By changing to polar coordinates, evaluate the double integral {eq}\iint_{D} (x^2 + y^2)^\frac{3}{2} \, \mathrm{d}x \ \mathrm{d}y {/eq}, where {eq}D {/eq} is the disk {eq}x^2 + y^2\leq 36 {/eq}.
Answers
The expression inside the integral, we get {eq}r^3 \sqrt{r^2} = r^{\frac{7}{2}} {/eq}. Evaluating the integral, we get:{eq}\int_{0}^{2\pi} \int_{0}^{6} r^3 \sqrt{r^2} \, \mathrm{d}r \, \mathrm{d}\theta = \int_{0}^{2\pi} \left[\frac{2}{9}r^{\frac{9}{2}}\right]_{0}^{6} \, \mathrm{d}\theta = \frac{2}{9}(6^{\frac{9}{2}}-0) \int_{0}^{2\pi} \mathrm{d}\theta = \boxed{432\pi} {/eq}
To change to polar coordinates, we need to express {eq}x {/eq} and {eq}y {/eq} in terms of {eq}r {/eq} and {eq}\theta {/eq}. Using the conversion formulas, we have {eq}x = r\cos{\theta} {/eq} and {eq}y = r\sin{\theta} {/eq}. The limits of integration also change to reflect the new coordinate system. In polar coordinates, the disk {eq}x^2 + y^2\leq 36 {/eq} becomes {eq}0\leq r\leq 6 {/eq} and {eq}0\leq \theta\leq 2\pi {/eq}. Substituting these values, we get:
{eq}\iint_{D} (x^2 + y^2)^\frac{3}{2} \, \mathrm{d}x \ \mathrm{d}y = \int_{0}^{2\pi} \int_{0}^{6} r^3 \sqrt{r^2} \, \mathrm{d}r \, \mathrm{d}\theta {/eq}
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Related Questions
For the transformation T, write the T-1. T: (x, y) ( 2x, y + 5) T -1 (x, y) (x - 2, y - 5) (2x - 1, y + 4) (½x, y - 5)
Answers
=====================================
Explanation:
The original transformation (2x, y+5) takes any x value and doubles it. So the inverse of this is to cut the x value in half. We can say x/2 since division is the opposite of multiplication. The value x/2 is the same as ½x
For the y coordinate, we add on 5 for the original transformation. Subtraction undoes addition meaning the inverse will have y-5.
Side note: the inverse notation \(T^{-1}\) can be written as T^(-1).
Simplify (x + y)² - (x - y)² + 2xy - 3x²
Answers
Answer:
\(\huge\boxed{\sf 6xy-3x^2}\)
Step-by-step explanation:
Given Expression:
(x + y)² - (x - y)² + 2xy - 3x²
Formulas used:
\((x+y)^2=x^2+2xy+y^2\)\((x-y)^2=x^2-2xy+y^2\)Expand the above expression according to the formulas
\(=x^2+2xy+y^2-(x^2-2xy+y^2)+2xy-3x^2\\\\= x^2+2xy+y^2-x^2+2xy-y^2+2xy-3x^2\\\\cancel \ out \ x^2 \ and \ y^2\\\\= 2xy+2xy+2xy-3x^2\\\\= 6xy-3x^2\\\\\rule[225]{225}{2}\)
Which of the following expressions represents "the difference of 7 and c"?
Answers
Answer:
Step-by-step explanation:
7-c because the difference of 7 and c
7 and c
7-c
EZ
Answer:
7 - c or c - 7
Step-by-step explanation:
The difference of two numbers is a non-negative number.
The difference of 7 and c is |7 - c|.
Since that is not a choice, you can choose 7 - c or c - 7.
help me asap! A parka that sold for $50 is marked up to $60. What is the percent of markup?
Answers
Answer:
the markup is 20 percent
Which number is greatest?6. 23 times 10 superscript 126. 23 times 10 superscript 86. 23 times 10 superscript negative 66. 23 times 10 superscript 3.
Answers
From the given numbers, the greatest number is 23 × 10^126
The first number = 23 × 10^126
The second number = 23 × 10^86
The third number = 23 × 10^66
The fourth number = 23 × 10^3
The scientific notation is defined as the easiest method to represents the very smallest or the largest number. The scientific notation consist of a whole number multiplied by the power of ten
Here, the whole number is same in all cases, only the power of the 10 is different . To find the largest number we have to find the number with largest power of 10
The number with largest power of 10 = 23 × 10^126
Hence, the greatest number is 23 × 10^126
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Add 3x4 - 7x3 + 12x - 9
GUEST, GUEST
to
The sum is closed because
Roxanne wants to test the idea
that polynomials are closed
under addition. Her work and
explanation are shown.
are
and by definition
the sum is a polynomial.
