Using the Integral Test, check the convergence of the given series by verifying the necessary conditions of integral test. 00 2n Σ [Sin²2+n²+ cos²2] n=1
Answers
To check the convergence of the series using the Integral Test, we need to verify the necessary conditions.
The series in question is:
∑ [sin²(2 + n²) + cos²(2)]
We can rewrite the series as:
∑ [1]
Since sin²(2 + n²) + cos²(2) simplifies to 1 for all terms, the series becomes an infinite geometric series with a common ratio of 1.
The conditions of the Integral Test are:
The terms of the series are positive.
The terms of the series are decreasing.
The integral of the terms of the series is finite.
Let's verify these conditions:
The terms of the series, which are all equal to 1, are positive.
To check if the terms are decreasing, we compare consecutive terms:
1 ≥ 1
The terms are not strictly decreasing, but they are constant. Therefore, the terms are not increasing either. So, we can say the terms are non-increasing.
We need to evaluate the integral of the terms to check if it is finite:
∫ [1] dn
Integrating 1 with respect to n gives us n + C, where C is the constant of integration.
The integral is not finite as it grows without bound. Thus, the integral of the terms is not finite.
Since the third condition of the Integral Test is not satisfied, we cannot conclude anything about the convergence of the series using this test.
In this case, we cannot determine the convergence or divergence of the series using the Integral Test. Other convergence tests, such as the Comparison Test or the Ratio Test, may be more suitable for analyzing this series.
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Related Questions
Mrs. Kephat's sixth grade class has been collecting aluminum cans. They receive a dollar a can. What percent of the goal still needs to be achieved?
Answers
Answer: A. 40%
amount achieved: 600/1000 = 3/5
amount not achieved = 2/5
2/5 as percent is 40%
Angle
x
= 076° and angle
y
= 111°.
Find the bearing of point A from point O.
Answers
The bearing of point A from point O is 256°.
What are bearings?In mathematics, a bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.
Given that, angle x= 076° and angle y = 111°.
Now, the bearing of point A from point O is
180°+ 076°
= 256°
Therefore, the bearing of point A from point O is 256°.
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Please help me! Please!
Answers
Answer:
here is your aneswer
the answer. will be 40
if the probability of david passing his exam is 1/4 what is the probabilty of him failing
Answers
Answer:
3/4
Step-by-step explanation:
4/4-1/4=3/4
i hoped this helped :)
Answer:
3/4
Step-by-step explanation:
2 over 9 minus 1 over 3 in simplest form
Answers
Answer:
2/9 - 1/3 (If you want to solved: -1/9)
Step-by-step explanation:
2 over 9 is 2/9 minus is just - and 1 over 3 is 1/3 so the equation looks like this: 2/9-1/3
To solve this you need to multiply the 1/3 by 3 on both the denominator and numerator: 2/9-3/9
simplify: -1/9
Hope this helps!
In a survey, 200 people were asked to choose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number
Answers
Using the probability concept, it is found that:
The theoretical probability of choosing a card with the number 4 was of 0.20 = 20%.The experimental probability of choosing a card with the number 4 was of 0.24 = 24%.What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these number of outcomes are taken from previous trials. Researching the problem on the internet, it is found that 48 of the 200 trials resulted in the number 4 being chosen, hence:
pE = 48/200 = 0.24.
For the theoretical probability, we consider that each card is equally as likely to be picked, hence:
pT = 1/5 = 0.2.
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5w-11/3=-4w
What is w
Answers
Answer:
Step-by-step explanation:
Exact Form:
w
=
11/3
Decimal Form:
w
=
3.6 (6 is repeated)
Mixed Number Form:
w
=
3 2/3
When you have a repeating decimal, what is one thing you must put to
show that it is repeating before submitting your answer?
Answers
Answer:
you need to put a line over the numbers that are repeating or if you can't put a line you can put this "..."
Step-by-step explanation:
You are considering purchasing instead of renting. Currently, you pay $1,500 each month in rent. The home you are interested in purchasing is valued at $248,000. You have determined the monthly payment will only be $1,331 if you take out a 30 year loan at 5%. The only thing you haven't considered is your monthly property tax bill.
You know the assessed value is 29% for residential property and you determine that the mill rate in your county is 32.45%0.
Calculate your yearly and monthly property tax and determine if it will be a better deal to continue to rent or to purchase this home based on your monthly cash output.
Yearly property tax: $
Monthly property tax: $
Which is less per month cost? Continue renting or Buying the house.
