evaluate the integral. (use c for the constant of integration.) e4θ sin(5θ) dθ

Answers

Answer 1

The value of the integral is [tex]-(16/41) e^{(4\theta) }cos(5\theta) + c[/tex]

How to evaluate the integral ∫[tex]e^{(4\theta)}[/tex] sin(5θ) dθ?

To evaluate the integral ∫ [tex]e^{(4\theta)}[/tex] sin(5θ) dθ, we can use integration by parts.

Let's assign u = sin(5θ) and dv = [tex]e^{(4\theta)}[/tex] dθ.

Differentiating u with respect to θ, we have du = 5 cos(5θ) dθ.

Integrating dv with respect to θ, we have v = (1/4) [tex]e^{(4\theta)}[/tex].

Now, we can use the integration by parts formula:

∫ u dv = uv - ∫ v du

Applying the formula, we have:

∫ [tex]e^{(4\theta)}[/tex] sin(5θ) dθ = - (1/4) [tex]e^{(4\theta)}[/tex] cos(5θ) - ∫ (1/4) [tex]e^{(4\theta)}[/tex] (5 cos(5θ)) dθ

Simplifying further:

∫[tex]e^{(4\theta)}[/tex] sin(5θ) dθ = - (1/4) [tex]e^{(4\theta)}[/tex]cos(5θ) - (5/4) ∫[tex]e^{(4\theta)}[/tex] cos(5θ) dθ

Now, we have a new integral to evaluate: ∫[tex]e^{(4\theta)}[/tex]cos(5θ) dθ.

Using integration by parts again with u = cos(5θ) and dv = [tex]e^{(4\theta)}[/tex]dθ, we obtain:

du = -5 sin(5θ) dθ

v = (1/4) [tex]e^{(4\theta)}[/tex]

Applying the integration by parts formula:

∫ [tex]e^{(4\theta)}[/tex]cos(5θ) dθ = (1/4) [tex]e^{(4\theta)}[/tex]cos(5θ) - (5/4) ∫[tex]e^{(4\theta)}[/tex] sin(5θ) dθ

Substituting this back into the previous equation, we have:

∫[tex]e^{(4\theta)}[/tex]sin(5θ) dθ = - (1/4)[tex]e^{(4\theta)}[/tex] cos(5θ) - (5/4) [(1/4) [tex]e^{(4\theta)}[/tex] cos(5θ) - (5/4) ∫ [tex]e^{(4\theta)}[/tex]sin(5θ) dθ]

Now, let's solve for the remaining integral:

(1 + (25/16)) ∫[tex]e^{(4\theta)}[/tex]sin(5θ) dθ = - (1/4)[tex]e^{(4\theta)}[/tex] cos(5θ)

Simplifying:

(41/16) ∫ [tex]e^{(4\theta)}[/tex] sin(5θ) dθ = - (1/4) [tex]e^{(4\theta)}[/tex]cos(5θ)

Finally, dividing both sides by (41/16), we get:

∫[tex]e^{(4\theta)}[/tex]sin(5θ) dθ = - (16/41)[tex]e^{(4\theta)}[/tex] cos(5θ) + c

Therefore, the value of the integral ∫[tex]e^{(4\theta)}[/tex]sin(5θ) dθ is -(16/41) [tex]e^{(4\theta)}[/tex] cos(5θ) + c, where c is the constant of integration.

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Related Questions

France had 8,306,000 visitors while Australia had 15,976,000 visitors. How many combined visitors did they have?

Answers

Answer:

24,282,000 visitors (total)

Step-by-step explanation:

Add these two counts together:

8 306 000

15 976 000

------------------

24 282 000 total number of visitors

Answer:

Add the number of France visitors and Australia visitors and you will get...

