Answer:
The integral of the volume is:
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
The result is: [tex]V = 78.97731[/tex]
Step-by-step explanation:
Given
Curve: [tex]x^2 + 4y^2 = 4[/tex]
About line [tex]x = 2[/tex] --- Missing information
Required
Set up an integral for the volume
[tex]x^2 + 4y^2 = 4[/tex]
Make x^2 the subject
[tex]x^2 = 4 - 4y^2[/tex]
Square both sides
[tex]x = \sqrt{(4 - 4y^2)[/tex]
Factor out 4
[tex]x = \sqrt{4(1 - y^2)[/tex]
Split
[tex]x = \sqrt{4} * \sqrt{(1 - y^2)[/tex]
[tex]x = \±2 * \sqrt{(1 - y^2)[/tex]
[tex]x = \±2 \sqrt{(1 - y^2)[/tex]
Split
[tex]x_1 = -2 \sqrt{(1 - y^2)}\ and\ x_2 = 2 \sqrt{(1 - y^2)}[/tex]
Rotate about x = 2 implies that:
[tex]r = 2 - x[/tex]
So:
[tex]r_1 = 2 - (-2 \sqrt{(1 - y^2)})[/tex]
[tex]r_1 = 2 +2 \sqrt{(1 - y^2)}[/tex]
[tex]r_2 = 2 - 2 \sqrt{(1 - y^2)}[/tex]
Using washer method along the y-axis i.e. integral from 0 to 1.
We have:
[tex]V = 2\pi\int\limits^1_0 {(r_1^2 - r_2^2)} \, dy[/tex]
Substitute values for r1 and r2
[tex]V = 2\pi\int\limits^1_0 {(( 2 +2 \sqrt{(1 - y^2)})^2 - ( 2 -2 \sqrt{(1 - y^2)})^2)} \, dy[/tex]
Evaluate the squares
[tex]V = 2\pi\int\limits^1_0 {(4 +8 \sqrt{(1 - y^2)} + 4(1 - y^2)) - (4 -8 \sqrt{(1 - y^2)} + 4(1 - y^2))} \, dy[/tex]
Remove brackets and collect like terms
[tex]V = 2\pi\int\limits^1_0 {4 - 4 + 8\sqrt{(1 - y^2)} +8 \sqrt{(1 - y^2)}+ 4(1 - y^2) - 4(1 - y^2)} \, dy[/tex]
[tex]V = 2\pi\int\limits^1_0 { 16\sqrt{(1 - y^2)} \, dy[/tex]
Rewrite as:
[tex]V = 16* 2\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
Using the calculator:
[tex]\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy = \frac{\pi}{4}[/tex]
So:
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
[tex]V = 32\pi * \frac{\pi}{4}[/tex]
[tex]V =\frac{32\pi^2}{4}[/tex]
[tex]V =8\pi^2[/tex]
Take:
[tex]\pi = 3.142[/tex]
[tex]V = 8* 3.142^2[/tex]
[tex]V = 78.97731[/tex] --- approximated
What percent of 84 is 42
PLS HELP ME
The smallest hummingbird is the Bee hummingbird. It has a mass of about 1
1
4
grams. The mass of a larger type of hummingbird is about 6 times the mass of the Bee hummingbird.
What is the mass of the larger hummingbird?
Answer:
The mass of the larger hummingbird is 7 1/2 or 15/2.
Step-by-step explanation:
Bee hummingbird = 1 1/4g
Larger hummingbird = 6x that
So,
1 1/4 x 6 = 7.5
7.5 as fraction = 7 1/2 or 15/2
3^x=2 solve for x without using calculating utility?
here is a tree diagram showing the sample independent events how many outcomes are there for the second event
8
1
2
4
Which algebraic expression is a polynomial?
3m^2 n - 2m/n + 1/n
4m^3/n^2 - 3mn^5 + square root of 8
7mn + 3m/2 + 5n/4
Answer: The answer is 7mn+3m/2+5n/4
7mn + 3m/2 + 5n/4 is the algebraic expression which is a polynomial
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
A polynomial is an expression with variables and coefficients separated by addition and subtraction.
The following are used when determining if an expression is a polynomial:
i) Variables of a polynomial must not have negative exponent.
ii) Variables of a polynomial must not have fractional exponent.
iii) Dividing by an exponent is not allowed
iv) Exponent radicals are not allowed.
7mn + 3m/2 + 5n/4 is a polynomial because it has variables and seperated by operators addition and subtraction.
