Solve the Anti derivative.
Answer:
[tex]\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C[/tex]
General Formulas and Concepts:
Algebra I
FactoringCalculus
Antiderivatives - integrals/Integration
Integration Constant C
U-Substitution
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Trig Integration: [tex]\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integral] Factor fraction denominator: [tex]\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx[/tex][Integral] Integration Property - Multiplied Constant: [tex]\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx[/tex]Step 3: Identify Variables
Set up u-substitution for the arctan trig integration.
[tex]\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx[/tex]
Step 4: Integrate Pt. 2
[Integral] Substitute u-du: [tex]\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du[/tex][Integral] Trig Integration: [tex]\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C[/tex][Integral] Simplify: [tex]\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C[/tex][integral] Multiply: [tex]\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C[/tex][Integral] Back-Substitute: [tex]\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C[/tex]Topic: AP Calculus AB
Unit: Integrals - Arctrig
Book: College Calculus 10e
What’s the total area of a rectangular prism with a height of 17 feet, a width of 12feet, and a thickness of 10feet?
Answer:
988 feet________________
Complete each equation so that it is true for no values of x.
x - 2 = -(__- x)
nswer:
(x +5)^2 = -2
Step-by-step explanation: w t f
We can subtract the constant to get ...
x^2 +10x = -27
Then add the square of half the x-coefficient:
x^2 +10x +5^2 = -27 +5^2
(x +5)^2 = -2 . . . . . . write as a square
PLS I NEED HELP! If y varies direct to x and y = 12 and x = 3, then what does x equal when y is 80?
Answer:
20
Step-by-step explanation:
12 divided by 3 = 4
therefore 80 divided 4 is 20
Answer:
x=10
Step-by-step explanation:
If I have 8 cans of soup and I gave 1/2 to sue and 1/4 to mark how many do I have left
Answer:
6 1/2 (a.k.a 6.5)
1/4 = 2/2 + 1/2 = 3/2 = 1 1/2
8 - 1 1/2 = 6 1/2
The product of-9/4 with another number is 7/3.what is the other number
Answer:
Step-by-step explanation:
(-9/4)x = 7/3
x = (7/3) · (-4/9) = -28/27
URGENT URGENT!!!!! PLEASE HELP
Answer:
2x+3y=T
Step-by-step explanation:
t= total
the total number of points depending on how many 3 points are shot makes up the score.
The tape diagram a way to model 5/8x11
Answer:
55/8
Step-by-step explanation:
here u gooo good luck
Sam puts $500 in the bank and does not put any more money in or take any out for elght years. He receives 6% Interest
yearly, compounded semi-annually. How much money will be in the account after elght years?
O $793.44
$796.92
O $800.52
O $802.36
Answer:
$793.44
Step-by-step explanation:
Factor -7x^3+21x^2+3x-9 by grouping what is the resulting expression
Answer:
Step-by-step explanation:
You want to group things that can actually be factored. You dont want to group -7x^3 and -9 because that would just be a mess and wouldnt give you the right answer.
[tex](-7x^3+21x^2)+(3x-9)\\-7x^2(x-3)+3(x-3)\\(-7x^2+3)(x-3)[/tex]
X + Y = 2. y =2x + 5 write the solution as a ordered pair
Answer:
(-1, -2)
x=-1
y=-2
Step-by-step explanation:
x+y=2
y=2x
Knowing this information, we can substitute y for 2x+5 in the first equation.
x+2x+5=2
3x+5=2
3x=-3
x=-1
Now, plug x into the second equation.
y=2(-1)
y=-2
1.)
Line up the numbers in the table.
Then order the numbers from least to
greatest
A= 4.28
B = 4.03
C = 4.4
D= 4.74
Write the letters in order to make the sentence true.
Answer:
the answer is c=4.4
Step-by-step explanation:
use books
Which expression is equivalent to 4(3x + 2y) + 5(2x – 4y)?
A 222 - 12y
B 14.2 - 9y C 22x – 2y D 172 4y
Answer:
22x-12y
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THANK YOU.
Solve for the missing side of the triangle
sin53=x/15
0.798×15=x
x=11.98is your answer
Does the following table represent an exponential decay or growth function?
Answer:
It shows the growth function I think because the are increasing
Step-by-step explanation:
It is not a exatly
Find all real square roots of -36
Answer:
The answer is ±6.
Step-by-step explanation:
The positive and negative square roots of 36 are 6. and −6. Both 6, and −6 are square roots of 36 since they both give 36 when squared:...
6^2=6×6=36
(−6)2=(−6)×(−6)=36
All positive real numbers have a positive and negative real square root which are additive inverses of one another.
The principal square root is the positive one and is the one meant when we use the √... symbol. So:...
