We are integrating f(x) = 9cos(9x) + 3x²: [tex]\int\ {9cos(9x)+3x^{2} } \, dx[/tex]
a) Apply the sum rule
[tex]\int\9cos(9x)} \, dx +\int\ 3x^{2} } \, dx[/tex]
b) Calculate each antiderivative
First integral
[tex]\int\ {9cos(9x)} \, dx[/tex]
1. Take out the constant
[tex]9\int\ {cos(9x)} \, dx[/tex]
2. Apply u-substitution, where u is 9x
[tex]9\int\ {cos(u)\frac{1}{9} } du[/tex]
3. Take out the constant (again)
[tex]9*\frac{1}{9} \int{cos(u)} du[/tex]
4. Take the common integral of cos, which is sin
[tex]9*\frac{1}{9}sin(u)}[/tex]
5. Substitute the original function back in for u and simplify[tex]9*\frac{1}{9} sin(9x) = sin(9x)[/tex]
6. Always remember to add an arbitrary constant, C, at the end
[tex]sin(9x) + C[/tex]
Second integral
[tex]\int3x^{2} } \, dx[/tex]
1. Take out the constant
[tex]3\int{x^{2} } \, dx[/tex]
2. Apply the power rule, [tex]\int{x}^{a} \, dx =\frac{x^{a+1} }{a+1}[/tex], where a is your exponent
⇒ [tex]3*\frac{x^{2+1} }{2+1} = x^{3}[/tex]
3. Add the arbitrary constant
[tex]x^{3} + C[/tex]
c) Add the integrals
sin(9x) + C + x³ + C = sin(9x) + x³ + C
Notice the two arbitrary constants. Since we do not know what either constant is, we can combine them into one arbitrary constant.
Answer:F(x) = sin(9x) + x³ + C
Answer:
[tex]g(x)=sin(9x)+x^3+C[/tex], choose a constant that is any number you want for C
Step-by-step explanation:
So we have a function, [tex]f(x)=9cos(9x)+3x^2[/tex] An antiderivative is also called an integral, so to find the antiderivative of f(x) we find the integralso we will say g(x) is equal to the integral (antiderivative) of f(x)Then [tex]g(x)=\int\ {(9cos(9x)+3x^{2}) } \, dx[/tex] Which can be written as [tex]g(x)=\int\ {9cos(9x)} \, dx +\int\ {3x^{2} } \, dx[/tex] So let's do the first part integral [tex]\int\ {9cos(9x)} \, dx[/tex] which can be written as [tex]9*\int\ {cos(9x)} \, dx[/tex] Then we use u substitution integration, and [tex]u=9x,\frac{du}{dx} =9,dx=\frac{1}{9}*du[/tex] so we replace dx and 9x so that [tex]9*\int\ {cos(9x)} \, dx =9*\int\ {\frac{1}{9}cos(u) } \, du=9*\frac{1}{9}*\int\ {cos(u)} \, du[/tex] Leaving [tex]\int\ {cos(u)} \, du=sin(u)+C[/tex] then replace u with 9x, so [tex]sin(9x)+C[/tex]Now for the second part integration[tex]\int\ {3x^2} \, dx =3 *\int\ {x^2} \, dx=3*\frac{x^{2+1}}{2+1}+C=3*\frac{x^{3}}{3}+C=x^3+C[/tex] so [tex]g(x)=sin(9x)+C+x^3+C=sin(9x)+x^3+C[/tex] so [tex]g(x)=sin(9x)+x^3+C[/tex] is a general solution antiderivative to f(x)Drag and drop each square root value to its approximate location on the number line. Not all pieces will be used
Answer:
Its a kanono on this one hope this helps
Step-by-step explanation:
i wonie
Three students have started a fence-painting business. Working together,
Pragnesh and Qazi can paint the fence in 2 hours. Similarly, Pragnesh and Ronghui can paint the
fence in 3 hours when they work together. Finally, when Qazi and Ronghui work together, they can
paint the fence in 4 hours. How long would it take if all three students worked together to paint the
Answer:
4 1/2 hours
Step-by-step explanation:
Pragnesh = 30 minutes
Qazi = 1 1/2 hours
Ronghui = 2 1/2 hours
add them and that gets you 4 1/2 hours. You can also check this yourself by putting this in the number problem. :)
Determine the x- and y- intercepts for the graph defined by the given equation.
y = x + 8
a. x-intercept is (0,8)
c. x-intercept is (-8, 0)
y-intercept is (-8, 0)
y-intercept is (0,8)
b. x-intercept is (0, -8)
d. x-intercept is (8,0)
y-intercept is (8,0)
y-intercept is (0, -8)
Answer:
y-intercept is (0,8)
c. x-intercept is (-8, 0)
Step-by-step explanation:
y=x+8
x=0
y+0=8
y=8
y=0
y=x+8
0=x+8
x=-8
What is 1700 m to 40 minutes the unit rate the rate unit
Answer:
42.5
thas the answer, u welcome
find the midpoint of A and B where A has coordinates (-5,3) and B has coordinates (3,-1)
Let M = midpoint
M = (-5+3/2, -1+3/2)
M = (-2/2, 2/2)
M = (-1, 1)
If David can prepare 2 gallons of juice and 4 days how many cups of juice can you prepare per day
Answer:
32
Step-by-step explanation:
because if he did 16 cups both days
hopefully this helps
A game is played using ne die. If the die is rolled and shows 3, the player wins $45. If the die shows any number other than 3, the player wins nothing. If there is a charge of $9 to play the game, what is the game's expected value?
Answer:
-$13.5
Step-by-step explanation:
Let x be a random variable of a count of player gain.
- We are told that if the die shows 3, the player wins $45.
- there is a charge of $9 to play the game
If he wins, he gains; 45 - 9 = $36
If he looses, he has a net gain which is a loss = -$9
Thus, the x-values are; (36, -9)
Probability of getting a 3 which is a win is P(X) = 1/6 since there are 6 numbers on the dice and probability of getting any other number is P(X) = 5/6
Thus;
E(X) = Σ(x•P(X)) = (1/6)(36) + (5/6)(-9)
E(X) = (1/6)(36 - (5 × 9))
E(X) = (1/6)(36 - 45)
E(X) = -9/6 = -3/2
E(X) = -3/2
This represents -3/2 of $9 = -(3/2) × 9 = - 27/2 = -$13.5
Complete the sentence.
9 is 18% of
Answer:
the answer is 50
Step-by-step explanation:
Answer:
9 is 18% of 50
Step-by-step explanation:
All you need to do is divide 9 by 18, and multiply the answer by 100
In ΔGHI, the measure of ∠I=90°, the measure of ∠G=31°, and IG = 6.3 feet. Find the length of HI to the nearest tenth of a foot.
Answer:.
Step-by-step explanation:
- 2.5(4w - 4) = -6 Check:
Answer:
Step-by-step explanation:
- 2.5(4w - 4) = -6
-2.5×4w+2.5×4=-6
-10w+10=-6
-10w=-6-10
-10w=-16
Cancel the -sign from both side soqe get
10w=16
W=16/10
W=1.6
So the value of w is 1.6
What is the answer to
2 3/4 divided by 3
Answer: 8/9 or .8
Advice for the future, use math w a y next time for stuff like this.
The list of ordered pairs below represents a function
(12, 6), (3, 1), (2,-2), (5, 10), (-8, -4) (_,_)
Which of the following could be the missing ordered pair?
A. (2,1)
B. (12,7)
C. (-8,8)
D. (-3,-4)
Answer:
D. (-3,-4)Step-by-step explanation:
GivenOrdered pairs
(12, 6), (3, 1), (2,-2), (5, 10), (-8, -4) (_,_) To findThe missing pairSolutionSince it is a function, the missing pair can't repeat input values with different output, therefore only option D is unique so is the correct choice
A school had 225 students enrolled last year. This year, 260 students are enrolled. Find the percent of change to the
nearest percent.
