Answer:
[tex] I = \dfrac{1}{3}sin(3x) - 3cos(x) + C[/tex]
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]
Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx .Rewrite using du and u .[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]
Answer:
[tex]\displaystyle \large{\frac{\sin 3x}{3} - 3\cos x + C}[/tex]
Step-by-step explanation:
We are given the indefinite integral:—
[tex]\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx}[/tex]
Important Formulas
[tex]\displaystyle \large{\int f(ax+b) \ dx = \frac{1}{a} F(ax+b) + C}\\\displaystyle \large{\int \cos(ax) \ dx = \frac{1}{a} \sin (ax) + C \ \ \tt{(a \ \ is \ \ a \ \ constant.)}}\\\displaystyle \large{\int \sin x \ dx = - \cos x + C}\\\displaystyle \large{\int [f(x) \pm g(x)] \ dx = \int f(x) \ dx \pm \int g(x) \ dx}\\\displaystyle \large{\int kf(x) \ dx = k \int f(x) \ dx \ \ (\tt{k \ \ is \ \ a \ \ constant.})}[/tex]
Therefore, from the integral, apply the properties above:—
[tex]\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \int \cos 3x \ dx + \int 3 \sin x \ dx}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \int \cos 3x \ dx + 3 \int \sin x \ dx}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \frac{1}{3} \sin 3x + 3\cdot -\cos x + C}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \frac{\sin 3x}{3} - 3\cos x + C}[/tex]
Hence, the solution is:—
[tex]\displaystyle \large \boxed{\frac{\sin 3x}{3} - 3\cos x + C}[/tex]
e) que cantidad aumenta en 25 de como resultado 65
Answer:
40
Step-by-step explanation:
The triangle shown below has an area of 40 units. Find the missing side.
8 and 9 are both sides (help meeee)
Can some explain how to do this?
Answer:
Exact Area = 210.25pi - 210Approximate Area = 450.185The units for the area are in square inches or in^2. The approximate value shown above is when using pi = 3.14
=============================================================
Explanation:
Use the pythagorean theorem to find the length of the hypotenuse
a = 20b = 21c = unknowna^2 + b^2 = c^2
20^2 + 21^2 = c^2
400 + 441 = c^2
c^2 = 841
c = sqrt(841)
c = 29
The hypotenuse is 29 inches long. This is the diameter of the circle. Half of that is the radius at r = d/2 = 29/2 = 14.5 inches.
The area of the circle is...
A = pi*r^2
A = pi*(14.5)^2
A = pi*210.25
A = 210.25pi
Which is exact in terms of pi
We'll subtract off the triangular region as this isn't shaded in. The area of the triangle is base*height/2 = 20*21/2 = 420/2 = 210 square inches.
So the shaded region is therefore 210.25pi - 210 square inches
This approximates to 210.25*3.14 - 210 = 450.185 when using the approximation pi = 3.14; use more decimal digits of pi to get a more accurate value.
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
30
you can easily find out the answer by multiplying 2/3 by 10 on both the numerator and denominator to get 20/30 which is the amount of people that like the chip flavor. the other 10 is the people that don't like it.sorry if I gave you a stroke but 20 people like the chip and 10 people don't so theres 30 people in total
what is the value of y in the following system of equations ? 2x + 3y = 6 2x + y = -2
y = 4
Step-by-step explanation:
2x + 3y = 6. #1
2x + y = -2. #2
Subtract Eq 2 from Eq 1,
3y - y = 6 - (-2)
2y = 8
or
y = 4
Answer:
y = 4
Step-by-step explanation:
2x + 3y = 6
2x + y = -2
Let's set the second equation equal to y. This means that y will be alone on one side of the equal sign.
2x + y = -2
Subtract 2x from both sides.
y = -2x - 2
Now that we have y as an expression, plug it into the first equation.
2x + 3y = 6
2x + 3(-2x - 2) = 6
Distribute the 3 across the parentheses by multiplying.
2x - 6x - 6 = 6
Combine like terms.
-4x = 12
Divide both sides by -4.
x = -3
Now we have solved x.
To solve for y, plug x back into one of the equations.
y = -2x - 2
y = -2(-3) - 2
Multiply.
y = 6 - 2
Subtract.
y = 4
Check your answer by plugging both values back into the original equations.
2x + 3y = 6
2(-3) + 3(4) = 6
Multiply.
-6 + 12 = 6
Add.
6 = 6
Your answer is correct.
Hope this helps!
What is the answer to this ?
Answer:
the answer is 180
Step-by-step explanation:
Can someone please help.
