Numer 72
69, 70, 71, and 72 Find the volume obtained by rotating the region bounded by the curves about the given axis. 69. Y sin r, y=0, x/2
Answers
To find the volume obtained by rotating the region bounded by the curves about the given axis, we need to determine the integration limits and set up an integral.
The region is bounded by the curves y = sin(x), y = 0, and x/2.
To find the limits of integration, we need to determine the x-values where the curves intersect. The curve y = sin(x) intersects the x-axis at x = 0, π, 2π, and so on. Since we are considering the interval from 0 to x/2, our limits of integration will be from 0 to π. The radius of rotation is given by r = y. In this case, r = sin(x). The volume V obtained by rotating the region can be calculated using the formula: V = π ∫[a, b] r^2 dx
Substituting the values, the integral becomes: V = π ∫[0, π] (sin(x))^2 dx
Simplifying further: V = π ∫[0, π] sin^2(x) dx
This integral can be evaluated to obtain the volume V. After integrating, the volume obtained by rotating the region bounded by the curves about the given axis will be determined.
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Related Questions
Craig just purchased a new car. He financed $45000 and must pay it back over 5 years with 11% interest.
How much will he have paid for his car, including interest, after 5 years?
Answers
Answer:
$49950
Step-by-step explanation:
you do 45000(.11) which equals 4950. and then you add 4,950 to 45000, and then you get your answer
Due May 4Attendance Question (5/4/21) A cab company charges a$5 boarding rate in addition to its meter which is $3 forevery mile. What equation represents the rate of thiscompany?
Answers
Explanation
Step 1
Let x represents the number of hours
Let y represents the rate of the company
and
cost per hour = $3
so, the total cost per time is
cost per time= 3* number of hours
cost per time==3x
now, the company charges a $5 boarding rate
so, the rate is
\(\begin{gathered} \text{rate= boarding rate}+\text{cosper times} \\ reaplce \\ y=\text{ \$5+\$3x} \\ \text{reorder} \\ y=\text{ \$3x}+\text{\$5} \end{gathered}\)I hope this helps you
The pearson correlation is calculated for a sample of n = 25 individuals. what value of df should be used to determine whether or not the correlation is significant?
Answers
The correlation is a significant non-zero value.
The number of samples is n.
n = 25
The correlation of the coefficient is r.
r = -0.40
When correlation is significant,
\(H _{0} : p = 0\)
When correlation is non-zero,
\(H _{ \alpha } : p ≠0\)
The test statistic is,
\(TS = \frac{r \times \sqrt{n - 2} }{ \sqrt{1 - r {}^{2} } } \)
\( = \frac{0.4 \times \sqrt{25 - 2} }{ \sqrt{1 - ( - 0.4) ^{2} } } \)
\( = \frac{ - 1.918 }{ \sqrt{0.84} } \)
= -2.093
The test statistic is -2.093.
The correlation is,
\(H _{ \alpha } : - 2.93 ≠0\)
The correlation is not equal to zero and is significant.
Therefore, the correlation is a significant non-zero value.
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the vector sum of two or more other vectors is called the
Answers
Answer: resultant
Step-by-step explanation:
Can somone answer my question please: 3cm squared onverted to 100mm squared = 300cm squared?
Answers
Answer:
hi you can solve this sum by 4×side formula
Step-by-step explanation:
plz solve and check you equation
10000mm < 90000cm
10000mm < 900000mm
Find the equation for the
following parabola.
Focus (3, 4)
Directrix y = 2
A. (x-3)2 = 2(y-2.5)
B. (x-3)2 = 4(y-3)
C. (x-3)2 = (y-4)
D. (y-3)2 = 4(x-3)
Answers
Option A is correct.The equation for the parabola is A.(x - 3)^2 = 2(y - 2.5)
The equation for a parabola with a focus (h, k) and a directrix y = a can be expressed as:
(x - h)^2 = 4a(y - k)
The focus is (3, 4) and the directrix is y = 2, we can substitute these values into the equation:
(x - 3)^2 = 4(2)(y - 4)
Simplifying:
(x - 3)^2 = 8(y - 4)
The correct equation for the parabola is:
(x - 3)^2 = 8(y - 4)
Therefore, the answer is option A. (x - 3)^2 = 2(y - 2.5)
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Which characteristic of data is a measure of the amount that the data values vary?.