√36=6
If we want to refer to the negative square root, then just put a minus sign in front:...
−√36=−6
The two square roots of -36 are 6i and -6i, where i is the imaginary unit.
What is Number system?A number system is defined as a system of writing to express numbers.
Since the square of any real number is always non-negative, there is no real number whose square is equal to a negative number.
Therefore, the expression √(-36) has no real square roots.
However, we can express the square root of -36 using imaginary numbers.
By definition, the imaginary unit "i" is equal to the square root of -1. Using this definition, we can rewrite √(-36) as:
√(-36) = √(36) × √(-1) = 6i
Therefore, the two square roots of -36 are 6i and -6i, where i is the imaginary unit.
To learn more on Number system click:
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A set of 6 number cards contains the numbers 2,5,7,8,9, and 11. Which ratio of odd number cards to total cards in the set?
Bobby decides to sell lemonade on a hot summer day. If Bobby sells 20 glasses of lemonade for $2.00 per cup, and his average total cost is $1.70, what are Bobby's economic profits for the day?
Bobby's economic profit for the day is $6.
Bobby's economic profit is total revenue less total cost.
Economic profit = total revenue - total cost
Total revenue = price x glasses of lemonade sold
20 x $2 = $40
Total cost = average total cost x glasses of lemonade sold
$1.70 x 20 = $34
Economic profit = $40 - $34 = $6.
A similar question was answered here: https://brainly.com/question/14918805?referrer=searchResults
What’s 720 x 0.1? Please answer
Answer:
72
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
720 x 0.1 would be 72 because the 0 doesnt show when you times it. your welcome lol.
What decimal does the model represent?
The model below is shaded to represent 2
A 25.6
2.056
2.56
0.256
Answer:
2.56
Step-by-step explanation:
7. If AJKL - ANMP, find the value of x.
P x +5 N
49
14
M
J 9x + 1 L
Answer:
Since they are similar their sides are corresponding,
9x + 1 / x + 5 = 49 / 14
or, 14 ( 9x + 1 ) = 49 ( x + 5 ) { cross multiply}
or, 126x + 14 = 49x + 245
or, 77x = 231
or, x = 231/77
or, x = 3
Hope it helped
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Mr. Barrientos can run 2 ½ miles in 2 hours. How many miles can he run in 6 hours? Show your work.
Answer:
7 1/2 miles
Step-by-step explanation:
A container has 360 gallons ; daniel took 1/3 of water to give to the animals in the ranch; how many gallons of water are left? I NEED IT TO BE EXPLAINED AND I WILL MAKE YOU THE BRAINLIEST
Answer: 240 gallons
Step-by-step explanation:
From the question, we are informed that the container has 360 gallons and that Daniel took 1/3 of water to give to the animals in the ranch. Therefore, the amount of water that Daniel took will be:
= 1/3 × 360
= 120 gallons
Since we have 360 gallons at the beginning and Daniel has taken 120 gallons, the amount of gallons that'll be left will be:
= 360 - 120
= 240 gallons
What is the absolute value of |-2+4|
Answer:
2
Step-by-step explanation:
The absolute value of a number is its distance from zero, since distance is always positive, the absolute value is always positive.
| -2 + 4 |
Simplify,
|2|
= 2
If our school has about 300 seventh graders, about how many would be expect to watch 4 to
8 hours of television weekly?
A. 55
B. 116
C. 138
D. 165
Answer:
55
Step-by-step explanation:
Casper write the algebraic expression 5b + 3.79. I represents the total cost, in dollars, of buying 5 bagels and a container of cream cheese. Identify any variables, coefficients, and termsin the expression.
Answer:
yes
Step-by-step explanation:
In a shop for every pant there are 3 shirts and for every 9 shirts there are 27 pairs of shoes. Express the ratio of pants to shirts to shoes in the shop.
Answer:
1 : 3 : 9
Step-by-step explanation:
For every Pant = 3 shirts
If
Pant = x ; shirt = 3x
For :
Every 9 shirts = 27 pairs of shoes
Simplifying further :
1 shirt = 3 pairs of shoes
3 shirts = 3 * 3 = 9 pairs of shoes
Expressing as ratio:
1 Pant = 3 shirts = 9 pairs of shoes
1 : 3 : 9
Hair colors are an example of which type of data?
Answer:
Nominal data are used to label variables without any quantitative value. Common examples include male/female (albeit somewhat outdated), hair color, nationalities, names of people, and so on. In plain English: basically, they're labels (and nominal comes from "name" to help you remember). You have brown hair (or brown eyes).
b.) -1, 6, -36, ....
digits to write the value of the 5 in this number.587,096
Answer: what does the question even mean
Step-by-step explanation: