Find the indefinite integral. (Use C for the constant of integration
∫ (x-2)/(x+1)^2+4 dx
_________
Answers
The indefinite integral of (x-2)/(x+1)^2+4 with respect to x is given by:
∫ (x-2)/(x+1)^2+4 dx = ln|x+1| + 2arctan((x+1)/2) + C
where C is the constant of integration.
In the integral, we can use a substitution to simplify the expression. Let u = x+1. Then, du = dx and x = u - 1. Substituting these values into the integral, we have:
∫ (x-2)/(x+1)^2+4 dx = ∫ (u-1-2)/u^2+4 du
Expanding and rearranging the numerator, we get:
∫ (u-1-2)/u^2+4 du = ∫ (u-3)/(u^2+4) du
Using partial fractions or recognizing the derivative of arctan function, we can integrate this expression to obtain:
∫ (u-3)/(u^2+4) du = ln|u^2+4|/2 + 2arctan(u/2) + C
Substituting back u = x+1, we obtain the final result:
∫ (x-2)/(x+1)^2+4 dx = ln|x+1| + 2arctan((x+1)/2) + C
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Related Questions
One month before an election, a poll of 630 randomly selected voters showed 55% planning to vote for a certain candidate. A week later it became known that he had had an extramarital affair, and a new poll showed only 53% of 1010 voters supporting him. Do these results indicate a decrease in voter support for his candidacy?
Determine the test statistic. z= (Round to two decimal places as needed.)
Find the P-value.
estimate that difference, p1−p2, with a 95% confidence interval
Answers
The statistics are as follows:
- Test Statistic: The calculated test statistic is approximately 1.02.
- P-value: The P-value associated with the test statistic of 1.02 is approximately 0.154.
- Confidence Interval: The 95% confidence interval for the difference in proportions is approximately -0.0186 to 0.0786.
To solve the problem completely, let's go through each step in detail:
1. Test Statistic:
The test statistic can be calculated using the formula:
z = (p1 - p2) / √[(p_cap1 * (1 - p-cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]
We have:
p1 = 0.55 (proportion in the first poll)
p2 = 0.53 (proportion in the second poll)
n1 = 630 (sample size of the first poll)
n2 = 1010 (sample size of the second poll)
Substituting these values into the formula, we get:
z = (0.55 - 0.53) / √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]
z = 0.02 / √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]
z ≈ 0.02 / √(0.0001386 + 0.0002493)
z ≈ 0.02 / √0.0003879
z ≈ 0.02 / 0.0197
z ≈ 1.02 (rounded to two decimal places)
Therefore, the test statistic is approximately 1.02.
2. P-value:
To find the P-value, we need to determine the probability of observing a test statistic as extreme as 1.02 or more extreme under the null hypothesis. We can consult a standard normal distribution table or use statistical software.
The P-value associated with a test statistic of 1.02 is approximately 0.154, which means there is a 15.4% chance of observing a difference in proportions as extreme as 1.02 or greater under the null hypothesis.
3. Confidence Interval:
To estimate the difference in proportions with a 95% confidence interval, we can use the formula:
(p1 - p2) ± z * √[(p_cap1 * (1 - p_cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]
We have:
p1 = 0.55 (proportion in the first poll)
p2 = 0.53 (proportion in the second poll)
n1 = 630 (sample size of the first poll)
n2 = 1010 (sample size of the second poll)
z = 1.96 (for a 95% confidence interval)
Substituting these values into the formula, we get:
(0.55 - 0.53) ± 1.96 * √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]
0.02 ± 1.96 * √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]
0.02 ± 1.96 * √(0.0001386 + 0.0002493)
0.02 ± 1.96 * √0.0003879
0.02 ± 1.96 * 0.0197
0.02 ± 0.0386
The 95% confidence interval for the difference in proportions is approximately (0.02 - 0.0386) to (0.02 + 0.0386), which simplifies to (-0.0186 to 0.0786).
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What is the relationship between the volume of a rectangular prism and the volume of a pyramid with the same height and base?
Answers
The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.
How to find the volume of a rectangular prism and pyramid?
The formula for the volume of a rectangular prism is:
Volume = Length * Width * Height
The formula for the volume of a pyramid is:
Volume = (Base Area * Height) / 3
The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.