Hence, 7mn + 3m/2 + 5n/4 is the algebraic expression which is a polynomial
To learn more on Polynomials click:
https://brainly.com/question/11536910
#SPJ5
Question 2
There are 8 students in a discussion section: 3 boys and 5 girls.
If the teacher picks a group of 1 at random, what is the probability that everyone in the
group is a boy?
3/8
1/3
110
Submit answer
Exit
wl
Chin
Answer:
3/8
Step-by-step explanation:
this is because there are 8 students in all and only three of them are boys
The slope of the line shown below is 1/2
Someone Please Help Me
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 2
Explanation:
Remember Rise/Run
1/2
So if they went "Run" 4 units
then the equivalent to 1/2 is 2/4
Therefore the value of a is 2!
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Can anyone help me with my homework
Help this is due today
Which of the following expressions is equivalent to 32 ÷ 4• 4 ÷ 2 • 2?
Answer:
128
Step-by-step explanation:
32 ÷ 4• 4 ÷ 2 • 2
8 .4.2.2
128
A line has a slope of 2 and y-intercept of -3/4 . Which if the following is an equation of the line ?
Answer: y = 2x - 3/4
Step-by-step explanation:
y = mx + b where m is the slope, and b is the y-intercept.
y = 2x - 3/4
Use slopes and y-intercepts to determine if the lines 4x−3y=6 and y=43x−1 are parallel.
Answer:
Since they have the same slope, they are parallel.
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope. If two lines are parallel, they have the same slope.
4x−3y=6
Placing into the above format:
[tex]3y = 4x - 6[/tex]
[tex]y = \frac{4x - 6}{3}[/tex]
[tex]y = \frac{4x}{3} - 2[/tex]
The slope [tex]m = \frac{4}{3}[/tex]
y=4/3x−1
The slope is [tex]m = \frac{4}{3}[/tex]
Since they have the same slope, they are parallel.
Which of the following is a TRUE statement about check cashing stores?
please help!!! and show work!!
Answer:
x = 17
Step-by-step explanation:
area = L x W
45 = (x-2)(x-14)
45 = x² - 14x - 2x + 28
simplify:
x² -16x - 17 = 0
(x + 1)(x -17 ) = 0
x = -1 not applicable
x = 17
Proof:
(17-2)(17-14) = 45
15 x 3 = 45
45 = 45
circle A is defined as (x+5)^2+(y-6)^2=16, and circle B is defined as (x+3)^2+(y+2)^2=9. which transformation of circle A shows that circle B is similar
Answer: the answer is D “The center of circle A is translated left 2 and up 8, and the radius is enlarged by a scale factor of 4/3.”
Step-by-step explanation:
A process manufactures ball bearings with diameters that are normally distributed with mean 25.14 mm and standard deviation 0.08 mm. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on
Answer:
The diameter is in the 77th percentile.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
25.14 mm and standard deviation 0.08 mm.
This means that [tex]\mu = 25.14, \sigma = 0.08[/tex]
A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on?
This is the pvalue of Z when X = 25.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25.2 - 25.14}{0.08}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a pvalue of 0.77.
The diameter is in the 77th percentile.
I need help plz math
Answer:
Q1 = 40
Step-by-step explanation:
Set up numbers from least to greatest
21, 40, 52, 58, 72, 75, 96
First, find the median,
Median is: 58
Now Q1 is all numbers before the median (without counting the median)
21, 40, 52
The median here is 40
Answer:
D/40
Step-by-step explanation:
The answer is D because if you were to put them in the correct order it would be
21, 40, 52, 58, 72, 75, 96
Q1 Q2 Q3
Q1 is quartile 1 so the answer is 40
Hope this helps!
A company has a maximum advertising budget of $100,000 for the year. It
will be using two different platforms of advertising: online ads and billboards. Each online ad purchased will cost $15,000 for the year, and each billboard will cost $10,000 for the year. The company will not spend more than 60% of its overall budget on one of the platforms.Given that x represents the number of online ads purchased and y represents the number of billboards purchased, create a system of inequalities modeling the scenario. Select all that apply.
