Answer:
[tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = 3x^\bigg{\frac{4}{3}} - \frac{3x^\bigg{\frac{2}{3}}}{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
IntegralsIndefinite 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]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = \int {4x^\bigg{\frac{1}{3}}} \, dx - \int {x^\bigg{\frac{-1}{3}}} \, dx[/tex][1st Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = 4\int {x^\bigg{\frac{1}{3}}} \, dx - \int {x^\bigg{\frac{-1}{3}}} \, dx[/tex][Integrals] Reverse Power Rule: [tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = 4 \bigg( \frac{3x^\bigg{\frac{4}{3}}}{4} \bigg) - \frac{3x^\bigg{\frac{2}{3}}}{2} + C[/tex]Simplify: [tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = 3x^\bigg{\frac{4}{3}} - \frac{3x^\bigg{\frac{2}{3}}}{2} + C[/tex]Step 3: Check
Differentiate the answer.
Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx} \bigg[ 3x^\bigg{\frac{4}{3}} \bigg] - \frac{d}{dx} \bigg[ \frac{3x^\bigg{\frac{2}{3}}}{2} \bigg] + \frac{d}{dx} \bigg[ C \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle 3\frac{d}{dx} \bigg[ x^\bigg{\frac{4}{3}} \bigg] - \frac{3}{2}\frac{d}{dx} \bigg[ x^\bigg{\frac{2}{3}} \bigg] + \frac{d}{dx} \bigg[ C \bigg][/tex]Basic Power Rule: [tex]\displaystyle 3 \bigg( \frac{4}{3}x^\bigg{\frac{1}{3}} \bigg) - \frac{3}{2} \bigg( \frac{2}{3}x^\bigg{\frac{-1}{3}} \bigg)[/tex]Simplify: [tex]\displaystyle 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}}[/tex]∴ we have found the answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
The set of all numbers on a number line are called?
Answer:
This second number line is called an integer number line, since integers are the set of numbers including all whole numbers and their negative opposites. Two opposite numbers are the same distance from zero on the number line, but on opposite sides. For example, 3 and -3 are opposites.
Step-by-step explanation:
I hope it's help u
Grandma Marlene and Grandpa Gary are putting holiday lights on the gutters of their house. Grandma Marlene leans a 16-foot ladder up against the house, which makes the base of the ladder 9 feet from the house. How far up the house is the ladder?
Answer: 48
Step-by-step explanation: if i did the math correct 1/3 times the base (9) times 16 is 48. the formula is 1/3 x Bh
HELP MEEE
What is the probability of spinning a blue on
the above spinner and flipping heads?
.....................
Answer:
Final volume, V2 = 8.57 liters
Step-by-step explanation:
Given the following data;
Initial volume, V1 = 7.7 liters
Initial pressure, P1 = 6.9 atm
Final pressure, P2 = 6.2 atm
To find the new volume V2, we would use Boyles' law.
Boyles states that when the temperature of an ideal gas is kept constant, the pressure of the gas is inversely proportional to the volume occupied by the gas.
Mathematically, Boyles law is given by;
[tex] PV = K[/tex]
[tex] P_{1}V_{1} = P_{2}V_{2} [/tex]
Substituting into the equation, we have;
[tex] 6.9 * 7.7 = 6.2*V_{2} [/tex]
[tex] 53.13 = 6.2V_{2} [/tex]
[tex] V_{2} = \frac {53.13}{6.2}[/tex]
[tex] V_{2} = 8.57 [/tex]
Final volume, V2 = 8.57 liters
Therefore, the new volume is 8.57 liters.
Answer:
just greeting so that the other one can get a brainliest (would be kind if the favor would be returned :D )
What is the equation of the curve that best fits the data? Round to the nearest hundredths, when appropriate. picture*
Answer:
.....
Step-by-step explanation:
Up and down
An expression is shown. Which one of the expressions below is equivalent?
