Use cylindrical coordinates. ∭_e x^2 dv .where E … solid thati x2 dV, where E is the solid that lies within the cylinder x^2 + y^2=4, above the plane z = 0, and below the cone z^2 4x^2 + 4y^2
The value of the triple integral ∭_E x² dV over the given solid E is 64π/5.
To evaluate the triple integral ∭_E x^2 dV, where E is the solid that lies within the cylinder x² + y² = 4, above the plane z = 0, and below the cone z² = 4x² + 4y², we can express the integral in terms of cylindrical coordinates.
In cylindrical coordinates, we have:
x = r cos(theta)
y = r sin(theta)
z = z
The limits for the cylindrical coordinates are as follows:
0 ≤ r ≤ 2 (limits for the radius)
0 ≤ theta ≤ 2π (limits for the angle)
0 ≤ z ≤ sqrt(4r²) = 2r (limits for the height, as per the cone equation)
Now let's express the integral in cylindrical coordinates:
∭_E x² dV = ∭_E (r cos(theta))² r dz dr d(theta)
Let's evaluate the integral step by step:
∫[0 to 2π] ∫[0 to 2] ∫[0 to 2r] (r³ cos²(theta)) dz dr d(theta)
We can simplify the innermost integral with respect to z:
∫[0 to 2π] ∫[0 to 2] [r³ cos²(theta)z] |[0 to 2r] dr d(theta)
= ∫[0 to 2π] ∫[0 to 2] (r³ cos²(theta)(2r)) dr d(theta)
= 2 ∫[0 to 2π] ∫[0 to 2] (2r⁴ cos²(theta)) dr d(theta)
Now, let's integrate with respect to r:
2 ∫[0 to 2π] [(1/5) r⁵ cos²(theta)] |[0 to 2] d(theta)
= 2 ∫[0 to 2π] [(1/5)(32 cos²(theta))] d(theta)
= (64/5) ∫[0 to 2π] cos²(theta) d(theta)
To evaluate the remaining integral, we can use the identity cos²(theta) = (1 + cos(2theta))/2:
(64/5) ∫[0 to 2π] [(1 + cos(2theta))/2] d(theta)
= (64/10) ∫[0 to 2π] (1 + cos(2theta)) d(theta)
= (64/10) [(theta + (1/2)sin(2theta))] |[0 to 2π]
= (64/10) [(2π + (1/2)sin(4π)) - (0 + (1/2)sin(0))]
= (64/10) (2π + 0 - 0)
= (64/10) (2π)
= 128π/10
= 64π/5
Therefore, the value of the triple integral ∭_E x² dV over the given solid E is 64π/5.
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Read the question and answer below. Remember that one measure of center is better than another when you have outliers in the data set. *
A. A
B. B
C. C
D. D
Answer:
C
Step-by-step explanation:
The population of a small town is decreasing by 2% per year. The population in the year 2017 was 3,850. A. By how many people will be the population decrease from 2027 to 2018? B. What will be the populatiom of the town in 2018?
Answer:
A. 77
B. 3,773
Step-by-step explanation:
According to the problem, computation of given data are as follows,
Population in 2017 = 3,850
Decrease rate = 2% per year
(A) We can calculate number of population decrease from 2017 to 2018 by using following formula,
Number of population decrease = Population in 2017 × Decrease rate
= 3,850 × 2%
= 77
(B). Total population in 2018 = 3,850 - 77
= 3,773
A package of 12 pencils costs $0.96. At this rate, how much would 100 pencils cost?
A. $8.35
B. $10.80
C. $9.60
D. $8.00
Answer:
B
Step-by-step explanation:
Please Give brainliest
Answer:
D
Step-by-step explanation:
What is the area of the rectangle below?
5/6 m H
2/3 m L
Answer:
5/9
Step-by-step explanation:
Answer:
A = 0.55 or 5/9
Step-by-step explanation:
Area = HL
A = (5/6)(2/3)
A = 0.55 or 5/9
Please help! Will give Brainliest! SHOW ALL WORK
Factor:
2x^(2)+ay-ax^(2)-2y
Answer:
(2 - a) (x² - y)
Step-by-step explanation:
2x² + ay - ax² - 2y
=> 2x² - 2y + ay - ax²
=> 2 (x² - y) + -a (-y + x²)
=> 2 (x² - y) + -a (x² - y)
=> (2 - a) (x² - y)
The equation of a line in the form y = a number creates this kind of line.
Answer:
a diagonal one??? like its linear uhm okay here i have a picture one sec
Step-by-step explanation:
Find the critical t-value that corresponds to 95% confidence. Assume 15 degrees of freedom.