Answer:
15.5%
Step-by-step explanation:
No of students that had enrolled last year = 225
This year, 260 students are enrolled.
We need to find the percent of change in the number of students. It can be calculated as :
P = (change in no of students/initial no of students)×100
[tex]\%=\dfrac{260-225}{225}\times 100\\\\=15.5\%[/tex]
So, the percent change is 15.5%.
Find the mean of 3, 11, 6, 13, 14
Answer:
9.4
Step-by-step explanation:
To find the mean, add the values up and then divide them by the number of values there are:
3 + 11 + 6 + 13 + 14 = 47
47/5 = 9.4
The mean is 9.4
Hope this helps :)
For the volume of soap in a bottle, Ryan determined the margin of error as 354.85 mL to 354.95 mL. What was the volume of soap that he measured? 354.8 mL 354.85 mL 354.9 mL 354.95 mL
Answer:
Correct answer is option C. 354.9 mLThe volume of soap that Ryan measured is 354.9 mL. Therefore, option C is the correct answer.
Given that, for the volume of soap in a bottle, Ryan determined the margin of error as 354.85 mL to 354.95 mL.
We need to find the volume of soap that he measured.
What is the margin of error?A margin of error tells you how many percentages points your results will differ from the real population value.
Now, the margin of error is 354.85 - 354.95
The volume=354.9 mL (Mid value of 354.85 - 354.95 )
The volume of soap that Ryan measured is 354.9 mL. Therefore, option C is the correct answer.
To learn more about the margin of error visit:
https://brainly.com/question/10501147.
#SPJ2
First to answer correct gets Brainiest!!
In a three-digit number, the tens digit is the same as the hundreds digit. The ones digit of this number is equal to 1/3 of the sum of the other two digits. Find the number if the sum of all its digit is equal to 24.
Answer:
996
Step-by-step explanation:
the three digit number is;
996
Step-by-step explanation:
The three digit can be written xyz
ones digit is equal to 1/3 the sum of the two other digits
z = 1/3(x + y)
x + y + z = 24
Tens digit is same as hundreds digit
That means x = y
z = 1/3 (x + x) = 2x/3
So;
2x/3 + x + x = 24
Multiply through by 3
2x + 3(2x) = 72
8x = 72
x = 72/8
x = 9
x = y = 9
z = 1/3(18)
z = 6
What is 256 heartbeats in 4 mins in unit rates
Answer:
64 beats per min or 64/min
Step-by-step explanation:
256/4=64
The solution to 3.2x = 11.52 is x =
Answer:
11.52/3.2=3.6
x=3.6
I hope this is good enough:
Farmer Jones wants to make a circular corral for his horses. If the diameter is to be 500 m,
how many meters of fencing is needed? Round to the nearest whole number? Use 3.14 for .
Answer:
1571mStep-by-step explanation:
Step one:
given data
the diameter of the farm= 500m
the radius will be d/2
= 500/2
r=250m
Step two:
Required
The perimeter fence for the farm
this is also the same as the circumference of the farm
C=2πr
C=2*3.142*250
C=1571m
Hence the needed length of fence is 1571m
Amanda purchased a prepaid phone card for $20. Long distance calls cost 11 cents a minute using this card. Amanda used her card only
once to make a long distance call. If the remaining credit on her card is $16.81, how many minutes did her call last?
minutes
Answer:
29 minutes?
i divided 3.19 by 11 (20 - 16.81 is 3.19) and i got 29 so i think it is that amount of minutes
M is the midpoint of line segment LN. Find the length of LN
Answer:
Step-by-step explanation:
Here is the complete question;
M is the midpoint of line segment LN. If LM= 3x + 5 and LN= 5x + 40, find the length of LN.