Answers
Variation is characteristic of data is a measure of the amount that the data values vary.
What is variation?
Variation is a measure of how spread out the data is around the center of the data.
The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set. Variance is often depicted by this symbol: σ
The coefficient of variation is a more representative measure of dispersion than the previous ones, because it is an abstract number.
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represent the number of books a student buys at the next book fair. what is the expected value of
Answers
The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.
How to determine a discrete probability distribution's expected value?The sum of each result of a discrete probability distribution times its corresponding probability is the distribution's anticipated value.The distribution is stated as follows based on the histogram provided by the picture just at end of the answer:P(X = 1) = 0.285P(X = 2) = 0.333P(X = 3) = 0.168P(X = 4) = 0.136P(X = 5) = 0.063P(X = 6) = 0.015The random variable b's expected value is then calculated as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X) = 2.404 books.
Thus, the expected value of discrete probability distribution is 2.404 books.
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The graph for the question is attached.
Are the following functions analytic? Use (1) or (7). 2. f(z)=iz
z
ˉ
3. f(z)=e
−2x
(cos2y−isin2y) 4. f(z)=e
x
(cosy−isiny) 5. f(z)=Re(z
2
)−iIm(z
2
) 6. f(z)=1/(z−z
5
) 7. f(z)=i/z
8
8. f(z)=Arg2πz 9. f(z)=3π
2
/(z
3
+4π
2
z) 10. f(z)=ln∣z∣+iArgz 11. f(z)=cosxcoshy−isinxsinhy
Answers
The following functions are analytic:
1. f(z) = iz
2. f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y^)\)
4. f(z) = \(e^x(cosy - isiny)\)
5. f(z) = \(Re(z^2) - iIm(z^2)\)
8. f(z) = \(i/z^8\)
11. f(z) = cos(x)cos(hy) - isin(x)sin(hy)
Analytic functions are those that can be expressed as power series expansions, meaning they have derivatives of all orders in their domain. In the given list of functions, we need to determine if each function satisfies this criterion.
f(z) = iz: This function is linear and can be expressed as a power series, therefore it is analytic.f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y)\): This function can also be expressed as a power series expansion and has derivatives of all orders, making it an analytic function. f(z) = \(e^x(cosy - isiny)\): Similarly, this function can be written as a power series expansion and has derivatives of all orders, making it analytic. f(z) = \(Re(z^2) - iIm(z^2)\): Although this function involves the real and imaginary parts of \(z^2\), both of these components can be expressed as power series expansions, implying that f(z) itself can be written as a power series and is thus analytic.f(z) = \(i/z^8\): This function can be rewritten as i*\((1/z^8)\) , where \(1/z^8\) can be expressed as a power series expansion. Since the multiplication of a constant (i) and an analytic function (\(1/z^8\)) results in an analytic function, f(z) is analytic. f(z) = cos(x)cos(hy) - isin(x)sin(hy): This function consists of the multiplication and addition of trigonometric functions, which are themselves analytic. Therefore, f(z) is an analytic function.Learn more about Analytic functions
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the product of permutation matrices is again a permutation matrix. True/False
Answers
The statement which is given as , "The product of permutation matrices is again a permutation matrix." is True.
A permutation matrix is a square matrix whose entries are either 0 or 1 and has exactly one "1" in each row and each column. In other words, it is a matrix that represents a permutation of the rows (or columns) of the identity matrix.
