Answer:
[tex]\displaystyle \frac{2 \cdot sin2x-cos2x}{5e^x} + C[/tex]
Step-by-step explanation:
The integration by parts formula is: [tex]\displaystyle \int udv = uv - \int vdu[/tex]
Let's find u, du, dv, and v for [tex]\displaystyle \int e^-^x \cdot cos2x \ dx[/tex] .
[tex]u=e^-^x[/tex][tex]du=-e^-^x dx[/tex] [tex]dv=cos2x \ dx[/tex] [tex]v= \frac{sin2x}{2}[/tex]Plug these values into the IBP formula:
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = e^-^x \cdot \frac{sin2x}{2} - \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex] [tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex]Now let's evaluate the integral [tex]\displaystyle \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex].
Let's find u, du, dv, and v for this integral:
[tex]u=-e^-^x[/tex] [tex]du=e^-^x dx[/tex] [tex]dv=\frac{sin2x}{2} dx[/tex] [tex]v=\frac{-cos2x}{4}[/tex]Plug these values into the IBP formula:
[tex]\displaystyle \int -e^-^x \cdot \frac{sin2x}{x}dx = -e^-^x \cdot \frac{-cos2x}{4} - \int \frac{-cos2x}{4}\cdot e^-^x dx[/tex]Factor 1/4 out of the integral and we are left with the exact same integral from the question.
[tex]\displaystyle \int -e^-^x \cdot \frac{sin2x}{x}dx = -e^-^x \cdot \frac{-cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx[/tex]Let's substitute this back into the first IBP equation.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \Big [ -e^-^x \cdot \frac{-cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx \Big ][/tex]Simplify inside the brackets.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \Big [ \frac{e^-^x \cdot cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx \Big ][/tex]Distribute the negative sign into the parentheses.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4} - \frac{1}{4} \int cos2x \cdot e^-^x dx[/tex]Add the like term to the left side.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx + \frac{1}{4} \int cos2x \cdot e^-^x dx= \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4}[/tex] [tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4}[/tex]Make the fractions have common denominators.
[tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x}{4} - \frac{e^-^x \cdot cos2x}{4}[/tex]Simplify this equation.
[tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{4}[/tex]Multiply the right side by the reciprocal of 5/4.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{4} \cdot \frac{4}{5}[/tex]The 4's cancel out and we are left with:
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{5}[/tex]Factor [tex]e^-^x[/tex] out of the numerator.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x(2 \cdot sin2x-cos2x)}{5}[/tex]Simplify this by using exponential properties.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2 \cdot sin2x-cos2x}{5e^x}[/tex]The final answer is [tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2 \cdot sin2x-cos2x}{5e^x} + C[/tex].
Answer:
[tex]\displaystyle\int e^{-x}\cos(2x)\, dx=\frac{2\sin(2x)-\cos(2x)}{5e^x}+C[/tex]
Step-by-step explanation:
We would like to integrate the following integral:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx[/tex]
Since this is a product of two functions, we can consider using Integration by Parts given by:
[tex]\displaystyle \int u\, dv =uv-\int v\, du[/tex]
So, let’s choose our u and dv. We can choose u base on the following guidelines: LIATE; or, logarithmic, inverse trig., algebraic, trigonometric, and exponential.
Since trigonometric comes before exponential, we will let:
[tex]u=\cos(2x)\text{ and } dv=e^{-x}\, dx[/tex]
By finding the differential of the left and integrating the right, we acquire:
[tex]du=-2\sin(2x)\text{ and } v=-e^{-x}[/tex]
So, our integral becomes:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=(\cos(2x))(-e^{-x})-\int (-e^{-x})(-2\sin(2x))\, dx[/tex]
Simplify:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\int e^{-x}\sin(2x)\, dx[/tex]
Since we ended up with another integral of a product of two functions, we can apply integration by parts again. Using the above guidelines, we get that:
[tex]u=\sin(2x)\text{ and } dv=e^{-x}\, dx[/tex]
By finding the differential of the left and integrating the right, we acquire:
[tex]du=2\cos(2x)\, dx\text{ and } v=-e^{-x}[/tex]
This yields:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\Big[(\sin(2x))(-e^{-x})-\int (-e^{-x})(2\sin(2x))\, dx\Big][/tex]
Simplify:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\Big[-e^{-x}\sin(2x)+2\int e^{-x}\cos(2x)\, dx\Big][/tex]
We can distribute:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)-4\int e^{-x}\cos(2x)\, dx[/tex]
The integral on the right is the same as our original integral. So, we can isolate it:
[tex]\displaystyle \Big(\int e^{-x}\cos(2x)\, dx\Big)+4\Big(\int e^{-x}\cos(2x)\, dx)\Big)=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)[/tex]
Combine like integrals:
[tex]\displaystyle 5 \int e^{-x}\cos(2x)\, dx=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)[/tex]
We can factor out an e⁻ˣ from the right:
[tex]\displaystyle 5\int e^{-x}\cos(2x)\, dx=e^{-x}\Big(-\cos(2x)+2\sin(2x)\Big)[/tex]
Dividing both sides by 5 yields:
[tex]\displaystyle \int e^{-x}\cos(2x)\, dx=\frac{e^{-x}}{5}\Big(-\cos(2x)+2\sin(2x)\Big)[/tex]
Rewrite. We of course also need the constant of integration. Therefore, our final answer is:
[tex]\displaystyle\int e^{-x}\cos(2x)\, dx=\frac{2\sin(2x)-\cos(2x)}{5e^x}+C[/tex]
Last year, the debate club had 16 members. This year, the club has 10 members. What is the percent of change in the number of club members?
Answer:
-60%
Step-by-step explanation:
The formula for percent change is [ x2-x1/x1 ].
10-16/10
-6/10 or -0.6
~Multiply by 100%
-0.6 * 100% = -60%
Best of Luck!
The campus bookstore knows from the past several semesters that a certain elementary statistics book has a demand that is approximated by a normal distribution with a mean of 250 and a standard deviation of 40. They buy these books for $105 each and sell them to unsuspecting undergraduates at $222 each. All demand for this book is realized by the middle of the semester, at which point the bookstore bundles them up and sells them to a vendor in another country for $40 each. What is the probability of sale for the last book that the bookstore should purchase for sale to a student
Answer:
0.357
Step-by-step explanation:
The computation of the probability of sale for the last book that the bookstore should purchase for sale to a student is shown below
Probability is
= 1 - ((Cs ) ÷ (Cs + co))
= 1 - (($225 - $105) ÷ ($117 + ($105 - $40)))
= 1 - 0.6428
= 0.357
Here Cs represent the notional loss in the case when the demand is underestimated
And Co represent the notional loss in the case when the demand is overestimated
The equation 22j + 8s = 150 is used to determine the number of jeans j and the number of shirts s that can be bought for $150. You purchase 5 pairs of
jeans. Select all the steps that may be used when solving for the number of shirts purchased
A Add 22 to both sides.
B. Subtract 22; from both sides.
C. Substitute 5 for j in the equation
D. Multiply both sides by 8
E Divide both sides by 8.
Answer:
C. Substitute 5 for j in the equation
Step-by-step explanation:
22(5)+8s =150
110+8s=150
8s = 40
s=5
or
110+8s=150
sam was charged $1050 in interest on a loan with a 2.5% interest rate. what was the original amount of the loan if he took 5 years to pay it back?
Answer:
$8,400=amount of loan
Step-by-step explanation:
Key:
P=Money borrowed
T=5 years (time passed)
R=0.025 (interest rate)
I=$1050 (interest charged)
Formula: I=P*R*T
Work:
1,050=P*0.025*5
1,050=P*0.125
1,050/0.125=8,400
Check
8,400*0.025*5=1,050
(thank you 7th grade math last year haha)
Mrs. Cameron's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?
23 x 3 =
57 + 12 =
47 + 22 =
Find the range of the function for the given domain.
f(x) = 3x -6;{-2,-1,0,1,2}
What is the range? Choose the correct answer below.
A. {-13, - 9,-6,-3,1)
B. {-12, - 8,-6,- 2,0}
C. {-12, - 8, -7,-2,0)
D. {-12,-9,-6,-3,0}
=================================================
Explanation:
The domain is the set of allowed x inputs. The range is the set of possible y outputs.
The set {-2,-1,0,1,2} represents all the possible x inputs
Let's plug each of those into the equation y = 3x-6 to find the corresponding paired out puts.
Note: y = f(x), so f(x) = 3x-6 is the same as y = 3x-6.
---------------
If x = -2, then,
y = 3x-6
y = 3(-2)-6
y = -6-6
y = -12
We see that x = -2 and y = -12 pair up together.
The value -2 in the domain maps to -12 in the range.
----------------
If x = -1, then,
y = 3x-6
y = 3(-1)-6
y = -3-6
y = -9
The input x = -1 in the domain maps to the output y = -9 in the range
So far the range consists of {-12, -9} in either order.
The answer is between A and D
-----------------
If x = 0, then,
y = 3x-6
y = 3(0)-6
y = 0-6
y = -6
So -6 is also part of the range. We have {-12, -9, -6} so far. The answer is still between A and D.
------------------
If x = 1, then,
y = 3x-6
y = 3(1)-6
y = 3-6
y = -3
The range updates to {-12, -9, -6, -3}
A and D are still equally valid
-------------------
We have one more x value to try
If x = 2, then,
y = 3x-6
y = 3(2)-6
y = 6-6
y = 0
Since y = 0 is in the range, instead of y = 1, this rules out choice A
The answer is therefore D. {-12, -9, -6, -3, 0}
Which theorem, term, or corollary is represented by the picture? The bold lines in the pictures represent the hypothesis of the theorem or corollary.
A. Corollary to the isosceles triangle theorem
B. Corollary to the converse of the isosceles triangle theorem
C. CPCTC
D. Isosceles triangle theorem
E. Converse to the isosceles triangle theorem
Answer:
Pictured is the equilateral triangle with 3 sides and 3 angles being same
This should be equilateral triangle theorem, but it is not captured by answer choices
ARIHANNAL
Session 2: Calculator
Question 22
X+Y
Line
Guide
Jason took out an $800 loan from his bank two years ago. He recently paid $860 back to the bank. This included the original loan amount
and the simple interest charged to him.
What was the annual interest rate of Jason's loan?
a 3%
D 3.75%
7.5%
15%
Answer:
I think its 3 or 3.75 you can check
Step-by-step explanation:
The linear regression equation for a data set is y=1.6x-4.1. If the actual value at x=3 is 0.9,
what is the residual value at x=3?
Answer:
0.2
Step-by-step explanation:
Given the regression model :
y = 1.6x - 4.1
At x = 3
Predicted value = 1.6(3) - 4.1 = 0.7
If actual value at x = 3 is 0.9
The residual value at x = 3 ;
Residual value is the difference between the actual and predicted value :
Actual at x = 3 minus predicted at x = 3
Hence, Residual = 0.9 - 0.7 = 0.2
Residual is the difference between the predicted value and the actual value of the response variable
The residual at x = 3 is 0.2
The linear regression is given as:
[tex]y = 1.6x - 4.1[/tex]
The predicted value at x = 3 is calculated by substituting 3 for x in the linear regression
So, we have:
[tex]y = 1.6 \times 3 - 4.1[/tex]
[tex]y = 4.8 - 4.1[/tex]
[tex]y = 0.7[/tex]
The actual value is given as 0.9.
So, the residual is calculated using:
[tex]Residual =Actual - Predicted[/tex]
This gives
[tex]Residual =0.9 - 0.7[/tex]
[tex]Residual =0.2[/tex]
Hence, the residual at x = 3 is 0.2
Read more about residuals at:
https://brainly.com/question/9315325
Which expression is equivalent to 2(x + 7) – 18x + 3?
Answer:-16x+17
Step-by-step explanation:
The square of 15 is 225. The square of what other number is 225?
Answer:
-15
Step-by-step explanation:
-15²
= -15×-15
= 225
hope it helps!!
Answer:
-15
Step-by-step explanation:
Any number times itself is a positive number. The square of any number will be the same as the square of that number times -1
example:
2^2=4
-2^2=4
1. Using the numbers 1-20, and only using a number once, fill in the blanks. There may be multiple correct answers
a) (x +
D(x+
b) (x + (x +
2. Using the numbers 1-40, and only using a number once, fill in the blanks. There may be multiple correct answers
a) (x+2)CL_X+5) =
b) CX+ 2XL X+5) =
kingston made a pot of 29 1/2c of gumbo soup. His family ate some of the gumbo for lunch. this changed the amount of the pot by -7 3/4c. then he gave some gumbo to his neighbors. This changed the amount in the pot by -6 1/2c. How many cups of gumbo are left in the pot?
please answer quickly!!!!!!!
Answer:
29 1/2-7 3/4 is 21.75
Then 21.75-1/2 is 21.25
Step-by-step explanation:
There is [tex]15\frac{1}{4}[/tex]c of gumbo soup left after Kingston's family ate and he shared some with his neighbor.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Kingston made a pot of [tex]29\frac{1}{2}[/tex] of gumbo soup.
His family ate some of the gumbo for lunch. this changed the amount of the pot by [tex]-7\frac{3}{4}[/tex].
So, Reaming gumbo soup is ([tex]29\frac{1}{2} - 7\frac{3}{4}[/tex]).
= (59/2 - 31/4).
= (118 - 31)/4.
= 87/4c of gumbo soup.
Then he gave some gumbo to his neighbors. This changed the amount in the pot by -6 1/2c.
= (87/4 - 13/2)c.
= (87 - 26)/4c.
= 61/4.
= [tex]15\frac{1}{4}[/tex]c of gumbo soup.
learn more about fractions here :
https://brainly.com/question/10354322
#SPJ2
I need help?...........
Answer:
J. 2(×-3)=22...........
Answer:
J. 2( x - 3 ) = 22
Step-by-step explanation:
All you need to do, is substitute the x with 14
2 ( x - 3 ) = 22
2 ( 14 - 3 ) = 22
use PEMDAS
2 * 14 - 2* 3 = 22
28 - 6 = 22
22 = 22
So this problem is the correct one
Hope this helped!
P.S Do you want me to show you the work for the others so you can see how I know there wrong?
If I had 1 banana then I ate that banana how many of the banana would I have hint the peal First person gets brainliest
1 peal 0 banana
eeeeeeeeeeeeee
please help me urgent!!
[tex] \sf \longmapsto S_{ 20} = \dfrac{n}{2} \times 2a + (n - 1)d \\ \\ \sf\longmapsto S_{20}= \dfrac{20}{2} \times 2(2) + (20 - 1)6 \\ \\ \sf\longmapsto S_{20} = 10 \{ 4 + 114 \} \\ \\ \sf \longmapsto \boxed{\bf{S_{20} = 1180}}[/tex]
Hope it helps :)
Luis buys 6 pizza's for $36.90 at the Italian restaurant, how much does 1 pizza cost?
Answer:
$6.15 for 1 pizza.
Step-by-step explanation:
The answer is 6.15 because 36.90 divided by 6 is 6.15.
P.S Can I have brainliest?
what is 1% of 73023.60
Answer:
730.236
the answer
Sam saved $50 from his summer job to buy video games. He bought 3 video
games and the cashier gave him $12.80 in change. If each game cost the same
amount, how much was each video game?
Answer:
$12.40
subtract 12.80 from 50 to get 37.20 then divide by 3
What is the origional price of an object if the total is 878.74 and the tax is 0.07.
My problem/find X
X × 0.07 =b
X + b =$878.78
Answer:
The original price was $821.25
Step-by-step explanation:
The price of an object is $878.74 including a tax of 7%.
We are required to find the original price.
If the tax is 7%, then the total price is 100+7=107% of the original price.
Thus, $878.74 is the 107% of the original price x, thus:
x = $878.74/107*100 = $821.25
The original price was $821.25
Which statement is correct?
Α. ΔΑGT = ΔQΜΕ
Β. ΔTAG = ΔΕΜW
C. ΔGTA = ΔQΜΕ
D. ΔΑGT = ΔΜΕΟ
Answer:
C
Step-by-step explanation:
We already know the triangles are congruent because all of the sides of one triangle correspond directly with another. Then, this is a problem of correct labling. GTA goes from point G (top) to T (bottom) to A (left). If we rotate the triangle MEQ, it is laid out in the same way: point Q (top) to point M (bottom) to point E (left or right).
Our correct answer is GTA = QME
If s varies directly as t2, and s = 294 when t = 7, find s when t is 9
Answer:
If you need to find s when t is 9, its simple.
Step-by-step explanation:
All ypu need to do is see what t is
t equals 2
you want to find what s is when t is 9
when t is 2, s is 294
when t is 9, all you have to do is find what times 2 equals 9, then times that number by 294
Help pls I need help asap
Which statement is true regarding the graphed functions?
chris types 350 words in 4 minutes. Which equation can be used to find w, the number of words chris can type in 20 minutes if he continues to type at the same speed rate?
Answer:
Chris will type 7,000 words in 20 minutes. You can use 350 x 20 to find your answer.
Step-by-step explanation:
Write a linear function for each line that relates to y to x
Answer:
Please check the complete explanation below.
Step-by-step explanation:
We know that the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
ANALYZING TABLE 1
Part A)
Given table 1
x 0 1 2 3
y 1 3 5 7
From table 1, the y-intercept can be determined by setting x=0 and checking the corresponding y-value.
so at x = 0, y = 1
Thus, the y-intercept is (0, 1).
From the graph, it is clear that the line W has a y-intercept (0, 1).
Therefore, table 1 represents the line W.
Part B)
Taking two points (0, 1) and (1, 3) to find the slope using the formula
m = (y₂-y₁) / (x₂-x₁)
m = 3-1 / 1-0 = 2/1 = 2
now substituting m = 2, and b = 1 in the slope-intercept form
y = mx+b
y = 2x+1
Thus, table 1 represents the line W with the equation line y = 2x+1
ANALYZING TABLE 2
Part A)
Given table 2
x 0 1 2 3
y 0 3 6 9
From table 2, the y-intercept can be determined by setting x=0 and checking the corresponding y-value.
so at x = 0, y = 0
Thus, the y-intercept (0, 0).
From the graph, it is clear that line F has a y-intercept (0, 0).
Therefore, table 2 represents the line F.
Part B)
Taking two points (0, 0) and (1, 3) to find the slope using the formula
m = (y₂-y₁) / (x₂-x₁)
m = 3-0 / 1-0 = 3/1 = 3
now substituting m = 3, and b = 0 in the slope-intercept form
y = mx+b
y = 3x+0
y = 3x
Thus, table 2 represents the line F with the equation y = 3x
ANALYZING TABLE 3
Part A)
Given table 1
x 0 1 2 3
y 2 3 4 5
From table 3, the y-intercept can be determined by setting x=0 and checking the corresponding y-value.
so at x = 0, y = 0
Thus, the y-intercept (0, 2).
From the graph, it is clear that line N has a y-intercept (0, 2).
Therefore, table 3 represents line N.
Part B)
Taking two points (0, 2) and (1, 3) to find the slope using the formula
m = (y₂-y₁) / (x₂-x₁)
m = 3-2 / 1-0 = 1/1 = 1
now substituting m = 1, and b = 2 in the slope-intercept form
y = mx+b
y = (1)x+2
y = x+2
Thus, table 2 represents the line N with the equation y = x+2
how many times larger is 2.4 x 10^8 than 6 x 10^7?
Identify the angles of rotational symmetry for the figure.
+
Rotational symmetry
Answer:
144
Step-by-step explanation:
Answer:
90 180 270
Step-by-step explanation:
PLEASE HELP ME I AM BEING TIMED I WILL GIVE YOU BRAINILIEST!!!!!!
On a road trip a family drives 350 miles per day how many days D must they travel to reach the distance of at least 1400. Solve the inequality what does the solution represent in this situation?
(Just in case you wanted to see the question I put a picture)
Answer:
The family will travel at least 4 days.
Step-by-step explanation:
The inequality would look like this:
350d ≤ 1400
it's ≤ because the problem said that they had to travel AT LEAST a distance of 1400.
To solve the inequality, use inverse operations.
350d ÷ 350 ≤ 1400 ÷ 350
d ≤ 4
the family will travel at least 4 days.
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!