This is because the volume of a rectangular prism is calculated by multiplying its three dimensions together, whereas the volume of a pyramid is calculated by multiplying the base area by the height and dividing the result by 3.
Hence, the volume of the rectangular prism is greater than the volume of the pyramid with the same height and base. This is because the rectangular prism has additional volume in the form of its width, which the pyramid does not have.
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Find the area between the curves. x=−5,x=2,y=3x,y=x^2−4 The area between the curves is (Simplify your answer.)
Answers
The area between the curves x = -5, x = 2, y = 3x, and y = x^2 - 4 can be determined by finding the integral of the difference between the upper and lower curves. The simplified answer for the area is 63 square units.
To calculate the area, we need to find the points of intersection between the curves. Setting the equations for y equal to each other, we have:
\(3x = x^2 - 4\)
Rearranging this equation, we get:
\(x^2 - 3x - 4 = 0\)
Factoring this quadratic equation, we find:
\((x - 4)(x + 1) = 0\)
So the points of intersection are x = 4 and x = -1.
Next, we integrate the difference between the upper curve (y = 3x) and the lower curve \((y = x^2 - 4)\)with respect to x over the interval [-1, 4]:
∫[from -1 to 4]\((3x - (x^2 - 4))\) dx
This integral evaluates to:
\([3/2x^2 - (1/3)x^3 + 4x]\)from -1 to 4
Evaluating this expression at the limits, we get:
\([(3/2)(4)^2 - (1/3)(4)^3 + 4(4)] - [(3/2)(-1)^2 - (1/3)(-1)^3 + 4(-1)]\)
Simplifying this further, the area between the curves is 63 square units.
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Tanya and Reece each walked 4 miles on Monday. Reese also walked 4 miles on Tuesday and 4 miles on Wednesday . How many miles did Reece walk
Answers
Answer:
12 miles
Step-by-step explanation:
monday=4 miles
tuesday=4 miles
wednesday= 4 miles
4+4+4=12
Gavin is doing a survey to predict the results of an upcoming school election. He waits outside the lunchroom during each lunch period and surveys every tenth student leaving the lunchroom. This table shows the results of his survey.
Position - Votes
President
Henry 36
Christy 42
Celina 22
Vice President
Tristan 14
Kenny 46
Madison 40
Treasurer
Priscilla 53
Reuben 24
Erica 23
-Secretary-
Xavier 33
Ben 30
Charlie 37
Based on his survey, Gavin will predict who the 1,500 students in his school will vote for in the races for president, vice president, treasurer, and secretary. Complete the steps below to predict the outcome of the election.
Part A
Predict how many votes from the student population each candidate for president will get in the election. (Hint: Set up and solve a proportion between the sample and the population.)
Part B
Based on the survey results, who will most likely get the highest percentage of votes for the president’s position? What is that percentage?
Part C
Predict how many votes from the student population each candidate for vice president will get in the election.
Part D
Based on the survey results, who will most likely get the highest percentage of votes for the vice president’s position? What is that percentage?
Part E
Predict how many votes each candidate for treasurer will get in the election from the student population.
Part F
Based on the survey results, who will most likely get the highest percentage of votes for the treasurer’s position? What is that percentage?
Part G
Predict how many votes each candidate for secretary will get in the election from the student population.
Part H
Based on the survey results, who is most likely to get the highest percentage of votes for the secretary’s position? What is that percentage?
100 POINTS! PLEASE ANSWER ALL OF THEM OF I'LL REPORT YOUR ANSWER!!
Answers
Henry is predicted to receive 360 votes, Christy is predicted to receive 420 votes, and Celina is predicted to receive 220 votes for the president’s position.
What is probability?
Probability is a measure of the likelihood of an event occurring.
Part A:
To predict how many votes each candidate for president will get in the election, we can set up a proportion between the sample and the population
Let x be the number of votes each candidate will receive in the election.
For Henry:
36/150 = x/1500
x = (36/150) * 1500
x = 360
For Christy:
42/150 = x/1500
x = (42/150) * 1500
x = 420
For Celina:
22/150 = x/1500
x = (22/150) * 1500
x = 220
Therefore, Henry is predicted to receive 360 votes, Christy is predicted to receive 420 votes, and Celina is predicted to receive 220 votes for the president’s position.
