Evaluate the iterated integral by changing to cylindrical coordinates. ∫ 0 2 ∫ √ 0 4 − y2 ∫ 16-x^2-y^2 0 1 dz dx dy
Answers
The iterated integral by changing to cylindrical coordinates of ∫ 0 2 ∫ √ 0 4 − y2 ∫ \(16-x^2-y^2\) 0 1 dz dx dy is \(-\frac{64}{3}\sqrt{2}\pi\).
To convert to cylindrical coordinates, we replace \($x$\) and \($y$\) with \($r\cos\theta$\) and \($r\sin\theta$\) respectively, and replace \($z$\) with \($z$\). We also replace \($dV$\) with \($r,dz,dr,d\theta$\).
So the limits of integration become:
\(0\leq & r\leq 2\0\leq & \theta\leq 2\pi\0\leq & z\leq 16-r^2\)
And the integral becomes:
\(\iiint_E 1, dV &= \int_0^{2\pi} \int_0^2 \int_0^{16-r^2} r,dz,dr,d\theta,\sqrt{4-r^2}\quad\text{(substituting } \sqrt{4-y^2}=r\quad\text{)}\)
\(&= \int_0^{2\pi} \int_0^2 r(16-r^2),dr,d\theta,\sqrt{4-r^2}\)
\(&= \int_0^{2\pi} \left[-\frac{1}{4}(16-r^2)^2\right]_0^2,d\theta,\int_0^2 r\sqrt{4-r^2},dr\)
\(&= \int_0^{2\pi} 24,d\theta,\int_0^2 \sqrt{4-r^2},d(-\frac{1}{3}(4-r^2)^{\frac{3}{2}})\)
\(&= \int_0^{2\pi} 24,d\theta,[0-\frac{8\sqrt{2}}{3}]\)
\(&= -64\sqrt{2}\pi/3\end{align*}\)
So the iterated integral evaluates to \(-\frac{64}{3}\sqrt{2}\pi\).
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Related Questions
2. Tino charges $2 for the first mile, plus 50 cents for
each additional mile. Is this a proportional
relationship?
Answers
The given situation for the price according to the distance is not proportional.
Describe the term proportional relationship?Relationships between 2 factors that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value.Let the total distance covered by Tino is 'x'.
Let the total price be 'y'.
Then,
y = fixed price + additional price
y = $2 + $0.5x
For x = 1; y = $2.5 ---> x/y = 1/2.5
for x = 1; y = $3 ---> x/y = 2/3
for x = 3; y = $3.5 -----> x/y = 3/3.5
In all situations, ratio x/y is not constant.
Thus, the given situation for the price according to the distance is not proportional.
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Write y=2/3x+7 in standard form
Answers
Step-by-step explanation:
y = 2/3x + 7
Multiply both sides by 3 to get rid of the fraction 2/3
3y = 2x +21
subtract 2x from both sides
3y - 2x = 21
Answer ofc is 3x - 2y = 21
Please rate if you get the answer right.
Could someone help me find the length of each segment and which statements are true?
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
calculate the lengths using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )
JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)
= \(\sqrt{(3+3)^2+(-8+7)^2}\)
= \(\sqrt{6^2+(-1)^2}\)
= \(\sqrt{36+1}\)
= \(\sqrt{37}\)
repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )
MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)
= \(\sqrt{(-1)^2+(-6)^2}\)
= \(\sqrt{1+36}\)
= \(\sqrt{37}\)
repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )
PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)
= \(\sqrt{(-2+8)^2+1^2}\)
= \(\sqrt{6^2+1}\)
= \(\sqrt{36+1}\)
= \(\sqrt{37}\)
(b)
JK ≅ MN ← true
JK ≅ PQ ← true
MN ≅ PQ ← true
Kirito's Clothing Store buys coats for $80 and sells them for $140.
What is the percent markup on the price of the coats?
Answers
Answer:
75%
Step-by-step explanation:
80 x 0.75 = 60
80 + 60 = 140
Sam pushes crates starting from rest across the floor of his classroom of 3 s with a net force as shown above.
For each crate, rank impulses delivered from greatest to least
For each create, rank changes in momentum from greatest to least
For each crate, rank final speeds grom greatest to least
For each crate, rank momenta in 3 s from greatest to least
Answers
To rank the given quantities from greatest to least, we need to understand the definitions of each term:
(a) Impulse delivered: Impulse is defined as the change in momentum of an object. It can be calculated by multiplying the force applied to the object by the time interval over which the force is applied.