Step-by-step explanation:

24,282,000 visitors

The Scenario: Your cousin Caleb has a dog-walking business, and you'd like to start one in your own neighborhood. Caleb has had his business for more than a year and has experimented with different prices for his services. He is willing to share what he has learned with you as you begin to plan your business. The Project: Use the information provided in the Performance Task to learn more about your competition and the costs of your business. See what you can discover by looking at Caleb's sales records to help you decide how to set up and price your own dog-walking services. Use the questions below to help you gather information and get your new business off to a profitable start. Understanding the Competition 1. Explore the three competitors in your area to learn more about the services they offer and how they reach their customers. Fill in the table below to help you compare their businesses. (12 points: 1 point for each table cell)
Outward HoundA1-Pet Services Debbie's Daily Dog Walks What services does the business offer? What do you know about the type of business and its staff? Who are the target customers? How much does the business charge?2. Now that you know a bit about the competition, it's time to get more specific about your business offering. (6 points: 3 points for describing services, 1 point for each of the other questions)
List three services you would like to offer. Do any of these services require you to buy special items? If so, what would you need to buy? Describe the type of customer you believe your business will appeal to and explain why. If you had to guess now, how much do you think you should charge for a 30-minute dog walk? Calculating Your Business Costs 3. Use the table below to summarize your monthly business costs. Record each option you choose in the "Options selected" column. (9 points: 1 point for each completed table cell)
Cost type Total cost per month Options selected Advertising Goods Transportation Licensing TOTAL 4. Explain the choices you made that determined your business costs in each cost category. (4 points: 1 point for each explanation) In your explanation, be sure to describe: ❑ Your advertising choices ❑ The goods you will purchase ❑ Your transportation needs
❑ Whether you chose bonding ❑ The reasons for your choices Advertising: Goods: Transportation: Bonding:
loading...
With every price decrease of $1, Caleb (gained/lost) ___________ customers. 6. Write a profit equation for Caleb's business. Profit = Price • Number of customers – Cost To write the profit equation, use the following assumptions: ❏ Express price and number of customers in terms of the same variable, x. ❏ Let x = the change in price from the price that gave Caleb the greatest revenue. Use the information in the table to answer these questions. (9 points: 1 point per blank) a. At what price did Caleb make the most revenue per month? How many customers did he serve at that price? Price: _________ Number of customers: _________ b. Write an expression for price. Use the price identified in part a. Let x represent the change in Caleb's price from this price. Price = __________ + ____________ c. Write an expression for the number of customers. Use the number of customers identified in part a, and the decrease in number of customers when Caleb increases his price by $1 (from question 5). Number of customers = _________ – __________x d. Write Caleb's profit equation. Use the expressions you identified in parts b and c. Assume Caleb's costs amounted to $200 each month. Profit = Price • Number of customers – Cost Profit = ___________ • ____________ – _________
Maximizing Your Profits You've done a lot of research. Now it's time to try to maximize the profit of your new business. 7. Write and simplify your personalized profit equation. Complete the profit equation, using the price and customer expressions from question 6 and your total cost from question 3. (6 points: 1 point for each element: price, number of customers, and cost; 3 points for writing and simplifying the profit equation) 8. Now find the maximum point on the graph of your profit equation (the vertex). (5 points: 1 point for each box in part a; 2 points for part b) a. b. Substitute x into the profit function to find the maximum profit. Maximum profit: . According to your model, what price should you charge to maximize profit? Explain how you know this is the best price. (Hint: Remember that x represents change in price from $22, not price.) (3 points: 1 point for price and 2 points for explanation) 10. What are the break-even points of the profit function (the values of x where profit equals 0)? Use the quadratic formula. (4 points: 2 points for each x-value) 11. According to your model, between what two prices should you price your service? Why would you want to keep your price between those limits? (4 points: 2 points for the break-even values, and 2

.
+
1

Answers

Answer:

Here is the answer. :)

Please do mark me brainlist.

Answer:

3.7.2 Project: Your Dog-Walking Business Project

Algebra I Sem 2 (S4982522) Ahmad Anwar

Points possible: 80 Date: 3/27/19

The Scenario: Your cousin Caleb has a dog-walking business, and you'd like to start one in your own

neighborhood. Caleb has had his business for more than a year and has experimented with different

prices for his services. He is willing to share what he has learned with you as you begin to plan your

business.

