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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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?
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
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
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%
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
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
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
Why are the two triangles congruent?
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:
HELP I NEED HELP ASAP
All of the following expressions are equivalent except _____.
7 - x
x - 7
- x + 7
7 + (- x)
Answer:
x - 7
Step-by-step explanation:
7 - 1= 6
1 - 7= -6
-1 + 7= 6
7 + (-1) =6
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?
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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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.
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.
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?
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
Sue read 125 pages. Sal read 128 pages. Steve read 122 pages. What is the average number of pages that the students read
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
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
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.
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?
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
Simplify the expression.
4(5x + 2) + 7x + 6 =
12x + 8
27x + 14
27x + 8
27 + 14x
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?
Step-by-step explanation:
What is the question? You have not stated the question.
Which property justifies the statement below?
"If -4x = 28, then 28 = -4r"
A. Commutative Property
B. Symmetric Property
C. Identity Property
D. Transitive Property
Answer:
Commutative Property
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?
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
need helpppppp
plz and thank u
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
Please hurry I need help with this
The problem is a word problem: The sum of two consecutive odd numbers is 72. find the numbers
Answer:
35 and 37
Step-by-step explanation:
consecutive ODD numbers, 35 then 37.. 35+37 = 72
Please help!!! I'll give brainliest, if you help U_U
Tysm for the help xD
Answer:
x is 122
Step-by-step explanation:
France had 8,306,000 visitors while Australia had 15,976,000 visitors. How many combined visitors did they have?
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
help lol i cant read the text, please tell me how u did it too <3
I can't read the text either, can you zoom in a bit?
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:
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.
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.
IS THIS RIGHT? PLS HELP
Step-by-step explanation:
yes your answer is absolutely correct ..the value of x comes out to be -1 and 7 ..
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
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)
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
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!!
find the slope of the line that passes through
(-5,8) and (2,-6)
Answer:
Slope is -2
Step-by-step explanation:
Formula is y2 - y1 / x2 - x1
Hope this helps. Pls give brainliest.
Can anyone help with this problem ?
[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.