Answer:7-10
Step-by-step explanation:
In this question it is asking what is the biggest change in the temperature that happened "next to the other one" on the table
And the change from 7-10 is the highest change that is "next to each other"
Explain the meaning of probability. What does it mean if an event has a probability of 0? Give an example. What does it mean if an event has a probability of 1? Give an example. What does it mean if an event has a probability of 1/2? Give an example. (LONG ANSWERS ONLY)
Answer:
If an event has a probability of 0 it means that it is impossible. For example when they say there is 0% of rain. It is very unlikely it is going to rain. If an event has a probability of 1 it means that it is certain. For example, if they say there is a 100% chance it is going to rain. It is very certain that it's going to rain. If an event is 1/2 then it means there it is likely as it is unlikely. For example, if they say there is a 50% chance of rain. Then it might not rain, but there is a chance that it might rain as well.
Step-by-step explanation:
Hope this helps!
Probability can simply be defined as the chances of an event a, occuring with respect to event b, with respect to event n, given an nth number of possible outcomes.
Probability can be calculated using the following expression:
[tex] \frac{freq \: of \: event \: n}{freq \: of \: total \: number \: of \: events} [/tex]
When an event has a probability of 0, it means that by no chance or condition will the event be true. For example, the probability of a person who is a boy has 0 probability that he is a girl.
When an event has a probability of 1, it means that with every chance or condition, the event will be true. For example, the probability that a person who is a boy has a probability of 1 that he is a boy.
An event that has a probability of 1/2 means that the event could either return a probability of 0 or 1 on different chances or conditions. For example, the probability of a fuetus whose gender is not known has a probability of 1/2 for being a boy and 1/2 for being a girl.
Okay can somebody please me fast with this problem
Answer:
3
Step-by-step explanation:
I don't know plz correct me If I'm wrong
Also brainliest?
Step-by-step explanation:
skakisjsjsjjajabbajaj
please tell me where to graph this!! (include if i open circle or not please) (NO FILE ANSWER!!!)
Answer:
1.Make the circle open
2.put the dot on 5
3. change direction
Step-by-step explanation:
A solid dot on a number line graph indicates that the given number should be included as a possible solution, whereas an open dot indicates that the given number cannot be a solution. For example, if you graph x > 7, you place an open dot at 7.
Have a nice day! :-)
Answer:
closed circle on 3 with line pointing right
Step-by-step explanation:
the number can be greater than or equal to 3 so it means that includes 3 so closed circle on 3 and then it points right towards the bigger numbers because it can be greater than 3
ughhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
Hello! answer: 260.66
Step-by-step explanation:
I dont know for sure but I'd assume you would add them all up for the total so 260.66 is the total when adding them up
8. At a wholesale food distribution center, the price of sugar has increased 6.3% annually since 1980.
Suppose sugar cost $0.43 per pound in 1980 and this growth continues. What will a pound of sugar
cost in 2017? Use y = a(1 + r) and round to the nearest cent.
a. $4.12 b. $1.21
c. $0.42 d. $3.30
Answer: A. $4.12
Step-by-step explanation:
Y=a(1+r/n)^nt is the equation we use to solve this.
a= $0.43
t=37 - take 1980 and subtract it from 2017
r= .063 - the 6.3% goes into a decimal
n = 1
Y= ?
Y= 0.43( 1+ .063/1) ^1*37
Y= 0.43 (1.063) ^37
Y= 4.12
Graph y =-7x-1 il do anything
Answer:
here you go!
on a piece of paper graph......
What is the same ration of 2/3
Answer:
4/6
Step-by-step explanation:
Answer:
4/6
Step-by-step explanation:
PLS HELP!!!
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
6 yd
13 yd
17 yd
Answer:
36
Step-by-step explanation:
A man earns 15000 in a month. if he spends 20% on food and 10% in his children's education.
a) what is his total expenditure?
b) how much does he save in a month?
Step-by-step explanation:
Total money=15000
food=20%
edu.=10%
food AMT=20% of 15000
=20/100*15000
= 3000
education AMT= 10/100*15000
=1500
savings = 15000-1500-3000
=Rs10500
total expenditure=1500+3000
=4500
5. (08.02 MC) Which of the following graphs shows a pair of lines that represents the equations with the solution (3, -6)? (1 point)
Answer:
Hello, it appears you did not attach an image that would provide the necessary information for me to answer your question. I cannot see the graphs, so I'm afraid unless you present a photograph, I'm cannot help you. If you show me the graphs, I'd be more than happy to help you!
Step-by-step explanation:
Solve for the x variable
Answer:
5x-5.2=7.3
5x=7.3+5.2
5x=12.5
x=12.5÷5
x=2.5
Answer: x = 2.5
Step-by-step explanation:
Try to get x by itself
5x - 5.2 = 7.3
5x = 7.3 + 5.2
5x = 12.5
x = 12.5 / 5
x = 2.5
carol rolled a dice 150 times she rolled a six 39 time
Answer:
nice
Step-by-step explanation:
whats the rest of the problem or is it just that she rolled a dice
50 persons 2 glass. Each glass 150 milliliter. How many liters
Answer:
1.5 liters
Step-by-step explanation:
300 mL per person
50 people
300 x 50 = 1500
1500 mL = 1.5 L
Watch "How Wolves Changed Rivers" on YouTebe
***And answer the following question please ASAP ASAP please
1. Why did the "deer" (they are really elk) leave the valleys when the wolves were re-introduced to Yellowstone?
2. When the elk left the valleys, what happened to the vegetation? Give specific examples.
3. Once the vegetation changed, what wildlife came back?
4. How did the wolves change the rivers?
5. How did the elk change the rivers when the wolves were removed from Yellowstone National Park?
You Are Not Allowed To Put Links Or To Tell To Go To Other Websites according To The Rules
Please answer the math question about the Pythagorean theorem
**Template**
B. Answer
C. Answer
D. Answer
E. Answer
F. Answer
G. Answer
H. Answer
Answer:
B) 289 C) 29 D) 7.28 (round as necessary) E)400 F) 7.81 (round as neccessary) G) 10 H) 3.31 (round as neccessary)
Step-by-step explanation:
Here is what you use to find the LONG SIDE ONLY
Pythagorean Theorem: A squared + B squared = C squared. After this, find the square root of C using a radical.
Answer:
B = 17
C= 29
D= 7.28
E= 20
F= 7.81
G= 10
H= 3.32
Step-by-step explanation:
c=a2+b2
What is the volume of a cube with a side length that measures 1 1/2 ft? Enter your answer in the box.
9514 1404 393
Answer:
3 3/8 ft³
Step-by-step explanation:
The volume of a cube is the cube of the side length.
V = s³
V = (1.5 ft)³ = 3.375 ft³ = 3 3/8 ft³
1. The radius of the circular base of a cylinder tank is 0.7 m and its height is 5 m. What is
its surface area??
A. 20.5572 sqm
B. 22.5072 sqm
C. 25.0572 sqm
D. 27.0552
2. An ice cream cone has a radius of 7 cm and a slant height of 10 cm. What is its surface
area?
A. 337.66 sq cm
B.373.66 sq cm
C.376.36 sq cm
D. 376.66 sq cm
help, it's just 1-3 :( with solution please :(
3. A cubical wooden box has a surface area of 600 square cm. What is the measurement
of each
edge?
B. 6 cm
C. 10 cm
A. 5 cm
D. 100 cm
Answer:
C)
B)
C)
Step-by-step explanation:
Question-1:recall the surface area formula of cylinder
[tex] \displaystyle A _{S} = 2\pi r(h + r)[/tex]
given that,h=5 and r=0.7
substitute:
[tex] \displaystyle A _{S} = 2\pi (0.7)(5 + 0.7)[/tex]
simplify parentheses:
[tex] \displaystyle A _{S} = 2\pi (0.7)(5 .7)[/tex]
simplify multiplication:
[tex] \displaystyle A _{S} =25.0572 sqm[/tex]
hence, our answer is C
Question-2:remember the surface area formula of cone
[tex] \displaystyle A _{S} = \pi r(r + s)[/tex]
given that,r=7 and s=10
substitute:
[tex] \displaystyle A _{S} = \pi (7)(7+ 10)[/tex]
simplify parentheses:
[tex] \displaystyle A _{S} = \pi (7)(17)[/tex]
simplify multiplication:
[tex] \displaystyle A _{S} =373.66sqcm[/tex]
hence, our answer is B
Question-3:now for the question-3 we need a little bit understanding
remember the surface area formula of cube
[tex] \displaystyle A _{S} =6 {a}^{2} [/tex]
we are given that,[tex]A_S=600[/tex] Thus
substitute:
[tex] \displaystyle 6 {a}^{2} = 600[/tex]
divide both sides by 6:
[tex] \displaystyle {a}^{2} = 100[/tex]
square root both sides:
[tex] \displaystyle {a}^{} = 10[/tex]
hence, the measurement of each
edge is 10 cm therefore our answer is C)
Answer two questions about Equations A and B:
A. 5x = 3x
B. 5 = 3
1) How can we get Equation B from Equation A?
A. Add/subtract the same quantity to/from both sides
B. Add/subtract a quantity to/from only one side
C. Multiply/divide both sides by the same non-zero constant
D. Multiply/divide both sides by the same variable expression
2( Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
A. Yes
B. No
Find the surface area of each sphere shown below. Round you
32 yd
Help me pleaaaaaseeee
A riddle for the day
I am less than 7 tens and more than 4 tens I am a odd number if you add both my digits you will get 11 which number am I?
47
65
67
74
Answer:
two of them are possible which one is the correct
Joe is recording the percentages he earned on each quiz In his math class. Here are his results for the last 7 quizzes. 72, 82, 65, 67, 80, 81, 67 Find the range of the data set.