Drag an expression and phrases
to the boxes to complete the
statement.
5x2 - (2x)3 + (4x)-1
(2x)3 + 2.1x2 - 11
-8x-2 f(3x)3 - 12x6 + 7
the exponents
the variables
the coefficients
integers
whole numbers
real numbers
Answers
The complete statements are:
Add \(\mathbf{3x^4 -7x^3 + 12x - 9}\) to \(\mathbf{(2x)^3 +2.1x^2-11}\).The sum is closed because the exponents are whole numbers, And by definition, the sum is a polynomialThe polynomial is given as:
\(\mathbf{3x^4 -7x^3 + 12x - 9}\)
Polynomials are closed under addition.
This means that, when the polynomial is added to another, the exponents do not change.
The above highlight mean that:
\(\mathbf{3x^4 -7x^3 + 12x - 9}\) cannot be added to \(\mathbf{5x^2 -(2x)^3 + (4x)^{-1}}\) and \(\mathbf{-8x^{-2} +(3x)^3 -12x^6+ 7}\), because they are not polynomials, and they have negative exponents
However, \(\mathbf{3x^4 -7x^3 + 12x - 9}\) can be added to \(\mathbf{(2x)^3 +2.1x^2-11}\)
The sum will give:
\(\mathbf{3x^4 -7x^3 + 12x - 9 + (2x)^3 +2.1x^2-11 = 3x^4 + x^3+2.1x^2 + 12x - 20}\)
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Alberto is painting a square canvas. What is the length of each side of the canvas?
A = 121 in^2
Answers
Answer:
Step-by-step explanation:
Area = 121 in²
Length = √121 in = 11i in
a can contains 24 fluid onces of fruit juice . how many pints of fruit juice does the can contain
A. 3 pt
B. 1 1/2 pt
C. 12 pt
D. 1/3 pt
Answers
Answer:
B 1 1/2 pts
4 fluid ounces = 0.25 pints
24 fluid ounces = 6 pt
What is the coefficient in the expression x² - 6?
Answers
Your answer would be 1/x^2 -6
Sketch the graph of a relation that’s is a function
Answers
Answer:
See attached
Step-by-step explanation:
Refer to attachment
One relation is a linear function
Second one is a graph of non-functional relation
Answer:
below
Step-by-step explanation:
For the first graph, we can use a linear function as it means "straight" lines so when we use the vertical lines test, it passes it (shown below).
We can use a U shaped line so it when we use the vertical line test, it passes through two points to resemble its not a function (shown below).
Best of Luck!
x−5y=4
−2x+10y=k (a) For what value(s) of k does the system have a unique solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The given system has a unique solution for k= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The given system has a unique solution for all real values k. C. There is no value of k that will give the system a unique solution. (b) For what value(s) of k does the system have no solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The given system has no solution for all real numbers k except for k= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The given system has no solution for all real numbers k. C. The given system has a solution for all real values k. (c) For what value(s) of k does the system have infinitely many solutions? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The given system has infinitely many solutions for k= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The given system has infinitely many solutions for all real numbers k except for k= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. The given system has infinitely many solutions for all real numbers k.
Answers
The system of equations given by x - 5y = 4 and -2x + 10y = k has no unique solution for any value of k. It has a solution for all real values of k and infinitely many solutions for all real numbers k.
To determine the values of k for which the system of equations has a unique solution, no solution, or infinitely many solutions, let's analyze the given equations:
x - 5y = 4
-2x + 10y = k
We can observe that equation 2 is a scalar multiple of equation 1. Multiplying equation 1 by -2, we obtain:
-2(x - 5y) = -2(4)
2x - 10y = -8
Comparing this with equation 2, we see that both equations represent the same line. This implies that the system of equations has infinitely many solutions for any value of k, as both equations are equivalent and represent the same line.
Therefore, for part (a), there is no value of k that gives the system a unique solution. The correct choice is C: There is no value of k that will give the system a unique solution.
For part (b), since the system has infinitely many solutions for all values of k, the correct choice is C: The given system has a solution for all real values k.
For part (c), we have already determined that the system has infinitely many solutions for all values of k. Therefore, the correct choice is C: The given system has infinitely many solutions for all real numbers k.
