)
C.
Option b. The Companies would tend to repurchase their own stock if they feel the stock is been undervalued by the market
Step-by-step explanation:
a. Computation for return on equity for 2015
Using this formula
Return on equity = The Net income amount /The Average stockholders' equity amount
Let plug in the formula
Return on equity=2,634.4/[(5,605+6,151)/2]
Return on equity=2,634.4/(11,756/2)
Return on equity=2,634.4/5,878
Return on equity=0.4482×100
Return on equity= 44.82%
b. In a situation where they repurchased over $1.4 billion of its common stock in the year 2015 this means that the RETURN ON EQUITY will usually tend to increases reason been that the repurchase of shares will often reduces the denominator (average stockholders' equity)
Therefore the repurchase increase Starbucks’ Return On Equity.
c. In a situation where Starbucks had not repurchased common stock in the year 2015, what their Return On Equity would have been is that they will repurchase their own stock if they feel the stock is been undervalued by the market
What is the value of x in the equation 6(x + 1) - 5x = 8 + 2(x - 1)?
A100
12
Answers
Answer:
x=0
Step-by-step explanation:
First, we distribute on both sides
6x+6-5x=8+2x-2
simplify
x+6=2x+6
subtract x from both sides
6=x+6
subtract 6 from both sides
x=0
(plz give brianliest ty)
Answer:
x = 0
Step-by-step explanation:
6 ( x + 1 ) -5x = 8 + 2 ( x - 1 ) (Distribute)
6x + 6 - 5x = 8 + 2x - 2 (Rearrange expression)
6x - 2x - 5x = 8 - 6 - 2 (Combine like terms)
-1x = 0 (Divide)
x = 0
Inverse of g(x)=-x^5-3
Answers
Answer:
[tex] {g}^{ - 1} (x) = \sqrt[5]{ - x - 3} [/tex]Step-by-step explanation:
[tex]g(x) = - {x}^{5} - 3[/tex]To find the inverse of g(x) equate g(x) to y
That's
[tex]y = - {x}^{5} - 3[/tex]Next interchange the terms
x becomes y and y becomes x
We have
[tex]x = - {y}^{5} - 3[/tex]Next make y the subject
Multiply both sides by - 1
That's
[tex] {y}^{5} + 3 = - x[/tex]Send 3 to the right side of the equation
That's
[tex] {y}^{5} = - x - 3[/tex]
Find the 5th root of both sides
That's
[tex] \sqrt[5]{ {y}^{5} } = \sqrt[5]{ - x - 3} \\ y = \sqrt[5]{ - x - 3} [/tex]We have the final answer as
[tex] {g}^{ - 1} (x) = \sqrt[5]{ - x - 3} [/tex]Hope this helps you
What is the measure of x? 37° 67° 97° 107°
Answers
Answer:
97°
Step-by-step explanation:
The angles of any quadrilateral will add up to 360°. Since we already know 3 out of the 4 angles (the bottom two are both 90°), we can easily find the measure of x.
[tex]90 + 90 + 83 +x = 360[/tex]
[tex]263 + x = 360\\\\x = 97[/tex]
Hope this helped!
Answer:
Value of x = 97 degrees
Step-by-step explanation:
In the given quadrilateral
One angle = 83
2 other angles = 90 degrees each
Sum of all the four angles in a quadrilateral = 360 (Angle Sum Property of quadrilaterals)
=>90+90+x+83= 360
=>180+83+x = 360
=> 263+x= 360
=>x= 360-263
=>x=97
Hi! I really need help with this question and please help me if u can. I'll mark you as BRAINLIEST.
Answers
Answer: The answer is 148 square feet.
Step-by-step explanation:
So if we are given the information to the area of the composite figure, we just first have to find the area of the smaller shapes and then add them all together to achieve the total.
1. The larger rectangle is a 10 by 14 rectangle.
2. The smaller rectangle is a 1 by 8 rectangle.
How did I get around to 8 feet?
Subtract 3 and 3 from 14, and you'll get 8 for the side.
Now just find the areas of each of the rectangles:
1. 10 times 14 = 140
2. 1 times 8 = 8
Now add them together:
140 + 8 = 148
The answer is 148 square feet.
-1(-2x + 4) = 6
Hellooooooooooo
Answers
Answer:
x=5
Step-by-step explanation:
First we distribute
2x-4=6
isolate x
2x=10
divide both sides by 2
x=5
(plz give brianliest ty)
Answer:
X=5
Step-by-step explanation:
2x+(-4)=6
2x=6+4
2x=10
X=10/2
X=5
You earned a 40% on your French quiz. How would you respond to "ça va?"
Answers
Answer:
D
Step-by-step explanation:
6p^{2}-(3p^{2}+2q)p=1,q=5
Answers
Answer: 24p ² r + 20 a s - 5 ar / ar
Step-by-step explanation:
If x=2y=3z then x:y:z equals what?
Answers
Answer: x=6 y=3 z=2
Step-by-step explanation: The question is very vast so im guessing that its just finding 3 whole numbers that can equal the same ammount being multipied by 2 and 3. I chose 6. But theres many others. The answer should be correct because if we replace the letters with the numbers i put in the answer it should look like this: 6=2•3=3•2
When we do simplify this we should get 6=6=6 which is true.
Again you can use different numbers for example 12 as X. Then you need to divide 12 by whats behind the Y. So 12÷2 is 6. So Y is equal to 6. To find Z all you need to do is follow the same steps as Y. Find the number behind Z (3) and divide that into 12. So it would be 12÷3. And if you do the math right it should look like this: X=12, Y=6, Z= 4. And when you imput the numbers to thier corresponding letter it should look like this 12=2(6)=3(4) which simplified looks like 12=12=12 which is true.
The length of a rectangle is 4 inches less than 4 times the width. If the perimeter is 72 inches, find the length and the width of the rectangle.
Answers
Answer:
Length is 28. Width is 8.
Step-by-step explanation:
The perimeter of a rectangle is given by the following formula:
[tex]P=2l+2w[/tex]
We know that the length is 4 inches less than 4 times the width. Therefore:
[tex]l=4w-4[/tex]
Substitute this for l. Let's also substitute 72 for P. Therefore:
[tex]72=2(4w-4)+2w[/tex]
Distribute:
[tex]72=8w-8+2w[/tex]
Combine like terms:
[tex]72=10w-8[/tex]
Add 8 to both sides:
[tex]80=10w[/tex]
Divide both sides by 10:
[tex]w=8[/tex]
Therefore, the width is 8.
The length is 4 less than 4 times the width. Thus: "
[tex]l=4(8)-4[/tex]
Multiply:
[tex]l=32-4[/tex]
Subtract:
[tex]l=28[/tex]
Therefore, the length is 28 and the width is 8.
And we're done!
A box rectangular prism has an end that is 3 by 5 ft in dimension it’s length is 10 feet what is the volume of the prism
Answers
Answer:
150
Step-by-step explanation:
Multiply 3 x 5 x 10
A plot of land is in the shape of a triangle. If one side is x meters, a second side is (5x - 2) meters and a third side is (7x-3) meters, express the perimeter of the lot as a simplified expression in x.
Answers
Hey there! I'm happy to help!
The perimeter is the distance around a shape. Let's add up the lengths of our sides to ind it.
x+5x-2+7x-3
We combine all of the x values.
x+5x+7x=13x
And all of the constants.
-2-3=-5
Therefore, the perimeter is 13x-5.
Have a wonderful day! :D