Answer:
C
Step-by-step explanation:
Age of each person in Kidz Zone
6
5
4
2
1
20
25
0
0 5 10 15
Number of years
In which interval is the median age?
Choose 1 answer:
0-5
5 - 10
Answer:
10-15
Step-by-step explanation:
Median is the middle of the numbers (or in this case, number sets)
The middle number set is the third.
Thus, the interval would be 10-15.
Answer: 5-10
Step-by-step explanation:
the median for 11 data points would be the sixth data point which falls into the 5 to 10 years interval
Charles has 24 marbles. He has 6 more yellow marbles than blue marbles.
Which equation represents this situation?
Answer:
n+(n+6)=24
Step-by-step explanation:
we know that he has 24 in total so it has to equal 24
we also know that he has 6 more marbles meaning he has n number of yellow marbles plus 6 and that will give you the total of the blue marbles he also has n number of yellow marbles that he has to add to the number of blue marbles to get the total of 24
The question is in the picture (Alegbra 1)
Answer:
[tex]\frac{s}{s-4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{s^2+6s}{s^2+10s+24}[/tex] ÷ [tex]\frac{s-4}{s+4}[/tex] ( factor and simplify fraction on left )
= [tex]\frac{s(s+6)}{(s+4)(s+6)}[/tex] ÷ [tex]\frac{s-4}{s+4}[/tex] ← cancel (s + 6) on numerator/ denominator
Leave first fraction, change division to multiplication, turn second fraction upside down
= [tex]\frac{s}{s+4}[/tex] × [tex]\frac{s+4}{s-4}[/tex] ← cancel (x + 4) on numerator/ denominator
= [tex]\frac{s}{s-4}[/tex]
29x-7y=-17 solve for x
Answer:
[tex]x= -\frac{17}{29} +\frac{7y}{29}[/tex]
Step-by-step explanation:
[tex]29x-7y=-17[/tex]
[tex]x= -7y/29 + -17/29[/tex] Divide every number by x except
maths question is here
9+92*12312
Answer:
it would be 101 i believe
Answer:
1,132,713
Step-by-step explanation:
9+ 92 * 12312
= 9 + 1,132,704
= 1,132,713
The annual per capita consumption of bottled water was 32.6 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.6 and a standard deviation of 12 gallons. The probability that someone consumed more than 33 gallons of bottled water is?
Answer:
0.4867
Step-by-step explanation:
Given an approximately normal distribution:
Z = (x - mean) / standard deviation
Mean = 32.6 ; Standard deviation = 12
For :
P(x > 33)
Z = (33 - 32.6) / 12
Z = 0.4 / 12
Z = 0.0333
Hence, using the Z distribution table :
P(Z > 0.0333) = 1 - P(Z < 0.333)
P(Z > 0.0333) = 1 - 0.51328
P(Z > 0.0333) = 0.48672
The sum of a number and twenty-one is sixty-four.
What is the value of the number?
The number equals
Answer:
43
Step-by-step explanation:
64-21= 43 :))))) ez
Answer:
43
Step-by-step explanation:
I hope you pass your test!
EDG2021 <3
A jar contains 6 red marbles numbered 1 to 6 and 4 blue marbles numbered 1 through 4. A marble is drawn at random from the jar. Find the probability of the given event as a simplified fraction.
A. The marble is red
b. The marble is odd-numbered
c. The marble is red and odd-numbered
What is the median of the following numbers: 15, 51, 35, 25, 58, 33, 64, 43, 29, 14, 13, 11, 4, 10?
Answer:
(25+29)/2 = 27
Step-by-step explanation:
Answer:25+29=54
54/2=27
Step-by-step explanation:
4, 10, 11, 13, 14, 15, 25, 29, 33, 35, 43, 51, 58, 64
25+29=54
54/2=27
Answer: 27
An engine runs for 3.2 hours. How many seconds did it run?