(b) Change in momentum: Change in momentum is the difference between the final momentum and initial momentum of an object. It can be calculated by subtracting the initial momentum from the final momentum.
(c) Final speed: The final speed of an object is the magnitude of its velocity at the end of a given time period.
(d) Momentum in 3 s: Momentum is the product of an object's mass and velocity.
- Impulse delivered is directly related to the net force acting on the crate. If the net force is higher, the impulse delivered will also be higher.
- Change in momentum is equal to the impulse delivered to the object. So, the ranking of impulse and change in momentum will be the same.
- Final speed depends on the initial conditions of the crate and the net force acting on it. If the net force is significant and acts in the direction of motion, the final speed will be higher.
- Momentum in 3 seconds depends on the initial momentum, net force, and time. Without specific values, it is challenging to determine the exact ranking.
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The total number of fans is attendance at a Wednesday baseball game was 48,268. The game had 12,568 more fans than the Tuesday game the day before. How many fans attended each game?
Answers
35,700+48,268=83,969.
PLZZ HELP FOR BRAINLIEST
What is the y-intercept of the graph?
Answers
Answer:
-5
Step-by-step explanation:
Please help!
Question 2
Geometric sequences are a subset of:
Question 2 options:
Linear Functions
Exponential Functions
Linear and Exponential Functions
Answers
Answer:
B.
Step-by-step explanation:
Exponential Functions
Help ON. NUMBER 1 PLSSSSSS ASAP
Answers
Find the Mean, Median, and Mode
Answers
mean is the average and can be calculated by adding the scores and then dividing by the total number of scores.
for this take the total number of childrena and divide by the number of families which should give 3.5.
median is the middle number when the scores are put in order.
an easy way to find it from this data set is to just add the number of families from top down and bottom up and seeing where they meet which should be 3.
mode is the number that occurs the most in a data set.
for this data set it would be where the greatest number for number of families is which is 3 as there is 82 families.
-x/5-8=12
Show work
And check
Answers
Answer:
\(\huge\boxed{\sf x = -100}\)
Step-by-step explanation:
Given equation:\(\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}\)
What is the graph for f (x)=-2(x-3)2+4
Answers
Answer:
hnahnahnahnahhnahnahnahnah
A museum groundskeeper is creating a semicircular statuary garden with a diameter of 25 feet. There will be a fence around the garden.The fencing costs $8.00 per linear hundredth. Use 3.14 for pie
Answers
we have that
The fence around the garden is equal to
\(P=\frac{1}{2}\cdot\pi\cdot D+D\)where
pi=3.14
D=25 ft
substitute
\(\begin{gathered} P=\frac{1}{2}\cdot3.14\cdot25+25 \\ P=64.25\text{ ft} \end{gathered}\)To find out the cost, multiply 64.25 ft by $8.00 per linear foot
so
64.25*8=$514
the answer is $514Consider the equation:
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+4x+10, equals, x, squared, plus, 4, x, plus, 1
1) Rewrite the equation by completing the square.
Your equation should look like
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2) What are the solutions to the equation?
Choose 1 answer:
Choose 1 answer:
Answers
We can rewrite the equation as:
(x + 2)² = 3
The solutions to the equation is:
-2 ± √3
How to rewrite the equation by completing the square?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
We have:
0 = x² + 4x + 1
x² + 4x + 1 = 0
We can rewrite the equation by completing the square as follow:
x² + 4x + 1 = 0
x² + 4x = -1
Add the square of the half of the coefficient of x to both sides.
x² + 4x + (2)² = -1 + (2)²
x² + 4x + (2)² = -1 + 4
x² + 4x + (2)² = 3
(x + 2)² = 3 [Factorize]
Here, c = 2 and d = 3
Let's find the solutions to the equation:
(x + 2)² = 3
x + 2 = ±√3
x = -2 ±√3
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Complete Question
Check attached image
What is the sum of the absolute values of -14 and 10?
What is the absolute value of the sum of -14 and 10?
Answers
Answer:
|-14| + |10| = 24
|-14 + 10| = 4
Step-by-step explanation:
The sum of each absolute value makes the values positive before adding them together, producing 24.
For the second one, you have to find the sum then take the absolute value afterwards. The sum of -14 and 10 is -4 and the absolute value makes -4 positive, producing 4.