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Market researchers sent out a survey to college students in Ohio to assess their preferences in regard to three different brands of honey. When examining the average preference of the respondents, which measure of central tendency is most likely to be used to describe them
Answers
The measure of central tendency most likely to be used to describe the average preference of the respondents in the survey of college students in Ohio regarding three different brands of honey is mean.
The mean is a commonly used measure of central tendency that calculates the average value by summing up all the preference scores and dividing it by the total number of respondents. It provides an overall view of the central tendency of the data and is sensitive to extreme values or outliers.
In this survey, the market researchers would collect preference ratings from each college student for the three brands of honey. By calculating the mean preference score for each brand, they can determine the average preference for each brand among the respondents. This information can be valuable for understanding which brand of honey is most preferred overall among college students in Ohio.
Other measures of central tendency, such as the median or mode, may also be considered depending on the nature of the data and the specific research objectives. However, when examining the average preference of the respondents, the mean is commonly used as it takes into account the magnitude of the preference scores and provides a comprehensive representation of the central tendency.
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Hi Help please asap!!!!!!!
Answers
Answer:
5.213
Step-by-step explanation:
bruh just search up right triangle calculator
PLEASE HELP ME PUT THESE WHERE THEY GO ILL GIVE BRAINLIESST
Answers
Answer:
volume of rectangular prism: 8 x 4 x 11= 352
volume of triangular prism: 4 x 8 x 7= 224/2= 112
Volume of composite figure: 352 + 112= 464
Answer:
see explanation
Step-by-step explanation:
volume of rectangular prism = lbh ( l is length, b is breadth, h is height )
Here l = 11, b = 8 , h = 4
V = 11 × 8 × 4 = 352 ft³
volume of triangular prism = Al ( A is area of triangular end and l is its length )
A = \(\frac{1}{2} \) bh ( b is base and h is height )
Here b = 8, h = 4 and l = 7
A = \(\frac{1}{2} \) × 8 × 4 = 4 × 4 = 16 ft² , then
V = 16 × 7 = 112 ft³
volume of composite figure = 352 + 112 = 464 ft³
In one area along the interstate, the number of dropped wireless phone connections per call follows a Poisson distribution. From four calls, the number of dropped connections is 2 0 3 1 (a) Find the maximum likelihood estimate of 2. (b) Obtain the maximum likelihood estimate that the next two calls will be completed without any ac- cidental drops.
Answers
The solution involves calculating the likelihood function, maximizing it, and using the estimated value to find the probability of no dropped connections in the next two calls.
(a) To find the maximum likelihood estimate of λ, the mean number of dropped connections per call, we need to use the Poisson distribution to calculate the likelihood function L(λ) for the given data. The Poisson distribution is given by:
P(X = x | λ) = (λ^x * e^(-λ)) / x!
where X is the random variable representing the number of dropped connections per call, λ is the parameter representing the mean number of dropped connections per call, and x is the observed number of dropped connections in a call.
The likelihood function for four calls with observed numbers of dropped connections 2, 0, 3, and 1 can be expressed as:
L(λ) = P(X = 2 | λ) * P(X = 0 | λ) * P(X = 3 | λ) * P(X = 1 | λ)
= (λ^2 * e^(-λ)) / 2! * (e^(-λ)) / 0! * (λ^3 * e^(-λ)) / 3! * (λ^1 * e^(-λ)) / 1!
= (λ^6 * e^(-4λ)) / 6
Taking the derivative of L(λ) with respect to λ, setting it equal to zero, and solving for λ.
d/dλ [L(λ)] = d/dλ [(λ^6 * e^(-4λ)) / 6]
= [(6λ^5 * e^(-4λ) - 4λ^6 * e^(-4λ)) / 6]
Setting this derivative equal to zero, we get:
2λ - 3λ^2 = 0
λ = 0 or λ = 2/3
Since λ = 0 is not a valid solution for a Poisson distribution, the maximum likelihood estimate of λ is λ = 2/3.
Therefore, the maximum likelihood estimate of the mean number of dropped connections per call is 2/3.
(b) To obtain the maximum likelihood estimate that the next two calls will be completed without any accidental drops, we can use the estimated value of λ = 2/3 to calculate the probability of no dropped connections in each of the next two calls, using the Poisson distribution:
P(X = 0 | λ = 2/3) = (2/3)^0 * e^(-2/3) / 0! = e^(-2/3) ≈ 0.5134
P(both calls have no drops | λ = 2/3) = P(X = 0 | λ = 2/3)^2 ≈ 0.2637
Therefore, the maximum likelihood estimate that the next two calls will be completed without any accidental drops is approximately 0.2637.
