(1 point)
Find the area enclosed by the curve r=2 sin(0) + 3 sin(90).

Answers

Answer 1

If the 0's are indeed zeroes, then it would appear that you're using degrees, so that the equation

r(θ) = 2 sin(0°) + 3 sin(90°)

describes a circle r = 3 (since sin(0°) = 0 and sin(90°) = 1). In this case, the area would simply be π r ² = 9π.

But I suspect you meant to use θ, so the curve has the far more interesting equation,

r(θ) = 2 sin(θ) + 3 sin(9θ)

Since sin(9θ) has a period of 2π/9 and sin(θ) has a period of 2π, their sum has a period of 2π. (That is, 2π times the LCM of 1 and 1/9, which is 1.) But we observe r(θ) is odd, since

r(-θ) = 2 sin(-θ) + 3 sin(-9θ)

… = -2 sin(θ) - 3 sin(9θ)

… = - r(θ)

which tells us that the curve closes itself over a half-period. So the area bounded by the curve is given by the integral,

[tex]\displaystyle\int_0^\pi\int_0^{r(\theta)}r\,\mathrm dr\,\mathrm d\theta[/tex]

If you're not familiar with double integrals yet, all you need to know is that this reduces to the area formula you may/should be familiar with,

[tex]\displaystyle\frac12\int_0^\pi r(\theta)^2\,\mathrm d\theta[/tex]

Compute the integral:

[tex]=\displaystyle\frac12\int_0^\pi(2\sin(\theta)+3\sin(9\theta))^2\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac12\int_0^\pi(4\sin^2(\theta)+12\sin(\theta)\sin(9\theta)+9\sin^2(9\theta))\,\mathrm d\theta[/tex]

Apply some identities:

sin²(θ) = (1 - cos(2θ)) / 2

sin(θ) sin(9θ) = (cos(9θ - θ) - cos(9θ + θ)) / 2 = (cos(8θ) - cos(10θ)) / 2

sin²(9θ) = (1 - cos(18θ)) / 2

[tex]=\displaystyle\frac14\int_0^\pi(4(1-\cos(2\theta))+12(\cos(8\theta)-\cos(10\theta))+9(1-\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac14\int_0^\pi(13 - 4\cos(2\theta) + 12\cos(8\theta) - 12\cos(10\theta) - 9\cos(18\theta))\,\mathrm d\theta[/tex]

[tex]=\dfrac14 \left(13\theta-2\sin(2\theta)+\dfrac32\sin(8\theta)-\dfrac65\sin(10\theta)-\dfrac12\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac1{40} \left(130\theta-20\sin(2\theta)+15\sin(8\theta)-12\sin(10\theta)-5\sin(18\theta)\right)\bigg|_0^\pi[/tex]

[tex]=\dfrac{130\pi-20\sin(2\pi)+15\sin(8\pi)-12\sin(10\pi)-5\sin(18\pi)}{40}[/tex]

= 13π/4


Related Questions

Type the answer in the box.

d = 6 y = 10 g = 8

Answers

Step-by-step explanation:

[tex](6) + \frac{1}{2} (10 + 8)[/tex]

[tex]6 + \frac{1}{2} (18)[/tex]

[tex]6 + \frac{18}{2} [/tex]

[tex]6 + 9[/tex]

[tex]15[/tex]

Answer:

15

Step-by-step explanation:

an electronics store is having a 20%-off on all cell phones. the original price of a cell phone is x dollars. which expression represents the sale price of a cell phone?

a. x - 0.2
b. x - 0.8
c. 0.2*x
d. 0.8*x​

Answers

Answer: x*.2

Step-by-step explanation:

When you are trying to find the sale price you want to multiply the origanal price of the cellphone to the percentage you are getting off. Hope this helped!

When a famous artist was just beginning her career, she sold a painting for $250. Her artwork has been increasing in value by 15% every year as her popularity has grown. If this rate continues, how much will the painting be worth in 10 years? Round your answer to the hundredths place if needed.