Answer:
Step-by-step explanation:
An insurance office buys paper by the ream, 500 sheets, for use in the copier, fax, and printer. Each ream lasts an average of 4 days, with standard deviation 1 day. The distribution is normal, independent of previous reams. a. Find the probability that the next ream out- lasts the present one by more than 2 days. b. How many reams must be purchased if they are to last at least 60 days with probability at least 80%
Answer:
a) the probability that the next ream out- lasts the present one by more than 2 days is 0.0787
b) the number of reams that must be purchased is 19
Step-by-step explanation:
Given the data in the question;
Lets X₁ and X₂ be the two random variables that represents the first and second ream lasts
given that both random variables follow normal distribution with mean 4 and standard deviation 1.
a)
Find the probability that the next ream out- lasts the present one by more than 2 days.
P( X₂ - X₁ > 2 ) = P( [(X₂ - X₁ - E(X₂ - X₁)) / √(V(X₂ - X₁)] > [ (2-E(X₂ - X₁))/√(V(X₂ - X₁) ]
= 1 - P( Z ≤ [2-(μ₂ - μ₁)] / [√( V(X₂) + V(X₁) ) ] )
= 1 - P( Z ≤ [2-(4 - 4)] / [√( 1 + 1 )] )
= 1 - P = ( Z ≤ 2 / √2 )
= 1 - p( Z ≤ 1.4142 )
from excel; p( Z ≤ 1.41 ) = 0.9213
P( X₂ - X₁ > 2 ) = 1 - 0.9213
P( X₂ - X₁ > 2 ) = 0.0787
Therefore, the probability that the next ream out- lasts the present one by more than 2 days is 0.0787
b)
How many reams must be purchased if they are to last at least 60 days with probability at least 80%
total value is 4n
standard deviation is nσ
so
P(nX ≥ 60 ) = 0.80
P( nX-nμ /nσ ≥ 60-nμ/nσ) = 0.80
P( Z ≥ 60-4n/n) = 0.80
1 - P( Z ≥ 60-4n/n) = 0.80
P( Z < z ) = 0.20
now since z = 60-4n/n
from standard normal table
critical value of z corresponding to cumulative area of 0.20 is -0.841
so
z = - 0.841
60-4n/n = -0.841
60 - 4n = -0.841n
60 = -0.841n + 4n
60 = 3.159n
n = 60 / 3.159
n = 18.99 ≈ 19
Therefore, the number of reams that must be purchased is 19
Find the rate of change in table plsss helppp!!!!
Answer:
.25 is the answer
Step-by-step explanation:
.5/2=.25
At burns high school 3/5 of the students are females of the female students 1/3 of them play volleyball what fraction of the students in burn high school are girls that play volleyball
3/5 of 1/3 means 3/5 x 1/3
[tex]\frac{3}{5} \times \frac{1}{3} = \frac{3}{15}[/tex]
3/15 simplifies to 1/5
So 1/5 of the students in the high school are girls who play volleyball
If Q1=5 and Q3=15, what is the Interquartile range (IQR) and what does it tell you about the data?
Will give Brainliest .
a.188.5 cubic units
b. 204.2 cubic units
c. 1,021.0 cubic units
d. 942.5 cubic units
Answer:
d. 942.5 cubic units
Step-by-step explanation:
Volume of the oblique cylinder = πr²h
h = 12
r = 5
Plug in the values
Volume = π × 5² × 12
Volume = 942.477796
Volume = 942.5 cubic units (nearest tenth)
Come I need answers
The sum of three consecutive positive numbers is 147. Find the product of the greatest and the
smallest number.
Answer:
any how there are three consecutive positive numbers
3/5+1/4
Give your answer as a fraction in its simplest form
Answer:
5.25/5 i think
Step-by-step explanation:
3/5 = 8/10 and 1/4 = 2.5/10
So if I do 8/10 + 2.5 / 10.
My reply is 10.5/10
And if I reduce as max, my reply is: 5.25 / 5
Rewrite the number in Standard form
6 x 10^8
Answer:
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 x 6 = 600,000,000.
Answer:
600000000
Step-by-step explanation:
10^8=100000000
6×100000000=600000000
hope this helps
I need help with the questions I circle only.
Answer:
3:12
4:36
Step-by-step explanation:
( pls dont report me let me kno if it wrong and i will fix it
(20 points)
What is the measure of ^1?
☁︎
A:230
☁︎
B:130
☁︎
C:125
☁︎
D:115
Step-by-step explanation:
I want to say B) 130 but not 100% sure. Sorry if my answer is wrong.
A private beach is 6/7 mile in length and 1/4 mile in width. What is the area of the private beach? (Don't forget to simplify)Immersive Reader
(20 Points)