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how many degrees is the measurement of angle 1? show you work GVING BRAINLY
Answers
Answer:
m<1 = 79°
Step-by-step explanation:
12x + 19 + 22x - 9 = 180
add the numbers
34x + 10 =180
minus 10
34x = 170
divide by 34
x = 5
plug 5 into the equation of angle 1
12(5) + 19 =
79
Line m is represented by the equation y + 2 = 3/2(x + 4). Select all equations that
represent lines perpendicular to line m.
A. y = -3/2x +4
B. y = -2/3x +4
C. y = 2/3x +4
D. y = 3/2x +4
E.y+1=-4/6(x+5)
F.y+ 1 = 3/2(x + 5)
Answers
The equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
What is the Slope of Perpendicular Lines?Lines that are perpendicular to each other have slopes that are negative reciprocal of each other.
For example, if a line has a slope of 2, the slope of a line that is perpendicular to it would be, -1/2 (negative reciprocal of 2).
Determine the slope of the given line whose equation is, y + 2 = 3/2(x + 4). Rewrite the equation in slope-intercept form [y = mx + b]:
y + 2 = 3/2x + 6
y = 3/2x + 6 - 2
y = 3/2x + 4
The slope is therefore 3/2.
Negative reciprocal of 3/2 is -2/3.
Examine each of the equations given and see which equation has a slope of -2/3.
A. y = -3/2x +4, the slope is -3/2.
B. y = -2/3x + 4, the slope is -2/3. (perpendicular)
C. y = 2/3x +4, the slope is 2/3.
D. y = 3/2x +4, the slope is 3/2.
E. y+1=-4/6(x+5), rewrite in slope-intercept form
y+1=-4/6x + 20/6
y + 1 = -2/3x + 10/3
The slope is -2/3. (perpendicular)
F. y+ 1 = 3/2(x + 5), the slope is 3/2.
Therefore, the equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
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hello please help i’ll give brainliest
Answers
Answer:
C.
Step-by-step explanation:
PLEASE BRAINLIESTWhich equation represents the line that contains the point ( 7 , − 1 ) ( 7 , − 1 ) and is parallel to the line represented by 3 x + y = 4
Answers
Answer:
Step-by-step explanation:
3x+y = 5
slope of line is -3
slope of any parallel to the line is also -3
point-slope equation for line of slope -3 that passes through (7,-1):
y+1 = -3(x-7)
You haven't provided the choices, but one of them is equivalent to the point-slope equation.
3 ( X + 6 ) = 24
What is X
Answers
I mode
Simplify the expression.
2(8 + 24) = 23 x 4
X
X
ngles.
How do you simplify this?
Answers
Answer:
okay so IM not 100 percent sure but I think its 64 = 92
Determine whether or not the function is one-to-one, and if it is, determine its inverse function
Answers
Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.
What is a horizontal line test?It is simple to establish whether the inverse of a function is also a function using the horizontal line test.
Because it fails the vertical line test, a function's inverse might not actually be a function.
Graph of the line
f\left( x \right) = - x + 2
f(x)=−x+2.
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Find the surface area of the following cylinder. Round your answers to the nearest tenth.
Answers
Answer: 628
Step-by-step explanation:
2πr^2+2πrh
2(3.14)(5)^2+2(3.14)(5)(15)
2(3.14)(25)+2(3.14)(75)
2(78.5)+2(235.5)
157+471
628
the rate of college enrollment immediately after high school completion was 67
Answers
The statement " Rate of college enrollment immediately after completing high school was 67% by 1997" is an example of (a) Descriptive Statistics.
The Descriptive statistics involves the use of measures, such as averages, proportions, and frequencies, to summarize and describe the main features of a set of data.
In this statement, the rate of 67% is a summary statistic that describes the proportion of high school graduates who enrolled in college immediately after completing high school in 1997.
Whereas; the inferential statistics involves making inferences or predictions about a population based on a sample of data.
The statement provides a summary statistic for the rate of college enrollment for a specific year, 1997, but it does not provide any inferences or predictions about the rate of college enrollment for other years or other populations , so it denoted a Descriptive Statistics .
The given question is incomplete , the complete question is
What type of Statistics does the statement "the rate of college enrollment immediately after high school completion was 67" represents ?
