Use the Table of Integrals to evaluate the integral 兀 x3 sin(x) dx 0
Answers
Using the Table of Integrals to evaluate the integral 兀 x3 sin(x) dx 0, the value is:
∫x^3 sin(x) dx = 3(x^2 sin(x) - 2x cos(x) + 2 sin(x)) - x^3 cos(x) + C
Using integration by parts,
∫x^3 sin(x) dx = - x^3 cos(x) + 3 ∫x^2 cos(x) dx
Now, using integration by parts again,
∫x^2 cos(x) dx = x^2 sin(x) - 2 ∫x sin(x) dx
One more integration by parts gives us:
∫x sin(x) dx = x cos(x) - ∫cos(x) dx = x cos(x) - sin(x)
Putting these results together, we get:
∫x^3 sin(x) dx = - x^3 cos(x) + 3(x^2 sin(x) - 2x cos(x) + 2 sin(x)) + C
where C is the constant of integration.
Evaluating this expression at x = 0 gives:
∫0 x^3 sin(x) dx = 0
Therefore,
∫x^3 sin(x) dx = 3(x^2 sin(x) - 2x cos(x) + 2 sin(x)) - x^3 cos(x) + C
where C is the constant of integration.
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Related Questions
What is the image point of (−8,−1) after a translation left 3 units and up 4 units?
Answers
Answer:
i think it is
( 3,-11) or
(-4,-4) as
the
answer
Determine the total number of roots of each polynomial function using the factored form.
f(x) = (x+5)³(x-9)(x + 1)
Answers
The polynomial function f(x) = (x+5)³(x-9)(x + 1) has a total of three distinct roots when considering the factored form.
To determine the total number of roots of the polynomial function f(x) = (x+5)³(x-9)(x + 1) using the factored form, we can examine the factors individually.
The factor (x+5)³ has a triple root at x = -5, meaning it touches the x-axis but does not cross it. Therefore, it contributes only one unique root.
The factor (x-9) has a single root at x = 9, contributing one unique root.
The factor (x + 1) has a single root at x = -1, also contributing one unique root.
To find the total number of roots, we add up the number of unique roots contributed by each factor: 1 + 1 + 1 = 3.
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The gateway arch in st. Louis, mo is approximately 630 ft tall. How many u. S. Nickels would be in a stack of the same height? each nickel is 1. 95 mm thick.
Answers
The gateway arch in st. Louis, MO is approximately 630 ft tall, the same height of the Nickels would be in a stack is 98474.
Height of Gateway Arch in St. Louis, MO = 630ft tall
We are asked, how many nickels would be in a stack of the same
height when 1 nickel is 1.95 mm thick.
Convert height in ft to mm
1 ft = 304.8 mm
630ft = X
After Cross Multiply,
630ft × 304.8mm/1ft
= 192024 mm.
To find how many nickel would be in a stack of the same height
= Total thickness/ Thickness of 1 US dime
= 192024 mm/1.95mm
= 98473.8
≈98474 nickels
Therefore, the number of nickel that would be in a stack of the same height is 98474.
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15. Find m
X=3
please help due today
Answers
Answer:
11x - 2 = 6x + 13 (corresponding angles)
5x = 15
x = 3
Enter the number that belongs in the green
box as you solve the equation for x.
2(5x + 4) = 8
First, use the
Distributive Property! [?]X + [ ] = 8
Answers
The equivalent expression using the property is 10x + 16 = 8
Distributive propertyThis a property where a value is distributed over the values in parenthesis.
Given the following expression
2(5x+8) = 8
Using the Distributive property;
2(5x + 8) = 8
2(5x) + 2(8) = 8
10x + 16 = 8
Subtract 16 from both sides
10x = 8 - 16
10x = -8
x = -8/10
Hence the equivalent expression using the property is 10x + 16 = 8
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-1.6, 5/2, -7/8, 0.9, -6/5 from least to greatest
Answers
Answer:
starting with least...
-1.6
-6/5
-7/8
9/10
5/2
...to greatest.
Step-by-step explanation:
start by putting the decimals into fractions:
-1.6 = -8/5
0.9 = 9/10
and then find a common denominator to compare them fairly.
the number that they all end up going into is 40, which will be your common demoninator.
-8/5 (aka -1.6) = -64/40
5/2 = 100/40
-7/8 = -35/40
9/10 (aka 0.9) = 36/40
-6/5 = -48/40
Swimming Pool On a certain hot summer's day, 140 people used the public swimming pool. The daily prices are $1.25 for children and $2.00 for adults. The
receipts for admission totaled $214.00. How many children and how many adults swam at the public pool that day?
