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]
explanation please?!?!
Answer:
third option
Step-by-step explanation:
[tex]first\:one:\\\\2x+10=-2x+10 \rightarrow\leftarrow\\\\second:\\\\-2(x+5)=2x-10\\\\-2x-10=2x-10\rightarrow\leftarrow\\\\third:\\\\-2x-10=-2(x+5)\\\\-2x-10=-2x-10 \\\\fourth:\\\\-2(x-5)=-2x-10\\\\-2x+10=-2x-10\rightarrow\leftarrow[/tex]
Note: this symbol [tex]\rightarrow\leftarrow[/tex] means contradiction, you can take it as doesn't work
I hope that i explained enough
What’s the measure for x
find the length of the third side to the nearest tenth 6 and 9
Hello, i do believe that you are asking me to do pythagorean theorem.
I'm not too sure if we are solving hypotenuse or a/b so i'll do both.
[tex]\boxed{\underline{Hypotenuse...}}\\\\\\A^2+B^2=C^2\\6^2+9^2=C^2\;\\36+81=117[/tex]
[tex]\sqrt{117}=10.816\\Round-\;10.8[/tex]
[tex]\boxed{\underline{a/b...}}\\\\\\A^2=C^2-B^2\\A^2=9^2-6^2\\A^2=81-36\\A^2=45\\\sqrt{45}= 6.708\\Round-\;6.7[/tex]
Hope it helps!
which property is this example (1+2)+3=1+(2+3)
Answer
Associative property of addition
Step-by-step explanation:
Please need it finshed i will give brainliest to whoever right.
Answer:
40 + -40 = 0
Step-by-step explanation:
hope this helps!
Answer:
40 + -40 =0 (your answer)
2538494 + -2538494 = 0 (example)
4 + -4 = 0 (example)
-18 + 18 = 0 (example)
-82 + 82= 0 (example)
just as long as the first number and the second number are the same, and one is negative and the other is positive, added together the two numbers will equal zero.
What's this? I don't understand
Answer:
There are two solutions
Step-by-step explanation:
The two equations intersect in two points therefore you willl have two solutions
Answer:
C. two solutions
Step-by-step explanation:
Hope this helped have an amazing day!
Please help I’ll appreciate it thank you
Answer:
107*
Step-by-step explanation:
assuming QOP is 73 degrees then NOP is 107 degrees
a straight like is 180* then - 73* = 107*
Find the volume of a pyramid with a square base, where the side length of the base is
14.7 in and the height of the pyramid is 17.2 in. Round your answer to the nearest
tenth of a cubic inch.
Answer:
1238.9
Step-by-step explanation:
The volume of pyramid with square a square base is 1239 [tex]inch^{3}[/tex]
What is pyramid with square base?A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid
We have
Side length of base(L) = 14.7 inch
Height of pyramid(H) = 17.2 inch
Given ,Base is a square then
length=width(w)=14.7 inch
We know the formula of volume of pyramid = 1/3(L×W×H)
= 1/3 (14.7 × 14.7 × 17.2)
= 1/3 × 3716.748
= 1238.916
= 1239 [tex]inch^{3}[/tex]
Hence, The volume of pyramid is 1239 [tex]inch^{3}[/tex]
To learn more pyramid from here
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Translate the sentence into an inequality.
A number c increased by 3 is greater than -27.
Answer:
Inequality: c + 3 > -27
A researcher is interested in the relationship between time spent browsing items in an online store and the total amount purchased from the store. The researcher selects a random sample of visitors to the online store and records the time spent browsing and the total amount of their purchase. The researcher will conduct a t-test for the slope of a regression line, where time spent browsing is the explanatory variable and total amount of purchase is the response variable. Which of the following would be an indication that the normality condition has been met?
A. A sample size that is less than 30
B. A histogram of the residuals that is centered at 0 and strongly right skewed
C. A dotplot of the residuals that is centered at 0, unimodal, and symmetric
D. A boxplot of the residuals that is centered at 100 and does not provide evidence of skewness or outliers
E. A scatterplot where total amount of purchase is the explanatory variable and time spent browsing is the response variable
Answer:
C
Step-by-step explanation:
AP Classroom
please help me will mark brainliest
How can you use an inequality to describe the dimensions of a figure?
A scalene triangle can be identified by the inequality of the lengths of its sides and size of its angles.
Tired asl I need some help, thanks.
Answer:
C
Step-by-step explanation:
y=5-2x
3x-y=15
Substitute
3x-(5-2x)=15
Which expression is equivalent to 25?
2 + 2 + 2 + 2 + 2
5+5
0 2.2.2.2.2
5.5
DONE
Answer:
It's C because its 2 to the power of 5
Step-by-step explanation:
2x2x2x2x2
20 of the 80 coffee mugs at Carson's Pancake House are dirty. What percentage of the coffee mugs at the pancake house are dirty?
Answer:
25%
Step-by-step explanation:
20/80 in can be reduced to 1/4 and 1/4 equals 25%.
We have:
[tex]\dfrac{20}{80} = \dfrac{\%} {100}[/tex]
Solving for %:
[tex]\% = \dfrac{20\cdot 100}{80} = 25\%[/tex]
R/ 25% of coffee mugs are dirty.
Complete the table.
y = f(g(x))
u = g(x)
y = f(u)
y = 8 tan(itx5) u =
I
y = 8 tan u
9514 1404 393
Answer:
u = x +14 u = πx^5Step-by-step explanation:
I find it easiest to match the patterns. You could also work this by finding inverse functions.
1.
[tex]y=u^{-1/2}\\\\y=\dfrac{1}{\sqrt{u}}=\dfrac{1}{\sqrt{x+14}}\\\\u=x+14 \qquad\text{match radical contents}[/tex]
__
2.
[tex]y=8\tan{u}=8\tan{(\pi x^5)}\\\\u=\pi x^5 \qquad\text{match tangent arguments}[/tex]
Jared bakes 2 apple pies. He cuts the two pies into pieces. Each piece is 1/8 of a pie. Enter the number of pie Jared cuts.
Answer:
16 pieces
Step-by-step explanation:
Please give me brainliest
this is so emaruballos can be marked brainliest and yes the answer is 16
The Ulis family spends $1,632 a year for gym memberships. How much does the family spend in 4 years?
Enter your answer in the box.
Help me please.
Best answer gets brainiest. Ariel hiked to a famous point with a beautiful view. It took 2 hours and 20 minutes to hike to the viewpoint and 55 minutes to hike back. Ariel spent 1 hour and 40 minutes enjoying the view at the top. She finished the hike at 2:55 P.M. What time did Ariel start the hike to the viewpoint?
Include A.M. or P.M. in your answer.
Answer:
10: 00 AM
Step-by-step explanation:
2 hr 20 minutes +55 min= 3 hours 15 minutes
3. 15+ 1 hr 40 min= 4 55 min
2: 55 pm- 4 hours and 55 minutes= 10 am
Answer:
Ariel starts hiking at 10:00am
Step-by-step explanation:
2hr 20min
+ 55min
+ 1hr 40min
————————
4hr 55min total time spent hiking.
14:55 - 4hr 55min = 10:00
2:55 pm - 4hr 55min = 10:00am
skateboard is priced for $38. They are having a sale for 20% off. how much is the discount and what is the selling price
Answer:
18$
Step-by-step explanation:
Find an equation of the line that passes through the point (23, 22) and is
parallel to 2x=3-5y
Answer:
The equation of the line is y= -2/5x+156/5
Step-by-step explanation:
y=mx+b
m= -2/5 ( 23,22)
y-y=m(x-x¹)
y-22=-2/5(x-23)
y-22=-2/5x+46/5
+22 +22
y= -2/5x+156/5
there are 120 cars in a multi storey car park given that 30% of them are blue find the number of cars which are not blue
Answer:
84 cars
Step-by-step explanation:
30% are blue, which means (100-30=70) 70% are not blue
(70/100)×120= 84
hence, 84 cars are not blue
hope it helps!!!!
What's the ratio equivalent to 15 to 60.
Answer:
1:4
Step-by-step explanation:you can simplify the ratio by finding the LCM on both sides and dividing the number by the lcm in which this case is 15.
15/15=1
60/15=4
so 1:4
The answer to the question is 1:4
Step-by-Step explanation:
We have to divide each number over here by the LCF of 15.
The LCF (Least Common Factor) of 15 is 5.
Given the LCF of 15 is 15, we will divide both given numbers by 15.
[tex]\text {60 / 15 = 4 and 15 / 15 = 1}[/tex]
We will put the numbers back in order from least to greatest.
The ratio we find is 1:4, and the answer to your question is 1:4.
Carry on Learning!
Hayden plans to take a loan out to buy his Ultimate PC
Gaming Desktop. He will borrow $6,200 from the bank
at a rate of 3.5% annually. The length of the loan will be
5 years. How much interest will Hayden have to pay on
the loan? What is the total that Hayden will have to pay
the bank back?
Give step by step plz
Answer:
The rate of simple interest for loan was 8%
Step-by-step explanation:
Given
Principal amount = p = $6200
Time = t = 1 year
Amount after interest = $6696
We have to calculate the amount of interest first
So,
Interest amount =I= Amount after interest - principal amount
= 6696-6200
=$496
The formula for simple interest is:
The rate of simple interest for loan was 8%
Keywords: Simple interest, percentage
Learn more about simple interest at:
determine the coordinates
Answer:
Thus, the rule of a point P(x, y) reflected over the line y = -x
P(x, y) → P'(-y, -x)
we conclude that:
A(3, 4) → A'(-4, -3)B(3, 2) → B'(-2, -3)C(-1, 2) → C'(-2, 3)Step-by-step explanation:
We know that If a point P(x, y) is reflected over the line y = -x, the x-coordinate and y-coordinate tend to change places and the signs are reverses.
Thus, the rule of a point P(x, y) reflected over the line y = -x
P(x, y) → P'(-y, -x)
Thus, we conclude that:
A(3, 4) → A'(-4, -3)B(3, 2) → B'(-2, -3)C(-1, 2) → C'(-2, 3)The equation y = 12x represents a proportional relationship. What is the
constant of proportionality? will give brainliest
Answer:
D
Step-by-step explanation:
Proportional relationships come in the form
[tex]y=kx[/tex]
and [tex]k[/tex] is the constant of proportionality. By comparing the general case [tex]y=kx[/tex] and your specific case [tex]y=12x[/tex], you can see that in your case [tex]k=12[/tex].
In the equation y = 12x the constant of proportionality is D. 12.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Let y = kx.
∴ k = y/x.
Given, y = 12x.
12 = y/x.
So, the constant of proportionality is 12.
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Which of the following is an appropriate line of fit for the data?
1
T
2
3
4
5
6
y
8
15
23
28
37
44
Oy= 5x + 1
y = 7x + 2
2
Oy= -62 +5
Oy= 6.52
Answer:
123idbd8dbokeofyccbdid12332
What is an equation parallel to y=3x-5
Answer:
ANY line that has a slope of 3, and any y intercept other than -5.
Step-by-step explanation:
Parallel lines have the same slopes, but different y intercepts.
So, it would be ANY line that has a slope of 3, and any y intercept other than -5.
here are a few examples:
y=3x-17
y=3x+4
y=3x+3293248032843209.3432492384032984032984023840398249082
y=3x+5
y=3x-1
y=3x
Mr. Garza bought paper cups for his food truck. He bought 5 cartons of blue cups and 4 cartons of green cups. He ordered a total of 1,008 cups. How many cups are in each carton?
Answer:112
Step-by-step explanation:Divide 1008 by 9
Explain how Sergio use three lengths of a ribbon 2 ½ feet long to wrap packages. How many feet of ribbon did he us
Answer:
rate this 5 stars or your gay
Step-by-step explanation:
Just do it
identify the type of pair of angles labeled as 1 and 2 in the figure. will give brainliest!!!!!