(a) Descriptive
(b) Inferential
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factorise 12x²+15xy.
Answers
Answer:
3x(4x+5y)
Step-by-step explanation:
to factorise this equation you have to remove the common terms,or the common factors in this case the common factor for both sides is 3 and the common letter is x
12x²+15xy
3x(4x+5y)
I hope this helps
A manufacture has been selling 1750 television sets a week at $450 each. A market survey indicates that for each $26 rebate offered to a buyer, the number of sets sold will increase by 260 per week. a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price. p(x) 1 = b) How large rebate should the company offer to a buyer, in order to maximize its revenue? dollars c) If the weekly cost function is 131250 + 150x, how should it set the size of the rebate to maximize its profit? dollars
Answers
The function representing the demand p(x) is p(x) = 450 - x/10
The rebate that maximizes the revenue is 2250
The rebate that maximizes the profit is 1500
Finding the function representing the demand p(x)From the question, we have the following parameters that can be used in our computation:
Initial price = 450
Rate = 260 for each $26
So, we have
p(x) = 450 - 26x/260
Evaluate
p(x) = 450 - x/10
(b) The rebate that maximizes the revenueThe revenue function is calculated as
R(x) = x * p(x)
So, we have
R(x) = x(450 - x/10)
Evaluate
R(x) = 450x - x²/10
Differentiate and set to 0
450 - 2x/10 = 0
So, we have
2x/10 = 450
Evaluate
x = 2250
So, the size of the rebate is 2250
(b) The rebate that maximizes the profitThe profit is calculated as
Profit = Revenue - Cost
So, we have
Profit = 450x - x²/10 - (131250 + 150x)
Differentiate
Profit = 450 - 2x/10 - 150
Set to 0
450 - 2x/10 - 150 = 0
So, we have
300 - 2x/10 = 0
This gives
2x/10 = 300
Solving for x, we have
x = 300 * 10/2
x = 1500
So, the size of the rebate is 1500
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|x-(-12)| if x<-12
help
Answers
The requried absolute value function |x-(-12)| = |x+12| when x is less than -12.
If x is less than -12, then x-(-12) will result in a negative number. However, the absolute value of any number is always positive, so we can simplify |x-(-12)| by making the expression inside the absolute value bars positive.
Since x is less than -12, x-(-12) can be simplified as follows:
x - (-12) = x + 12
So, |x-(-12)| = |x+12| when x is less than -12.
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Linda works at the U-Pick Berry Farm selling strawberries and raspberries. Her first customer of the day bought 3 quarts of strawberries and 2 quarts of raspberries for $22.00. The second customer bought 5 quarts of strawberries and 4 quarts of raspberries for $39.00. Which system of equations can be used to find the costs of a quart of strawberries and a quart of raspberries? 3 x + 2 y = 39. 5 x + 4 y = 22. 2 x + 3 y = 39. 5 x + 4 y = 22. 3 x + 2 y = 22. 5 x + 4 y = 39. 2 x + 3 y = 22. 5 x + 4 y = 39.
Answers
Answer:
Sorry about the person above. The answer would be:
C. \(3x + 2y = 22\) and \(5x + 2y = 39\)
Explanation:
I just did the test.
Answer:
C
Step-by-step explanation:
A correlation coefficient of \( -0.84 \) between the variables "impulsivity" and "hours spent viewing TV" indicates A weak relationship \& the more impulsive, the less TV viewing A strong refationship
Answers
The correlation coefficient of -0.84 between the variables "impulsivity" and "hours spent viewing TV" indicates a strong relationship, suggesting that the more impulsive an individual is, the less time they spend viewing TV.
What does a correlation coefficient of -0.84 indicate about the relationship between impulsivity and hours spent viewing TV?The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, a correlation coefficient of -0.84 indicates a strong negative relationship between impulsivity and hours spent viewing TV.
The negative sign indicates an inverse relationship, meaning that as one variable (impulsivity) increases, the other variable (hours spent viewing TV) decreases.
The magnitude of -0.84 indicates a relatively strong relationship. Since the correlation coefficient is close to -1, it suggests that there is a strong tendency for individuals with higher levels of impulsivity to spend less time viewing TV.
Conversely, those with lower levels of impulsivity tend to spend more time watching TV.
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please help i will give you brain list pleaseeeee!
Answers
Answer:
-30x^17
Step-by-step explanation:
if multiply
Answer:
-60x^16
Step-by-step explanation:
You're welcome lol