The critical t-value that corresponds to a 95% confidence level with 15 degrees of freedom is approximately 2.131.
To find the critical t-value that corresponds to a 95% confidence level with 15 degrees of freedom, we can use a t-table or a statistical software.
Using a t-table or a statistical software, we look up the critical t-value for a two-tailed test with a confidence level of 95% and 15 degrees of freedom.
For a two-tailed test, we divide the desired confidence level by 2 to account for both tails of the t-distribution. In this case, we divide 95% by 2, which gives us 0.475.
Looking up the critical t-value for a confidence level of 0.475 and 15 degrees of freedom, we find that the critical t-value is approximately 2.131.
Therefore, the critical t-value that corresponds to a 95% confidence level with 15 degrees of freedom is approximately 2.131.
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The figure shows a tank in the form of a rectangular prism that is 25% full of water. How many more gallons of water will it take to fill the tank? (1 gallon 231 in.)
Answer:
if it is one gallon then it will take 75 more percent
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Question is in picture
a box in mrs booths class contains 200 loose white or yellow golf balls
Answer:
Dot Plot
Step-by-step explanation:
Libby can finish a paper in 2 hours. Ethan can finish the same paper in 4 hours. How
long will it take them to finish a paper if they work together?
Answer:
1.33333 hours
Step-by-step explanation:
Given :
Time taken by Libby = 2 hours
Time taken by Ethan = 4 hours
rate = 1 / time taken
Libby's rate = 1 /2
Ethan's rate = 1/4
Combined rate = Libby's rate + Ethan's rate
Combined rate = 1/2 + 1/4 = 3/4
Time taken = 1 / combined rate
Time taken = 1 / (3/4)
Time taken = 4 /3
Time taken = 1.33333 hours
Mr. Singh needed to understand the trend of his students’ latest test scores. Find the mean and median for each set of data, and then determine which gives a better picture of the scores.
Scores: 89, 99, 80, 5, 90, 0, 100, 95
Answer:
See explanations below
Step-by-step explanation:
Mean is the average of the data
Mean = sum of data/sample size
Sum of data = 89+99+80+5+90+0+100+95
Sum of data = 558
Sample size = 8
Mean = 558/8
Mean = 69.75
Median is the data value in the middle after rearrangement
Rearrange
0 , 5, 80) 89, 90, (95, 99 100
Median = 89+90/2
Median = 89.5
The parameter that gives a better picture of the scores is the Mean since all the given datas are taken into consideration
The mean test score is
✔ 69.75
.
The median test score is
✔ 89.5
.
Which measure of center best represents the test data?
✔ median
I hope this helps!
For a fixed confidence level, when the sample size decreases, the length of the confidence interval for a population mean decreases.
a. True
b. False
The given statement "For a fixed confidence level, when the sample size decreases, the length of the confidence interval for a population mean decreases." is false, length of CI increases in this case.
When the sample size decreases, the length of the confidence interval for a population mean actually increases, not decreases.
The length of a confidence interval is influenced by several factors, including the sample size, the variability of the data, and the desired level of confidence. A confidence interval provides a range of values within which the population mean is estimated to lie.
When the sample size is smaller, there is less information available to estimate the population mean accurately. As a result, the confidence interval needs to be wider to accommodate the increased uncertainty. This wider interval allows for a larger range of potential values for the population mean.
On the other hand, as the sample size increases, there is more data available to estimate the population mean. This increased amount of information leads to a more precise estimate, allowing for a narrower confidence interval.
Therefore, for a fixed confidence level, as the sample size decreases, the length of the confidence interval for a population mean generally increases, not decreases.
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hiiii pppplease help i’ll give brainliest
Answer:
Step-by-step explanation:
For observers right at the north pole and the south pole, there are only two seasons – an almost six-month long winter night followed by an almost six-month long summer day!
Paper lanterns are $3.50 each. Write
a direct proportion equation using p
for paper lanterns and c for total
cost.
A. 3.50c = p
B. 3.5pc
C. 3.50 + p = C
D. 3.50p = 0
Answer:
it's probably C
Step-by-step explanation:
️♀️
Plz help ASAP and thank you!
Answer:
Plot attached
Step-by-step explanation:
We want to locate √36 and ∛36 on the given number line
Now, √36 = 6.
And ∛36 = 3.3
I have attached a plot number line both values as we are told in the question
Find the perimeter of rectangle with length 6 inches and width 3 inches.
