the answer is m=2.4r. I HOPE THIS HELPS YOU OUT
Integrate the following problem:
[tex]\int {e^{-x} \cdot cos(2x)} \, dx[/tex]
P.S:
Have fun Lauren (and possibly Kelvy)!
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]
A equation of a line in slope intercept form with the given slope and Y-intercept slope: -4, Y-intercept : -9
Answer:
y = -4x - 9
Step-by-step explanation:
Use slope intercept form, y = mx + b, where m is the slope and b is the y intercept.
Since we are already given the slope and y intercept, we just have to plug them into the equation to find the equation:
y = mx + b
y = -4x - 9
So, y = -4x - 9 is the equation of the line in slope intercept form
A group of friends ordered two pizzas, one with pepperoni and one with mushrooms and green peppers. A plain pizza costs $9. Each topping costs $1. How much did the two pizzas cost?
A.
Answer:
21$
Step-by-step explanation:
2 pizzas =18 plus 3 toppings which equals 21$
I need help need it done in 20 minutes will give 20 points each
Answer:
Lets start by isolating for one variable In this case I chose y -7x-2y=14 -2y=14+7x y=-7 -3.5x (1)Next plug the y into the second equation to solve for x
6x+6(-7 -3.5x) =186x+(-42)+ (-21x) =18 6x-21x= 60 -15x=60x=-4Now we know x and we can plug into the original equation (1)
x= -4 y= -7 - 3.5× -4 y= 7Rate brainlist and drop a follow for future help
Answer:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
6*x-6*y-(18)=0
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
6x - 6y - 18 = 6 • (x - y - 3)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true:
2.1 Solve : 6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve x-y-3 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
Step-by-step explanation:
x= 1 y= 1
hope am right if i am, pls brainliest
I will give you brainliest if you answer this right.
Just Some e-dgenuity i need to get done
Answer:
Check mark number
2
4
5
Please help me thank you so much I appreciate it
Answer:
12
Step-by-step explanation:
To find perimeter, add the lengths of each side. 5 + 4 + 3 = 12
Answer:
12
Step-by-step explanation:
5+4+3
Harper is a salesperson who sells computers at an electronics store. She makes a base pay amount of $100 per day regardless of sales and she earns a commission of 1% of the dollar amount of sales that she makes. Write an equation for P, in terms of x, representing Harper’s total pay on a day which she sells x dollars worth of computers
Answer:
100x-p*1%
Step-by-step explanation:
Is this correct if not correct me
help me answer these questions please 15, 19 and 20 please
Answer:
15) K'(t) = 5[5^(t)•In 5] - 2[3^(t)•In 3]
19) P'(w) = 2e^(w) - (1/5)[2^(w)•In 2]
20) Q'(w) = -6w^(-3) - (2/5)w^(-7/5) - ¼w^(-¾)
Step-by-step explanation:
We are to find the derivative of the questions pointed out.
15) K(t) = 5(5^(t)) - 2(3^(t))
Using implicit differentiation, we have;
K'(t) = 5[5^(t)•In 5] - 2[3^(t)•In 3]
19) P(w) = 2e^(w) - (2^(w))/5
P'(w) = 2e^(w) - (1/5)[2^(w)•In 2]
20) Q(W) = 3w^(-2) + w^(-2/5) - w^(¼)
Q'(w) = -6w^(-2 - 1) + (-2/5)w^(-2/5 - 1) - ¼w^(¼ - 1)
Q'(w) = -6w^(-3) - (2/5)w^(-7/5) - ¼w^(-¾)
I need help with these too questions
Number 1
Number 2
Answer:
Step-by-step explanation:
-6n + 2.9 = 11
subtract 2.9 from both sides
-6n = 8.1
divide both sides by -6
n = -1.35
2/3n - 3 = 8
add 3 to both sides
2/3n = 11
multiply both sides by 3
2n = 33
divide both sides by 2
n = 16.5
hope this helps <3
Answer:
left side:
-6n = 11 - 2.9
-6n = 8.1
n = - 8.1/6
n = - 1.35
right side:
2/3 n = 8 + 3
2/3 n = 11
n = 33/2
n = 16.5
What postulate/theorem can be used to prove the following triangles congruent?
