Answers
Step-by-step Explanation:
We are going to solve this problem using integration by parts. We can write the integrand as
[tex]\dfrac{4x}{x^2+4x+3} = \dfrac{4x}{(x+3)(x+1)}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{A}{x+3} + \dfrac{B}{x+1}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{Ax + A + Bx + 3B}{x^2+4x+3}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:=\dfrac{(A+B)x + (A+3B)}{x^2+4x+3}[/tex]
Comparing the above term to the left hand side, we can see that
(A + B)x = 4x
A + 3B = 0
Solving for A and B, we find that A = 6 and B = -2 so our integrand becomes
[tex]\dfrac{4x}{x^2+4x+3} = \dfrac{6}{x+3} - \dfrac{2}{x+1}[/tex]
We can now easily integrate this expression as follows:
[tex]\displaystyle \int{\dfrac{4x}{x^2+4x+3}}dx = 6\int{\dfrac{dx}{x+3}} - 2\int{\dfrac{dx}{x+1}}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:= 6\ln|x+3| - 2\ln|x+1| + C[/tex]
Related Questions
A car travels at an average speed of 48 miles per hour. How long does it take to travel 180 miles?
Answers
Answer:
3 hours and 45 minutes
Step-by-step explanation:
mark me a brainliest answer
De enero a junio, 46200 inmigrantes solicitaron la ciudadanía. Durante este mismo período el año pasado, se postularon 120000 inmigrantes. ¿Cuál es el porcentaje de disminución?
Answers
Usando el concepto de porcentaje, se encuentra que el porcentaje de disminución es de 61.5%.
El porcentage de disminución es la disminución multiplicada por 100% y dividida por la cantidad inicial.
Disminución de 120000 imigrantes para 46200 imigrantes, entonces:
[tex]P = \frac{(120000 - 46200)}{120000} \times 100\% = 61.5\%[/tex]
El porcentaje de disminución es de 61.5%.
Un problema similar es dado en https://brainly.com/question/24547889
PLEASE HELP!!!!
Given A and B, use your knowledge of sets to determine which one of the following numbers is not in
AUB.
A = {-10, 8, 12, 26, 29}
B = {-8, - 1,5, 26, 36}
A.18
B. -10
C. 26
D. 36
E. None of the above
Answers
===========================================================
Explanation:
The set A U B represents the list of items that are either in set A, set B or both sets at the same time. The "U" is the union symbol.
Set A U B looks like this
A U B = {-10, 8, 12, 26, 29, -8, - 1,5, 26, 36}
I basically started with set A, then tacked on the stuff in set B shown in bold.
From here, we toss out the duplicate item 26 and we can optionally sort the set
A U B = {-10, -8, -1, 5, 8, 12, 26, 29, 36}
We see that the number 18 is not in this final set, which is why choice A is the answer.
--------------------
Put another way: the number 18 is neither in set A nor set B, so it cannot be in set A U B.
Something like -10 is in set A, so it's going to be in set A U B as well. We can rule out choice B for this reason. Choices C and D follow a similar idea as choice B.
pls help, this is for khan acd
Answers
Answer: Carys earns $10 per hour and earn $1 in hour .
Step-by-step explanation:
Given: Carys calculates the total amount E, in dollars, that she earns for working h hours.
She use the equation to calculate the total amount .
Foe h=1,
hence, she earns $10 in one hour.
Therefore, Carys earns $10 per hour.
Let she earn $1 then put E=1 in the equation, we get
Hence, she earn $1 in hour .
-4 2/3 • 1 4/5
Help me with this
Answers
the answer is -42/5 :D
can't type because im lazy
A store buys 10 shirts at a whole sale price of $5 each. They want to mark up the price by 50%. How much do they sell each t-shirt for?
A.$55
B.$5.50
C.$100
D.$7.50
Answers
Answer:
d)
Step-by-step explanation:
100%=$5
200%=5x2=10
200-50=150%
150/200x10=7.50
Hope this helps! Thanks.
Rewrite the formula to solve for the positive value of r in terms of h and v
*click photo to see question*
Answers
Answer
[tex] | \sqrt \frac{3v}{\pi \: h} | = r[/tex]
The given formula for the volume of cone can be written as [tex]\sqrt{\frac{2V}{\pi h} }[/tex] in terms of V and h for r.
What is transposing a term in an expression or transpose method?To bring a term from one side of an equation to the other, with corresponding change in sign or by doing opposite operations is called transposing a term in an expression.
According to the given question.
We have a formula for the volume of cone
[tex]V = \frac{1}{2} \pi r^{2} h[/tex]
To solve the the above formula for r we use transpose method.
Therefore,
[tex]V = \frac{1}{2} \pi r^{2} h[/tex]
⇒ [tex]2V = \pi r^{2}h[/tex] (multiplying by 2 both the sides)
⇒ [tex]\frac{2V}{\pi h} =r^{2}[/tex] (dividing both the sides by πh)
⇒ [tex]r=\sqrt{\frac{2V}{\pi h} }[/tex]
Hence, the given formula for the volume of cone can be written as [tex]\sqrt{\frac{2V}{\pi h} }[/tex] in terms of V and h for r.
Find out more information about transpose method here:
https://brainly.com/question/2263930
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About how many years did it take to pay off this account if...
Principal = $1582
Rate = 2.5%
Interest = $79.10
Answer:
years
Answers
Answer:
2 years
Step-by-step explanation:
Simple Interest=P×r×n
where:
P=Principal amount
r=Annual interest rate
n=Term of loan, in years
so with the givens, 79.10=1582*0.025*x
79.10/(1582*0.025)=x
x=2 years
please do number 4 !!! Giving Brainlist
Answers
you just find the spot that point is at!
Answer:
(4,3)
Step-by-step explanation:
Which of these represent the statement, "36 is 4 times as many as 9"?
Answers
Answer:
36=4*9
Step-by-step explanation:
5.2500000000 -2 1/67
Answers
Answer:
3.23507462687
Step-by-step explanation:
The length of a rectangle is 7 feet less than four times with width. The Perimeter of the
rectangle is 146 feet. Find the length and width of the rectangle. ( P = 2L +2W)
Answers
Answer:
Step-by-step explanation:
p = 2L+ 2W
length
(7-4)
3 feet
p = 2L+ 2W
146 = 2*3 + 2* w
146 = 6 + 2w
146-6 = 6-6 +2w
140 = 0+ 2w
140 = 2w
70 feet = w
width is 70 feet
p= 2L+2W
146 = 2*a +2* 70
146 = 2a + 140
146-140 = 2a + 140-140
6 = 2a
3 feet = a
length is 3 feet
width is 70 feet.
The owner of a large restaurant is considering a new “no tipping” policy and wants to survey a sample of employees. The policy would add 20% to the cost of food and beverages and the additional revenue would be distributed equally among servers and kitchen staff.
Answers
A) The strata to be used in this survey by the employer is; Type of Staff
B) Stratified Random Sampling will be preferred because the opinions of the staffs on the tipping policy may be the same within each type but differ across the different types of staffs.
A stratified random sampling is a type of sampling that divides a population into groups known as strata.Now, from the question, we see that after adding a 20% to the cost of food and beverages, that the additional revenue will be distributed equally among the kitchen and server staffs.
This means the strata here will be the type of staff because the opinions of the staffs on the tipping policy may be the within each type but differ across both types of staffs.
Read more at; https://brainly.com/question/1954758
Write 1.6 x 10 in standard form.
Answers
Answer:
[tex]1.6 \times 10 = 16 \\ [/tex]
To multiply a decimal by 10, move the decimal point in the multiplicant by one place to the right. Here we multiplied the number 1.6 by 10 so we move 1 place to the right.
To multiply a decimal by 100, move the decimal point in the multiplicant by two places to the right.
PLEASE HELP!!!!!
will mark brainliest!!!!!
Answers
Answer:
(-9,-6) ,(-3,0),(-2,1),(4,7)(6,9)
Answer:
x = -9 —> f(x) = – 6
x = -3 —> f(x) = 0
x = -2 —> f(x) = 1
x = 4 —> f(x) = 7
x = 6 —> f(x) = 9
Step-by-step explanation:
x = -9 —> f(x)= x+3 —> f(-9)= -9+3 = -6 —> f(x) = – 6
x = -3 —> f(x)= x+3 —> f(-3)= -3+3 = 0 —> f(x) = 0
x = -2 —> f(x)= x+3 —> f(-2)= -2+3 = 1 —> f(x) = 1
x = 4 —> f(x)= x+3 —> f(4)= 4+3 = 7 —> f(x) = 7
x = 6 —> f(x)= x+3 —> f(6)= 6+3 = 9 —> f(x) = 9
I hope I helped you^_^
In the year 2008, a person bought a new car for $26500. For each consecutive year
after that, the value of the car depreciated by 12%. How much would the car be worth
in the year 2010, to the nearest hundred dollars?
Answers
Answer:
$20500
Step-by-step explanation:
26500-(.12*26500)=23320 For 1 year
23320-(.12*23320)=$20521.60 For 2 years
PLS HELP ME UNDERSTAND THIS quUESTION!!
Answers
Answer:
-2 11/35
GOOD LUCK!!
In a triple batch of mix there are 6 teaspoons garlic and 15 teaspoons of salt how much salt is used with 8 teaspoons of garlic
Answers
Answer:
20
Step-by-step explanation:
6:15
2:5
*4
8:20
"Sierra has recipe she wants to make. She has to use eggs and sticks of butter. The ratio for these ingredients is 12 to 4 batches. What will the equivalent ratio be if she wants to make 8 batches"
"What is she wants to make 2 batches"
please help me get my grade up by answering this question I'll mark brainliest whoever answers first!<3
Answers
Answer:
24:8
Step-by-step explanation:
Given the following data;
Batch = eggs + sticks of butter
4 batches = 12:4
8 batches = 2 * 4 batches
Therefore, 8 batches = 2*(12:4)
8 batches = 24:8
Hence, the equivalent ratio Sierra would use if she wants to make 8 batches is 24 eggs to 8 sticks of butter.