Answer:
18
Step-by-step explanation:
Formula
P = 2 * (L + W)
Solution
L = 6
W = 3
P = 2 (6 + 3)
P = 2 (9)
P = 18
1 3/4 cups of flour for one batch but he wants to make 1 1/2 batches. How many more cups of flour will he need
Answer:
[tex]2\frac{5}{8} cups = 1\frac{1}{2}\ batches[/tex]
Step-by-step explanation:
Given
[tex]1\frac{3}{4} cups = 1\ batch[/tex]
Required
Number of cups for [tex]1\frac{1}{2}[/tex] batches
[tex]1\frac{3}{4} cups = 1\ batch[/tex]
Multiply both sides by [tex]1\frac{1}{2}[/tex]
[tex]1\frac{1}{2} * 1\frac{3}{4} cups = 1\ batch * 1\frac{1}{2}[/tex]
[tex]1\frac{1}{2} * 1\frac{3}{4} cups = 1\frac{1}{2}\ batches[/tex]
Express fractions as improper fractions
[tex]\frac{3}{2} * \frac{7}{4} cups = 1\frac{1}{2}\ batches[/tex]
[tex]\frac{21}{8} cups = 1\frac{1}{2}\ batches[/tex]
Express fraction as improper fraction
[tex]2\frac{5}{8} cups = 1\frac{1}{2}\ batches[/tex]
2) given that z is a standard normal random variable, compute the following probabilities. a. p(z ≤ -1.09) = b. p(z ≤ -1.5) = c. p(z ≥ 1.3) = d. p(z ≥ 2.54) = e. p(-0.71 < z ≤ 2.54) =
The probability of z being less than or equal to,-1.09 is approximately 0.1379,-1.5 is approximately 0.0668, 1.3 is approximately 0.0968.2.54 is approximately 0.0057,-0.71 and 2.54 (exclusive) is approximately 0.6467.
To compute these probabilities, we can use the standard normal distribution table or a statistical software. In the standard normal distribution table, we look up the given z-values and find the corresponding probabilities.
For (a), the probability of z being less than or equal to -1.09 is approximately 0.1379.
For (b), the probability of z being less than or equal to -1.5 is approximately 0.0668.
For (c), the probability of z being greater than or equal to 1.3 is approximately 0.0968.
For (d), the probability of z being greater than or equal to 2.54 is approximately 0.0057.
For (e), we subtract the probability of z being less than or equal to -0.71 from the probability of z being less than or equal to 2.54. This gives us approximately 0.6467.
These probabilities provide information about the likelihood of certain values occurring in a standard normal distribution.
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hehe guess it right;)
Answer:
I don't understand this at all but I wanted to take a stab at it anyway.
It's not an even number, it's less than 50, it has to be divisible by six or three in order to be 5 more than a perfect square, and it has to be two or three digits that equal 40.
Sounds hard.
Okay first I want to get all the odd numbered equations that could equal 40
1+39 19+21
3+37 17+23
5+35 15+25
7+33
9+31
11+29
13+27
This is taking so much brain power, wow... So none of those so far would work, which makes me think that it would be a single digit equation to make it double digit, but nothing, not even 9+9 equals 40, so at least one of the numbers would have to be double digit but that makes no sense because then the number would have to have three digits, which makes it more than 100!
This is impossible. I think I have to rephrase my answer above in saying that the number has to be more than 100, but that means I have no idea what that first line means...
I'm so frustrated by this imao... Asker of the question, if you've figured out the answer please let me know because I am so confused.
Answer:
I DONT KNOW
Step-by-step explanation:
hehe
A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should move his token forward on the board, three of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board.
The total area of the sectors that do not allow the player to move his token is 45. 1 inches squared.
What is the radius of the spinner?
Enter your answer, rounded to the nearest tenth of an inch, in the box
Answer:
The radius is 9.28 inches.
Step-by-step explanation:
Since there are 7 Move Ahead zones, and 3 Go Backwards zones on the spinner, there must be 2 other zones (the Freeze! +Bonus pts)
2 out of 12 zones are Freeze! +Bonus pts. That is 1/6 of the spinner. They said the area of the the Freeze!+Bonus pts is 45.1 inches squared.
45.1 × 6
= 270.6
The entire spinner has the area 270.6
The area of a circle is:
A = pi•r^2
We are looking for r. Thats the radius they asked for in the question.
270.6 = pi•r^2
pi is a number, I'm using the pi button on the calculator bc it is most exact.
270.6 = pi•r^2
Divide both sides by pi.
86.134655 = r^2
square root both sides.
9.28 = r
The radius is 9.28 inches.
The Consumer Reports National Research Center conducted a telephone survey of 2000 adults to learn about the major economic concerns for the future (Consumer Reports, January 2009). The survey results showed that 1760 of the respondents think the future health of Social Security is a major economic concern. a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern (to 2 decimals)
Answer:
The point estimate is 0.88
Step-by-step explanation:
Given
[tex]n = 2000[/tex] -- sample size
[tex]x = 1760[/tex] -- adults who think future health of social security is a major economic concerm
Required
Determine the point estimate
This is calculated as:
[tex]\hat p= \frac{x}{n}[/tex]
[tex]\hat p= \frac{1760}{2000}[/tex]
[tex]\hat p = 0.88[/tex]
The point estimate is 0.88
Eric needs $10 to buy a book. He has $6 already. How much more money does Eric
need?
Answer: $4
Step-by-step explanation: Since he needs 10 dollars and he already has 6 dollars, we can subtract to find the remaining amount, which is 4 dollars.
Necesito un dibujo donde se muestren los ángulos agudos obtusos rectos y llanos
Answer:
El dibujo se encuentra adjuntado al término de este documento, después de las explicaciones previas.
Step-by-step explanation:
Por Geometría sabemos lo siguiente:
Angulo recto - Dos semirrectas con origen común y cuya medida angular es mayor a 0° y menor a 90°.
Angulo obtuso - Dos semirrectas con origen común y cuya medida angular es mayor a 90° y menor a 180°.
Angulo recto - Dos semirrectas con origen común y cuya medida angular es igual a 90°.
Angulo llano - Dos semirrectas con origen común y cuya medida angular es igual a 180°.
Finalmente, presentamos un dibujo representativo de los cuatro tipos de ángulos.
en que consiste la jerarquía de operaciones?
Answer:
La jerarquía de operaciones es un método para resolver operaciones con múltiples operadores; saber realizarla te servirá para resolver los diversos problemas que te presenten en tu examen CENEVAL EXANI-II. En primer lugar, se deben resolver las operaciones de potencias y raíces.
Step-by-step explanation:
You spin the spinner twice what is the probability of landing on a three and then landing on a number greater than three
Answer:
2/4
Step-by-step explanation:
which criterion is least likely to be used in choosing bins (classes) in a frequency distribution?
The criterion that is least likely to be used in choosing bins (classes) in a frequency distribution is personal preference or subjective judgment.
When constructing a frequency distribution, it is important to consider objective criteria based on the nature of the data and statistical principles. Common criteria used for choosing bins include the range of the data, the desired number of bins, the shape of the data distribution, and the purpose of the analysis. These criteria help ensure that the bins effectively capture the variation in the data and provide meaningful insights. Personal preference or subjective judgment, on the other hand, may introduce bias and lack objectivity in determining the bin boundaries. It is essential to rely on objective criteria and statistical guidelines to make informed decisions when choosing bins for a frequency distribution.
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Which graph represents the function f(x) = 4|x|?
Answer:
A
Step-by-step explanation:
got it correct in edu
Which graph represents an equation in the form =?
Please help me!!
That's a question about graphs.
In the Cartesian coordinate system, we have two axes: The x-axis (horizontal) and the y-axis (vertical).
When we want to represent a equation in the cartesian coodinate system, we associate a point in the x-axis and other in the y-axis. The Cartesian coordinate is represented by (x, y).
To represent some equation in a graph, we need at least two points to draw a line that cross these 2 points.
For example: To represent the equation [tex]y = x +1[/tex], let's replace the value of x:
When x = 0 → [tex]y = 0 + 1 = 1[/tex]. Therefore, the coordenate is (0, 1).When x = 1 → [tex]y = 1 + 1 = 2[/tex]. Therefore, the coordenate is (1, 2).Finally, if we draw a line tha cross these 2 points, we will have the graph that represents [tex]y = x +1[/tex].
Now you know about it, let's solve our problem?
In that question, we should to find the graph that represents the equation [tex]y = kx[/tex], but we don't know the value of k, so what should we do? It's easy:
k is a constant. That means that the value of k never changes. Now, let's analyze a specific case:
If x = 0, so y = 0 as well. But why? We know that any number multiplied by 0 is equal 0. Therefore:
When If x = 0 → [tex]y = 0 \times k = 0[/tex]. So, this graph cross the coordinate (0,0).With the informations that the problem give to us, these are the unique things that we can find, but that's enough.
When we look at the options, just the second graph have a line that cross the coordenate (0, 0). Therefore, the correct answer is the graph below:
I hope I've helped. :D
Enjoy your studies! \o/