Positive and negative linear associations from scatter plots— question:
What is the best description of the relationship in the scatterplot below?
Answers
Answer:
C
Step-by-step explanation: dots goes down then up
HELPPPPPP
1 Gobble 1 chocolate comes in a package shaped
like a triangular prism, as shown. Each triangular face of the prism has a base of 2 inches and a height of 2.5 inches.
What is the volume of the package?
A 25 in.³
B 8 in.³
C 50 in.3
D 12.5 in.3
Answers
Answer:
A
Step-by-step explanation:
Volume = 1/2 x 2 x 2.5 x 10
V = 25
Please help me answer these questions and explain why... I will mark you brainliest and rate you five stars
Answers
How you calculate this is this:
So, any two given sides much be greater than the other side.
7. The answer is no. 1 plus 5 is 6 right? 6 is less than 11, so it can never be a triangle.
8. The answer is yes. 3 plus 6 is greater than 7. 3 plus 7 is greater than 6. 6 plus 7 is greater than 3.
9. The answer is yes. 9 plus 11 is greater than 12. 9 plus 12 is greater than 11. 11 plus 12 is greater than 9.
A sample of adults was asked to choose their favorite sport to watch from a list of four sports. Age Range 18-30 31-50 51 Total Sport Football 15 19 17 51 Baseball 7 12 18 37 Basketball 15 8 11 34 Soccer 12 9 6 27 Total 49 48 52 149 What proportion of those surveyed chose basketball as their favorite sport? StartFraction 34 Over 149 EndFraction StartFraction 15 Over 49 EndFraction StartFraction 18 Over 52 EndFraction StartFraction 37 Over 149 EndFraction
Answers
The proportion of those surveyed who chose basketball as their favorite sport is 34.149 (option a)
Let's denote the proportion of adults who chose basketball as their favorite sport as P(Basketball). To calculate P(Basketball), we need to divide the total number of adults who chose basketball by the total number of surveyed adults. Mathematically, it can be represented as:
P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)
To calculate the number of adults who chose basketball, we sum up the values from the age range categories:
Number of adults who chose basketball = Number of adults (18-30) who chose basketball + Number of adults (31-50) who chose basketball + Number of adults (51 and above) who chose basketball
Looking at the table, we find that the number of adults (18-30) who chose basketball is 15, the number of adults (31-50) who chose basketball is 8, and the number of adults (51 and above) who chose basketball is 11. Adding these values together, we get:
Number of adults who chose basketball = 15 + 8 + 11 = 34
Now, let's calculate the total number of surveyed adults. We can sum up the values from the age range categories:
Total number of surveyed adults = Total number of adults (18-30) + Total number of adults (31-50) + Total number of adults (51 and above)
From the table, we find that the total number of adults (18-30) is 49, the total number of adults (31-50) is 48, and the total number of adults (51 and above) is 52. Adding these values together, we get:
Total number of surveyed adults = 49 + 48 + 52 = 149
Now, we have the values we need to calculate the proportion:
P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)
= 34 / 149
Hence the correct option is (a).
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one bit can represent 0 or 1. how many different combinations of 0 and 1 can be represented with three bits?
Answers
In binary code, a bit can represent either 0 or 1, which means that each bit has two possible values. Therefore, for three bits, we can represent 2 x 2 x 2 = 8 different combinations of 0 and 1.
To visualize this, we can list out all the possible combinations:
000
001
010
011
100
101
110
111
Each combination represents a unique value in binary code, ranging from 0 to 7. This is important in computer science and information technology, where binary code is used extensively for data storage and transmission. By using multiple bits, we can represent larger numbers and more complex information.
In summary, three bits can represent 8 combinations of 0 and 1, essential building blocks for binary code and computer operations.
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plz help will give brainliest
CDE is reflected over the Y- Axis
Answers
Answer:
The answer to this question is A
The new coordinates will be C( 3 ,0), D( 7,1) , E(2,4) , Option A is the correct answer.
What is the meaning of Reflection ?When a object or a figure is reflected , it means an mirror image if the object is being created , the shape and size of the object remains same , Only the coordinates change on the basis of the axis used for Reflection.
The figure is given in the question.
The coordinates of the figure is
C( -3 ,0)
D( -7,1)
E(-2,4)
When reflection is done along any axis , the coordinates of the other axis change sign.
so in this case ( x,y ) -----> ( -x,y)
The new coordinates will be
C( 3 ,0)
D( 7,1)
E(2,4)
Therefore Option A is the correct answer.
