find the area inside the polar curve r=3cos(3theta)

Answers

Answer 1

The area inside the polar curve r=3cos(3θ) is (3/8)π + (3/8).

To find the area inside the polar curve r=3cos(3θ), we need to integrate the equation of the curve with respect to θ from 0 to π/6

The area formula in polar coordinates is:

A = (1/2) ∫[a,b] (r(θ))^2 dθ

where r(θ) is the equation of the curve and a and b are the limits of integration.

In this case, the limits of integration are 0 and π/6, and the equation of the curve is r = 3cos(3θ), so the area formula becomes:

A = (1/2) ∫[0,π/6] (3cos(3θ))^2 dθ

Simplifying, we get:

A = (9/2) ∫[0,π/6] cos^2(3θ) dθ

Using the trigonometric identity cos^2(θ) = (1/2)(1 + cos(2θ)), we can rewrite the integral as:

A = (9/4) ∫[0,π/6] (1 + cos(6θ)) dθ

Evaluating the integral, we get:

A = (9/4) [θ + (1/6)sin(6θ)] [0,π/6]

Plugging in the limits of integration, we get:

A = (9/4) [(π/6) + (1/6)sin(π/2) - 0 - 0]

Simplifying, we get:

A = (3/8)π + (3/8)

So the area inside the polar curve r=3cos(3θ) is (3/8)π + (3/8).

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Related Questions

Please help fast 15 points math homework

Answers

Answer:

Letter C

Step-by-step explanation:

Math expert please provide the product in standard form

Answers

Here’s the answer to your question

HELP PLEASE WITH MY ASSIGNMENT

Answers

10 dollars per hour

(HELP!!!) 1. 20 % of the total number of pupils in a class is 6, How many pupild are there in the class altogether? (with explanation pls)

Answers

if 20% is 6, then that means that 1/5 of the class is 6 students. in order to get to 100% (all of the students in class) we would need to multiply 6 x 5, since 6 is only 1/5 of the class, and we want to find the total number of the entire class. 6 x 5 = 30, meaning there are 30 students in the class altogether

Answer:

Step-by-step explanation:

this is the explanation

6÷20% = 30

can someone help me with this? Thank you!

Answers

Answer:

10.

Step-by-step explanation:

As the 2 Figures are similar the correspond sides are in the same ratio.

We see that BC = 5.0 and FG = 2.5, so each side in EFGH is 1/2 of its correspond side in ABCD.

Perimeter of EFGH , therefore, is

2.5 + 2 + 4 + 1.5

= 10.

How does the denominator of the F-ratio (the error term) differ for a repeated-measures ANOVA compared to an independent-measures ANOVA

Answers

The main difference between the denominator of the F-ratio (the error term) for a repeated-measures ANOVA and an independent-measures ANOVA lies in the way variability is accounted for within the groups.

In a repeated-measures ANOVA, the same participants are exposed to multiple conditions or measured at different time points. Therefore, this design accounts for individual differences, leading to a smaller error term in the denominator of the F-ratio.

The error term in repeated-measures ANOVA represents the variability due to individual differences and the residual error, but not the variability between participants. In contrast, an independent-measures ANOVA involves separate groups of participants for each condition, meaning that variability between participants is included in the error term.

As a result, the error term for the independent-measures ANOVA is larger than that of the repeated-measures ANOVA. This difference in the denominator of the F-ratio affects the sensitivity of the statistical test, with the repeated-measures ANOVA being more sensitive due to its smaller error term.

In summary, the denominator of the F-ratio (the error term) differs for a repeated-measures ANOVA compared to an independent-measures ANOVA in terms of the variability accounted for within groups. The repeated-measures ANOVA error term is smaller, as it controls for individual differences, while the independent-measures ANOVA error term is larger because it includes variability between participants.

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I NEED HELP AGAIN PLEASE!!

Answers

Answer:

Step-by-step explanation:

You borrow $30,000 to buy a car. The loan is to be paid off in 10 equal quarterly payments at 6% interest annual interest rate. The first payment is due one quarter from today. What is the amount of each quarterly payment (rounded)? A. $1,777. B. $2,803. C. $3,253. D. None of the above.

Answers

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).

To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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help me with this please

Answers

Answer:

C. 7.5m

Step-by-step explanation:

$8m \: up= 3m \: above \\ 12m \: up = x \: above$

Cross multiply

$8x = 12 \times 3 \\ 8x = 36$

Divide both sides of the equation by 8

$ \frac{8x}{8} = \frac{36}{8} \\ x = 4.5 \\ 3 + 4.5 = 7.5m$

Hobby Lobby offered a 15% discount off the regular price of a lamp. The amount of the discount is $12. What is the regular price of the lamp?