Answers

Answer:625 dollars

Step-by-step explanation:

Drag each tile to the correct box. Ross has a box of movies in four genres: romance, comedy, drama, and science fiction. The table gives the probability of picking a movie of each genre. Movie Genre Probability romance 0.38 comedy 0.1 science fiction 0.22 drama 0.3 As part of an experiment, Ross picks a movie at random and then replaces it. He repeats the process 200 times. Place the following events in order from the event with the lowest predicted frequency to the event with the highest predicted frequency. picking a romantic movie picking a comedy movie picking a science fiction movie picking a dramatic movie , , ,

Answers

Answer:

0.1

0.3

0.22

0.38

Step-by-step explanation:

Answer:

1ST BOX Picking a Comedy movie

2ND BOX picking a science  fiction movie

3RD BOX picking a dramatic movie

LAST BOX Picking a romantic movie

Step-by-step explanation:

I took the test

A news report states that the 99% confidence interval for the mean number of daily calories consumed by participants in a medical study is (1850, 2000). Assume the population distribution for daily calories consumed is normally distributed and that the confidence interval was based on a simple random sample of 18 observations. Calculate the sample mean, the margin of error, and the sample standard deviation based on the stated confidence interval and the given sample size. Use the t distribution in any calculations and round non-integer results to 4 decimal places.

Answers

Answer:

The sample mean is of 1925 calories.

The margin of error is of 75 calories.

The sample standard deviation is of 109.7992 calories.

Step-by-step explanation:

Sample mean:

The sample mean is the mean value of the two bounds of the confidence interval. So

[tex]M = \frac{1850 + 2000}{2} = 1925[/tex]

The sample mean is of 1925 calories.

The margin of error

Difference between the bounds and the sample mean. So

2000 - 1925 = 1925 - 1850 = 75 calories.

The margin of error is of 75 calories.

Sample standard deviation:

Here, I am going to expand on the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.898

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Since [tex]M = 75, T = 2.898, n = 18[/tex]

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]75 = 2.898\frac{s}{\sqrt{18}}[/tex]

[tex]s = \frac{75\sqrt{18}}{2.898}[/tex]

[tex]s = 109.7992[/tex]

The sample standard deviation is of 109.7992 calories.

5x + 4 = 3x + 10 how would you solve for the value of x? How would you prove your solution is correct? How would you prove another value is incorrect? Explain in as much detail as possible.

Answers

5x+3=3x+10 the first thing we're going to do it to subtract 3 from both sides which would look like this

5x+3-3x=10 (the minus because it changed place)

from 5x and 3x we get 2x so the next step is 2x=10-3 which is 7

so now we have

2x=7

x=7/2

Answer:

x=3

Step-by-step explanation:

5x+4 = 3x+10

2x = 6

therefore, x = 3

Verification:

5 * 3 + 4 = 3 * 3 + 10

15+4 = 9+10

19=19

Therefore, LHS= RHS

Hence Proved!

in the following figure, the value of x is ____

Answers

Answer:

it should be 20 i hope it helps but im nt 100% sure

Step-by-step explanation:

LAST QUESTION I NEED! Should be easy (I don’t think the answer is 4 might be wrong if given an explanation)

Answers

Answer:

2

Step-by-step explanation:

because 2 square is 4 then that was needed for the other squares but this one is doubled

Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800; SSTR = 4560.
Set up the ANOVA table for this problem (to 2 decimals, if necessary).
Source of Variation Sum of Squares Degrees of Freedom Mean Square F
Treatments
Error
Total
Use {Exercise 13.07} Three different methods for assem = .05 to test for any significant difference in the means for the three assembly methods.
Calculate the value of the test statistic (to 2 decimals).
The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 11
What is your conclusion?
SelectConclude not all means of the three assembly methods are equalCannot reject the assumption that the means of all three assembly methods are equal
Item 12are my calculations correct?