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In testing whether each individual independent variables (Xs) in a multiple regression equation is statistically significant in explaining the dependent variable (Y), one uses F-test Durbin-Watson test t-test z-test
Answers
Option c T test
In testing whether each individual independent variables (Xs) in a multiple regression equation is statistically significant in explaining the dependent variable (Y), one uses T-test.
A T-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero.
Each independent variable is subjected to the T-test to determine whether the null hypothesis that the slope is 0 is true. This suggests that the independent and dependent variables do not significantly interact.
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In a survey, 100 people were asked how many car accidents they had in the past year. The estimated probability distribution for the number of accidents is shown in the table.
Using the data from the table, what is the probability of having exactly 1 accident in a year?
A 2-column table has 4 rows. The first column is labeled Accidents: X with entries 0, 1, 2, 3. The second column is labeled Probability: P x (x) with entries 0.905, 0.080, 0.010, and 0.005.
Answers
The probability of having exactly 1 accident in a year would be = 0.080.
What is probability?Probability is defined as the likelihood or the possibility of an event to occur or not to take place.
The number of people that were surveyed on how many car accidents they have had in the past year = 100
Using the 2-column table above, the probability that only 1 accident will happen in a year is calculated as follows:
The total probabilities of the various accidents (X) = 0.905+0.080+0.010+0.005 = 1
The probability that only 1 accident will occur in the year = 0.080/1 = 0.080.
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Evaluate the given expression when x=-4 and y=-1: 3x to the second power - xy + 2y to the second power
A. 54
B. 46
C. -32
D. -42
Answers
Answer:
The answer to the statement provided is 46.
kim makes $12 per hour . write an equation showing the relationship between her total pay (p) and the number of hours she works (h)
Answers
Answer:
C) P = 12H
Step-by-step explanation:
This is because she makes 12 dollars every hour so it'll be 12 times the number of hours.
step by step explanation:
it asks you to find the pay, and because we don’t know how many hours she worked we would use H. the total pay is P.
P is determined by 12 x the amount of hours she works
hope this helps
square root of 31-4√21
Answers
Hope that helps
Answer:
-12.762538417
Step-by-step explanation:
Consider this system of equations.
p=2n
p-5 = 1. 5n
What value of n makes the system of equations true?
Enter your answer in the box.
Answers
Therefore, the value of n that makes the system of equations true is n = 10.
Given:
p = 2n
p - 5 = 1.5n
Substituting the value of p from the first equation into the second equation, we have:
2n - 5 = 1.5n
Next, we can solve for n by subtracting 1.5n from both sides of the equation:
2n - 1.5n - 5 = 0.5n - 5
Simplifying further:
0.5n - 5 = 0
Adding 5 to both sides of the equation:
0.5n = 5
Dividing both sides by 0.5:
n = 10
Therefore, the value of n that makes the system of equations true is n = 10.
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7+3x5-4(divided by)2+3 USING PEMDAS SHOW YOUR WORK
WILL MAKR BRAINLIEST
Answers
Answer:
23
Step-by-step explanation:
(PEMDAS)
No parentheses
No exponents
Multiply 3*5= 15
Divide -4/2 = -2
Rewrite equation
7+15-2+3➡22-2+3➡20+3
23
Answer: 23
Step-by-step explanation: Multiply 3*5= 15
Divide -4/2 = -2
After, rewrite the equation
7+15-2+3 22-2+3 20+3
Answer : 23
a line has a slope of 5 and passes through the points (3,y) and (1,-6) solve for y
Answers
Answer:
y = 4
Step-by-step explanation:
Using the slope, m = 5, and the given point, (1, -6), plug in these values into the point-slope formula:
y - y1 = m(x - x1)
y - (-6) = 5(x - 1)
y + 6 = 5x - 5
Subtract 6 on both sides of the equation to isolate y:
y + 6 - 6 = 5x - 5 - 6
y= 5x - 11
Therefore, the linear equation in slope-intercept form is y = 5x - 11.
To find the value of the y-coordinate in point (3, y ):
Plug in the value of x = 3 into the equation, y = 5x - 11
y= 5x - 11
y= 5(3) - 11
y = 15 - 11
y = 4
Therefore, the value of the y-coordinate in point (3, y) is 4.
(3x+1)(3x^2-6x-8) in standard form
Answers
Answer:
3s3x2+6x+4.3x2+6x+4