Answers

15% = 0.15
12/0.15 = 80
Solution: regular price is $80

A count went from 605 to 203. What was the approximate percent decrease? Round the numbers to find an estimate of the percent decrease.
A. The percent decrease was approximately 25%.
B. The percent decrease was approximately 33%.
C. The percent decrease was approximately 50%.
D. The percent decrease was approximately 66%.

Answers

IT'S D

HOPE THIS HELP MARK ME BRAINLIST

Sabrina is going to rent a bicycle while in vacation. There are two rental companies she can choose from. The first company charged $10 plus a rate of $2 per hour until the bicycle is returned. The second company’s rental charges can be represented by the equation c=3h+6 where c represents the rental cost and h represents the number of hours the bicycle is rented. If Sabrina plants to bicycle for 3 hours, what is the least amount she could pay in rental fees?

Answers

Answer:

pretty sure its 16 but im not sure.

Step-by-step explanation:

Graph the systemY= 0.5 x + 5x - 2y=8find the solution to the system if there is no solution put no solution if there is infinite put infinitelable the system as consistent or inconsistent

Answers

We have the next system of equations

$\begin{cases}y=0.5x+5\ldots(1) \\ x-2y=8\ldots(2)\end{cases}$

To solve the systme we must replace equation (1) in equation (2)

$x-2(0.5x+5)=8$

Simplifying,

$\begin{gathered} x-\lbrack2(0.5x)+2(5)\rbrack=8 \\ x-\lbrack x+10\rbrack=8 \\ x-x-10=8 \\ -10=8\text{ } \\ \text{this, is false. So, the system has no solution} \end{gathered}$

To graph the system we must graph equation (1) and (2)

- equation (1)

x-intercept: (-10, 0)

y-intercept: (0, 5)

-equation (2)

x-intercept

The graphs never intersect, we can confirm that the system has no solution.

Graph the systemY= 0.5 x + 5x - 2y=8find the solution to the system if there is no solution put no solution

XY has endpoints at X(2, -3) and
Y(-1, 2). What is the length of XY?

A. 2 units
B. 10 units
C. 34 units

Answers

Answer:

Step-by-step explanation:

I did this, but I'm not 100% sure.

what is negitive 7 minus positive 2

Answers

Given

Negative 7 = -7

Positive 2 = +2

To Find The Difference Of The Number

After Evaluating We Get

$ - 7 - ( + 2) \\ \\ = - 7 - 2 \\ \\ = - 9$

Hope This Helps You

Please help with this

Answers

Answer:

CORRECT STATEMENTS:

Step-by-step explanation:

can someone help me with these answers please

Answers

since we were given the key ( how it should be sort out or used )

then we get all the numbers out which are:

21, 23, 30, 32, 32, 35, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53, 55

then we go ahead to answer the questions:

a) Range = highest number minus Lowest number

55 - 21 = 34

b) 17 (by counting all individual ages ).

c) Median = the middle age

(but before that, we must arrange the ages either a cording to their sizes either from biggest to smallest (descending order) or from smallest to biggest (ascending order)

so we arrange in ascending order but the numbers are already arranged so we don't have to stress ourselves:

Median = 46 (the number in the middle ).

Hope you ace your tests, Good luck ✅.

brainlyest, plus 5 points
PLEASE STEP BY STEP
Evaluate x/2+5y-1.5 when x = 10 and y = 8

Answers

Answer:

43.5

Step-by-step explanation:

x/2+5y-1.5

10/2+5×8-1.5

5+40-1.5

5+38.5

=43.5

Answer:

43.5

Step-by-step explanation:

x ÷ 2 + 5y - 1.5

Start by replacing the x's and y's

10 ÷ 2 + (5 · 8) - 1.5

Start with parenthesis

10 ÷ 2 + 40 - 1.5

Then do the division

5 + 40 - 1.5

Then go left to right

45 - 1.5

43.5

I hope this helps!!!

What is the total of the equation : 5 wholes and 2/3 x 3/4?

Answers

The total of the equation 5 wholes and 2/3 x 3/4 is 4 1/4

How to find the total of the equation

The total of the equation is found by multiplication of fractions.

Fractions are system of numbers used to represent a number in forms which has two basic parts

The numerator The denominator

The fraction required are:

5 wholes and 2/3 = 5 2/3

3/4

The multiplication

= 5 2/3 * 3/4

The first step is done by converting the mixed number to improper fraction = = 5 2/3 = 17/3

= 17/3 * 3/4

= 17/4

17/4 is an improper fraction and 4 1/4 as a mixed number

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Joey went to the county fair last weekend. When he got there, he had to walk 1/2 of a mile from the car to the entrance. Then he walked 11/16 of a mile to the carnival rides and 1/2 of a mile from the carnival rides to the farm animal show. Next, he walked 3/4 of a mile back to the car. How many miles did Joey walk in all?