Answer:
11520 seconds
Step-by-step explanation:
3.2 x 60= 192 minutes
192 x 60= 11520 seconds
You want to put a 2 inch thick layer of topsoil for a new 17 ft by 30 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order
Plz help me well mark brainliest if correct.......????
Answer:
D
Step-by-step explanation:
shows change over time
Identify the unlike terms in the expression:
3a + 11b + 30 + 4a + 3b
Answer: 7a+14b+30
How to: Combine like terms
Have a great day and stay safe ! sorry if im wrong
Evaluate the following
6!
Answer:
Mind showing a picture?
Thank you!
Part A: Students from 4 towns attend a conference. Each town is assigned a number from 1 to 4. Drag yes or no next to the first sentence.
Yes or No
A number is drawn and replaced 6 times. Is this a fair way to pick 6 members to give each town representation? __________
Part B: What is the probability that Town 1 will have at least 1 representative after 6 number draws, to the nearest percent?
probability = __________ %
Answer:
Part A - No
Part B - 100 %
Step-by-step explanation:
Part A.
This is because, a fair chance requires that each member has the same probability of being picked.
Since there are 4 towns, a fair chance would be 1/4.That is, 1 out of every town.
Part B
The probability of at least 1 representative after 6 number draws is P(at least 1) = 1 - P(none from Town 1)
P(none from town 1) = 0
P(at least 1) = 1 - P(none from Town 1)
P(at least 1) = 1 - 0 = 1
In percentage 1 × 100 % = 100 %
The number of residents in a city is 57,000 people. The population is increasing each
year by 1.2%. Write an equation to model this situation.
Please help If using the method of completing the square to solve the quadratic equation
22 - 142 – 40 = 0, which number would have to be added to "complete the
square"?
A and B are mutually exclusive events.
P(A) = 0.60 and P(B) = 0.30. What is P(A or B)?
A. 0.90
B. 0.15
C. 0.18
O D. 0.72
The value of P(A or B) if the probabilities are mutually exclusive is 0.9
Mutually exclusive eventsGiven the following probability values shown below;
P(A) = 0.60
P(B) = 0.30
If A and B are mutually exclusive, hence;
P(A or B) = P(A)+P(B)
P(A or B) = 0.6 + 0.3
P(A or B) = 0.9
Hence the value of P(A or B) if the probabilities are mutually exclusive is 0.9
Learn more on mutually exclusive events here: https://brainly.com/question/27588497
#SPJ1
tessa burned 357 calories in 42 minutes on the elliptical. ashley only spent 0 minutes on the elliptical and burned 267 calories. who burned calories at a faster rate
Answer:
ashley
Step-by-step explanation:
because she didnt spend any time
Find the measure of arc TV
What is the area of the following picture ( HELP PLEASE )
Answer:
area=l*b
10*8
80#
Step-by-step explanation:
hope you like it
Jerome solved the equation below using the steps shown. Step 1: 3x + 6 = 18 step 2: 3x = 12 step 3: x = 4 what operation did her perform to get from step 2 to step 3
Answer:
divided both sides of the equation by 3
Step-by-step explanation:
does 2, 5, and 7 make a right triangle
Answer: No, we don't have a right triangle
==========================================================
Explanation:
If a triangle with sides a,b,c makes the equation a^2+b^2 = c^2 true, where c is the longest side, then this triangle is a right triangle. This is the converse of the pythagorean theorem.
Here we have a = 2, b = 5 and c = 7.
So...
a^2+b^2 = c^2
2^2+5^2 = 7^2
4+25 = 49
29 = 49
The last equation is false, so the first equation is false for those a,b,c values. Therefore, we do not have a right triangle.
------------
In contrast, consider the classic 3-4-5 right triangle
a = 3, b = 4 and c = 5 would make a^2+b^2 = c^2 true because 3^2+4^2 = 5^2 is a true equation (both sides lead to 25).
what is the area of this figure
Answer:
A=162.56in^2
Step-by-step explanation:
make sure u separate the different shapes