1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
8x − 4/x(x2 + 1)2
2. Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration).
2x3 - 16x2 - 39x + 20/x2 - 8x - 20 x dx
3. Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration).
x2/x4 - 42x2 - 343 x dx
Answers
Answer:
Step-by-step explanation:
1.
To write the form of the partial fraction decomposition of the rational expression:
We have:
[tex]\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}[/tex]
2.
Using partial fraction decomposition to find the definite integral of:
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx[/tex]
By using the long division method; we have:
[tex]x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }[/tex]
[tex]- 2x^3 -16x^2-40x[/tex]
[tex]x+ 20[/tex]
So;
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}[/tex]
By using partial fraction decomposition:
[tex]\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}[/tex]
[tex]= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}[/tex]
x + 20 = A(x + 2) + B(x - 10)
x + 20 = (A + B)x + (2A - 10B)
Now; we have to relate like terms on both sides; we have:
A + B = 1 ; 2A - 10 B = 20
By solvong the expressions above; we have:
[tex]A = \dfrac{5}{2}[/tex] [tex]B = \dfrac{3}{2}[/tex]
Now;
[tex]\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}[/tex]
Thus;
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}[/tex]
Now; the integral is:
[tex]\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx[/tex]
[tex]\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}[/tex]
3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.
Please check to the attached image below for the solution to question number 3.
Related Questions
23) What is the equation of the line below?
24) What is the equation for the table below?
Answers
First of all, you need to find the slopes of each. To do this, we need to take 2 points from each and plug them into y2 -y1/ x2 - x1.
For the graph we will take the points given (0,5) (4,0)
0 - 5 / 4 -0 = -5/4 = your slope for the graph
For the table, we will take the first three points. (-1,-1) (0,3) (1,7)
7 - 3 / 1 - 0 = 4 / 1 = 4
3 - - 1 / 0 - - 1 = 4 / 1 = 4
Therefore, the slope of the table is 4.
Now, for the y-intercepts.
These are normal be the points (0, y)
For the graph this would be (0,5) and for the table it would be (0,3)
Slope - intercept form = y = mx + b, where m is the slope and b is the y-intercept form.
Soo,
For the graph, it would be;
Y = -5/4x + 5
And for the table, it would be;
Y = 4x + 3
Madeline has two different candles made by two different companies. The length in centimeters of the first candle depends on its burning time t (in hours) according to the formula f(t)= 20-1.5t. The length (in centimeters) of the second candle over time
Answers
Answer:
I needed help with this answer well, because im on it right now.
Step-by-step explanation:
I'm in algebra and I don't understand how to solve this equation or problem :(
does anyone know what the warnings on your profile are for
Answers
Answer:
it is when you do something very bad like make a rude comment
Step-by-step explanation:
hope this helps!!!!
What type of triangle can have one right angle?
Answers
Answer:
A right triangle and an isosceles
Step-by-step explanation:
Simon's phone plan costs him $27.50 per month plus $0.15 per text message he sends or receives. If Simon wants to spend a maximum of $65 on his monthly phone bill, what is the maximum number of text messages he can send or receive?
Answers
Answer:
250 text messages
Step-by-step explanation:
There are several bowls containing various amounts of grapes on a table. When 12 of the bowls each had 8 more grapes added to them, the mean (average) number of grapes per bowl increased by 6.How many bowls of grapes are on the table?
Answers
Answer:
There are 16 bowls
Step-by-step explanation:
Number of bowls = x
Total grapes added = 12 x 8 = 96
The average increased by 6
So 96/6 = 16
There were 16 bowls of grapes on the table
OR
12 x 8 = 96
96/6=16
1. Which number is divisible by 2, 3, 5, and 9? A. 1,640 B. 1,999 C. 2,430 D. 3,666
Answers
Answer:
C
Step-by-step explanation:
I need help with whole thing teacher is putting pressure on me and I have a 10 in her class
Answers
Answer:
So... for problem 15. im gonna help you and maybe you'll understand how to do it:) So the X axis is the horizontal line and the Y axis is the vertical line.
So when it says X -4
Y 5
Then the point would be at -4 on the horizontal line and 5 positive points on the Y axis (vertical line)
Step-by-step explanation:
I really hope this helps you its hard to describe over type:(
Good luck:))
the tax on a purchase of $20 is 1.12. how much will tax be on a purchase of $45.50
Answers
Answer:
$ 1,593.75
Step-by-step explanation:
this is the advanced sale calculation if you wan a simple one i can write that in the comments! hope this help you! :D
How did they figure out the answer was 4 for the fraction problem solving. There are 36 people in the Newtown Hiking Club. 2/3 of the club must vote yes if the club is to hike the Northern Trail. 20 people have voted yes. How many more yes votes are needed?