Answers

Given :

Number of methods, k = 3

Number of the observations, n = 30

Degrees of freedom Treatment = k - 1

                                                     = 3 - 1 = 2

Degrees of freedom for error = n - k

                                                 = 30 - 3 = 27

[tex]$SSTR = 4560, \ SST = 10800$[/tex]

[tex]$SSE = SST - SSTR$[/tex]

       = 10800 - 4560

       = 6240

[tex]$SSE_{treatment} = MS_{treatment } \times DF_{treatment}$[/tex]

[tex]$MS_{treatment} = \frac{4560}{2}=2280$[/tex]

[tex]$MS_{error}=\frac{SSE_{error}}{DF_{error}}$[/tex]

             [tex]$=\frac{6240}{27}=231.1$[/tex]

[tex]$F=\frac{MS_{treatment}}{MS_{error}}$[/tex]

  [tex]$=\frac{2280}{231.1}=9.865$[/tex]

Source variation   Sum of square  Degrees of freedom  Mean square     F

Treatment                   4560                          2                         2280       9.8653

Error                            6240                         27                   231.11111111

Total                            10800

The critical value of F for the 0.05 sig level and df (227) is 3.354

Since the test stat > critical value of F, so we reject null hypothesis and state that there is a significant difference in the means of the three assembly methods.

Consider the function graphed below.

What is the average rate of change of the function over the interval [1, 3] ?

A.36

B. 48

C.72

D.96

Answers

Answer:

A. 96

Step-by-step explanation:

By using slope formula we got that  average rate of change of the function over the interval [1, 3] is 48 .

What is the average rate of change?

the rate at which one variable of a function changes in relationship to another variable  is called average rate of change.

Here we can see in graph that

when x =1 y=12

and when x= 3 ,y=108

Now we know that rate of change is same as slope of straight line passing through that points

So average rate of change can be calculated as

[tex]=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]=\frac{108-12}{3-1}\\\\[/tex]

[tex]\frac{96}{2}[/tex]

=48

By using slope formula we got that  average rate of change of the function over the interval [1, 3] is 48 .

To learn more about rate of change visit :https://brainly.com/question/8728504

The number of that grow sugar beet =12

Answers

Answer:

I think question is not proper

you should check it again

hope your day will fine

Answer:

Whatttt

Step-by-step explanation:

An elementary school is offering 3 language classes: one in Spanish, one inFrench, and one in German. The classes are open to any of the 100 students inthe school. There are 28 students in the Spanish class, 26 in the French class,and 16 in the German class. There are 12 students that are in both Spanish andFrench, 4 that are in both Spanish and German, and 6 that are in both Frenchand German. In addition, there are 2 students taking all 3 classes.(a) If a student is chosen randomly, what is the probability that he or she isnot in any of the language classes

Answers

Answer:

0.5 = 50% probability that he or she is not in any of the language classes.

Step-by-step explanation:

We treat the number of students in each class as Venn sets.

I am going to say that:

Set A: Spanish class

Set B: French class

Set C: German class

We start building these sets from the intersection of the three.

In addition, there are 2 students taking all 3 classes.

This means that:

[tex](A \cap B \cap C) = 2[/tex]

6 that are in both French and German

This means that:

[tex](B \cap C) + (A \cap B \cap C) = 6[/tex]

So

[tex](B \cap C) = 4[/tex]

4 French and German, but not Spanish.

4 that are in both Spanish and German

This means that:

[tex](A \cap C) + (A \cap B \cap C) = 4[/tex]

So

[tex](A \cap C) = 2[/tex]

2 Spanish and German, but not French

12 students that are in both Spanish and French

This means that:

[tex](A \cap B) + (A \cap B \cap C) = 12[/tex]

So

[tex](A \cap B) = 10[/tex]

10 Spanish and French, but not German

16 in the German class.