Question 8 of 10
Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark ( as the fraction bar if necessary.
Answers
Answer:
2/4 or 1/2
Hope this helps!
The slope of the line that passes through (-2, -3) and (2, -1) will be 1/2.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
From the graph, the points are (-2, -3) and (2, -1). Then the slope of the line is calculated as,
m = (- 3 + 1) / (-2 - 2)
m = 2/4
m = 1/2
The slope of the line that passes through (-2, -3) and (2, -1) will be 1/2.
More about the slope link is given below.
https://brainly.com/question/3605446
#SPJ7
Help please (I have to write something so that I can post a question) .
Answers
Step-by-step explanation:
answers: -9
the ground
^^^^^^^^^^^
According to a survey, 59% of parents say their teens are addicted to using their cell phones. Write this percent as a ratio and do not simplify.
Answers
Answer:
1/10
Step-by-step explanation:
show your work” below and solve the given equation for x showing all your steps.
3.5(6 – x) + 14 = 7 – 1.5(5x + 16)
please make the steps as clear as you can for brainliest!
Answers
Answer:
x=-13
Step-by-step explanation:
21-3.5x+14=7-7.5x-24
21+14-3.5x=7-24-7.5x
35-3.5x=-17-7.5x
35+17=3.5x-7.5x
52=-4x
-4. -4
x=-13
Help me with this lol
Answers
Answer:
here are answers of 21 22,23,24
Step-by-step explanation:
11 ,21,15,9
1/16 1/14 1/2 1/6 1/50 1/30 1/8 1/40 1/20 1/5 1/100 1/625 1/25 1/45 1/125 1/12 1/32 1/7 1/28 1/24 1/64 1/11 1/4 1/21
Determine which fractions in the list can be written as terminating decimals.
List these fractions in order from greatest to least.
Answers
Answer:None
Step-by-step explanation:
Excel tells me that all of the numbers have terminating decimals. One might ask for a definition of what is considered terminating. Is 1/14=
0.0714285714285714000000000 going too many places before concluding it is not terminating?
X 1/X
16 0.0625000000000000000000000
14 0.0714285714285714000000000
2 0.5000000000000000000000000
6 0.1666666666666670000000000
50 0.0200000000000000000000000
30 0.0333333333333333000000000
8 0.1250000000000000000000000
40 0.0250000000000000000000000
20 0.0500000000000000000000000
5 0.2000000000000000000000000
100 0.0100000000000000000000000
625 0.0016000000000000000000000
25 0.0400000000000000000000000
45 0.0222222222222222000000000
125 0.0080000000000000000000000
12 0.0833333333333333000000000
32 0.0312500000000000000000000
7 0.1428571428571430000000000
28 0.0357142857142857000000000
24 0.0416666666666667000000000
64 0.0156250000000000000000000
11 0.0909090909090909000000000
4 0.2500000000000000000000000
21 0.0476190476190476000000000
Which rule explains why these triangles are congruent?
ASA
AAS
SSS
SAS
These triangles cannot be proven congruent.
Answers
Answer:
ASA .................explains these 2 triangles are congruent to each other.
Angle UST=Angle SUV{given in the figure}
side SU= side SU{common side}
angle TUS= Angle USV{given in the figure}
A group of elderly citizens turn it off but for $160. Unfortunately, eight of them fell ill and had to miss the trip. As a consequence the other citizens had to pay an extra one dollars each. How many elderly citizens went on the trip?
Answers
Each minute there is one diamond ring sold on website.find the number of diamond rings sold in 60 days
Answers
Answer:
there are 60 rings sold
Step-by-step explanation:
becuse 1x60 is 60
What is the slope-intercept form of the following equation?
2x+2y=20
Question 2 options:
y= x+10
2y= -2x+20
y= -x-10
y= -x+10
Answers
Answer:
[tex]y=-x+10[/tex]
Step-by-step explanation:
First we must know the format of slope-intercept form!
This is: [tex]y=mx+b[/tex] (where "m" is the slope and b is the y-intercept)
Given this equation: [tex]2x+2y=20[/tex] we must convert this into the format of slope-intercept form.
First, we should move the "2x" to the other side of the equation, we do this by subtracting -2x from 2x and proceed to move it to the other side.
This would be result in: [tex]2y=-2x+20[/tex]
Next, we need to isolate the "y" variable by dividing the 2 off of it.
What you do to one side you do to the other!
-2 / 2 is -1 so this will just be "-x"
20 / 2 is 10
Therefore, our resulting equation will be: [tex]y = -x+10[/tex]
I hope this helped! Feel free to ask questions if you feel the need!
Brody's fishing cooler is shaped like a rectangular prism. The inside of the cooler is 10 inches wide, 18 inches long, and 6 inches tall. What is the volume of the cooler?