7. Determine whether each improper integral converges or diverges. If it converges, find the value to which it converges. Use limit notation. a) Si" (2x+1)= dx 1 • 3x2 (3x+1) lise substitution to integrate り 1 2 1 30) (311) 11) b) Sex dx = 1 e b -) Soda Inxľ inli)=0 In 1) ar
Answers
The given improper integral converges to the finite value of 0.0833... by using u-substitution and evaluating the limit as the upper limit approaches infinity.
We can determine whether the given improper integral converges or diverges by evaluating the limit of the integral as the upper limit approaches infinity
∫(1 to ∞) 1/(3x+1)^2 dx = lim t→∞ ∫(1 to t) 1/(3x+1)^2 dx
To evaluate the integral, we can use u-substitution, letting u = 3x + 1 and du = 3dx
∫(1 to t) 1/(3x+1)^2 dx = (1/3) ∫(4 to 3t+1) u^(-2) du
= (1/3) [-u^(-1)] from 4 to 3t+1
= (1/3) [(3t+1)^(-1) - 4^(-1)]
Taking the limit as t approaches infinity
lim t→∞ (1/3) [(3t+1)^(-1) - 4^(-1)]
= (1/3) * 0.25 = 0.0833...
Since this limit exists and is finite, the improper integral converges to 0.0833...
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--The given question is incomplete, the complete question is given
" 7. Determine whether each improper integral converges or diverges. If it converges, find the value to which it converges. Use limit notation. a) integral limit from infinity to 1 {1/ (3x+1)^2}dx "--
Related Questions
dave earns his salary by making a 12.5% commision on all of his sales.if he sells $25000 this month,how much did he earn this month
PLEASE SHOW WORK
Answers
The total amount did he earn this month is $3125.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Dave earns his salary by making a 12.5% commission.
sales= $25000 this month.
According to given question we have
The basic formula is
Sales × Commission Percent/100 = Commission
$25000 ×12.5/100= Commission
Commission=$3125
Therefore, the total amount did he earn this month is $3125.
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Why did oslo go to the sled and sleigh auction
Answers
Oslo went to the sled and sleigh auction because he needed to find a mode of transportation for his upcoming winter camping trip.
He had been searching for weeks for the perfect sled or sleigh that would be durable enough to carry all of his gear and withstand the harsh winter conditions. The auction offered a variety of options and he was able to find a sled that met all of his requirements.
Additionally, attending the auction allowed him to network with other winter enthusiasts and gain valuable insight into the best equipment and techniques for winter camping.
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Which point represents the ordered pair (-2 1/4, 2/3)?
A. Point Q
B. Point R
C. Point S
D. Point T
Answers
Answer: c. Point S
Step-by-step explanation:
Answer:point s
Step-by-step explanation:
customers send emails to a help desk of an online retailer every 2 minutes, on average, and the standard deviation of the inter-arrival time is also 2 minutes. the online retailer has three employees answering emails. it takes 4 minutes to write a response email, on average. the standard deviation of the service times is 2 minutes. this is a g/g/k queue. what is the arrival rate? what is the service rate?
Answers
The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.
It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.
It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.
Therefore the arrival rate per hour is given by the following relation:
Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes
Given here,
No. of minutes in an hour = 60 minutes
Inter arrival time of the email taken in minutes = 2 minutes
∴ Arrival rate in 1 hr = 60 / 2
= 30 emails / hr
Hence the arrival rate is 30 emails per hour.
Now for finding out the service rate we have the following formula:
Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email
Given here,
No. of minutes in an hr = 60 minutes
No. of employes answering = 3
Average time that for writing response email = 2 minutes
∴ Service rate = 60 * 3 / 4
= 45 emails / hr
Hence the service rate is 45 emails per hour.
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Write an equation to find the total hours of video games played by William in any number of days.
Answers
The equation is H=d*h total hours of video games played by William.
We'll abbreviate William's daily video game playing as "d." The total amount of hours he plays can be expressed mathematically as follows:
Hours = H
H = d * h
where "h" stands for the daily number of hours he plays.
A period of time equal to \(\frac{1}{24}\) (a twenty-fourth) of a day. 1 Day = 24 Hours. 1 Hour = 60 minutes
Therefore, the equation to get the total number of hours William spent playing video games in any number of days is:
H = d * h
Where d is the number of days and h is the daily playing time.
Therefore, the equation is d*h.
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2) You go out to breakfast and order a meal that costs $7.24
and a coffee that costs $2.65. You want to leave a 15% tip.
How much will you leave for a tip?
Answers
Answer:
$1.48
Step-by-step explanation:
Meal cost: $7.24
Coffee cost: $2.65
Total cost: $9.89
Now we need to find 15% of 9.89.
This is a percentage question, we need to first multiply 9.89 with 15% then divide it by 100%:
9.89 × 15 ÷ 100 = 1.48 approximately.
PLEASE HELP ME ASAPPPPPPP!!!!!!!!!!!!!!!
TY :)
Answers
Answer:
I’m pretty sure it’s A.