When two permutation matrices are multiplied, the result is another square matrix with exactly one "1" in each row and each column. To see why this is true, consider two permutation matrices, A and B. Suppose that A is a m x m matrix and B is a m x m matrix. The product of these two matrices is another m x m matrix, C = AB.
Each entry in the matrix C is given by the dot product of the corresponding row in A and the corresponding column in B. If the row in A has a "1" in the i-th position and the column in B has a "1" in the j-th position, then the i,j-th entry in C will be "1".
Since both A and B are permutation matrices, each row in A and each column in B has exactly one "1". This means that each row in C will have exactly one "1", and each column in C will also have exactly one "1". Hence, C is also a permutation matrix.
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solve for x, Give your answer as a fraction or decimal rounded to the nearest hundredth.
Answers
Using the fact that the triangles are similar, we will see that:
x = 5.626
How to find the value of x?On the image we can see two triangles, such that one is inscribed on the other.
Just because of that, it is obvious that the two triangles are similar.
And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:
3/x = 8/15
The quotient is "left side over the bottom side"
We can solve that equation for x:
3/x = 8/15
3 = (8/15)*x
(15/8)*3 = x
45/8 = x
5.625 = x
That is the value of x.
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Estimate the value of the square root of 15.9÷3.8
Answers
Step-by-step explanation:
lets round up for even square roots.
16 and 4 have even square roots
the square root of 16 is 4 and the square root of 4 is 2
4÷2 is 2
i estimate that the square root of 15.9÷3.8 is about 2
question 3 on a railway line, peak ridership occurs between 7:00 am and 5:00 pm. the fairness of a passenger survey could be improved by over-sampling data from which group?
Answers
To improve the fairness of a passenger survey on a railway line, it would be ideal to over-sample data from groups that are less likely to be represented in the regular ridership during peak hours of 7:00 am to 5:00 pm. One such group could be passengers who use the railway line during off-peak hours, such as early mornings or late evenings.
Over-sampling these groups will provide a more comprehensive picture of the ridership patterns and preferences of all passengers, rather than just those who use the railway line during peak hours. This approach will lead to a more accurate assessment of the passenger experience and needs and, therefore, allow for better decision-making when it comes to improving services and amenities.
Other groups that could be over-sampled include passengers with disabilities, seniors, and students who may have different transportation needs and experiences compared to the general ridership. By considering the unique experiences and needs of all passengers, railway companies can work towards creating a more inclusive and accessible transportation system.
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A die is loaded so that the probability of any side showing is proportional to the number on that side. If the die is rolled and you win 1 dollar for every dot showing, what is the probability distribution for X, the number of dollars won
Answers
To find the probability distribution for X, the number of dollars won, we need to determine the probabilities of winning different amounts of money.
Let's consider the sides of the die. We have numbers 1, 2, 3, 4, 5, and 6. The probability of each side showing is proportional to the number on that side.
To calculate the proportionality constant, we need to find the sum of the numbers on the die: 1 + 2 + 3 + 4 + 5 + 6 = 21.
Now, let's calculate the probability of winning $1. Since the die is loaded, the probability of rolling a 1 is 1/21. Therefore, the probability of winning $1 is 1/21.
Similarly, the probability of winning $2 is 2/21 (rolling a 2), $3 is 3/21 (rolling a 3), $4 is 4/21 (rolling a 4), $5 is 5/21 (rolling a 5), and $6 is 6/21 (rolling a 6).
In conclusion, the probability distribution for X, the number of dollars won, is as follows:
- Probability of winning $1: 1/21
- Probability of winning $2: 2/21
- Probability of winning $3: 3/21
- Probability of winning $4: 4/21
- Probability of winning $5: 5/21
- Probability of winning $6: 6/21
This distribution represents the probabilities of winning different amounts of money when rolling the loaded die.
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Please help and no links!!!!
Answers
Answer: 18
Step-by-step explanation:
what do i do with the negative? i completely forgot \(\frac{-yx^{3}z^{5} }{y^{2}z^{3} }\)
Answers
Answer:
Negative means focused on what is bad or lacking. A negative ad tells you bad things about the competition. A negative person loves to complain. In math, a negative number is less than zero.
Step-by-step explanation:
stores l and m each sell a certain product at a different regular price. if both stores discount their regular price of the product, is the discount price at store m less than the discount price at store l ?
Answers
The discount price at each store will depend on the regular price and the amount of the discount offered, and it is not possible to determine which store will have the lower discount price without knowing these factors.
Elaborate more your answer indetail?It is not necessarily true that the discount price at store M will be less than the discount price at store L. The relative discount prices will depend on the amount of the discount applied by each store.
For example, let's say that the regular price of the product at store L is $100 and the regular price at store M is $120. If store L offers a 20% discount, the discount price would be $80.
If store M offers a 15% discount, the discount price would be $102. Therefore, in this case, the discount price at store L is less than the discount price at store M.
On the other hand, if store L offers only a 10% discount, the discount price would be $90. In this case, the discount price at store M would be less than the discount price at store L.
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In the simulation in the Let’s Review section, select tan on the right. Select radians on the left. Activate the Labels option. Drag the red dot along the graph of the function at the bottom. What is the range of tanθ?
(-∞, ∞)
y > 0
[0, ∞)
Answers
Answer:
2
Step-by-step explanation:
A -10 nC charge is located at (x, y) = (1.2 cm , 0 cm).
What is the x-component of the electric field at the position (x, y) = (−4.1cm, 0 cm)?Express your answer to two significant figures and include the appropriate units.
Answers
We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:
E = k * Q / r^2
where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.
In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).
To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.
So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:
E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)
where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.
Substituting the given values, we get:
E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2
E_x ≈ -30,566.04 N/C
Rounding this to two significant figures and including the appropriate units, we get:
The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).
The value of Joe’s savings account is $25. To save more money, Joe plans to mow lawns in his neighborhood and charge $20 per lawn. How many lawns will Joe need to mow to reach a total of $200 in his savings account?
Answers
The number of lawns will Joe need to mow to reach a total of $200 in his savings accoun is 9.
A savings account is a deposit account that generally earns higher interest than an interest-bearing checking account. Savings accounts limit the number of certain types of transfers or withdrawals you can make from the account each monthly statement cycle. This is the most basic type of account you can open at any bank.
Calculation:-
value of Joe’s savings account is $25
charge per lawn is $20
The need amount =$200
Therefore, lawns will Joe need to mow to reach a total of $200 in his savings accoun = 200/20 = 10.
But he already have $25 in his account.
hence, 9 for $180.
A Savings Account by definition allows you to deposit your money safely with the bank so you don't have to carry it around with you or hide it in that rusted old steel safe at home.
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can you help me solve this?Identify the property being used
Answers
Solution
- The question asks us for which property is used in the following equation
\(2(RB)\cos \theta=2R(B\cos \theta)\)- The question uses the Commutative Property of Multiplication.
- This property is stated below:
\(A(DC)=C(AD)\)Final Answer
The answer is Commutative Property of Multiplication
Find the Surface area of the trapezoid
please help
show work
Answers
Answer:
259.5
Step-by-step explanation:
8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5
with a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?
Answers
The aim when choosing the model parameters:
Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line
The correct option is (b)
This is incomplete question
Complete question is this:
With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?
Only use models that produce values of r = 1Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line Maximize the size of the residualsFind the best fit line that crosses the y- axis at x = 0Choose the correct option:
Now, According to the question:
Hence, The aim when choosing the model parameters:
Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line
The correct option is (b).
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What is teh answer to 3X + 1 ?
Answers
Step-by-step explanation:
3x + 1 cannot be simplified further unless the variable 'x' has a constant value.
Therfore, 3x + 1 itself is the answer.
A spherical water tank holds 10,500 ft³ of water. What is the diameter of the tank?