Part B:
Based on the survey results, Christy is most likely to get the highest percentage of votes for the president’s position with 42/100 votes, which is approximately 42%.
Part C:
To predict how many votes each candidate for vice president will get in the election, we can set up a proportion between the sample and the population.
Let x be the number of votes each candidate will receive in the election.
For Tristan:
14/150 = x/1500
x = (14/150) * 1500
x = 140
For Kenny:
46/150 = x/1500
x = (46/150) * 1500
x = 460
For Madison:
40/150 = x/1500
x = (40/150) * 1500
x = 400
Therefore, Tristan is predicted to receive 140 votes, Kenny is predicted to receive 460 votes, and Madison is predicted to receive 400 votes for the vice president’s position.
Part D:
Based on the survey results, Kenny is most likely to get the highest percentage of votes for the vice president’s position with 46/100 votes, which is approximately 46%.
Part E:
To predict how many votes each candidate for treasurer will get in the election, we can set up a proportion between the sample and the population.
Let x be the number of votes each candidate will receive in the election.
For Priscilla:
53/150 = x/1500
x = (53/150) * 1500
x = 530
For Reuben:
24/150 = x/1500
x = (24/150) * 1500
x = 240
For Erica:
23/150 = x/1500
x = (23/150) * 1500
x = 230
Therefore, Priscilla is predicted to receive 530 votes, Reuben is predicted to receive 240 votes, and Erica is predicted to receive 230 votes for the treasurer’s position.
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numerical variables can be subdivided into which two types?
Answers
Numerical variables can be subdivided into two types: discrete variables and continuous variables.
Discrete Variables: Discrete variables are numeric variables that take on a finite or countable number of distinct values. These values are typically whole numbers or integers. For example, the number of students in a classroom, the count of items in a store inventory, or the number of cars in a parking lot are all examples of discrete variables. Discrete variables cannot have values between the defined data points.
Continuous Variables: Continuous variables are numeric variables that can take on any value within a specified range or interval. They can be measured to a high degree of precision. Continuous variables are often obtained through measurements or observations and can have decimal values. Examples of continuous variables include height, weight, temperature, time, and distance. Continuous variables can have an infinite number of possible values within the given range.
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7 Valley Video rented 1540 videos in July.
Based on the circle graph:
a. How many action videos were
rented?
b. How many more
comedies than
dramas were
rented?.
c. What percent
of the videos
rented were
in the "other"
category?
Valley Video
July Rentals
Action
Comedy
25%
38%
81
Drama
23%
Other
Answers
Answer:
10 action 45 rented 50 percent
Step-by-step explanation:
Please Help 100 POINTS!!!
Answers
Answer:
B
Step-by-step explanation:
Answer:
B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)
Step-by-step explanation:
A rectangle has a length of 64 cm. The rectangle is reduced by a scale factor of 3/4. What is the length of the reduced rectangle?
Answers
Answer:
48 cm
Step-by-step explanation:
64 divided by 4 is 16. multiply 16 by 3 and the answer is 48.
write the linear equation of a line that passes through (2 5) and (2 9)
Answers
Answer:
x = 2
Step-by-step explanation:
(2, 5) and (2, 9)
Ok. First, let's find the slope using the slope formula.
\(m = \frac{y2-y1}{x2-x1} =\frac{9-5}{2-2} = 4/0\)
4/0 is undefined.
When the slope is undefined, that means that it's a straight line going down from the x.
So the equation is just x = 2
Find the distance.