Answers

Answer:

39/16 or 2 7/16 miles

Step-by-step explanation:

find the common denominator between all fractions (16).

1/2 = 8/16

3/4 = 12/16

8 + 11 + 8 + 12 = 39

Therefore, Joey walked 39/16 or 2 7/16 miles in total

hi pls help last q..........

Answers

Answer:

ONLY B IS AN EQUATION.

Step-by-step explanation:

ONLY B IS AN EQUATION

B is answer to the question

Use the information to find and compare Δy and dy. (Round your answers to three decimal places. )
y = 0. 8x5 x = 1 Δx = dx = 0. 1
Δy = dy =

Answers

The computation shows that the values of Δy and dy will be 0.572 and 0.4 respectively.

How to compute the values?

The value of Δy will be computed thus:

Δy = y(x + Δx) - y(x)

= y(1.1) - y(1)

= 0.5(1.1)⁸ - 0.5(1)⁸

= 0.572

The value of dy will be:

= y'(x)dx

= (0.5)⁸ × x⁷(0.1)

= 0.4 (1)⁷

= 0.4

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$2\left(x+3\right)=x-4$

Answers

Step-by-step explanation:

Given that:

2(x + 3) = x - 4

Multiply the number outside of the brackets with numbers in the bracket on LHS.

⇛2x + 6 = x - 4

Shift all variables on LHS and constant on RHS, changing it's sign.

⇛2x - x = -4 -6

Subtract the number on LHS and RHS.

x = -10

Therefore, x = -10

Please let me know if you have any other questions.

which needs to occur on a consistent basis and at regular intervals to determine whether execuatin of goals

Answers

Exercise needs to be consistent and done at regular times. The body can adjust more effectively and swiftly when there is consistency. Exercise should ideally be performed 3-5 times per week.

What is Exercise ?

Exercise is any physical activity done to increase one's physical or mental fitness.

Exercise and physical activity not only aid to enhance physical health but also help to promote mental health.

A healthy mind follows from a healthy body.

By lowering body weight, frequent physical activity lowers the risk of developing serious conditions like heart attack, cardiovascular disease, diabetes, and high blood pressure. Regular exercise revitalizes the body and the mind.

Additionally, it raises energy levels, mood, and sleep quality.

Hence, Exercise must be performed consistently and at regular intervals. When there is consistency, the body can adjust more quickly and efficiently. The ideal number of times to exercise per week is three to five.

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Using the properties of triangles, prove that angle a is congruent to angle c in the drawing below.

Answers

Answer:

General conditions of congruency of triangles

Step-by-step explanation:

As no triangles are given, explaining the general rules to apply in congruency of all triangles.

Triangles are congruent on the basis of following conditions :

SSS : All 3 sides of two triangles are equal SAS : 2 sides & angle between them, of two triangles are equal ASA : 2 angles & corresponding side, of two triangles are equal HL : Hypotenuse & Leg of two right angled triangles are equal

A data set has these values: 7,9,9, 11, 11, 11, 11, 13, 13, 15. A histogram of
the distribution is shown.
4
Which statement does not describe the data set?
3
Frequency
2
A. It has a range of 16.
B. It has a median of 11.
0
6 8 10 12 14 16
c. It has a mode of 11.
O
D. It is symmetric.

Answers

Answer:

Step-by-step explanation:

Answer: It has a range of 16

Step-by-step explanation:

I just took it

Use the counterexample method to prove the following categorical syllogisms invalid. In doing so, follow the suggestions given in the text.

Some farm workers are not people who are paid decent wages, because no undocumented individuals are people who are paid decent wages, and some undocumented individuals are not farm workers.

Answers

To prove that the given categorical syllogism invalid using the counterexample method, we first need to check whether the syllogism follows the standard form of categorical syllogisms. The standard form of categorical syllogism is:

Premise 1: All A are B. (Major Premise)

Premise 2: All C are A. (Minor Premise)

Conclusion: All C are B.

Let's represent the given syllogism in the standard form:

Premise 1: No undocumented individuals are people who are paid decent wages. (Major Premise)

Premise 2: Some undocumented individuals are not farm workers. (Minor Premise)

Conclusion: Some farm workers are not people who are paid decent wages.

Now, we will use the counterexample method to disprove the given syllogism. We will use real-world examples that will make the premises true but will make the conclusion false. Suppose Premise 1 is "No birds can swim." and Premise 2 is "Some penguins are not birds". Then, the Conclusion will be "Some penguins cannot swim." which is true. Here, we see that the premises are true, and the conclusion is also true.

Let's take another example. Suppose Premise 1 is "No reptiles can fly." and Premise 2 is "Some birds are reptiles." Then, the Conclusion will be "Some birds cannot fly." which is false. Here, we see that the premises are true, but the conclusion is false.

Hence, the syllogism is invalid. Using the same method, we can disprove the given syllogism. Some farm workers are not people who are paid decent wages, because no undocumented individuals are people who are paid decent wages, and some undocumented individuals are not farm workers.

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. Write an equation in slope-intercept form that shows the cost y for flowers for x number
of arrangements.
ok

Answers

Answer:

He placed his most loyal subjects in government jobs. He developed civil service exams to reduce corruption. He enforced strict rules for workers to ensure job effectiveness.

Answer:

ahh

Step-by-step explanation:

What is y=6-2x-4x^2+5x^3 in standard form?

Answers

Y=6-2x-4x^2+5x^3
In standard form is……

Y=5x^3-4x^2-2x+6

(1 point) the volume of the solid obtained by rotating the region enclosed by y=x2, y=3x, about the line x=3 can be computed using the method of disks or washers via an integral

Answers

Evaluating this integral will give us the volume of the solid obtained by rotating the given region about the line x = 3.

The volume of the solid obtained by rotating a region enclosed by two curves about a line can be calculated using the method of disks or washers via an integral.

To apply the method, we consider the region between the curves y = x^2 and y = 3x. The line x = 3 acts as the axis of rotation. We want to find the volume of the solid formed by rotating this region.

The method of disks or washers involves dividing the region into infinitely thin slices perpendicular to the axis of rotation. Each slice represents a disk or washer. The volume of each disk or washer is calculated using its radius and thickness.

In this case, we choose the variable x as our integrating variable. The radius of each disk or washer is the distance between the axis of rotation (x = 3) and the corresponding curve. The thickness of each disk or washer is dx, representing an infinitely small change in x.

By integrating the volumes of all the disks or washers over the interval of x values that enclose the region, we can find the total volume of the solid. The integral will involve the square of the radius function and will depend on the limits of integration determined by the intersection points of the curves.

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For this project, you are going to create a program that asks the user for a list of ingredients. As the user enters the ingredients, you should store them in a list. Once the user is done entering their list, you need to pass this list to a function that will compare the ingredients to an already existing list of pantry items. Your Task The Shopping List For this problem, you are going to create a program that asks the user for a list of ingredients. As the user enters the ingredients, you should store them in a list. Once the user is done entering their list, you need to pass this list to a function that will compare the ingredients to an already existing list of pantry items. If all items are available in the pantry, print out that you dont need to go shopping. If any item is missing, print out that you need to go shopping and list the ingredients. While there is more than one way to complete this assignment, your answer must include the following: 1. A pre-created list for pantry items 2. User input into an ingredient list 3. Pass the ingredient list to a method 4. Use a conditional and loop in the method 5. Print out the results of whether the user needs to go shopping based on the items in the ingredient list that are not in the pantry. How do you find the time constant of an RC circuit? Lucy completed 36 out of 100 homework problems during class. Which fraction represents the completed part of her homework assignment?a 6256 over 25b 383 eighthsc 275027 over 50d 925 If you started with a 125g sample of u-235. 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Calculate the increase in the money supply associated with increases in bank reserves of $10. What is the money multiplier in this economy? Assume that individuals do not change their currency holdings.c. A general rule for calculating the money multiplier is:1. 1/(deposit ratio-desired reserve).2. 1/deposit ratio.3. 1/desired reserve.4. 1/(desired reserve-deposit ratio).d. Suppose the Fed wanted to reduce the money multiplier, perhaps because it believes that change would give it more precise control over the money supply. In order to achieve its goal, the Fed would:1. decrease the ratio of reserves to deposits.2. increase reserve requirements.3. increase the money supply.4. decrease reserve requirements. A technique is practiced frequently and creates little likelihood of severe injury. 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The change has no impact on the behavior of the method.b. After the change, the method will never check the first element in list b.c. After the change, the method will never check the last element in list b.d. After the change, the method will never check the first and the last elements in list b.e. The change will cause the method to throw an IndexOutOfBounds exception. I need help solving these Blank + 3Fe, reaction arrow, Fe3O4+4H2 How to complete this equation so that it is a Single displacement reaction A simple random sample of size n = 41 is obtained from a population with = 68 and = 3.1. Does the population need to be normally distributed for the sampling distribution of x bar to be approximately normally distributed? Why?a. No, because the Central Limit Theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases.b. 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The sampling distribution of x is uniform with x = _____ and x = _____. if the speed of light is nearly 3x108 m/s in air (300,000 km/s), what is its speed in glass with index of refraction 1.5? The line with the equation y=4x+5 undergoes a dilation with a scale factor of 2 and the center at (0,2). Determine the equation of the line that is a result of the dilation In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Meena sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.53 visitors purchased no costume.151 visitors purchased exactly one costume.22 visitors purchased more than one costume.Based on these results, express the probability that the next person will purchase exactly one costume as a percent to the nearest whole number.