The Project: Use the information provided in the Performance Task to learn more about your

competition and the costs of your business. See what you can discover by looking at Caleb's

sales records to help you decide how to set up and price your own dog-walking services.

Use the questions below to help you gather information and get your new business off to a

profitable start.

Understanding the Competition

1. Explore the three competitors in your area to learn more about the services they offer and how

they reach their customers. Fill in the table below to help you compare their businesses.

(12 points: 1 point for each table cell)

Outward Hound A1-Pet Services Debbie’s Daily Dog Walks

What

services

does the

business

offer?

Their unique services focus

on off-leash dog park play,

nature trails and wilderness

hikes, and social play with

other dogs

Their services include private

walks, distribution of food,

water, and medications,

stop-in pet sitting,

mail-pickup, and plant

watering

Her services include daily

leash-walks and playtime

supervision, distribution of

food and fresh water, mail

and newspaper pickup, and

turning house lights on and

off

What do you

know about

the type of

business

and its

staff?

Outward Hound is a small

business staffed by dog

lovers with extensive

training in animal behavior

and nutrition.

A1-Pet Services is a

nation-wide franchised

pet-service company. They

specialize in caring for pets

when their owners are away

from home.

Debbie's Daily Dog Walks is

a one person business. Her

services are available for a

day or an extended period of

time.

Who are the

target

consumers?

Outward Hound's

customers pay a premium

for their staff's expertise and

innovative services. They

are licensed, bonded, and

insured.

Their customers have pets

that need a strict schedule,

and the reliability of this

service is most important.

Her customers are

cost-conscious and

appreciate the low cost of her

services.

How much

does the

business

charge?

They charge per day at a

rate equivalent to $35 per

30 minutes.

Their rates are considered

average at $20 per 30

minutes.

She charges $12 per 30

minutes.

2. Now that you know a bit about the competition, it’s time to get more specific about your business

offering.

(6 points: 3 points for describing services, 1 point for each of the other questions)

List three services you

would like to offer.

The services I would like to offer are daily leash-walks and playtime supervision,

distribution of food and fresh water.

Do any of these

services require you to

buy special items? If so,

what would you need to

buy?

I need to buy leashes and leads, fetching toys, treats, cleanup bags.

Describe the type of

customer you believe

your business will

appeal to and explain

why.

The type of customer I believe my business appeals to is a casual person who

needs their dog watched by.

If you had to guess

now, how much do you

think you should charge

for a 30-minute walk?

I think I should charge around $20 for a 30-minute walk.

Calculating Your Business Costs

3. Use the table below to summarize your monthly business costs. Record each option you choose in

the “Options selected” column.

(9 points: 1 point for each completed table cell)

Cost-Type Total Cost per Month Options Selected

Advertising $12 Color flyers

Business website

Business cards

Social media advertising

Goods $37 Leashes and leads

Fetching toys

Treats

Cleanup bags

Transportation $75 Walking

Bicycle Maintenance

Bus/metro pass

Gas for vehicle

Licensing $160.75 Insurance

Business registration

Bonding

Total $284.75

4. Explain the choices you made that determined your business costs in each cost category.

(4 points: 1 point for each explanation)

In your explanation, be sure to describe:

❑ Your advertising choices

❑ The goods you will purchase

❑ Your transportation needs

❑ Whether you chose bonding

❑ The reasons for your choices

Advertising:

Goods:

Transportation:

Bondin

Step-by-step explanation:

please mark me brainliest!!

Why are the two triangles congruent?

Answers

Answer:

becuz they look the same, theyre the same shape, AND size.. thats what makes to shapes congruent.

Step-by-step explanation:

Brainliest, pretty please? hee hee

Answer:

All three pairs of corresponding sides are equal, have the same shape and dimensions.

Step-by-step explanation:

Please help!!! I'll give brainliest, if you help U_U
Tysm for the help xD

Answers

Answer:

x is 122

Step-by-step explanation:

Can anyone help with this problem ?