Answers
1. Calculating the yearly and monthly property tax to determine if it will be a better deal to continue to rent or to purchase this home based on the monthly cash output is as follows:
Yearly property tax: $2,334Monthly property tax: $194.50.2. To continue renting at $1,500 is less costly per month than buying the house with a monthly cash outflow of $1,525.50.
But the difference between renting and buying is minimal unless you factor in future maintenance costs.
How is the property tax computed?The property tax per year is based on the assessed value multiplied by the mill rate and divided by 1,000.
The annual property tax is then divided by 12 to obtain the monthly property tax.
Home value = $248,000
Assessed value = $71,920 ($248,000 x 29%)
Mill rate = 32.45%
Yearly property tax = $2,334 ($71,920 x 32.45/$1,000)
Monthly property tax = $194.50 ($2,334/12)
Comparison of Renting and Buying:Renting Purchase
Monthly payment $1,500 $1,331
Property tax 194.50
Total monthly payment $1,500 $1,525.50
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Aug 18, 10:56:17
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What is the value of the expression
2x2+4+6 × 3²?
Answer:
Answers
2x2+4+6x3^2
We do
4+4+6x3^2
4+4+36
=44
On average, Caryl's school bus arrives on time, although sometimes it is a bit early or late. If the arrival times are distributed on a normal curve, which of the following statistics would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day?
a. median
b. mean
c. standard deviation
d. correlation coefficient
Answers
If the arrival times of Caryl's school bus are distributed on a normal curve, the standard deviation would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.
The standard deviation is a statistic that measures the amount of variation or dispersion from the central tendency of a set of data values. A low standard deviation indicates that the data is tightly clustered around the mean or average, while a high standard deviation indicates that the data is more spread out.
The standard deviation is particularly useful when dealing with normally distributed data, as it allows us to estimate the probability of a certain range of values occurring. In this case, Caryl can use the standard deviation to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.
Hence, option c. standard deviation would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.
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Tonya went out to eat with her friends. The bill was $53 and they want to
leave a 20% tip. What is the total Tonya and her friends need to pay?
Explain how you found your answer.
marking as brainliest ^^
Answers
Answer:
A 20% tip plus the total of $53 would be $63.60
Step-by-step explanation: hope this helps<3
What is the value of I-9I?
Answers
Answer: 90
Step-by-step explanation:
91 - 1 = 90
Answer: 90
Step-by-step explanation:
If (x-9) is a factor of 2x^2 - 19x + k, what is the value of k?
Answers
Answer:
18
Step-by-step explanation:
Which of the following are equivalent to the function y = 3cOS X + 2? Check all that apply. A. y = 3cos(-x) + 2 B. y = -3cOS X-2 C. y = 3sin(x + 1) +2 + D. y = 3sin(x-7)+2
Answers
We need to plot the graphs of these functions on the same axis:
\(\begin{gathered} \text{From the graph, we s}e\text{ the function} \\ y\text{ = 3cosx + 2 has the same grap as } \\ y\text{ = 3sin(x + }\frac{\pi}{2})\text{ + 2} \\ \\ \text{Please note from angles in trigonometry:} \\ \sin \text{ (90 + }\theta)\text{ = cos }\theta \\ \cos x\text{ = sin (90 + x)} \end{gathered}\)Hence, the correct option
\(y\text{ = 3sin(x + }\frac{\pi}{2})\text{ + 2 (option }C)\)
, Which recursive sequence would produce the sequence
2,-6, 34
Answers
Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4
How can the recursive sequence be found?To identify a recursive sequence in which terms are defined using one or more preceding terms that are presented.Step 1, Find the nth term (an) of an arithmetic progression and the common discrepancy, d.Step 2, Use the formula an+1 = a + d to plug in the values and find the (n+1)th term, which will then reveal the following terms.A recursive formula is written in two parts: the first term is stated, and the formula connecting the succeeding terms is also stated. 10 through 35 in the following numerical order. Come up with a recursive formula. An arithmetic sequence is shown in this example (the same number, 5, is added to each term to get to the next term).Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4.To learn more about Recursive sequence refer to:
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See image below for question
Answers
Answer:
-1/3
Step-by-step explanation:
Rewrite as y = ax + b then inspect a
-y - (1/3)x = 0
y = (-1/3)x
so slope is -1/3
2. Find the domains of the functions. 1 (a). f(x) = √√/²2²-5x (b). f(x) = COS X 1–sinx
Answers
The domain of the function f(x) = √(√(22 - 5x)) is the set of all real numbers x such that the expression inside the square root is non-negative.