Step-by-step explanation:
Combine the like terms
3x+14x+4y-7+2
17x+4y-5
ABCD is a rectangle in which O is the point of intersection of the diagonals. Also, O is equidistant from A, B, C. Is this true? Explain.
Answers
Answer:
The correct answer is yes its true.
Step-by-step explanation:
Let ABCD is a rectangle which means rectangle have opposite sides of same length : AB = CD and AD = BC.
It is given that O is the point of intersection of the diagonals that means O is mid point of AC and DB,
Then, OA = OB = OC = OD which means O is at similiar distance from each A, B, C and D.
Thus, the correct answer is : True.
What is the difference between 85.23 and 2.675
Answers
Answer:
82.555
Step-by-step explanation:
Based on the given conditions, formulate:
85.23 - 2.675
Calculate the sum or difference: 82.555
I need help I’ll appreciate if you help thank you
Answers
Answer:
b
Step-by-step explanation:
u start at (0,9.5) and with every increasing x value the y value is decreasing by .5 units
a) Work out (5 × 10³) × (9 × 10')
Give your answer in standard form.
b) Work out (7 × 105) + (2 × 10²)
Give your answer in standard form.
Answers
B: 935
I HOPE THIS HELPED!!!
Mr.Reyes baked 4 batches of muffins for his class. Each batch had 12 muffins. If Mr.Reyes has 24 students, how many muffins will each student receive
Answers
Answer: Each student will receive 2 muffins
Step-by-step explanation: 4 x 12 = 48
48 ÷ 24 = 2
consider selecting two elements, a and b, from the set a = {a, b, c, d, e}. list all possible subsets of a using both elements. (remember to use roster notation. ie. {a, b, c, d, e})
Answers
Thus, the possible subsets of the set a = {a, b, c, d, e} using both elements a and b are: {a, b}, {a, b, c}, and {a, b, d}.
To find all possible subsets of the set a = {a, b, c, d, e} using both elements a and b, we need to consider all the possible combinations of these two elements with the remaining elements in the set.
There are three possible subsets that we can create using both elements a and b:
1. {a, b} - This is the subset that contains only the elements a and b.
2. {a, b, c} - This subset contains the elements a and b, along with the third element c.
3. {a, b, d} - This subset contains the elements a and b, along with the fourth element d.
Note that we cannot create any more subsets using both elements a and b because we have already considered all the possible combinations with the remaining elements in the set.
In summary, the possible subsets of the set a = {a, b, c, d, e} using both elements a and b are: {a, b}, {a, b, c}, and {a, b, d}.
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the point one (-1 , 4) is a reflected over the y-axis what are the coordinates of the new point
Answers
When a point is reflected over the y- axis, it keeps its y-coordinate, and its x coordinate is multiplied by -1. Thus the coordinates of the new point are
\((1,4)\)That is the reflection over the y-axis.
Which system is the only inconsistent system?
y = 3x-2
2y = 6x-4
1
O
y = x - 3
y = 3x - 1
y = 3x - 6
y = 3x + 6
y = x - 3
y = -x-1
Answers
Answer:
The only inconsistent system is:
2y = 6x - 4
y = 3x - 2
To see this, we can rewrite the first equation as:
y = 3x - 2
Substituting this into the second equation, we get:
y = 3x - 2
This is the same equation as the first equation, so the system has infinitely many solutions.
The other systems given are consistent and either have a unique solution or infinitely many solutions.
Step-by-step explanation:
is 62500 a perfect square by division method solution
Answers
find the expectation value of the position squared when the particle in the box is in its third excited state. answer this question with the correct coefficient of l2 for the expectation value.
Answers
The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.
The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),
where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to
\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).
This can be written as nine-eighths of the length of the box squared.
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I tried many times to solve this question: Joy makes 6,5 litres soup correct to the nearest 0.5 litres. She serves the soup in 280ml portions correct to the nearest 10ml. 22 people order this soup. Does joy definitely has enough soup to serve the 22 people. show how you decide Your final line must be written as joy definitely does have enough soup or joy may not have enough soup. If you can please explain it if not just give the answer.
Answers
Joy makes 6.5 litres soup correct to the nearest 0.5 litres. She serves the soup in 280ml portions correct to the nearest 10ml. 22 people order this soup. Does joy definitely has enough soup to serve the 22 people.
Answer:
Yes, Joy definitely does has enough soup
Step-by-step explanation:
From the question, we know,
Joy make 6.5 litres of soup
Serves it in 280ml portions
Step 1
We convert the portions to liters
1 ml = 0.001 litre
280 ml
= 280ml × 0.001 litre/1 ml
= 0.28litre
Step 2
We divide 6.5 liters by 0.28 to find out how many people can be served
= 6.5 ÷ 0.28
= 23.2142857143 people
We can see that 6.5 liters soup can serve 23 people approximately.