Answers

[tex] \frac{ {m}^{11} }{ {m}^{8} } = {m}^{3} [/tex]

[tex] {m}^{11 - 8} = {m}^{3} [/tex]

When you're dividing two exponents with like bases, all you have to do is substract the exponents.

need helpppppp
plz and thank u

Answers

5-1/10

Step-by-step explanation:

4-1/2+3/5=

9/2 + 3/5=

45/10+6/10=51/10=5-1/10

Jada has a stand in the marketplace where she sells ground cumin. Her weekly expenses are $300, and she sells her cumin at a fixed price per kilogram. If she sells 120 kilograms of cumin, her weekly net profit is $600.

Answers

Answer:

Step-by-step explanation:

The net profit of the marketplace is the difference between the revenue and the expenses. The revenue is the product of number of kilograms sold and the price per kilogram.

                           Profit  = Revenue - Expenses

                           600 = 120x - 300

The value of x from the equation is 7.5. The answer therefore for the first question is $7.5. Then, the number of kilogram of cumin she needs to sell to cover the expenses is $300/$7.5 and that is equal to 40.

A farmer sells 8.8 kilograms of apples and pears at the farmer's market. 1 4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

Answers

Answer: She sold 6.6kg of pears in the market.

Step-by-step explanation:

 Weight of apples and pears at the farmer's market.=8.8 kilograms

Weight of apples = 1/4

which is = 1/4 x 8.8kg = 2.2 kg

Weight of Pears =Weight of apples and pears - Weight of apples

= 8.8kg- 2.2kg

= 6.6kg

Pls help fast!!
Andrew is buying a new bike. The bike shop is having a special discount of 25% off all bikes. The bike Andrew wants usually sells for $550. What will be the final
price of the bike, including 6% sales tax? Be sure to write all answers to the nearest hundredth.
Discount Amount:
Tax Amount:
Final price:

Answers

the final price is $437.25

25%=0.25
1-0.25=0.75
550x0.75=412.5
6%=0.06
412.5x1.06=437.25$

A 25 m tall flagpole casts a shadow that is 10 m long. At the same time, a nearby office building casts a shadow that is 26 m long. What is the height of the building?

Answers

Answer:

kmjuhygtfcv nm,kljihuygbv njmihuygb

Step-by-step explanation:

The height of the office building is 65 meter.

What s proportionality in mathematics?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

If equivalent elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences are inversely proportional.

The shadow  of a 25 m tall flagpole casts is = 10 m.

Let  the height of the office  building = x m.

The  shadow  of a x m tall office  building is = 26 m.

From theory of directly  proportionality:

25 : 10 = x : 26

25/10 = x/26

x = (25/10)×26 = 65

Hence,  the height of the office building is 65 meter.

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Ali Clara and Shane raise money for new books for the school library all Ellie rays 20% more than Clara and $58 more than Shan Claries 1/4 times

Answers

Answer:

a. $435

b. 33.33%

Step-by-step explanation:

P.S - The exact question is -

Let Clara raised money = x

As given,

Ali raised 20% more than Clara

⇒Ali raised money =  [tex]x + \frac{20}{100}x = x + \frac{1}{5} x = \frac{6}{5}x[/tex]

Also given,

Clara raised [tex]\frac{1}{4}[/tex] times more than Shan

Clara raised money = Shan raise money + [tex]\frac{1}{4}[/tex] times shan raired money

⇒Clara raised money = [tex]\frac{5}{4}[/tex]  Shan raised money

⇒Shan raised money =  [tex]\frac{4}{5}[/tex] times Clara

⇒Shan raised money = [tex]\frac{4}{5}[/tex] x

As given,

Ali raised $58 more than shan

⇒[tex]\frac{6}{5}x = \frac{4}{5}x + 58[/tex]

⇒[tex]\frac{6}{5}x -\frac{4}{5} x = 58[/tex]

⇒[tex]\frac{2}{5}x = 58[/tex]

⇒x = (29)(5) = $145

∴ we get

Clara raised money = x = $145

Ali raised money = [tex]\frac{6}{5}x[/tex] = $174

Shan raised money =[tex]\frac{4}{5}[/tex] x  = $116

a.)

Total raised money = $145 + 174 + 116 = $435

b.)

Percentage of money Clara raised = [tex]\frac{145}{435}[/tex]×100% = [tex]\frac{1}{3}[/tex]×100% = 33.33%


Simplify the expression.

4(5x + 2) + 7x + 6 =
12x + 8
27x + 14
27x + 8
27 + 14x

Answers

Answer: =27x+14

Step-by-step explanation: hope this help :)

Let's simplify step-by-step.

4(5x+2)+7x+6

Distribute:

=(4)(5x)+(4)(2)+7x+6

=20x+8+7x+6

Combine Like Terms:

=20x+8+7x+6

=(20x+7x)+(8+6)

=27x+14

Answer:

=27x+14

0.7x-y=5.16 and 2-0.8x=0.4y round to the nearest hundredth? does anyone know this answer?

Answers

Step-by-step explanation:

What is the question? You have not stated the question.

All of the following expressions are equivalent except _____.

7 - x
x - 7
- x + 7
7 + (- x)

Answers

Answer:

x - 7

Step-by-step explanation:

7 - 1= 6

1 - 7= -6

-1 + 7= 6

7 + (-1) =6

white chocolate costs $2.00 per bar, and dark chocolate costs $2.50 per bar. If you buy 15 bars of chocolate for $34, how many of each bar did you buy?

Answers

Answer:

7 white and 8 dark bars

Step-by-step explanation:

x white bars

15-x dark bars

cost of white bars is 2 * x

cost of dark bars is 2,5 * (15-x)

Write an equation

2x + 2,5 * (15-x) = 34

2x + 37,5 - 2,5x = 34

-0,5 x = - 3,5

x = 7

So we have x = 7 white bars

and 15 - x = 15 - 7 = 8 dark bars

find the slope of the line that passes through
(-5,8) and (2,-6)​

Answers

Answer:

Slope is -2

Step-by-step explanation:

Formula is y2 - y1 / x2 - x1

Hope this helps. Pls give brainliest.

help lol i cant read the text, please tell me how u did it too <3

Answers

I can't read the text either, can you zoom in a bit?

I can’t read the text it’s too small sorry

16
The sum of two numbers is 1130. Their difference is 470. Write a system of equations that
could be used to find the value of the two numbers then find the value of the smallest number
(1 Point)
300
330
180
500
17

Answers

Answer:

x = 800 and y = 330

Step-by-step explanation:

Let two numbers be x and y.

Sum of two numbers is 1130.

Their difference is 470.

So,

x+y=1130 ...(1)

x-y = 470 ...(2)

Add equation (1) and (2).

x+y+x-y = 1130+470

2x = 1600

x = 800

Put the value of x in equation (1)

800+y=1130

y = 1130-800

y = 330

So, the smallest number is 330 and the largest number is 800.

Judy made 3 pans of brownies for her friends. She cut each pan into 8 equal pieces. Her friends ate 20/8 of the brownies. What fraction of the brownies are left?

Answers

Answer:

13/6

Step-by-step explanation: 8 pieces in 3 pan give us a total of 8/24, then minus 20/8. The writing of this equation is:

20/8- 8/24 or 8/24- 20/8 (both are good)

The common denominator here is 24 since it can divide 8 and divide itself.

Since you have 24 as denominator, you'll have to reconvert the fractions above by diving 24 by their previous denominator and multiply it by their numerator:

(24/8) × 20= 60 (numerator of the 1st fraction)

(24/24) × 8=  8 (numerator of the 2nd fraction)

The new fractions are then

60/24 - 8/24= 52/24

We could stop there but since we could find an irrational fraction as an answer, why not do it

52/24 (both divided by 2)= 26/12

26/12 can still be divided so we keep going

26/12 (both divided by 2) = 13/6

13 is a prime number and therefore can be divided only by itself, and 6 cannot be divided by 13 without having a decimal answer.

13/6 is the final answer

Which property justifies the statement below?
"If -4x = 28, then 28 = -4r"
A. Commutative Property
B. Symmetric Property
C. Identity Property
D. Transitive Property​

Answers

Answer:

Commutative Property

HELP I NEED HELP ASAP

Answers

What is that Sorry I can’t help

Sue read 125 pages. Sal read 128 pages. Steve read 122 pages. What is the average number of pages that the students read

Answers

Answer:

125 pages

Step-by-step explanation:

seu =125 pages

sal =128pages

Steve =122

average = (125+128+122 )/3

=375/3

= 125

average =125 pages

Guy please help me out so this is the question 3.  Last Sunday, the temperature at 8:00 a.m. was -3०C.  Between 8:00 a.m and 1:00 p.m., the temperature rose by 5०C.  By 6:00 p.m. the temperature was 2०C colder than it was at 1:00p.m.  Then, the temperature dropped 3०C each hour between 6:00 p.m. to 10:00 p.m.  What was the temperature at 10:00 p.m.? I got the answer -1 is that correct?​

Answers

Answer:

ayuda necesito lo mismo

Step-by-step explanation:

por favor algún voluntario

Answer:

-9C

Step-by-step explanation:

-3+5-2-3(3)=-9C

i think you made a mistake on "it got colder by 2C." If temperatures get colder, they drop, meaning you subtract it.

also, it said between the hours of 6-10pm, which is three hours, the temperature drops each hour by 3C. so, you multiply 3 to -3, and come up with -9

A man knows that his apple tree is 51 ft high. At 11:00 am the tree casts a shadow of 68 ft. What is the angle of elevation of the sun? Round to the nearest tenth

Answers

Answer:

36.9 degrees

Step-by-step explanation:

This problem can be solved by drawing a right triangle and doing trigonometry. We can draw our triangle with a height of 51 and a base of 68. In order to find the angle from the ground to the sun we can use arctangent (tan^-1). Since tan(angle)=opposite/adjacent we can find the angle by doing angle=tan^-1(51/68)

Quest
A teacher is peeling an orange at the front of a classroom. Where in the room
are the molecules from the orange most concentrated?
A. At the back of the room
B. In the second row of students
C. Near the orange
O D. By an open window
SUBMIT

Answers

D.By an open window

6th grade math plz help me
Grace made a dot plot showing the distances she ran each day for two weeks.
She says that she usually runs 7 miles each day because that is the distance that occurs most often.
Do you agree with Grace’s reasoning?
Use the drop-down menus to explain and show your answer.

Dot plot named as ALTDCDistances RunALTDC has number line from 1 to 7. 1 dot on 1, 3 dots on 2, 3 dots on 3, 3 dots on 4 and 4 dots on 7 are given.




The mode, which is (3,4, or 7) ,(is or is not) a typical distance for the data. The median, which is (3.5,4, or 7),(is or is not) a typical distance for the data. The mean, which is (3,4, or 7) ,(is or is not) a typical distance for the data. So, Grace’s reasoning(is or is not ) correct.

Answers

Answer:

The mode, which is 7, is not a typical distance for the data. The median, which is 3.5, is not a typical distance for the data. The mean, which is 4, is a typical distance for the data. So, Grace’s reasoning is not correct.

The problem is a word problem: The sum of two consecutive odd numbers is 72. find the numbers​

Answers

Answer:

35 and 37

Step-by-step explanation:

consecutive ODD numbers, 35 then 37.. 35+37 = 72

Please hurry I need help with this

Answers

answer is 2700 cubic feet. volume is base times width times height. so do the volume of the bigger square first to get 2420. and then the smaller one to get 280. then add them together to get 2700

IS THIS RIGHT? PLS HELP

Answers

Step-by-step explanation:

yes your answer is absolutely correct ..the value of x comes out to be -1 and 7 ..

Find the quotient of 3 2/5 and 3 1/6 . Express your answer in simplest form.
1 5/12
95/102
1 7/95
10 23/30

Answers

Answer:

1 7/95

Step-by-step explanation:

convert the fractions into improper fractions

3 2/5 = 17/5

3 1/6 = 19/6

[tex]\frac{17}{5}[/tex] divided by [tex]\frac{19}{6}[/tex] - invert second term and multiply

so 17 * 6 = 102

5* 19 = 95

answer is 102/95, or 1 7/95

Other Questions
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