In this case, we have 22 - 5x ≥ 0. Solving this inequality, we find x ≤ 4.4. Therefore, the domain of the function is (-∞, 4.4].
The domain of the function f(x) = cos(x)/(1 - sin(x)) is the set of all real numbers x such that the denominator, 1 - sin(x), is not equal to zero. Since sin(x) can take values between -1 and 1 inclusive, we need to exclude the values of x where sin(x) = 1, as it would make the denominator zero.
Therefore, the domain of the function is the set of all real numbers x excluding the values where sin(x) = 1. In other words, the domain is the set of all real numbers x except for x = (2n + 1)π/2, where n is an integer.
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Finding missing angles
please help!! i’m literally begging
Answers
Answer:
65
Step-by-step explanation:
the square means 90 add that to 25 and subtract from 180
Answer:
x = 65
Step-by-step explanation:
The measure of the entire angle is 180°. The angle on the furthest left (with a square in it) is a right angle, meaning that it is 90°.
All three of the angles (90°, x°, 25°) all add up to the measure of the line, which is 180°. So, we can write this equation.
90 + x + 25 = 180
Subtract 90 and 25 from both sides.
90 + x + 25 - 90 - 25 = 180 - 90 - 25
x = 65
Write the equation of a circle whose center is at (6,-7) and whose radius is 4.
Answers
Answer:
(x - 6)² + (y + 7)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (6, - 7 ) and r = 4 , then
(x - 6)² + (y - (- 7) )² = 4² , that is
(x - 6)² + (y + 7)² = 16
Suppose x has a poisson distribution with a mean of 6. determine the following probabilities. round your answers to four decimal places (e.g. 98.7654).
Answers
P(x) = =0.1033 , X has a Poisson distribution with a mean of 6.
Describe the Poisson distribution using an example?
A discrete probability distribution is a Poisson distribution. It provides the likelihood that an event will occur a specific number of times (k) over a predetermined period of time or area. The mean number of occurrences, denoted by the letter "lambda," is the single parameter of the Poisson distribution.Given mean =6
λ=6
To find the probability us ethe below formula
P(X=0)=60 e-6/0!=0.0025
P(X=1)=61e-6 /1!=6e-6 =0.0149
P(X=2)=62e-6 /2!=0.0446
P(X<=2)=P(X=0)+P(X=1)+P(X=2)
=0.0025+0.0149+0.0446
P(X<=2) =0.062
P(X=4)=64e-6/4!
=64e-6 /4.3.2.1
=64e-6 /24
P(X=4) =0.1339
P(X=8)=68 e-6/8!
=4163.351816/40320
=0.1033
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The complete question is -
Suppose X has a Poisson distribution with a mean of 6. Determine the following probabilities: P(x = 0) = P(x le 2) = P(x = 4) = P(X = 8) = Round your answers to four decimal places (e.g. 98.7654).
Solve the differential equation by variation of parameters. y + 2y' + y = e^-t ln t y(t)=
Answers
The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.
(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.
Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.
Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian
W(t) = e-2t, to derive the specific integral related to f(t) = e-t.
Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y
Obtain yp = (1/2)(t2)e-t for the given situation.
As a result, the general integral is provided by
y = C1e-t + C2te-t + (1/2)(t2)e-t.
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a car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time it takes the truck to travel the same distance. what is the speed of the car? how about the truck?
Answers
A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.
Define speed.You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).
Given,
A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.
Let s represent the truck's speed and (s+20) represent the car's speed.
to determine each vehicle's time
Time = Speed / Distance
truck time = 350/s
Time in an automobile is 350/(s+20)
Truck time - car time = 2 hours
So,
(350/s) - [350/(s+20)] = 2
LCM is s(s+20)
[350(s+20) - 350s]/s(s+20) = 2
Cross multiplying,
350(s+20) - 350s = 2s(s+20)
Simplifying the equation,
350s + 7000 - 350s = 2s² + 40s
Now, we have quadratic equation to simplify,
2s² + 40s - 7000 = 0
Dividing the equation by 2
s² + 20s - 3500 = 0
Factorizing,
s= 50
s= -70 (impossible because of the sign)
Hence the truck's speed is s = 50 km/h.
The speed of the car is s + 20 = 70 km/h.
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Which expression correctly represents "six more than the product of five and a number, decreased by one"? 6 5 n minus 1 6 5 n minus 1 6 5 (n minus 1) (6 5) n minus 1.
Answers
The expressioon correctly represents "six more than the product of five and a number, decreased by one" is 6 + 5 (n minus 1), the correct option is C.
What is expression?An expression is a sentence with a minimum of two numbers and at least one math operation.
This math operation can be addition, subtraction, multiplication, and division.
Given
The expression correctly represents "six more than the product of five and a number, decreased by one".
The expressioon correctly represents "six more than the product of five and a number, decreased by one" is;
= 6 + 5 (n minus 1)
Hence, the expressioon correctly represents "six more than the product of five and a number, decreased by one" is 6 + 5 (n minus 1).
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I need help with this please help if you can! I'm giving 40 points.
Find the length of the side CD in the pentagon ABCDE.
Answers
B
Explanation
Do you need me to show work?
Answer:
A.
Step-by-step explanation:
I chose letter c and d on two of my quizzes and those were wrong and I see that you chose B and got that wrong. So it leaves letter A. Hopefully its correct but its the only one left.
Please help me 50 points I’ve been struggling for so long..
Clayton hiked to the bottom of El Dorado canyon and spent some time exploring when he got there. Then, he hiked back to the top. This graph shows Clayton's elevation above sea level over time.
Increasing from minute 0 to 25
True or false
Constant from minute 25 to 60
True or false
Decreasing from minute 60 to 90
True or false
I’m so lost please help
Answers
Answer
True, True, False
Step-by-step explanation:
I am not quite sure but I hope this helps in any way.
I say True to the Increasing from minute to 25 because Clayton’s time starts at 0 and the time increases to 25 minutes.
I say True because if you see the point where it shows 25 minutes and stops at 60 minutes until Clayton goes back up, it shows the line regularly occurring which would make him be constantly moving to 60 minutes. (Constant means to regularly occur)
I say false because Clayton’s time is increasing into 90 minutes, not decreasing. Also its kinda like the same concept as the Increasing from minute 0 to 25.
If a city with a population of 50,00 doubles in size every 12 years, what will the population be 24 years from now?
Answers
Answer:
20,000
Step-by-step explanation:
5,000 x 2 = 10,000
10,000 x 2 = 20,000
Step-by-step explanation:
So this is the way I would look at this like, you could say that since it doubles by x2 every 12 years by 24 years it would or could be 200,00 since you have doubled once already from 50,000 to 100,000 on the 12 years your gonna multiple that by 2 as well since you have reached your year mark.
that's personally the way I would look at it but I'm sure other people will ne able to help aswell or change mine.
A family with 4 adults and 3 children spends 47 for movie tickets at the theater. Another family with 2 adults and 4 children spends 36 . What is the price of a child's ticket in dollars?
Answers
Answer:
The price of a child ticket in dollars $8.00
Step-by-step explanation:
-2.25x+8.75x+10-20 solve x pls
Answers
Answer:
im gonna assume the 10 - 20 is what the equation is = to if not x wouldnt be = to anything x = -1.5
Step-by-step explanation:
-2.25x + 8.75x = 10-20
-2.25x+ 8.75x = -10
6.50x = -10 divide both sides by 6.5
x = -1.5
why are there twice as many cycles in comparison with the previous part (two polarizers)?
Answers
In a system with two polarizers, there are twice as many cycles in comparison with the previous part (one polarizer) due to the way polarizers interact with light.
Let me explain this step-by-step:
1. A polarizer works by allowing light waves oscillating in a specific direction to pass through while blocking light waves oscillating in other directions.
2. When you have one polarizer, it filters the light, allowing only waves oscillating in the polarizer's axis direction to pass through.
3. When you add a second polarizer (called an analyzer) with its axis aligned to the first polarizer, the light waves that passed through the first polarizer will also pass through the second polarizer with minimal attenuation.
4. If you rotate the second polarizer's axis, it will block a certain percentage of light waves that passed through the first polarizer, creating a cycle of intensity variations as the angle between the polarizers changes.
5. The cycle of intensity variations is doubled when you introduce the second polarizer, as there are now two points in the rotation where the polarizers are parallel and perpendicular to each other, allowing for maximum and minimum light transmission.
In conclusion, there are twice as many cycles in a system with two polarizers compared to the previous part (one polarizer) due to the interaction of polarizers with light waves and the variation in light transmission as their axes are rotated relative to each other.
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