Answers
Answer:
Step-by-step explanation:
4 (-x+4) =12 solve for x
Thank you! Any help Is appreciated!
Answers
Answer:
X=4
Step-by-step explanation:
distribute the 4 to the ones in the parenthesis
-4x+28=12
move the 28 over and change the sign
-4x=-16
divide by -4
x=4
Evaluate the expression 2(2+2y)
Answers
Answer:
Step-by-step explanation:
4 + 4y
Answer:
4 + 4y
Step-by-step explanation:
2 times 2 equals 4
2 times 2y equals 4y
4 plus 4y
Which expression is equivalent to 20y - 5
A. 4(5y-1)
B. 20(y-5)
C. 5(4y-1)
D. y(20-5)
Answers
9514 1404 393
Answer:
C. 5(4y-1)
Step-by-step explanation:
The answer choices are all factored forms. The only common factor in 20y-5 is 5, so the factored form with 5 as a factor is the appropriate one:
5(4y -1)
Determine the resultant of the given vectors by component method. E = 23 km , 11 degrees N of E N = 25 km, 24 degrees E of N G = 19 km, 18 degrees S of W R = 27 km, 58 degrees W of N.
Answers
Answer:
The resultant of the given vectors by component method is [tex]\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km][/tex].
Step-by-step explanation:
First we define each vector by applying using rectangular form:
1) [tex]\|\vec E\| = 23\,km[/tex], 11º north of east.
[tex]\vec E = 23\,km\cdot (\cos 11^{\circ}\,\hat{i}+\sin 11^{\circ}\,\hat{j})[/tex] (Eq. 1)
2) [tex]\|\vec N\| = 25\,km[/tex], 24º east of north.
[tex]\vec N = 25\,km\cdot (\sin 24^{\circ}\,\hat{i}+\cos 24^{\circ}\,\hat{j})[/tex] (Eq. 2)
3) [tex]\|\vec G\| = 19\,km[/tex], 18º south of west.
[tex]\vec G = 19\,km\cdot (-\cos 18^{\circ}\,\hat{i}-\sin 18^{\circ}\,\hat{j})[/tex] (Eq. 3)
4) [tex]\|\vec R\| = 27\,km[/tex], 58º west of north.
[tex]\vec R = 27\,km\cdot (-\sin 58^{\circ}\,\hat{i}+\cos 58^{\circ}\,\hat{j})[/tex] (Eq. 4)
The resultant of given vectors is determined by vector sum, that is:
[tex]\vec U = \vec E + \vec N + \vec G + \vec R[/tex] (Eq. 5)
[tex]\vec U = 23\,km\cdot (\cos 11^{\circ}\,\hat{i}+\sin 11^{\circ}\,\hat{j})+25\,km \cdot (\sin 24^{\circ}\,\hat{i}+\cos 24^{\circ}\,\hat{j})+19\,km\cdot (-\cos 18^{\circ}\,\hat{i}-\sin 18^{\circ}\,\hat{j})+27\,km\cdot (-\sin 58^{\circ}\,\hat{i}+\cos 58^{\circ}\,\hat{j})[/tex]
[tex]\vec U = (23\,km\cdot \cos 11^{\circ}+25\,km\cdot \sin 24^{\circ}-19\,km\cdot \cos 18^{\circ}-27\,km\cdot \sin 58^{\circ})\,\hat{i}+(23\,km\cdot \sin 11^{\circ}+25\,km\cdot \cos 24^{\circ}-19\,km\cdot \sin 18^{\circ}+27\,km\cdot \cos 58^{\circ})\,\hat{j}[/tex]
[tex]\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km][/tex]
The resultant of the given vectors by component method is [tex]\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km][/tex].
А
y
B 4
D
In the pre-image of the parallelogram, the slope of AD is
-3 and the slope of BC is -3. The image is translated
down 7 units and then reflected over the y-axis.
The slope of A"D" is
The slope of B"C" is
What can you determine about the line segments A"D"
and B"C"?
21
С
4
16
2.
A
A"
-2
B
B"
D
D"
C C
Answers
Answer:The slope of A"D" is 3
The slope of B"C" is 3
What can you determine about the line segments A"D" and B"C"?
They are parallel.
Solve the equation for m: m-n=5
Answers
Answer:
m=n+5
Step-by-step explanation:
You just add n on both sides to get m because m is isolated on one side and variables and numbers on the other side of the equal sign.
Answer:
m=n+5
Step-by-step explanation:
m-n=5
add n on both sides
m=n+5
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon.
How many milliliters are in 3 gallons?
Label your answer in mL.
Answers
Answer:
11355mL
Step-by-step explanation:
It gives you how many milliliters are in one gallon. From there it gives extra information that isn't needed so you skip it and go to the question which is the amount of mL in 3 gallons. So you take the amount from the first sentence (3,785 mL) and multiply it by the amount that they ask in th equestion (3 gal) .
3785*3= 11355
Solve: C - 20 = 4 - 3c
Need to solve for C
C=___
Answers
Answer:
C = 6
Step-by-step explanation:
Here are steps
C - 20 = 4 - 3C
C + 3C = 4 + 20
4C = 24
C = 6
You need to make at least 360 wraps for a party. You can make 9 wraps per minute.
How long will it take you to make the number of wraps you need?
In two or more complete sentences write and solve an inequality for the situation and explain how you will solve the inequality.
Answers
Answer:
40 minutes
Step-by-step explanation:
What the person above/below me is saying, is you have to divide 360 and 9, to find x! X=40, 360/9=40! That's what they mean. I hope this helped you understand their answer!
It will take 40 minutes for me to make the 360 wraps that I need.
9x ≥ 360 ⇒ x ≥ 40
Step-by-step explanation:
I have to make at least 360 wraps for a party.
I can make 9 wraps per minute.
So, it will take minutes for me to make the 360 wraps that I need.
If I work for x minutes to make wraps, then I will be able to make 9x wraps.
So, the inequality that models the given condition is
9x ≥ 360
⇒ x ≥ 40 {Dividing both sides by 9}
Therefore, I need to work at least 40 minutes to reach my goal. (Answer)
Mrs. Daiz has 9 eggs. She cooks 5 how mich left
Answers
Answer:
You have for uncooked eggs left.
Step-by-step explanation:
9 (total amount of eggs) - 5 (eggs left after she cooks) = 4 eggs cooked.
There is a new truck worth $31,500 and it loses value at the rate of 2.7% per year.
1) Create an exponential model.
2) How much is the truck worth 5 years later?
3) How much is the truck worth 15 months later?
Answers
Answer:
For 2 it's 27,247 and for 3 it's 31393.86
Step-by-step explanation:
Find the variance for the given data. Round your answer to one more decimal place than the original data.
{12.4, 10.7, 14.5, 10.1, 16.5}
Answers
Answer:
5.6864
Step-by-step explanation:
Find the variance for the given data. Round your answer to one more decimal place than the original data.
{12.4, 10.7, 14.5, 10.1, 16.5}
3/8 + 7 1/2 =?
In simplest form
Answers
Answer:
63/8
Step-by-step explanation:
3/8+ 7 1/2 = 3/8+ 15/2= 3/8+60/8= 63/8
Answer: I think it’s 7 5/8 I’m not sure
Step-by-step explanation:
Whoever answer it correctly will get brainliest. :)
If 44 customer brought bread,67 workers also brought bread. And there were 2 bread left. How many breads were there before any of them brought one?
Answers
Answer:
69
Step-by-step explanation:
The answer is 113 assuming they all just bought 1 loaf :)
Find the slope. (4,2) (7, 6.5)
Answers
Answer:
B.
Step-by-step explanation:
m=y2-y1/x2-x1
6.5-2=4.5
7-4=3
4.5/3=1.5
the slope is 1.5
hope this helps :3
if it did pls mark brainliest
24 cycles in 2 cycle stands = cycles per cycle stand
Answers
Answer:
there are 12
Step-by-step explanation:
24/2 = 12 that means that there are 12 cycles per stand
Answer: 12 cycles
Step-by-step explanation:
need help with slopes..
Answers
Answer:
Step-by-step explanation:
y-intercept: -7
type of slope: 0
slope: y=0x-7
slope's hard ;_;
Solve for y x = 3y - 24
Answers
Answer:
y = 1/3x + 8
Step-by-step explanation:
Step 1:
x = 3y - 24 Equation
Step 2:
x + 24 = 3y Add 24 on both sides
Step 3:
1/3x + 8 = y Divide
Answer:
y = 1/3x + 8
Hope This Helps :)
six cats catch six mice in six minutes. how many cats are needed to catch 60 mice in 60 minutes
Answers
Answer:
10 cats
Step-by-step explanation:
If there are 10 cats, they all will catch 6 mice each, which means 60 mice in total. If they catch 6 mice in 6 seconds, that means they will catch 60 mice in 60 seconds. You need 10 cats to get this task done
Please give me the correct answer.
Answers
Answer:
33
Step-by-step explanation:
