Answer:
[tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsDefinite/Indefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx[/tex]
Step 2: Integrate Pt. 1
Set variables for u-substitution.
Set u: [tex]\displaystyle u = x^2 + 10x + 26[/tex][u] Differentiate [Addition/Subtraction, Basic Power Rule]: [tex]\displaystyle du = 2x + 10 \ dx[/tex]Step 3: Integrate Pt. 2
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{2(x + 5)}{x^2 + 10x + 26}} \, dx[/tex][Integrand] Expand: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{2x + 10}{x^2 + 10x + 26}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{1}{u}} \, du[/tex][Integral] Logarithmic Integration: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}ln|u| + C[/tex]Back-Substitute: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}ln|x^2 + 10x + 26| + C[/tex]Simplify: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Caroline spent $41.00 on groceries after using coupons and store discounts. Without the coupons and store discounts, the groceries would have cost $50.00. What is the total discount Caroline received at the grocery store? A. 22% B. 6% C. 9% D. 18% HELP PLEASE I DONT WANNA FAIL MY QUIZ :(=
Answer:
18% trust me i got you bro
Step-by-step explanation:
Find the missing exponent.
Answer:
-b^14 i think this is te answer but i am also consused
What are two things we look for in an equation that can tell us what's NOT in it's domain?
Answer:
1. Value for which denominator is 0.
2. Value for which we get negative sing inside the root or log.
Step-by-step explanation:
Domain is the set of input values.
If a function is not defined for a set of value then they are NOT in it's domain.
Two we look for in an equation that can tell us what's NOT in it's domain :
1. Value for which denominator is 0.
2. Value for which radicand is negative because negative values inside the square roots are not real. Value for which log values are negative because log is not defined for negative values.
Can someone tell me if I’m right?
Answer:
yesssssssssssssssssssss
The letter that form the word MISSISSIPPI are placed in a bowl. What are the odds of choosing a "P"
Answer:
11
Step-by-step explanation:
the answer is 11 because there are 11 words and 2 ps
100+5987+7899=please help me please ✌️
Answer:
13986
Step-by-step explanation:
hmmm... have you tried using a calculator
Answer:
The answer is 13986
Step-by-step explanation:Because 100+5987 is
5997 then 5997+7899 is
13986.
HOPE IT HELPS!
is 10/18 in decimal form a terminates or repeating decimal
Hey there! I'm happy to help!
To write a fraction as a decimal, you simply divide the numerator by the denominator.
10÷18=0.55555.... (the 5s never end!)
We see that the 5s repeat forever. This means that this is a repeating decimal.
Have a wonderful day! :D
24,40 find the GCF i want the gcf of 24
Answer:
The GFC would be 8
Step-by-step explanation:
12 - 1,2,3,4,5,6,7,8,12,24
40 - 1,2,4,5,8,10,20,40
mZDEF = 5x – 3 and mZFEG=2x+15
Answer:
x = 24
Step-by-step explanation:
Step 1:
5x -3 + 2x + 15 = 180
Step 2:
7x + 12 = 180
Step 3:
7x = 168
Answer:
x = 24
Hope This Helps :)
What is the square root of 45 rounded to the nearest hundredth
Answer:
your answer is fifteen
is the product of which of the following two radical numbers?
Answer:
The third line
Step-by-step explanation:
let's see all choices by solving them
1) The first one
[tex] \sqrt[ 3]{ - 5} \sqrt[3]{3} = \sqrt[3]{ - 15} (negative \: times \: positive \: is \: negative)[/tex]
2) The second one
[tex] \sqrt[3]{5} \sqrt[3]{ - 3} = \sqrt[3]{ - 15} (positive \: times \: negative \: is \: negative)[/tex]
3) The third one
[tex] \sqrt[3]{ - 5} \sqrt[3]{ - 3} = \sqrt[3]{15} (negative \: times \: negative \: is \: positive) \: this \: choice \: is \: the \: answer \: because \: the \: question \: asks \: positive \: radical \: number[/tex]
4) The fourth one
[tex] \sqrt[3]{ - 15} \sqrt[3]{1} = \sqrt[3]{ - 15} (any \: number \: multiply \: by \: one \: is \: it \: self [/tex]
hope u like it ❤️❤️❤️
For any question comment me
Answer:
Step-by-step explanation:
this mean answer is b
(-2ab^-5)(4a^-2b)^-2
Answer:
-a^5/(8b^7)
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^-b = 1/a^b
__
[tex](-2ab^{-5})(4a^{-2}b)^{-2}=(-2ab^{-5})(4^{-2}a^{-2(-2)}b^{-2})\\\\=\dfrac{-2}{16}a^{1+4}b^{-5-2}=\boxed{-\dfrac{a^5}{8b^7}}[/tex]
simplify the equation 3(u-6)-7u
Answer:
-4u-18
Step-by-step explanation:
which graph shows the function f(x)=x with an input of (f(x-3)
please help me asap!!
