Answer:
[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]
Step-by-step explanation:
We begin with the integral [tex]\int{sin^2(x)cos(3x)} \, dx[/tex]
First, we can apply the power reducing formula to [tex]sin^2(x)[/tex]
This formula states: [tex]sin^2(x)=\frac{1}{2} -\frac{1}{2} cos(2x)[/tex]
This gives us
[tex]\int{(\frac{1}{2} -\frac{1}{2} cos(2x))(cos(3x)} \, dx \\\\\int{(\frac{1}{2}cos(3x) -(\frac{1}{2} cos(2x)cos(3x)} \, dx \\\\\frac{1}{2} \int{cos(3x)} \, dx -\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]
Now, we can use integrate the first integral
[tex]\frac{1}{2} \int{cos(3x)} \, dx\\u=3x\\du=3dx\\\\\frac{1}{6} \int{3cos(u)} \, du\\\\\frac{1}{6} sin(u)+C\\\\\frac{1}{6} sin(3x)+C[/tex]
And now we can begin to integrate the second
[tex]-\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]
To integrate this, we need to use the Product-to-sum formula, which states
[tex]cos(\alpha )cos(\beta )=\frac{1}{2} [cos(\alpha +\beta )+cos(\alpha -\beta )[/tex] . For this formula, we will use [tex]\alpha =3x\\\beta =2x[/tex]
This gives us
[tex]-\frac{1}{2} \int{\frac{1}{2}[cos(5x)+cos(x)] } \, dx \\\\-\frac{1}{4} \int{[cos(5x)+cos(x)] } \, dx\\\\-\frac{1}{4}\int{cos(5x)} \, dx -\frac{1}{4}\int{cos(x)} \, dx[/tex]
We can then use the same process of u-substitution as the previous to get the answer of [tex]-\frac{1}{20} sin(5x)-\frac{1}{4} sin(x)+C[/tex]
Lastly, we can add the values of the two integrals together to give us the final solution of
[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]
Write a linear function f with the values f(2)=4 and f(−7)=9. A function is f(x)=
Answer:
f(x) = -5/9 x + 5 1/9
Step-by-step explanation:
f(2)=4 and f(−7)=9 means the line pass through (2,4) and (- 7,9)
f(x) = mx + b
m = (y-y') / (x-x') = (9 - 4) / (- 7 - 2) = - 5/9
for (2,4) : b = f(x) - mx = y - mx = 4 - (- 5/9) x 2 = 4 + 10/9 = 46/9 = 5 1/9
f(x) = -5/9 x + 5 1/9
check for (-7, 9) f(-7) = (-5/9) * (-7) + 5 1/9 = 35/9 + 46/9 = 81/9 = 9
Final answer:
The linear function that satisfies the given points f(2)=4 and f(-7)=9 is f(x) = (-5/9)x + (46/9).
Explanation:
To write a linear function f(x) that satisfies f(2)=4 and f(-7)=9, one must determine the slope and y-intercept of the line. A linear function has the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope using the two points (2, 4) and (-7, 9):
Slope (m) = (y2 - y1) / (x2 - x1) = (9 - 4) / (-7 - 2) = 5 / -9.
Now we have the slope which is -5/9. We can use one of the points and the slope to find the y-intercept (b). Let's use the point (2, 4):
4 = (-5/9)(2) + b
b = 4 + (10/9) = 46/9
Therefore, the linear equation of the function is:
f(x) = (-5/9)x + (46/9).
Brainliest!!!
Draw a tree diagram to show the sample space for each event.
a shirt with style choices crew-neck and v-neck and colors blue, yellow, or green
Answer:
3rd option
Step-by-step explanation:
We have two kind of necks and three different colours so the andswer would be 3rd option
Crew-neck :CB,CY,CG
V-neck : VB,VY,VG
Answer:
The 3rd one is correct.
Step-by-step explanation:
which of the following are true statements? Check all that apply logM^(p)=p*logM log ((M)/((N)))=logM-logN log ((M)/((N)))=(logM)/(logN) (logM)^(p)=p*logM
The expressions logM^(p)=p*logM and log ((M)/((N)))=logM-logN both correctly apply rules of logarithm, while log ((M)/((N)))=(logM)/(logN) and (logM)^(p)=p*logM don't.
Explanation:The subject matter involves logarithmic identities in Mathematics, specifically, rules of logarithms. Logarithms have certain properties that allow us to simplify complex expressions.
Let's go through each expression:
logM^(p)=p*logM: This is a correct identity. It's known as the power rule of logarithms, which states that the log of a number raised to an exponent is equal to the exponent multiplied by the log of the number. log ((M)/((N)))=logM-logN: This is also a correct identity. It's known as the quotient rule of logarithms, which states that the log of a quotient is the difference of the logs. log ((M)/((N)))=(logM)/(logN): This statement is false. It's an incorrect assumption about the rules of logarithms. (logM)^(p)=p*logM: This statement is also false. The power in this case refers to the exponent on the entire log term, which is different from the power rule. Learn more about Rules of Logarithms here:https://brainly.com/question/30287525
#SPJ12
Select the best answer for the question
17. A local supermarket sells shrimp for $4.50 per pound and lobster for $7.25 per pound.
You have a total budget of $95.75. If you buy 7 pounds of lobster, how many pounds of shrimp
can you purchase?
Answer:
10
Step-by-step explanation:
Multiply 7.25 and 7
that gets you 50.75
Then subtract 50.75 from 95.75
thats get you 45
Last divide 45 from 4.50
that gets you 10
paolo read 40 books in one year 35% of the books paolo read were non fiction. how many nonfiction and fiction books did he read?
Answer:
Paolo reads in total 26 fiction and 14 non- fiction books.
Step-by-step explanation:
Here, the total number of books read by Paolo = 40 books
The percentage of non-fiction books read = 35%
Now, 35% of total books read = 35% of 40
⇒ [tex]\frac{35}{100} \times 40 = 14[/tex]
So, the number of non -fiction books read by Paolo = 14
Now, the number of fiction booosk read
= Total books read - Non- Fiction books read
= 40 - 14 = 26
So, the number of fiction books read by Paolo = 26
Hence, Paolo reads in total 26 fiction and 14 non- fiction books.
What is the equation of a line in slope-intercept for that passes through (4,8) and (-1,-12)
Answer:
y=4x-8
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-12-8)/(-1-4)
m=-20/-5
m=4
y-8=4(x-4)
y=4x-16+8
y=4x-8
Shawn hike 12 miles and 4 hours at the same rate what is the total number of miles he could hike in 9 hours
Answer:
27 miles
Step-by-step explanation:
Find the rate or speed that Shawn hikes at. Find this reduced to lowest terms.
speed = distance / time
speed = 12 miles / 4h
speed = 3miles / h
Every hour, Shawn hikes 3 miles.
Multiply speed by time to find distance.
3mph X 9h = 27 miles
Therefore Shawn could hikes 27 miles in 9 hours.
Someoneee pleaseee helpp!!!
Answer:
(x, y ) → (x + 6, y + 12 )
Step-by-step explanation:
We require to determine the horizontal and vertical shift to go from one of the points on the line to the corresponding point on the image
Consider point V with x- coordinate - 8 and y- coordinate - 2
The corresponding point is V'
with x- coordinate - 2 and y- coordinate 10
Thus V → V' is 6 units right in the horizontal direction and 12 units up in the vertical direction.
These are the same shifts for W → W'
Thus the translation rule is
(x, y ) → (x + 6, y + 12 )
The equation which correctly represents this situation is
A) x2 = 306
B) 2x2 = 306
C) x2 + x = 306
D) 2x2 + x = 306
Answer:
C) x2 + x = 306
Step-by-step explanation:
x2 + x = 306
x2 + x - 306 = 0
x2 + 18x - 17x + 18 * (-17) = 0
x ( x + 18) - 17 (x +18) =0
(x + 18) (x - 17 ) = 0
x = -18 or 17
help please!!! really really important
Answer:
42. Graph a
43. Not possible.
44. Graph e
45. Graph c
46. Graph b.
Step-by-step explanation:
42. 7x + 13 ≥ 55
⇒ x ≥ 6
So, it matches graph a.
43. 12x - 8 > 4(3x + 2)
⇒ 12x - 8 > 12x + 8
Hence, d. not possible.
44. [tex]\frac{x}{- 4} - 3 < - 1[/tex]
⇒ [tex]\frac{x}{- 4} < 2[/tex]
⇒ x > - 8
Hence, graph e matches.
45. - 4(- 2x + 3) ≤ 5 + 8x
⇒ 8x - 12 ≤ 5 + 8x
⇒ - 12 ≤ 5
This is true for all values of x, hence that matches graph c.
46. - 4(x + 3) > 8(x + 3)
⇒ - 4x - 12 > 8x + 24
⇒ 12x < - 36
⇒ x < - 3
Hence, graph b matches the situation. (Answer)
Separate the number 41 and the two parts so that the first number is eight more than twice the second number what are the two numbers
The two numbers are 30 and 11
Solution:
Given that we have to separate the number 41 into two parts
Let the second number be "x"
Given that first number is eight more than twice the second number
first number = eight more than twice the second number
first number = 8 + twice the "x"
first number = 8 + 2x
So we can say first number added with second number ends up in 41
first number + second number = 41
8 + 2x + x = 41
8 + 3x = 41
3x = 41 - 8
3x = 33
x = 11
first number = 8 + 2x = 8 + 2(11) = 8 + 22 = 30
Thus the two numbers are 30 and 11
How to solve radicals
Answer:
Step-by-step explanation:
h(x)= 1/8x^3-x^2
What is the average rate of change of h over the interval −2≤x≤2?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The average rate of change of h(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [a, b ] = [ - 2, 2 ], thus
f(b) = f(2) = [tex]\frac{1}{8}[/tex] × 2³ - 2² = 1 - 4 = - 3
f(a) = [tex]\frac{1}{8}[/tex] × (- 2)³ - (- 2)² = - 1 - 4 = - 5
average rate of change = [tex]\frac{-3-(-5)}{2-(-2)}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
The average rate of change of h over the interval −2≤x≤2 is 1/2.
Here,
The function is [tex]h(x)= \frac{1}{8} x^3-x^2[/tex] and the interval −2≤x≤2.
We have to find, the average rate of change of h over the interval −2≤x≤2.
What is Average rate?
The Average rate of change of function f( x ) in the close interval [a, b ]
is, [tex]\frac{f(a)-f (b)}{b-a}[/tex]
Now,
The function is [tex]h(x)= \frac{1}{8} x^3-x^2[/tex] and the interval −2≤x≤2.
Hence, [tex]h(-2) = \frac{1}{8} *(-2)^{3} -( -2)^{2} = -5[/tex]
And, [tex]h(2) = \frac{1}{8} *(2)^{3} -( 2)^{2} = -3[/tex]
So, Average rate of change of function h(x) = [tex]\frac{-3-(-5)}{2-(-2)} = \frac{2}{4} = \frac{1}{2}[/tex]
The average rate of change of h over the interval −2≤x≤2 is 1/2.
Learn more about the Average rate of change visit:
https://brainly.in/question/40747816
#SPJ2
PLEASE HELP ME AND YOU'LL BE MARKED AS BRAINLIEST
PLEASE HELP ITS 10:45 PM AND I'M TRIED AND IF I DONT GET THIS DONE THEN MY TEACHER IS GONNA KILL ME SO PLEASE HELP ME.
1. Why is the wall special to the narrator and Lou?
2. Why don’t Lou and the narrator carry out their plan to recapture the wall?
3. Reread the final three paragraphs of the story - how do you think the two boys feel about having bought paint once they read the inscription on the wall? Explain.
4. Was the painter an “outsider” or a part of the community? Why?
Answer:
3 it teaches them a lesson by dont judge someone by how he looks
everyone was judging her cause of her religious and looks and in the end they admired the wall that she had painted cause it teaches them a lesson dont judge a book by it cover
4 Was the painter an “outsider” or a part of the community? Why? she was an outsider she came for a purpose and its to paint the wall text from the story "The painter lady has come to town ostensibly with the purpose of painting a mural."
What is the area of this triangle in square inches?
area of triangle = 1/2bh
area = 1/2(120)(252) = 15120 in²
answer: C
Answer:
C) 15,120 square inches
Step-by-step explanation:
To solve this problem we first need to convert both legs of the triangle to inches. 10 ft * 12 is 120 and 7 yards is roughly 21 ft and that times 12 is 252. All we have to do now is to plug these values into the formula for area of a triangle: 1/2(b x h) = 1/2(252 * 120) = 1/2(30240) = 15,120 square inches.
Complete this sequence: 88511, 16351, ?, 10251
Answer:
73155
Step-by-step explanation:
To complete the sequence, we need to know the pattern.
88511= [tex]8+8, 8-5, 5\times 1, \frac{1}{1} = 16351[/tex]
16351= [tex]1+6, 6-3, 3\times 5, \frac{5}{1} = 73155[/tex]
73155= [tex]7+3, 3-1, 1\times 5, \frac{5}{5} = 10251[/tex]
10251
∴ The missing number is 73155 and complete sequence is 88511,16351,73155, 10251
10.) A soccer team plays 104 tournaments in two
years, playing the same number of tournaments each
year. In each tournament they play 3 games. If they
won a total of 55 games in first year and 103 games
in the second year,A. how many games did they lose in
both years? B.Is the number of games won greater than
The number of games lost? Show your work below to
justify your anwser.
.
Answer:
A. The Number of Lost games = 154 Games
B. Number of games won is greater than the number of games lost.
Step-by-step explanation:
A. how many games did they lose in both years?
Total Number of games = 104 tournaments x 3 Games in each tournament
Total Number of games = 312 Games
The No. of Lost games= Total Games in 2 years - Games won in 1st year - Games won in 2nd year
The No. of Lost games = 312 - 55 - 103
The No. of Lost games = 154 Games
B. Is the number of games won greater than the number of games lost?
Total Number of Games won = 158 Games
Total Number of Games lost = 154 Games
Hence, Total Number of Games won is greater than the Total Number of Games lost.
Calculate the average rate of change of f(x) =x^2/4 - 5 for 3 ≤ x ≤ 5
Answer:
2
Step-by-step explanation:
Average rate of change of a function between x=a and x=b is:
[ f(b) − f(a) ] / (b − a)
On the interval 3 ≤ x ≤ 5:
[ f(5) − f(3) ] / (5 − 3)
[ (5²/4 − 5) − (3²/4 − 5) ] / (5 − 3)
(25/4 − 5 − 9/4 + 5) / (5 − 3)
(25/4 − 9/4) / (5 − 3)
(16/4) / 2
2
QUESTION 5 of 10: Your laptop died and you need a new one for work NOW! The one you need will cost $500. You do not have the cash in
your checking account, so you decide to borrow the money from your savings account. You have $9,000 in your savings account gaining
3% interest per year. If you don't replace the $500 in the savings account, how long will it take before the balance again reaches $9,000?
a) 1 year
b) 2 years
c) 5 years
Answer:
B
Step-by-step explanation:
9000-500 = 8500
8500 × (3/100) =255
8500 + 255 = 8755
8755 × (3/100) = 262.65
8755 + 262.65 = 9017.65
hence, the answer is B
*please correct me if im wrong ^^
Answer:
b) 2 years
Step-by-step explanation:
If you have $9000 in the saving account, and you take $500, you are left with:
$9000 - $500 = $8500
in one year you will have 3% more of the 8500 which is:
8500/100*3 = $255
so in one year the number on your savings account is:
8500 + 255 = $8755
and by the next year you will have 3% more of the 8755 which is:
8755/100*3 = $262.65
so in two years the number on your savings account is:
8755 + 262.65 = $9017.65
which is a little bit more than the $9000.
so it will take 2 years until the calance again reaches $9000
Need help on 5
Is it function and explain why.
Answer:
#5
It is not a function because the some x-values can have more than one possible y-value. The x-values can have the positive and negative y-value.
Step-by-step explanation:
The equation is the equation for a circle. When you graph a circle, it does not pass the vertical line test.
Example: if x is 6
6² + y² = 100
36 + y² = 100
y² = 100 - 36
y² = 64
y = ± √64 This is true because: (-8)² = 64 AND 8² = 64
y = -8 OR 8
By the way, for #4 it is not a function.
The points (13, 4) and (13, -4) mean that x will have more than one y value. The x-value 13 will have y-values 4 and -4.
one half the cost of a dress decreased by $12 is the same as 2/5 the cost of a dress. What is the cost of the dress?
Answer:
$120
Step-by-step explanation:
Let the cost of the dress be "c"
ONE HALF the cost DECREASED by 12, can be written as:
[tex]\frac{1}{2}c-12[/tex]
2/5th the cost of dress, can be written as:
[tex]\frac{2}{5}c[/tex]
Now, we equate both parts and solve for c to get cost of dress. Shown below:
[tex]\frac{1}{2}c-12=\frac{2}{5}c\\\frac{1}{2}c-\frac{2}{5}c=12\\\frac{5-4}{10}c=12\\\frac{1}{10}c=12\\c=\frac{12}{\frac{1}{10}}\\c=12*10\\c=120[/tex]
Thus,
The ccost of the dress is $120
Please help me.. I need help
1. I would multiply the dimensions of each room to find the area of each room. Then I can add up the areas to get the total area.
2. (24.5x16)+(15x12.75)+(10.5x10.5)
3. 392+191.25+110.25 = 693.5 ft²
which expression is equivalent to the given expression 13+6×7 after using the distributive property
Answer:
55
Step-by-step explanation:
13+6*7=13+42=55
Determine the type and number of solutions of x^2 + 10x − 25 = 0. A two real solutions B one real solution C two imaginary solutions
Answer:
two real solution
Step-by-step explanation:
x^2 + 10x − 25 = 0
we can solve this by finding out the value of x
lets assume the equation is a\times x^{2}+b\times x+c=0
x=-b\pm \sqrt{(b^{2}-4ac)}\div 2a
x=-10\pm\sqrt{100+4*25}\div2
x=-5\pm5\sqrt2
then we get both real value of x
so two real solution
If 10 minutes is how long it took Lisa to walk 1/4 of the way home, how long does it take to walk 2/3 of the way home?
Answer:
[tex]26\frac{2}{3}[/tex] minutes (or 26 minutes 40 seconds)
Step-by-step explanation:
This problem can be very easily solved with ratios and proportions.
We can create two ratios and equate them. Then we cross multiply and find the unknown.
Let the time it takes to walk 2/3rd of the way be "t".
We will keep minutes on top (numerator) and the fractional way on the bottom (denominator) when creating our ratios.
Simply put, 10 mins = 1/4th of the way, so "t" mins means 2/3rd of the way. Thus we can write:
[tex]\frac{10}{\frac{1}{4}}=\frac{t}{\frac{2}{3}}\\\frac{1}{4}t=10*\frac{2}{3}\\\frac{1}{4}t=\frac{20}{3}\\t=\frac{\frac{20}{3}}{\frac{1}{4}}\\t=\frac{20}{3}*\frac{4}{1}\\t=\frac{80}{3}\\t=26\frac{2}{3}[/tex]
sO, IT IS GOING to take [tex]26\frac{2}{3}[/tex] minutes to go 2/3rdof the way.
Or, 26 minutes and 40 seconds
Final answer:
To find out how long it takes to walk 2/3 of the way home, set up a proportion using the information given. so 26.7 minutes take to walk.
Explanation:
To find out how long it takes to walk 2/3 of the way home, we can set up a proportion using the information given. If 10 minutes is how long it took Lisa to walk 1/4 of the way, we can say that:
10 minutes = 1/4 of the way
To find out how long it takes to walk 2/3 of the way, we can set up another proportion:
x minutes = 2/3 of the way
We can cross multiply the proportions to solve for x:
10 * (2/3) = x * (1/4)
20/3 = x/4
To solve for x, we can multiply both sides of the equation by 4:
80/3 = x
So, it takes approximately 26.7 minutes to walk 2/3 of the way home.
3. What is the maximum of the sinusoidal function?
Please help thank you
Answer: -2
Step-by-step explanation:
This is the greatest value for f(x).
omplete the paragraph proof.
Given: M is the midpoint of
Prove: ΔPKB is isosceles
Triangle P B K is cut by perpendicular bisector B M. Point M is the midpoint of side P K.
It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because _____________. Finally, ΔPKB is isosceles because it has two congruent sides.
corresponding parts of congruent triangles are congruent
base angles of isosceles triangles are congruent
of the definition of congruent segments
of the definition of a right triangle
Answer:
Complete paragraph proof withe Diagram is below.
Δ PMB ≅ Δ KMB ...........SAS congruence theorem
∴ PB ≅ KG ......corresponding parts of congruent triangles are congruent
Step-by-step explanation:
Complete the paragraph proof.
Given: M is the midpoint of
Prove: ΔPKB is isosceles
Triangle P B K is cut by perpendicular bisector B M. Point M is the midpoint of side P K.
It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because __corresponding parts of congruent triangles are congruent _.
Finally, ΔPKB is isosceles because it has two congruent sides.
Δ PMB ≅ Δ KMB ...........SAS congruence theorem
∴ PB ≅ KG ......corresponding parts of congruent triangles are congruent
Answer: A
Step-by-step explanation:
Brook states that the distance on the line is 4 units. Caleb states that the whole line does not have a distance because it continues on forever. Vivian states that the line is 6 units long.
Answer:
kaleb is correct
Step-by-step explanation:
The awsner is Brook did the distance between L and M, Vivian however did the distance between M and N. Hope this helps you
Paige starts a stamp collection with 4 stamps. Every month, she adds 3 starps
to her collection. Which expression represents the number of stamps in Paige's
collection, if m represents the number of months that have passed? *
O A3m+4
O
B 4m+3
O
C 3m+3
D 4m+4
Answer:
3m + 4
Step-by-step explanation:
4 is the starting number of stamps and 3m represents 3 stamps per month
67+46
Find the solution and model how you found your answer
113
Step-by-step explanation:
7 plus 6 is 14 carry the one over to the 6 of the 67 then add the one the six and the four that equals 11
that gets you
113