Answers
Answer:
88 (children) and 52 (adults).
Step-by-step explanation:
1. if the number of the children is 'x' and the adults is 'y', then total number 140 people is x+y=140, - this is the first equation;
2. if the earned money is 214 USD and 1.25 USD for child and 2 USD for adult, then this means: 1.25x+2y=214, - this is the second equation;
3. using two equations above it is possible to make up and solve the next system of two equations:
\(\left \{ {{x+y=140} \atop {1.25x+2y=214}} \right. \ => \ \left \{ {{y=52} \atop {x=88}} \right.\)
4. Finally, the answers is:
children ('x') - 88; adults ('y') - 52.
Solve for x in 4^2x=2^5-x
Answers
Answer:
x=1.88
Step-by-step explanation:
x=1.88
Step-by-step explanation:
question 5: on a given day, there is a car accident reported at the intersection of victory blvd and richmond avenue with a probability 0.05. what is the probability that there are at most 2 car accidents reported thoughout a month?
Answers
The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:
Cumulative probability is equal to (number of events * e)/(average number of events per time period).
(Number of events / (-average number of events per time period)!)
In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:
Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.
That amounts to:
Probability total = 1 + 0.05 + 0.0025
which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.
can someone pls help me i really don't know how to do this
Answers
Answer:
option 2
Step-by-step explanation:
Since the sign is greater than or equal to it will be pointing to the right since it includes -9 it will be a closed circle
What's the slope of this chart?
Answers
Answer:
y= -2/7x +4
Step-by-step explanation:
Answer: -2/7
Step-by-step explanation:
1. Use the slope equation (y2-y1)/(x2-x1) you take 2 coordinates in the chart and use the second coordinates y output minus the first corrdinates y output and the same for the x inputs and whatever you get is your slope
1. Plug the first two coordinates into the slope formula:
(6-8)/(-7-(-14))
2. Solve:
-2/7!
I hope this helped :)
HEEELLLLP MEEEEE PLEASEEEE
Answers
The positive value of the distance between the two objects
is \(r = +\sqrt \frac{GM_1M_2}{F_g}\).
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, The formula to calculate the gravitational force between two objects
is \(F_g = \frac{GM_1M_2}{r^2}\) where r is the distance between the objects M is the individual masses and G is the gravitational constant.
Solving for r would result in two values one positive and one negative and distance can not be negative so we want the positive value.
\(F_g = \frac{GM_1M_2}{r^2}\).
\(r^2 = \frac{GM_1M_2}{F_g}\).
\(r = \pm\sqrt \frac{GM_1M_2}{F_g}\).
\(r = +\sqrt \frac{GM_1M_2}{F_g}\).
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17. Louis is offered an interest rate of 6.35%
for an investment with continuous
compounding. What is his equivalent rate
of interest with simple compounding?
[A] 1.23 or 12.3%
[B] 0.0593 or 5.93%
[C] 0.423 or 42.3%
ID] 0.0656 or 6.56%
[E] 0.0615 or 6.15%
Answers
The rate of interest for simple compounding if Louis is offered an interest rate of 6.35% for an investment with continuous compounding, is 0.0656 or 6.56%, so option D is correct.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
Louis is offered an interest rate of 6.35% for an investment with continuous compounding,
Here, P will be the same, the amount will be the same and the time period will be the same then,
The amount in simple compounding = The amount in continuous compounding
\(P(1 + r)^t = Pe^{rt}\)
Here, r is the rate of interest for simple compounding,
\(1 + r = e^{0.0635}\) (All same quantities get canceled)
r = 1.0656 - 1
r = 0.06556
r = 0.0656
r = 6.56%
Thus, the rate of interest for simple compounding is 6.56%.
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Suppose that each of n sticks is broken into one long and one short part. The 2n parts are arranged into n pairs from which new sticks are formed. Find the probability (a) that the parts will be joined in the original order, (b) that long parts are paired with short parts.
Answers
Given Information:Each of n sticks is broken into one long and one short part. The 2n parts are arranged into n pairs from which new sticks are formed.Pairing each long part with a short part gives n possible pairs.Explanation:a. Probability that the parts will be joined in the original orderWe have n sticks that are broken into 2 parts
each.So, total parts = 2nOut of 2n parts, we can select n parts in n! ways. (Order is important as we have to join them in the original order)For each such n! arrangement, there is only 1 main answer that is the original order of n sticks.Now, total number of ways to arrange the parts is 2n!.So, probability that the parts will be joined in the original order = Number of favourable outcomes / Total number of possible outcomes= n! / 2n! = 1 / 2n-1b. Probability that long parts are paired with short partsWe have n pairs out of which one part is long and other is short.Each long part can be paired with a short part in n ways.Out of n pairs, one pair can be selected in nC1 ways. Similarly, the other pairs can be selected in n-1 C 1 ways, n-2 C 1 ways and so on
Total number of ways to select n pairs is n * (n-1) * (n-2) *... * 1 = n!So, probability that long parts are paired with short parts= Number of favourable outcomes / Total number of possible outcomes= n! / 2n! = 1 / 2n-1Therefore, the main answer to the problem is:(a) Probability that the parts will be joined in the original order= n! / 2n!(b) Probability that long parts are paired with short parts= n! / 2n!
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help me find the answer, which numbers when put together make 405.
Answers
Answer:
19x23 = 437
437-23 = 414
414-9 = 405
Step-by-step explanation:
I believe this is what the question is asking. if not please let me know and tell me how the question works.
Frank and Linda just finished a meal and received their bill for $47. 60. They would like to leave their server a 20 percent tip. Which expression could be used to find the total bill including gratuity? 0. 2 (47. 60) 47. 60 minus left-bracket (0. 2) (47. 60) right-bracket 47. 60 left-bracket (0. 2) (47. 60) right-bracket 0. 8 (47. 60).
Answers
The result will be the original bill amount plus 20 percent of the bill amount, which represents the gratuity. To find the total bill including a 20 percent gratuity, we can use the expression: 47.60 + (0.2 * 47.60).
1. The expression (0.2 * 47.60) calculates 20 percent of the bill amount.
2. We multiply 0.2 by 47.60 to get the gratuity amount.
3. We then add the gratuity amount to the original bill amount of 47.60 to find the total bill including the gratuity.
Using the expression 47.60 + (0.2 * 47.60), we can calculate the total bill with the 20 percent tip. The result will be the original bill amount plus 20 percent of the bill amount, which represents the gratuity.
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The library sponsors a chess club for members of all ages and skill levels. Currently, the ages of the members are 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, and 22. The librarian uses a histogram to track the number of members in different age groups. For this situation, which is the appropriate way to label the age intervals on the x-axis?
Answers
Answer:
B. 7−10; 11−14; 15−18; 19−22
Step-by-step explanation:
What is the solution to the following system?
Answers
The solution to the system is x = 0, y =2, z = 5
How to find the solution to the system?Given the following system:
x+ 2y+z=9 -------- (1)
x- y+3z = 13 -------- (2)
2z = 10 -------- (3)
From (3):
2z = 10
z = 10/2 = 5
Put z = 5 into (1) and (2):
x+ 2y+z=9
x+ 2y+5 = 9
x +2y = 9-5
x +2y = 4 -------- (4)
x- y+3z = 13
x -y + 3(5) = 13
x-y + 15 = 13
x-y = 13 -15
x-y = -2 -------- (5)
Using elimination method on (4) and (5):
Subtracting (5) from (4):
x +2y = 4
x-y = -2
3y = 6
y = 6/3 = 2
Put y = 2 into (4):
x +2y = 4
x + 2(2) = 4
x + 4 = 4
x = 4-4 = 0
Therefore, the solution is x = 0, y =2, z = 5. The 3rd option is the answer.
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What percentage of people in the study started
saving for retirement at age 21 or before? How
does this compare with the how many of these
same people believe their children or
grandchildren should start saving at 21 or
before?
Answers
Answer:8% started saving at or before 21
30% believe their children or grandchildren should start saving at or before 21
Step-by-step explanation: on the graph, the ones in lighter color start saving for requirements
That is 3%+5%=8%
The second solution goes thus
13%+17%= 30%
the ones in dark colors believe their children or grandchildren should start saving before 21
Find The Measure Of Angle A In The Triangle
Answers
Answer:
∠A = 48°
Step-by-step explanation:
All angles in a triangle add up to 180°
Volume of Rectangular Prisms/Cylinders
Answers
\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=7\\ h=19 \end{cases}\implies V=\pi (7)^2(19)\implies V\approx 2924.8~ft^3\)
tyler's brother earns $12 per hour. the store offers him a raise -a 5% increase per hour . after the raise how much will tyler's brother make per hour
Answers
Answer:
12.50
Step-by-step explanation:
If Anita uses a total of 15 orange balloons how many green balloons should she use
Answers
Answer:
Step-by-step explanation:
So basically since she used 15 orange balloons she would have to use 10 green balloons
Your sister can get $30 per day, d, for selling clothes at the market. But she has to pay $60 at first for renting a stand. You can get $20 per day for helping your neighbor rake lawns. After how many days will your sister earn as much as you?