Since M is the midpoint of LN, hence LM + MN = LN and LM = MN
LM + LM = LN
2LM = LN ..... *
Given;
LM= 3x + 5
LN= 5x + 40
Substitute into the eqn *
2(3x+5) = 5x+40
6x+10 = 5x+40
6x-5x = 40-10
x = 30
Get the length LN
LN= 5x + 40
LN = 5(30)+40
LN = 150+40
LN = 190
Hence the length of LN is 190
Answer:
190
Step-by-step explanation:
If the function y = xa − 31 is a linear function, what is the value of a?
A. 1
B. 2
C. 3
D. 4
Answer:
a.1
i hope you get it right
Answer:
a
Step-by-step explanation:
Factor the expression completely. 5 - 45x^5
Answer:
5(9x-5)
Step-by-step explanation:
Each marble bag sold by Mary's Marble Company contains 5 blue marbles for every 4 purple
marbles. If a bag has 35 blue marbles, how many purple marbles does it contain?
Answer:
The total no. of purple marbles will be:
[tex] \boxed{ \underline{ \rm{28}}}[/tex]
Step-by-step explanation:
It is given that for every 5 blue marbles, we have 4 purple marbles. And similarly we have to find for the no. of purple marbles for 35 blue marbles.
First, Let's divide these 35 blue marbles in groups of 5. We will get:
➝ 35 ÷ 5 = 7 groups
For each group of 5 marbles, there are 4 purple marbles. So for 7 groups, No. of purple marbles will be:
➝ 4 × 7 = 28 purple marbles.
And we are done! :D
If DG = 60ft, solve for GO
35
7
None of the other answers are correct
25
6
Answer:
A: 35
Step-by-step explanation:
DG is the combined segments DO and OG. In other words:
[tex]DG=DO+OG[/tex]
We know that DG is 60. DO is (4x-3) and OG is (2x+21). So, substitute:
[tex]60=(4x-3)+(2x+21)[/tex]
Solve for x. Combine like terms:
[tex]60=6x+18[/tex]
Subtract 18 from both sides:
[tex]42=6x[/tex]
Divide both sides by 6. Hence, the value of x is:
[tex]x=7[/tex]
GO is defined as (2x+21).
So, to find GO, we can now substitute 7 for x and evaluate. Therefore:
[tex]GO=2(7)+21=14+21=35[/tex]
Hence, our answer is A.
e*****12345688954576665656556555555
a.
9x^2-4
F.(3x + 2)(3x - 2)
G.(3x + 2)2
H. (3x - 2)2
J.prime
Answer:
Step-by-step explanation:
I'm not entirely sure what the question is, but I suspect the answer is not prime.
9x^2 - 4
factors into two factors (3x + 2)(3x - 2)
Suppose x = 11 which is prime.
9*121 - 4
1085 which ends in a 5 so the expression is not prime.
In fact, the two factors are 3*11 + 2 = 35 and 3*11 - 2 = 31
31*35 = 1085
9514 1404 393
Answer:
F. (3x +2)(3x -2)
Step-by-step explanation:
The given expression is the difference of two squares, so can be factored accordingly.
9x^2 -4 = (3x)^2 -2^2 = (3x +2)(3x -2) . . . . . matches F
Help.please asap will mark brainliest!!!
During an election, Albert received 60% of the 30 votes cast. Anthony received the remaining votes. How many more votes did Albert receive?
Answer:
6 votes!
Step-by-step explanation:
Albert: 60% of 30= 18
Anthony: 40% of 30= 12
18 - 12= 6
please answer the image below .
Answer:
7Step-by-step explanation:
surface area of a square pyramid
= Area of base + 1/2 base perimeter * slant height
= (1 x 1) + (1/2 x (1*4) x 3)
= 1 + 6
= 7 yd²
How many exact tenths are in 21.34?
Answer: 3
Step-by-step explanation:
The tenths place in this number:
2 = tens place
1 = ones place
.
3 = tenths place
4 hundredths place
Answer is 3.
Look at each place value. The number shows you how much of each are there.
Tenths is the first column after the decimal point and it says 3.