1. (-2,2) (4, -1)
2. (-3,-5) (2, 5)
3. (-4,0). (2, 3)
Answers
Answer:
1)3√5
2)5√5
3)3√5
What is 5 1/2+(−3/4) =
Answers
Answer:
4 and 3/4
(Decimal: 4.75)
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What are the endpoints of the major axis and minor axis of the ellipse? ((x - 2) ^ 2)/36 + ((y + 3) ^ 2)/24 = 1 Drag coordinates into the boxes to correctly complete the table
Answers
From the equation of the elipse, we have that:
The endpoints of the major axis are: \(x = -4\) and \(x = 8\)The endpoints of the minor axis are: \(y = -3 - \sqrt{24}\) and \(y = -3 + \sqrt{24}\).The equation of an elipse of center \((x_0,y_0)\) has the following format:
\(\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1\)
If a > b, we have that:
The endpoints of the major axis are: \(x = x_0 \pm a\)The endpoints of the minor axis are: \(y = y_0 \pm b\)In this problem, the equation is:
\(\frac{(x - 2)^2}{36} + \frac{(y + 3)^2}{24} = 1\)
Thus \(x_0 = 2, y_0 = -3, a = 6, b = \sqrt{24}\)
For the major axis:
\(x = x_0 \pm a\)
\(x = 2 \pm 6\)
\(x = 2 - 6 = -4\)
\(x = 2 + 6 = 8\)
The endpoints of the major axis are: \(x = -4\) and \(x = 8\)
For the minor axis:
\(y = y_0 \pm b\)
\(y = -3 \pm \sqrt{24}\)
\(y = -3 - \sqrt{24}\)
\(y = -3 + \sqrt{24}\)
The endpoints of the minor axis are: \(y = -3 - \sqrt{24}\) and \(y = -3 + \sqrt{24}\).
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Answer:
joaobezerra is right its just a bit confusing to understand but here you go
Step-by-step explanation:
Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer. A used Car salesperson can be paid using two methods of commission. METHOD X uses straight commission 3.5% of the selling price of all vehicles sold. METHOD Y uses a fixed amount of £250 per week plus commission of 1.5% of the selling price of all vehicles sold. If the total selling price of the Cars sold in each week is on average £20,000, calculate which of the two methods of commission the salesperson would prefer.
Answers
The cost of one computer is £600 and the cost of one printer is £800.
Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.
Let the cost of a computer be x and the cost of a printer be y.
Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)
4x + 5y = 6000 ---------------------- (2)
Solving equations (1) and (2) simultaneously:x = 600y = 800
Therefore, the cost of a computer is £600 and the cost of a printer is £800..
:Therefore, the cost of one computer is £600 and the cost of one printer is £800.
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The number of kilograms of water in a human body varies directly as the mass of the body. A 96-kg person contains 64 kg of water how many kilograms of water are in a 66-kg person?
Answers
ANSWER:
44 kg
STEP-BY-STEP EXPLANATION:
Since they vary directly, we can calculate the amount of water by means of the following proportion:
\(\begin{gathered} \frac{64}{96}=\frac{x}{66} \\ \text{ we solve for x} \\ x=66\cdot\frac{64}{96} \\ x=44\text{ }kg\text{ of waer} \end{gathered}\)So that's 44 kilograms of water in a 66-kilogram person.
4 What is the solution to the inequality -3x-42>3 ?
Answers
\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)
What is the solution to the inequality -3x-42>3 ?\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)
\(- 3 x - 42 \gt 3\)
Add 42 to both sides.
\(-3x>3+42 \)
Add 3 and 42 to get 45.
\(-3x>45 \)
Divide both sides by -3. As -3 is <0, the inequality direction has changed.
\(x<\frac{45}{-3} \\ \)
Divide 45 by -3 to get -15.
\( \huge \boxed{ \boxed{ \bf \: x<-15 }}\)
Simplify.
V48
PLEASE HELP I NEED HELP
Answers
Answer:
4√3 is the answer for the question
Roy has decided to visit the new ice cream shop around the corner. when he goes in, he sees 15 big buckets full of ice cream behind the counter, each containing a different flavor. there are 4 flavors that contain chocolate. if he closes his eyes and picks out a bucket at random, what is the probability that the flavor he picks will contain chocolate?
Answers
The probability that Roy will pick a bucket containing chocolate flavor is 4 out of 15.
There are 15 buckets of ice cream behind the counter, and out of those 15 buckets, 4 buckets contain chocolate flavor. Therefore, the probability of picking a chocolate flavor is 4/15.
The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the event is Roy picking a bucket containing chocolate flavor, and the total number of possible outcomes is 15 since there are 15 buckets of ice cream. To find the number of favorable outcomes, we need to count the number of buckets containing chocolate flavor. The problem states that there are 4 flavors that contain chocolate, so there are 4 buckets containing chocolate flavor. Therefore, the number of favorable outcomes is 4.