Answer:
Step-by-step explanation:
B
The correct graph of the function is shown in option (B).
What is graph?A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.
The given function is,
f(x) = y = x (1)
To find the graph of f(x -3),
Substitute x = x- 3 in equation (1),
y = x- 3
The slope of the graph is 1,
And the y intercept at x = 0,
y = -3
So the graph of the function y = x - 3 can be plotted as,
Hence option (B) is correct option.
To know more about Graph on:
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On a map, 2.5 inches represents 300 miles. How many miles are represented by 6 inches?
А .05 miles
00
.40 miles
С
600 miles
D
720 miles
Answer:
D. 720 miles
Step-by-step explanation:
First, we know that 2.5 inches represents 300 miles. This means that we have to find out how much 1 inch represents in miles. So, we take 300/2.5. This results in 120. So, 1 inch represents 120 miles. Then, we take 6*120 which gets us 720 miles.
A map of 720 miles represented by 6 inches.
It is given that 2.5 inches represent 300 miles.
It is required to find the miles represented by 6 inches.
How many miles are represented by 6 inches?First we have to find how many miles we get in one inch. Then we find in how many miles does 6 inches have.
In 2.5 inches, the map represents 300 miles.
In 1 inch, a map represents 300/2.5 miles which are equal to 120 miles.
So, in 6 inches, a map represents (120×6) miles which are equal to 720 miles.
Thus in 6 inches, a map represents (120×6) miles which are equal to 720 miles.
Learn more about inches and miles it here:
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I NEED HELP PLEASE HELP ME.
Answer:
(a) 8
(b) 6
:>
A sock drawer contains 5 different colors of socks. It has 20 white, 10 black, 10 gray, 6 red, and 4 purple. If you reach into the drawer and choose a sock randomly, what is the probability you will get a black sock? P (black) = StartFraction Number of favorable outcomes over Total number of outcomes EndFraction P(black) =
Answer:
1/5
Step-by-step explanation:
Total number of socks = 50( 20+10+10+6+4)
Number of black socks = 10
Therefore, 10/50= 1/5
the probability of getting a black sock is 1/5.
Find the simplified product:[tex]\sqrt{2x^{3} }-\sqrt{18x^{5} }[/tex]
Correct Question: Find the simplified product: [tex] \sqrt{2x^3}*\sqrt{18x^5} [/tex]
Answer:
[tex] 6x^4 [/tex]
Step-by-step explanation:
Based on the rules of radicals, since [tex] \sqrt{2x^3} [/tex] and [tex] \sqrt{18x^5} [/tex] has the same index (square root), therefore:
[tex] \sqrt{2x^3}*\sqrt{18x^5} = \sqrt{2x^3 * 18x^5} [/tex]
To simplify this, multiply their bases together, and add their exponents.
[tex] = \sqrt{2*18x^{3+5} [/tex]
[tex] = \sqrt{36x^{8} [/tex]
Simplify further
[tex] = \sqrt{36}*\sqrt{x^8} [/tex]
[tex] = \sqrt{6*6}*\sqrt{x^4*x^4} [/tex]
[tex] = 6x^4 [/tex]
Answers For Entire Assignment:
--> Page 1: D, C
Page 2: B, C
Page 3: D
Page 4: B
Page 5: A, C
Page 6: B,C
Trust The Milk. Get that 100.
1. The average distance from the Earth to the moon is about 384,000 kilometers. What is this number written in scientific notation?
Answer:
3.84 x 10^5
Step-by-step explanation:
Answer:
3.84x10^5
Step-by-step explanation:
count how many times the decimal was moved to the right and that is the exponent
What is the answer to 1/7 x 8
Answer:
8/7
Step-by-step explanation:
What does the mean and median mean of numbers
Answer:
Mean is all numbers added up divided by the amount of numbers in the set.