Answer: SAS
Step-by-step explanation:
It is given that the two sides are congruent.
The angle between the two congruent sides is also congruent because of the vertical angle theorem.
Since a side, angle, and side are congruent, the theorem is SAS.
Company a charges 60$ plus 0.15 per mile company b charges 25$ per day or portion of a day .Jason has determined that it will cost him less to rent a car from company a for a weekend trip .is Jason's conclusion accurate?
Answer:
No
Step-by-step explanation:
A: C = 60 + 0.15m (C is total cost and m is no. of miles)
B: C = 25d (d is no. of days)
For a weekend trip, there are 2 days.
This means that the cost for B is 2*$25, which is $50.
It doesn't matter how many miles are driven for A because the cost will always be at least $60.
This means that B is cheaper and that Jason is inaccurate.
Find the unknown of the following
Step-by-step explanation:
For 4.
4b + 2b + 3b = 180°< Sum of angles of triangle >
9b = 180°
b = 180° / 9
b = 20°
4b = 4* 20° = 80°
2b = 2* 20° = 40°
3b = 3 * 20° = 60°
For 5.
x = 64° + 45° <Exterior angle of a triangle is equal to the sum of two opposite interior angles>
x = 109°
Hope it helps :)
Rob did 15 push-ups on Monday, but on Tuesday he did 3 more than on Monday. What was the percent change?
Answer:
20%
Step-by-step explanation:
A shop sells apple juice in cartons of two sizes. A 500 ml carton costs $1.30.
a) Work out the cost of 250 ml of this apple juice. A 750 ml carton costs $1.86.
b) Work out the cost of 250 ml of this apple juice.
c) Which carton is better value for money?
The sprit club is making school jackets to sell. The cost c (in dollars) for silkscreening supplies and jackets is c=20x+270, where x is the number of jackets. The club sells each jacket for $35. Write an equation for revenue R in terms of the number of jackets. How many jackets must the club sell to break even?
Answer:
The club must sell 18 jackets to break even
Step-by-step explanation:
Given:
C = 20x + 270
Where,
x = number of jackets
Equation for revenue R in terms of the number of jackets
Revenue = price × quantity
Price of the jacket = $35
Quantity of the jacket = x
Revenue = price × quantity
= 35 * x
R = 35x
Break even point is the point at which cost is equal to revenue, that is, no gain; no loss.
Cost = revenue
20x + 270 = 35x
270 = 35x - 20x
270 = 15x
x = 270 / 15
= 18
x = 18 jackets
The club must sell 18 jackets to break even
Answer:
torture
Step-by-step explanation:
I was just working on a prblem like this and I hate it
Answer this ASAP please. If you can’t see then zoom in. Giving out 25 points and Brainliest to the one who answers correctly. There is a PT2 to this, so you’ll have another chance to answer if you want.
Thank you in advance.
Answer:
Put 2 feet down for both of them and add 3 extra feet for nate
Step-by-step explanation:
Answer:
add 3 extra feet for Nate and put 2 feet from the both of them
Step-by-step explanation:
Which of the following MUST be true for two negative number?
A sailboat is 175 feet from the base of a lighthouse. If the angle of elevation to the top of the lighthouse is 23°, find the height of the lighthouse, to the nearest hundredth of a foot.
9514 1404 393
Answer:
74.28 ft
Step-by-step explanation:
The tangent of the angle is the ratio of opposite side (lighthouse height) to adjacent side (distance from lighthouse).
tan(23°) = height/(175 ft)
height = (175 ft)·tan(23°) ≈ 74.28 ft
n/ 39 = 8/13
Please select the best answer from the choices provided.
A: n = 32
B: n = 2 2/3
C: n = 24
D: n = 63 3/8
Answer:
24 is the correct answer
Which expressions represent the distance between-1 and 4? Choose ALL that apply. 14 - 11 | 4 – (-1) HH34 4342 0 3 5 |-1 - 4 |-1 - (-4)
Aaliyah is 3 times as old as AJ. 4 years ago, Aaliyah was 7 times as old as AJ. How old is Aaliyah now?
Answer:
Aaliyah is 18years old now
Step-by-step explanation:
let AJ's age=x
Aaliyah's age=3x
Four years ago,
AJ's age=x-4
Aaliyah's age=3x-4
3x-4=7(x-4)
3x-4=7x-28
3x-7x=-28+4
-4x=-24
x=6
Aaliyah's present age=3x=3×6=18
(b) Mrs. Young calculates that 5 nights will cost $1350. What is the percent error in Mrs. Young’s calculation? Round to the nearest percent. Show your work
Answer:
5 x 13,50= 6,750
Step-by-step explanation:
5,400 is the answer of the persentage. I subtracted 6,750 from 1350 and got 6,750
Cost of 1 night:-
[tex]\\ \sf\longmapsto \dfrac{1350}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{270}{1}[/tex]
[tex]\\ \sf\longmapsto 270[/tex]
Evaluate
f(x)=5x-3
f(5) =
f(x)=5x-3
use the substitution method
f(5)=(5)(5)-3
multiply the parentheses first
using: PEDMAS
P=Parentheses
E= Exponents
D=Division
M=Multiplication
A= Addition
S=Subtraction
(5)(5)=25
25-3
=22
answer:
f(5)=22
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
find the scale factor of the dilation
Answer:
k=1/2
It is a reduction
Step-by-step explanation:
To the scale factor, you simply divide the length of the post image by the image.
10/20=k
1/2=k
Kate Sanders, a researcher in the department of biology at PFW University, studied the effect of agricultural contaminants on the stream fish population in northeastern Indiana (April 2012). Specially designed traps collected samples of fish at each of four stream locations. A research question was: did the differences in agricultural contaminants found at the four locations alter the proportion of the fish population by gender
Full question attached
Answer and explanation:
Null hypothesis : all population proportions are equal, p1=p2=p3=p4
Alternative hypothesis : Not all population proportions are equal
To find our p-value using chi Square method, we first find expected frequencies from observed frequencies above
Expected Frequencies:
Gender A. B. C. D
Male. 46.81 46.81 44.21 43.17
Female 43.19. 43.19 40.79 39.83
Total = 348
chi Square for table = (observed frequency - expected frequency)²/expected frequency
Gender. A. B. C. D
Male. 0.10 0.17 0.52 0.40
Female 0.11 0.18 0.56 0.44
x²= 2.49
Degrees of freedom(df)= k – 1 = (4 – 1) = 3
Using the chi Square table with degree of freedom = 3, 2 and x²= 2.49 shows, the p –value = 0.4771 therefore we do not reject null hypothesis since p value is greater than significance level 0.08
We do not reject the null hypothesis
b. There is no evidence of differences in proportion
Then solve each problen
Situation 1: A pair of shoes is on sale for 80% of the original price.
The sale price is $60. What was the original price?
food drive
Answer:
75
a(0.80)=60
a=60/0.80
a=75
brainlist asap, please help i need to boost my grade in math ♡´･ᴗ･`♡
♡︎♡︎♡︎♡︎♡︎♡︎♡︎♡︎♡︎♡︎♡︎♡︎
question: mona borrowed $6000 for college expenses. After 2 1/2 years she will have paid $750 in interest. What is the interest rate? ______
Answer:
5250
i hope this is right.
Answer:
5250
Step-by-step explanation:
person on my top got it ^