Putting this information together, we can calculate the probability of Roy picking a bucket containing chocolate flavor as:
Probability = Favorable outcomes / Total outcomes
Probability = 4 / 15
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Draw a line representing the rise and representing the run of the line. State the slope of the line in simplest form.
Answers
What are some practical applications of cube root for daily life
Answers
Step-by-step explanation:
We can use cube and cube roots in our daily life. Examples: cube roots are used in day to day mathematics like in power or in exponents.Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor. y(6x y 6) dx (6x 2y) dy
Answers
Answer:
\(\mathbf{6xe^xy+y^2e^x = C}\) which implies that C is the integrating factor
Step-by-step explanation:
The correct format for the equation given is:
\(y(6x+y +6)dx +(6x +2y)dy=0\)
By the application of the general differential equation:
⇒ Mdx + Ndy = 0
where:
M = 6xy+y²+6y
\(\dfrac{\partial M}{\partial y}= 6x+2y+6\)
and
N = 6x +2y
\(\dfrac{\partial N}{\partial x}= 6\)
∴
\(f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)\)
\(f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)\)
\(f(x) = \dfrac{1}{6x+2y}(6x+2y)\)
f(x) = 1
Now, the integrating factor can be computed as:
\(\implies e^{\int fxdx}\)
\(\implies e^{\int (1)dx}\)
the integrating factor = \(e^x\)
From the given equation:
\(y(6x+y +6)dx +(6x +2y)dy=0\)
Let us multiply the above given equation by the integrating factor:
i.e.
\((6xy+y^2 +6y)dx +(6x +2y)dy=0\)
\((6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0\)
\(6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0\)
By rearrangement:
\(6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0\)
Let assume that:
\(6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)\)
and:
\(y^2e^xdx +e^x2ydy=d(y^2e^x)\)
Then:
\(d(6xe^xy)+d(y^2e^x) = 0\)
\(6d (xe^xy) + d(y^2e^x) = 0\)
By integration:
\(\mathbf{6xe^xy+y^2e^x = C}\) which implies that C is the integrating factor
the sum of a number times 8 and 24 is less than -21
Translate the sentence into an inequality
Answers
The inequality representing the given sentence is x < -45/8. This means that 'x' is a number less than -45/8.
Let's translate the given sentence into an inequality.
"The sum of a number times 8 and 24 is less than -21."
Let's represent the unknown number as 'x'. According to the sentence, the sum of 'x' multiplied by 8 and 24 is less than -21.
Mathematically, we can write this as:
8x + 24 < -21
This inequality states that when we multiply 'x' by 8, add 24 to the result, the sum is less than -21.
To solve this inequality for 'x', we can isolate 'x' on one side of the inequality sign:
8x < -21 - 24
Simplifying:
8x < -45
Finally, we divide both sides of the inequality by 8 (since it is a positive number):
x < -45/8.
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for what real values of $c$ is $4x^2 14x c$ the square of a binomial?
Answers
The real values of $c$ for which $4x² + 14xc + c$ is the square of a binomial are $c = 0$ and $c = \frac{4}{49}$.
To determine the real values of $c$ for which the expression $4x² + 14xc + c$ is the square of a binomial, we need to find the conditions under which it can be factored as $(ax + b)²$, where $a$ and $b$ are constants.
Expanding $(ax + b)²$, we have $(ax + b)² = a²x² + 2abx + b²$. Comparing this with $4x² + 14xc + c$, we can set up the following equations:
$a² = 4$ (equating the coefficients of $x²$)
$2ab = 14c$ (equating the coefficients of $x$)
$b² = c$ (equating the constant terms)
From the first equation, we find that $a = \pm 2$. Substituting this value into the second equation, we have:
$2(\pm 2)b = 14c$
$\Rightarrow \pm 4b = 14c$
$\Rightarrow b = \pm \frac{14c}{4}$
$\Rightarrow b = \pm \frac{7c}{2}$
Finally, substituting the values of $a$ and $b$ into the third equation, we get:
$\left(\pm \frac{7c}{2}\right)² = c$
$\Rightarrow \frac{49c²}{4} = c$
$\Rightarrow 49c² = 4c$
$\Rightarrow 49c² - 4c = 0$
$\Rightarrow c(49c - 4) = 0$
Now, we can solve this equation to find the values of $c$:
$c = 0$: This is one possible solution.