Median is the number that occurs the most in a set.
Step-by-step explanation:
A high school basketball team won 36% of the games that it played last season. The team won exactly 9 games last season. What is the total number of games that the team played?
Answer: REMEMBER TO RATE 5 STARS AND GIVE ME A HEART, THANKS!!!
The High Shcool Basketball team played a total of 25 games.
Step-by-step explanation:
You take the 9 from the games they won last season and divide it by .36 and that will give you the answer of 25. So 25 is the total games the "High School Basketball Team" won. If you want to double check your answer you can take the answer of 25 and times it by .36 which will equal 9.
Write 80% as a fraction in Simplest form
Answer:
Step-by-step explanation:
80/100 = 8/10= 4/5
The perimeter of a triangle is 105 cm. If each of the two legs is exactly twice the length of the
base, how long is each leg?
Greetings from Brasil...
According to the question of the statement, we can conclude that
PQ = 2B
QR = 2B
PR = base = B
Perimeter = P = 105
P = PQ + QR + PR
105 = 2B + 2B + B
B = 21
PQ = 2B = 42QR = 2B = 423^2 x^4 y^6 Which number is a base in the following expression?
Answer:
I believe it is 3
Step-by-step explanation:
That is the only number variable while the others are letter variables
BRAINLIEST ASAP! PLEASE HELP ME :)
I need help with Part 2 of the question.
Steps to solve:
6a + 12 = 3(2a + 1) + 5
~Distribute right sides
6a + 12 = 6a + 3 + 5
~Simplify
6a + 12 = 6a + 8
~Subtract 12 to both sides
6a = 6a - 4
~Subtract 6a to both sides
0 = 4
Therefore, there are no solutions.
Best of Luck!
PLease school is almost over HELP 30x+60x=?
Answer:
[tex]90x[/tex]
Step-by-step explanation:
[tex]30x+60x=?[/tex]
If you want to solve this easily, you can just remove x and add 30x + 60x.
[tex]30+60[/tex]
We know that 30 + 60 is 90. So we will add x to 90.
[tex]90x[/tex]
Now you have your answer!
Hope this helps!
Answer:
90x
Step-by-step explanation:
To solve, add 30+60.
30 + 60 is equal to 90.
Add x and it will be 90x.
That is your answer!
Hope I helped!
amy is scuba diving at a position 55.15 feet below sea level. she ascends 1.5 feet each minute for 15 minutes. what is amys position compared to the sea level after 15 minutes
Answer:
32.65 feet below sea level
Step-by-step explanation:
1.5x15=22.5
55.15-22.5=32.65
hope that helps
ANSWER AS SOON AS POSSIBLE PLEASE! Jessica has $19. She buys 4 apples for x dollars each. Levi has $30 and buys 7 apples for x dollars each. Write an expression of how much money altogether they would have left?
This is the same as -11x+49
=========================================================
Explanation:
1 apple = x dollars
4 apples = 4x dollars, after multiplying both sides by 4
If Jessica buys 4 apples, then she spends 4x dollars.
Jessica has $19, so she'll have 19-4x dollars leftover after buying those four apples.
Similarly, Levi will have 30-7x dollars leftover when buying 7 apples for x dollars each.
Add up the leftover amounts to get...
(jessica's leftovers) + (Levi's leftovers)
(19-4x)+(30-7x)
19-4x+30-7x
(19+30)+(-4x-7x)
49-11x
This is the same as -11x+49 since you can think of 49-11x as 49+(-11x), and we can add two terms in any order we want.
---------------------------
An alternative viewpoint
Pool up Jessica's and Levi's amount they start with to get 19+30 = 49 dollars
Jessica buys 4 apples and Levi buys 7 apples. In total, this is 4+7 = 11 apples. At x dollars an apple, they spend 11x dollars. So they'll have 49-11x dollars leftover after buying those 11 apples.
If (42)p = 414, what is the value of p? 7 8 12 16
Answer:
the correct answer is not there
Step-by-step explanation:
I'm not sure if "7, 8, 12, and 16" were answer choices but none of those are correct
Step-by-step explanation:
to find the value of p you'd need to divide 441 by 42 and the answer is 9.9