Answers
Answer:
6 days
Step-by-step explanation:
pay 60 = -60
Let d = the number of days
30d - 60 = sister
20d = me
Equation:
30d - 60 = 20d Move 30 to the other side
-30d -30d
-60 = 20d - 30d Combine liked terms
-60 = -10d
-10 -10 Divide
d = 6
A ship sails north for 2 hours, traveling a total of 15 miles. Then the ship turns south and travels 6 miles in an hour.
If north is taken as the positive direction, what is the velocity of the ship?
7 miles per hour , 7 miles per hour , ,
–3 miles per hour , –3 miles per hour , ,
3 miles per hour , 3 miles per hour , ,
–7 miles per hour
please help!!!
Answers
Answer:
3 miles per hour
Step-by-step explanation:
The half-life of Lead-218 is 0. 25 minute. This means that the amount of Lead-218 left from an initial sample of 100 mg can be modeled by A(t)=100(12)4t , where t is the number of minutes that have passed. What percent of the sample decays away every minute?
Answers
For a sample of Lead-218, with half-life time period of 0.25 minute, the percent of the sample decays away every minute is equals to the 93.75%.
We have a half-life time period of Lead-218 is equals to the 0.25 minute.
Initial sample amount of lead-218 = 100 mg
The equation which is used to modeled the situation or decay equation is written as \(A(t) = 100(\frac{1}{2})^{4t}\)
where, t --> time period ( in minutes)
We have to determine percent of the sample decays away every minute. So, we determine the decay value of A(t) at t = 1 minute then change the amount in percent form. Substitute, t = 1 minutes
=> \(A(t) = 100(\frac{1}{2})^{4× 1}\)
\(= 100(\frac{1}{2^4})\)
\(= \frac{100}{16}\)
= 6.25
Conversion in percentage : \( (\frac{100 - 6.25}{100})100%\)
= 93.75%
Hence, decay Percent is 93.75% in every minute.
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Rewrite the expression 16 + 32 as the product of the
greatest common factor and the sum of the remaining
numbers.
2(8 + 16)
4(4 + 8)
8(2 + 4)
16(1 + 2)
Answers
Answer:16(1+2)
Step-by-step explanation:
16 is the greatest common factor of 16 and 32. 16 divided by 16 is 1, and 32 divided by 16 is 2. THEREFORE, 16(1+2) after you distribute is 16+32.
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 point is deducted. Desiree did not leave any question unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
and the equation will have
.
Answers
Total number of multiple-choice questions that Desiree has to answer in Aptitude test = 50
Points given for every correct Answer = +3
Points deducted for every Incorrect Answer = -1
For every question unanswered ,
points Deducted = -0.5
Total Points Obtained by Desiree after Answering all the questions = 110
Number of Answers that Desiree answered correctly = x questions
Number of Incorrect Answers = (50 - x) questions
Then,the Equation representing above situation
→ 3 × x + ( -1 ) × ( 50 - x ) = 110
⇒3x - 50 + x = 110 ----------- equation that represents the given situation
⇒ 4x - 50 = 110
Adding 50, on both sides
→ 4x - 50 + 50 = 110 + 50
⇒ 4x = 160
Dividing both sides by, 4 we get
x = 40
Number of correct answers given by Desiree= 40 questions
Number of Incorrect Answers = 50 - 40
= 10 Questions .
Answer:
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 points is deducted. Desiree did not leave any questions unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
3(50 - x) + x = 110
and the equation will have
no solution
.
Step-by-step explanation:
the test statistic calculated in the process of a kruskall-wallis test is h.
T/F
Answers
The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups to determine if there is a significant difference between the medians of the groups. The test statistic used in this test is denoted by the letter "H," which is calculated based on the ranks of the data.
True. The test statistic calculated in the Kruskal-Wallis test is denoted by the symbol H, not to be confused with the Shapiro-Wilk test statistic denoted by W. The Kruskal-Wallis test is a non-parametric test used to compare the median ranks of three or more independent groups. The test statistic H is calculated by comparing the between-group sum of squares to the total sum of squares. H follows a chi-squared distribution with degrees of freedom equal to the number of groups minus one. The p-value obtained from the chi-squared distribution is used to determine whether to reject or fail to reject the null hypothesis that there is no significant difference between the groups.
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Which function is graphed ?
Answers
Answer:
its b :) then can i help you