This means that:

[tex](C - B - A) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 16[/tex]

[tex](C - B - A) + 2 + 4 + 2 = 16[/tex]

[tex](C - B - A) = 8[/tex]

8 in only German.

26 in the French class

[tex](B - C - A) + (A \cap B) + (B \cap C) + (A \cap B \cap C) = 26[/tex]

[tex](B - C - A) + 10 + 4 + 2 = 26[/tex]

[tex](B - C - A) = 10[/tex]

10 only French

28 students in the Spanish class

[tex](A - B - C) + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 16[/tex]

[tex](A - B - C) + 10 + 2 + 2 = 28[/tex]

[tex](A - B - C) = 14[/tex]

14 only Spanish

At least one of them:

The sum of all the above values. So

[tex](A \cup B \cup B) = 14 + 10 + 8 + 10 + 2 + 4 + 2 = 50[/tex]

None of them:

100 total students, so:

[tex]100 - (A \cup B \cup B) = 100 - 50 = 50[/tex]

(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?

50 out of 100. So

50/100 = 0.5 = 50% probability that he or she is not in any of the language classes.

7x10+2x1+6x1/10+3x1/1000

Answers

Answer:72.603

Step-by-step :

70 + 2 + 6 ÷ 10 + 3 ÷ 1000

=72.603

Answer this correctly I’ll give brainalist + 10 points

Answers

The Answer is 66

That small little box there that’s 90

You subtract 90 with 24 and you should get 66
The answer to your asked question is 66, 90-24=66. Hope this helped have a good day/night!

help do not scam me ok I will give 40 points

Answers

Answer:

C. Preform calculations on my own and compare them to Roberto’s.

Step-by-step explanation:

His calculations do not match the line plot. He doesn’t account for every mark on the plot.

Help plz....................

Answers

Answer:

x = 136°

y = 44°

Step-by-step explanation:

x + 44° = 180° (Adjacent angles of a parallelogram)

x = 180° - 44°

x = 136°

y = 44° (Opposite angles of a parallelogram)

Tina's bakery, sells cinnamon, banana, apple and blueberry muffins. Each day the bakery bakes 63 apple muffins, the apple muffins represent 42℅ of all the muffins baked each day, how many muffins are baked each day.

Answers

Ok. So if 42 % is apple, then 63 = 42%.

You can divide it by 42 to get 1%

63 / 42 = 1.5

Than times by 100 to get 100%

100% = 150.

150 Muffins per day

There are three numbers for the combination to the store's safe. The first number is 17. The two numbers can be multiplied together to give a product of 28. What are all of the possibilities for the other two numbers? IT IS MULTIPLICATION BTW

Answers

Answer:

1 28

2 14

4 7

Step-by-step explanation:

7 4

14 7

28 1

...........

I will mark someone brainliest!

Answers

Answer:

2nd option is the correct answer

Step-by-step explanation:

Oscillating powerful magnets within wire coils.

Answer:

Step-by-step explanation:

I think it's got to be coal because the power plants always have like smoke and d is the only one that burns something

Find each product mentally, using the distributive property, 4x51/8. (giving brainliest)

Answers

Answer:

25.5

Step-by-step explanation:

4 x 51 / 8

204/8

25.5

Answer:

Step-by-step explanation:

4×15/8 = 4×(1+⅞) = 4×1 + 4×⅞ = 4 + 7/2 = 4 + 3.5 = 7.5

The average daily balance of a credit card for the month of November was $700, and the unpaid balance at the end of the month was $1,400. If the monthly interest rate is 1.3% of the average daily balance, what is the total balance on the next billing date December 1? Round your answer to the nearest cent.

Answers

Answer:

This answer is on quizlet

Step-by-step explanation:

Answer:3255.20

Step-by-step explanation:

First, calculate the interest using the APR in decimal form (divided by 12) and the average daily balance.

Interest =0.27612×$2,400=$55.20

Then add the interest to the unpaid balance.

Total Balance =$3,200+$55.20=$3,255.20

can somebody help me?

Answers

Answer:

15x + 7

Step-by-step explanation:

i set this up

8x + 16 + 7x -9

the next step is to combine like terms

8x + 7x = 15x

16 - 9 = 7

15x = 7

15x + 7

the answer is going to be 15x + 7

A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members use each facility. A survey of the membership indicates that 75% use the golf course, 50% use the tennis courts, and 5% use neither of these facilities. One club member is chosen at random. What is the probability that the member uses the golf course but not the tennis courts

Answers

Answer:

0.45 = 45% probability that the member uses the golf course but not the tennis courts

Step-by-step explanation:

I am going to solve this question using the events as Venn sets.

I am going to say that:

Event A: Uses the golf courses.

Event B: Uses the tennis courts.

5% use neither of these facilities.

This means that [tex]P(A \cup B) = 1 - 0.05 = 0.95[/tex]

75% use the golf course, 50% use the tennis courts

This means, respectively, by:

[tex]P(A) = 0.75, P(B) = 0.5[/tex]

Probability that a member uses both:

This is [tex]P(A \cap B)[/tex]. We have that:

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]

So

[tex]P(A \cap B) = 0.75 + 0.5 - 0.95 = 0.3[/tex]

What is the probability that the member uses the golf course but not the tennis courts?

This is [tex]P(A - B)[/tex], which is given by:

[tex]P(A - B) = P(A) - P(A \cap B)[/tex]

So

[tex]P(A - B) = 0.75 - 0.3 = 0.45[/tex]

0.45 = 45% probability that the member uses the golf course but not the tennis courts

2 1/4 divided by 6
PLS I NEED HELP ASAP

Answers

Answer:

.375 which is 3/8

Step-by-step explanation: If you meant the mixed fraction 2 1/4 divided by 6 then that is the answer! 2 1/4 =2.25 and divide it by 6 and you get 0.375

Answer:

3/8

Step-by-step explanation:

convert mixed numbers to improper fractions

21/4 = 9/4

convert element to fraction

6=6/1

9/4 divided by 6/1

apply the fraction rule (hope you're familiar)

9/4 * 1/6

cross- cancel common factor 3

3*1 = 3

4*2 = 8

multiply the numbers

3/ 4*2

3/8

PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!

Answers

Answer:

B) one solution

Step-by-step explanation:

to understand thisyou need to know about:linear equationPEMDAStips and formulas:[tex]\sf\text{a system of linear equation has only one solution if $\frac{a_1}{a_2}\neq \frac{b_1}{b_2}$}[/tex]given:[tex] \begin{cases}2x - 4y = - 1 \\ 8x - 11y = - 19 \end{cases}[/tex]let's solve:

[tex] \sf substitute \: the \: value \: of \: a \: b : \\ \frac{2}{8} \ne \frac{ - 4}{ - 11} \\ [/tex]

[tex]\text{$\therefore$ the system of linear equation has only one solution}[/tex]

Lainey brought a set of 22 markers for $6. What is the cost of 1 marker? Round answers to the nearest hundredths where necessary.

Answers

The answer It’s about .360

what are prime factors

Answers

Answer:

Prime Factors is a  factor of a given integer which is also a prime number.

numbers like 9, 13, 7 and etc

Rashads teacher buys paperback books for her classroom library. Each book costs $6, and she spends a total of $150. Which equation models the number of books, n, she buys? A. 6n=150 B. n/6=150 C.150-n=6 D. 6•150=n

Answers

Answer:

A  

Step-by-step explanation:

6n=150

270 because yea hahahahaha

Helppppppppppppppppppppp

Answers

C hope that helps because if you look at your answers and compare your question to that there u go

. 16 is 20% of what number? Show your work and/or explain your reasoning.

Answers

Answer:

0.8

Step-by-step explanation:

.16/.2 = 0.8

check

0.8 x .2 = 0.16

Other Questions
Why was the Battle of Midway significant? PLZZZZZZZ HELP 50 POINTS FAST Assignment SummaryFor this assignment, you will ask questions about the factors that have caused a rise in global temperatures over the past century. Then, you will conduct research to answer your questions. You will also graph provided information, analyze the graphs, and make conclusions based on the graphs. Finally, you will write a paper describing the conclusions of your research and graphs.Background InformationGlobal temperature change is a gradual increase in the overall temperature of the Earth's atmosphere. Both human activity and natural processes have contributed to this temperature increase. Examples of human activities include the burning of fossil fuels, cement production, and agricultural activity. Examples of natural processes include changes in incoming solar radiation and volcanic activity.Scientists present evidence for the rise in global temperature in the form of tables, graphs, maps, and models. For example, scientists build climate models (computer simulations of climate systems) to explore the causes and effects of global temperature change and to predict future trends. These models predict that the Earths average surface temperature will rise as greenhouse gas concentrations continue to rise. Based on these models, scientists predict that average surface temperatures could rise by between 2C and 6C by the end of the 21st century.Step 2: Write your questions.You are familiar with some of the factors that have contributed to the rise in global temperatures over the past century. Think of three questions that will help you clarify your understanding of how these factors lead to an increase in global temperatures. Consider the following when you come up with your questions: Ways in which natural processes and human activity have affected global temperature change over the past centuryThe influence of these processes and activities on a gradual or sudden change in global temperatureWrite your questions in the space provided at the end of this document.Have your teacher review your questions. Once they are approved, you may begin Step 3.Step 3: Conduct research.Search for answers to each of your questions. Be sure to support your answers with scientific evidence from reliable sources.The following are examples of some reliable sources you might use:The National Oceanic and Atmospheric Administration (NOAA)The National Aeronautics and Space Administration (NASA)Nature magazineStep 4: Create graphs.Use the information in the tables below to create two-line graphs.The first graph should show the amount of carbon dioxide in the atmosphere from 20102017.The second graph should show the change in global temperature from 20102016.Table A. Carbon Dioxide (CO2) in the AtmosphereYearCarbon Dioxide (CO2) in Atmosphere (ppm*)20103902011392201239420133962014399201540120164042017406*parts per millionTable B. Change in Global TemperatureYearChange in Global Temperature (C)20100.7120110.6020120.6320130.6520140.7420150.8720160.99What happened to the amount of carbon dioxide in the atmosphere from 20102017?How did the global temperature change from 20102016?What is the relationship between the amount of carbon dioxide in the atmosphere and global temperature?Step 5: Create a typewritten paper.For each of your questions, write one paragraph summarizing the answer based on your research.Cite evidence and patterns in data that connect natural processes and human activity to the rise in global temperature. Be sure to include as evidence the trends that you observed in your graphs and the conclusion you made about the relationship between the amount of carbon dioxide in the atmosphere and change in global temperature.Discuss the relationship between these processes and activities, the production of greenhouse gases, and the effects of greenhouse gases on the atmosphere.Step 6: Evaluate your project using this checklist.If you can check each criterion below, you are ready to submit your presentation.YesNoEvaluation QuestionIs your name on your typewritten paper?Did you do research to answer your questions?Did you create a graph that shows the amount of carbon dioxide in the atmosphere from 2010-2017?Did you create a graph that shows the change in global temperature from 2010-2016?Did you write three total paragraphs answering your questions?Did you cite scientific evidence that connects natural processes and human activity to the rise in global temperature?Did you include as evidence the trends that you see in your graphs and the conclusion you made about the relationship between the amount of carbon dioxide in the atmosphere and the change in global temperature?Did you discuss the relationship between natural processes and human activities, the production of greenhouse gases, and the effects of greenhouse gases on the atmosphere? 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