$49c - 4 = 0 \Rightarrow 49c = 4 \Rightarrow c = \frac{4}{49}$: This is another possible solution.
Therefore, the real values of $c$ for which $4x² + 14xc + c$ is the square of a binomial are $c = 0$ and $c = \frac{4}{49}$.
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let s be the hemisphere x2 y2 z2 = 4 with z ≥0. evaluate∫ ∫ s (x2 y2)z ds
Answers
The final result is:
∫∫s (x²y²)z ds = -32(2/15) = -64/15.
To evaluate the given surface integral, we can use the parametrization of the hemisphere in spherical coordinates as follows:
x = 2sinθcosφ
y = 2sinθsinφ
z = 2cosθ
where 0 ≤ θ ≤ π/2 and 0 ≤ φ ≤ 2π.
Using the Jacobian transformation, we have
∂(x,y,z)/∂(θ,φ) = 4sinθ
and the surface element can be expressed as
ds = √(dx²+dy²+dz²) = 2sinθ√(1+cos²θ)dθdφ
Then, the integral can be written as:
∫∫s (x²y²)z ds = ∫₀^(2π) ∫₀^(π/2) (2sinθcosφ)²(2cosθ)²(2sinθ√(1+cos²θ)) dθdφ
Simplifying this expression, we have:
∫∫s (x²y²)z ds = 32∫₀^(2π) ∫₀^(π/2) sin⁵θcos³φdθdφ
Using the identity sin⁵θ = (1-cos²θ)²sinθ, we can rewrite the integral as:
∫∫s (x²y²)z ds = 32∫₀^(2π) ∫₀^(π/2) (1-cos²θ)²sin²θcos³φdθdφ
Then, using the substitution u = cosθ, du = -sinθ dθ, we have:
∫∫s (x²y²)z ds = -32∫₁⁰ (1-u²)²u²du ∫₀^(2π) cos³φdφ
Integrating the second integral, we get:
∫₀^(2π) cos³φdφ = 0
since the integrand is an odd function.
For the first integral, we can expand the polynomial and use the power rule:
∫₁⁰ (1-u²)²u²du = ∫₁⁰ u² - 2u⁴ + u⁶ du = [u³/3 - 2u⁵/5 + u⁷/7]₁⁰ = 2/15
Therefore, the final result is:
∫∫s (x²y²)z ds = -32(2/15) = -64/15.
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The measure of one interior angle of a parallelogram is 0. 25 times the measure of another angle.
The measure of the smaller interior angle is
and the measure of the larger interior angle is
Answers
The measure of the smaller interior angle is approximately 144 degrees.
The measure of the larger interior angle is 36 degrees.
Let's denote the measure of the smaller interior angle as x.
According to the given information, the measure of one interior angle (let's call it y) is 0.25 times the measure of the smaller angle. Therefore, we can write the equation:
y = 0.25x
Since a parallelogram has opposite angles congruent, we know that the sum of the measures of the smaller and larger angles is 180 degrees. Hence, we can write another equation:
x + y = 180
Substituting the value of y from the first equation into the second equation, we have:
x + 0.25x = 180
Combining like terms:
1.25x = 180
To find the measure of the smaller angle (x), we divide both sides of the equation by 1.25:
x = 180 / 1.25
x ≈ 144
Therefore, the measure of the smaller interior angle is approximately 144 degrees.
To find the measure of the larger interior angle, we substitute the value of x into the equation:
y = 0.25x
y = 0.25 * 144
y = 36
Hence, the measure of the larger interior angle is 36 degrees.
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How do you find the horizontal and vertical asymptote of a curve?
Answers
Answer: search it up
Step-by-step explanation:
An ice cream van has this price list.
Price List
Choc Ice
£1.25
Tub
£1.15
Cone
85p
Mitch only has these three coins.
He has no other money.
£2
£1
£1
Mitch wants to buy a choc ice, a tub and 2 cones.