Answers
The diameter of the sphere tank is 27.2 ft.
Volume of a sphere:Every point on the surface of the sphere is equally spaced from its center, making it a three-dimensional round solid object.
The capacity of a sphere is defined as its volume or the area that the sphere occupies. Cubic units are used to measure a sphere's volume.
The formula for the Volume of a sphere is given by
Volume of a sphere = 4/3 πr³
Here we have
A spherical water tank holds 10,500 ft³ of water.
Here capacity of the sphere = Volume of the sphere
As we know the volume of the sphere = 4/3 πr³
=> 4/3 πr³ = 10500
=> πr³ = 10500(3/4)
=> (22/7)r³ = 7875
=> 22r³ = 7875(7)
=> r³ = 55125/22
=> r³ = 2505
=> r = 13.6 (Approx)
As we know diameter = 2 × Radius
=> Diameter of sphere = 2(13.6) = 27.2 ft
Therefore,
The diameter of the sphere tank is 27.2 ft.
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is 4/7 an irrational number
Answers
Answer:
All rational numbers are whole numbers so yes, 4/7 is an irrational number
Irrational numbers are those real numbers which are not rational numbers. 4/7 is a rational number.
What is a rational number?Rational numbers are numbers which can be written in the form of a/b where a and b are integers.
Example: 1/2, 3.5 (which is writable as 7/5), 2(which is writable as 4/2), etc.
What is an irrational number?Irrational numbers are those real numbers which are not rational numbers.
For example √2, π, √13, etc.
It is important thing to Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.
Since Rational numbers are numbers which can be written in the form of a/b where a and b are integers. And 4/7 is written in p/q form and both 4 and 7 are natural numbers.
Hence, it can be concluded that 4/7 is a rational number.
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3. Owen’s parents were planning a big birthday party for him. (a) His parents spent $1.75 on each of 6 goodie bags. How much did they spend on goodie bags? Show your work. (b) They spent $130 to rent a bounce house for 8 hours. How much is the hourly rate for the rental? Show your work. (c) If the parents spent a total of $182.53 on the party, how much more did they spend than what was spent in parts (a) and (b)? Show your work.
Answers
Answer:
Step-by-step explanation:
(a) 2.49 * 6 = 14.94 <== what they spent on goodie bags
(b) 150 for 8 hrs = 150/8 = 18.75 per hr
(c) 182.53 - (150 + 14.94) = 182.53 - 164.94 = 17.59...they spent 17.59
express the following as a ratio in its simple form 1000 to 10 to 100
Answers
research topic 'the differential effect of inductive
instructions and deductive instructions'
Answers
The differential effect of inductive instructions and deductive instructions refers to the impact that these two types of instructional approaches have on learning and problem-solving abilities.
How to explain the informationInductive instructions involve presenting specific examples or cases and then drawing general conclusions or principles from them. This approach encourages learners to identify patterns, make generalizations, and develop hypotheses based on the observed data. Inductive reasoning moves from specific instances to a broader understanding of concepts or principles.
On the other hand, deductive instructions involve presenting general principles or rules first and then applying them to specific examples or cases. This approach emphasizes logical reasoning, where learners are guided to apply established rules to solve problems or make conclusions based on given premises. Deductive reasoning moves from a general understanding of concepts or principles to specific instances.
The differential effect of these two instructional approaches can vary depending on various factors, such as the learner's prior knowledge, cognitive abilities, and the nature of the task or subject matter.
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If 32 % of a is 1.12 then what is the value of a?
Answers
Answer:
4.5 is the value of A
Step-by-step explanation:
do it doing part/whole and cross crossing :)
32/100 because it’s a percentage and 1.12/x. 1.12 times 100 to get 112, and then 32 times x = 32x. your equation right now is 32x = 112, bur we want to get rid of that x, so we are going to divide 112/32 to get the whole of 3.5 for the value of A.