Therefore, Yes, Joy definitely does has enough soup to serve 22 people
37.6 x ???=3760
this question is basically:
thirty seven point six times ?what? equals three thousand seven hundred and sixty
15 POINTS AVALIBLE + BRAINLIEST !!!!
thanks :)
Answers
Answer:
The "what" is 100
Step-by-step explanation:
Rewrite this as 37.6y = 3760 and set out to determine y:
y = 3760/37.6 = 100
The "what" is 100
A family pass to the amusement park costs $54. Using Distributive Property, write an expression that can be used to find the cost in dollars of 8 family passes. (I'm actu
Answers
The cost of 8 family passes to the amusement park is $432 when a family pass to the amusement park costs $54.
To find the cost of 8 family passes to the amusement park, we can use the Distributive Property of multiplication over addition. The Distributive Property states that a(b + c) = ab + ac, where a, b, and c are numbers. In this case, we can use the Distributive Property to write:
8 x $54 = (5 x $54) + (3 x $54)
We can see that we have broken 8 down into two smaller numbers that we can multiply by $54 individually, and then add together. The first term, 5 x $54, represents the cost of 5 family passes, while the second term, 3 x $54, represents the cost of 3 family passes. Adding these two values together, we get:
(5 x $54) + (3 x $54) = $270 + $162 = $432
Therefore, the cost of 8 family passes to the amusement park is $432.
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find the surface area of each figure. Round to the nearest tenth if necessary.
Answers
Answer:
Step-by-step explanation:
Base of triangle = b = 8 cm
Height of triangle = h = 6 cm
Length of rectangle = l = 6 cm
Sides of the triangle : S1 = 6 cm ; S2 = 8 cm and S3 = 10 cm
Surface area of triangular prism= bh + l *(s1+ S2 + S3)
= 8 * 6 + 6*(6+8+10)
= 48 + 6*24
= 48 + 144
= 192 square cm
Write the sentence as an inequality. Three times a number r plus 8 is fewer than −12
Answers
Answer: \(3r+8<-12\).
Step-by-step explanation:
It is given that three times a number r plus 8 is fewer than −12.
We need to write the sentence as an inequality.
Three times a number r = 3r
Times a number r plus 8 = 3r+8
Fewer than = less than = <
So, the inequality for the sentence "three times a number r plus 8 is fewer than −12" is
\(3r+8<-12\)
Therefore, the required inequality is \(3r+8<-12\).
The inequality that describes the sentence is:
\(3r + 8 < -12\)
--------------------------------
3 times 1 is \(3 \times 1 = 3\), 3 times 2 is \(3 \times 2 = 6\), and so on, thus 3 times a number r is \(3 \times r = 3r\).The plus word means that we have an addition operation, plus 8, thus \(3r + 8\)Fewer than -12 means that the less than -12 completes the inequality, thus:\(3r + 8 < -12\)
Which is the inequality that describes this situation.
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a poll shows that of all voters approve of the mayor's work. on three separate occasions a pollster selects a voter at random. what is the probability that on exactly one of these three occasions the voter approves of the mayor's work?
Answers
The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:
0.189 = 18.9%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of these parameters in the context of this problem are given as follows:
n = 3, p = 0.7.
Then the probability of exactly one success is calculated as follows:
P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.
Missing InformationThe proportion of voters that approve the mayor's work is of 70%.
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1.5(2x – 4) = 2(4x + 2)
Answers
Answer: 2
Step-by-step explanation:
Answer:
x = -2
Step-by-step explanation:
Step-by-step on how to solve it is in the image below.
Hope this helps! :)
a screen test for breast cancer was administered to 400 women with biopsy proven breast cancer and to 400 women without breast cancer. the test results were positive for 100 of the proven cases and 50 of the women without breast cancer. the sensitivity of the screen test is a. 87.5% b. 25% c. 66.7% d. 53.9%
Answers
Therefore, the sensitivity of the screen test is 25%. So the correct answer to your question is option b. 25%.
To find the sensitivity of the screen test, we need to calculate the percentage of true positive results out of all the actual cases of breast cancer.
Given that the test results were positive for 100 of the proven cases (true positive) out of a total of 400 women with biopsy proven breast cancer, we can calculate the sensitivity as follows:
Sensitivity = (True Positive / Total Cases) * 100%
Sensitivity = (100 / 400) * 100%
Sensitivity = 0.25 * 100%
Sensitivity = 25%
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graph the inequality in the coordinate plane
x>7
Answers
Does anyone knows the answers to these
Answers
Range is 17.4
IQR is 6
help I hate math i have no clue what I'm do
Answers
Answer:
B when u graph it and when u do -2 will still be a -2 and when the 4 will be positive
Step-by-step explanation:
The half-life of strontium is 29 years. If strontium was released in the Chernobyl nuclear accident and 41.3% of it remains, how long ago did this accident occur? What year did it
happen?
Answers
Answer:
Happened in 1986
Maybe 37 years ago?
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS
Answers
Answer:
LN and RQ
Step-by-step explanation:
PQR is just an enlargened version of MLN
RQ is just LN but longer
RQ/LN and LM/RP
PR/ML and MN/PQ
RQ/LN and LN/RQ
I think this is the answer