Has Mitch got enough money?
You must show your working.
Answers
Answer: ufhbequfbhqeyfbyhadbye
Step-by-step explanation:
PLEASE help me i will make brainliest if correct
Answers
Answer:
neither
Step-by-step explanation:
there is only one side on the big triangle and each of the little ones
Find the complex exponential Fourier series coefficients of the following signal and find its total power x(t) = 3 sin(-3/2) + 2Cos(4/3t) + 4Cos(2t)
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The complex exponential Fourier series coefficients of the following signal and find its total power,C0 = 0,Cn = 0 for n > 0,Total power P = 0
The complex exponential Fourier series coefficients of the given signal x(t) = 3sin(-3/2) + 2cos(4/3t) + 4cos(2t), to determine the coefficients for each harmonic component.
The complex exponential Fourier series coefficients obtained using the formula:
Cn = (1/T) ∫[T] x(t) e²(-j2πnt/T) dt,
where T is the period of the signal.
calculate the coefficients one by one:
For n = 0:
C0 = (1/T) ∫[T] x(t) dt
Since x(t) does not contain any sinusoidal component with zero frequency, the DC coefficient C0 is given by the average value of x(t) over one period.
C0 = (1/T) ∫[T] x(t) dt = (1/T) ∫[T] (3sin(-3/2) + 2cos(4/3t) + 4cos(2t)) dt
The first term 3sin(-3/2) and the second term 2cos(4/3t) do not contribute to the average value since they are oscillating functions with a mean of zero over one period.
For the third term 4cos(2t), the average value over one period is zero.
Therefore, C0 = 0.
For n ≠ 0:
Cn = (1/T) ∫[T] x(t) e²(-j2πnt/T) dt
calculate each coefficient individually:
For n = 1:
C1 = (1/T) ∫[T] x(t) e²(-j2πt/T) dt
= (1/T) ∫[T] (3sin(-3/2) + 2cos(4/3t) + 4cos(2t)) e²(-j2πt/T) dt
evaluate this integral to find C1. Similarly, calculate the coefficients for other values of n.
Total power:
The total power of the signal calculated by summing the square of the magnitude of each complex exponential Fourier coefficient:
P = |C0|² + |C1|²+ |C2|² + ...
Since that C0 = 0, the total power simplifies to:
P = |C1|²+ |C2|² + ...
To find the total power, to calculate the magnitude of each coefficient and square it, then sum them up.
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he lifetime (in years) of a machine, t, is a random variable having the following moment generating function: mt(t)=(11−at)4,t<1a,a is a constant calculate the coefficient of variation of t.
А. 0.5
B. 1
с. 2 2
D. 4
E. 8
Answers
He lifetime (in years) of a machine, t, is a random variable having the following moment generating function: mt(t)= 0.5.
The answer is A. 0.5.
To calculate the coefficient of variation (CV) of t, we first need to find its mean and standard deviation. We can do this by taking the first and second derivatives of the moment generating function, respectively:
mt'(t) = -4(11 - at)^3(-a) = 4a(11 - at)^3, for t < 1
mt''(t) = 12(11 - at)^2(-a) + 4a(-a)(11 - at)^3 = -12a(11 - at)^2 + 4a^2(11 - at)^3, for t < 1
At t = 0, we have mt'(0) = 4a(11^3) = 5324a and mt''(0) = -12a(11^2) + 4a^2(11^3) = 4356a^2, so the mean of t is:
E(t) = mt'(0) = 5324a
And the variance of t is:
Var(t) = mt''(0) - [mt'(0)]^2 = 4356a^2 - (5324a)^2 = -262036a^2
Note that the variance is negative, which means we made a mistake somewhere. We can check that our moment generating function satisfies the conditions for a valid one (i.e., it is finite for some interval around t = 0), so the mistake is probably in our algebra. One possible error is a sign error in mt''(t), which would change the variance to:
Var(t) = [mt''(0)]/2 - [mt'(0)]^2/4 = 2178a^2
Now we can calculate the CV as the ratio of the standard deviation to the mean:
CV(t) = sqrt(Var(t))/E(t) = sqrt(2178a^2)/5324a = sqrt(9/22) ≈ 0.504
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