Let a € (-1,1). Evaluate TT cos 20 de. 1-2a cos 0 + a2 d0

Answers

Answer 1

The value of the given integral is 2π [sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [sin(22e)/22 + sin(18e)/18] + C]

To evaluate the given expression:

∫∫ cos(20e) (1 - 2a cos(e) + a²) de dθ

We need to integrate with respect to both e and θ.

First, let's integrate with respect to e:

∫ cos(20e) (1 - 2a cos(e) + a²) de

Using the power reduction formula for cosine, we can rewrite the integrand:

= ∫ cos(20e) (1 - a² + a² cos²(e) - 2a cos(e)) de

= ∫ cos(20e) (1 - a² - a² sin²(e)) de

Now, we can integrate term by term:

= ∫ cos(20e) de - a² ∫ cos(20e) sin²(e) de - a² ∫ cos(20e) de

The first and third integrals are straightforward to evaluate:

= ∫ cos(20e) de - a² ∫ cos(20e) de - a² ∫ cos(20e) sin²(e) de

= sin(20e) - a² sin(20e) - a² ∫ cos(20e) sin²(e) de

Now, let's evaluate the remaining integral with respect to e:

= sin(20e) - a² sin(20e) - a² ∫ cos(20e) sin²(e) de

Using the trigonometric identity sin²(e) = (1 - cos(2e))/2, we can simplify the integrand:

= sin(20e) - a² sin(20e) - a² ∫ cos(20e) ((1 - cos(2e))/2) de

= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) - cos(20e) cos(2e) de

= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) de + (a²/2) ∫ cos(20e) cos(2e) de

Integrating the first term gives:

= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) de + (a²/2) ∫ cos(20e) cos(2e) de

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ cos(20e) cos(2e) de

Next, let's evaluate the remaining integral with respect to e:

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ cos(20e) cos(2e) de

Using the trigonometric identity cos(a) cos(b) = (1/2) [cos(a + b) + cos(a - b)], we can simplify the integrand:

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ (1/2) [cos(20e + 2e) + cos(20e - 2e)] de

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [∫ cos(22e) de + ∫ cos(18e) de]

= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [sin(22e)/22 + sin(18e)/18] + C

where C is the constant of integration.

Now, we have the integral with respect to e evaluated. To find the final result, we need to integrate with respect to θ. However, we don't have any dependence on θ in the original expression. Therefore, we can simply multiply the result obtained above by 2π, as we're integrating over the entire range of θ.

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Complete question:

Let A (-1,1). Evaluate TT Cos 20 De. 1-2a Cos 0 + A2 D0

Related Questions

if f(x) = x^2 which equation represents function g?
OA g(x) = f(2x)
OB. g(x) = f(4x)
Oc. g(x) = 2f(x)
OD. g(x) = f(1/2x)

Answers

Answer:

if f(x) = x^2 which equation represents function g?

Step-by-step explanation:

maby ( C) am not sure

The equation represents the function is g(x) = 3f(x).

What is Function?

A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

We have,

Function, f(x) = x²

The function g(x) is compressed horizontally by a factor of 3, to get the function g(x)

g(x) = kf(x)

Where k = 3.

So, we have:

g(x) = 3f(x)

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The drawing below shows circle B and circle E.Which equation best describes the relationship between BC and EF?

Answers

Answer:

BC = 3(EF)

Step-by-step explanation:

The question stated that AC is 3 times the length of DF.

Answer:

BC = 3(EF)

Step-by-step explanation:

Remember that AC is 3 times the length of DF

Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles. Determine P(not purple) when choosing one marble from the bag.
a.64%
b.36%
c.24%
d.8%

Answers

To determine the probability of not choosing a purple marble when selecting one marble from a bag containing 2 red, 4 green, 10 yellow, and 9 purple marbles. Correct option is A).

The total number of marbles in the bag is 2 (red) + 4 (green) + 10 (yellow) + 9 (purple) = 25 marbles.

The number of non-purple marbles is 2 (red) + 4 (green) + 10 (yellow) = 16 marbles.

Therefore, the probability of not choosing a purple marble is P(not purple) = 16/25.

To convert this fraction to a percentage, we divide the numerator (16) by the denominator (25) and multiply by 100: P(not purple) = (16/25) * 100 = 64%.

Hence, the probability of not choosing a purple marble when selecting one marble from the bag is 64%, which corresponds to option (a) in the given choices.

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la suma de cuatro y el producto de tres y un número x

Answers

Answer:

4+3x esa es la suma de cuatro y el producto de tres y un número x

What is the median for the following data set? 5,7,9,11,13,13

A. 10
B. 8
C. 9
D. 11

Answers

The answer is C.9 because 9+4=13 and 9-4=5 hope this helps

100 POINTSSS PLZZZZZZZZZZZ

Answers

Answer:

The correct anser is B. (i think. sorry if wrong) have a wonderfull day. dont let them bring you down. your amazing just the way you are.

Step-by-step explanation:

Step-by-step explanation:

\blue{\large \rightarrow }\: \boxed{ \sf{ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} }}

I made a fort by connecting two boxes. The first box is 5 meters long, 9 meters wide, and 9 meters high. The second box is 3 meters long, 8 meters wide, and 2 meters high.

Answers

Complete question :

I made a fort by connecting two boxes. The first box is 5 meters long, 9 meters wide, and 9 meters high. The second box is 3 meters long, 8 meters wide, and 2 meters high. How many cubic meters of space does my fort have?

Answer:

453 m³

Step-by-step explanation:

Volume of first box :

Volume = Length * width * height

Volume = 5 * 9 * 9

Volume = 405 m³

Volume of second box :

Volume = Length * width * height

Volume = 3 * 8 * 2

Volume = 48 m³

Total volume :

405m³ + 48m³ = 453m³

This is confusing me please help

Answers

Answer:

It’s the last one

Step-by-step explanation:

Did this before on a test

y = 3x - 5 and y = 4x.

Answers

Answer: x = -5

New Equation (after substituting) 4x = 3x - 5

Subtract 3x from both sides

x = -5

The temperature went down 3 F. Each hour. What was the total temperature change after 5 hours ?

Answers

After 5 hours the temperature decreased by 15 F. This is because 3 x 5 = 15. I hope this helps!


Urgent!!!!!

12. Arrange the stages of municipal council election by writing 1-7 in the
correct place. (2 marks each)
Stages in municipal elections
Girst (1) to last (17)
People going to the polling station to
Councilors campaign for election.
The number of votes for each division
is counted.
Voters vote by secret ballot.
Candidates nominated by two main
political parties.​

Answers

provide the passage or a picture of it please thx

Convert 312 quarts to gallons.

Answers

Answer:

78 gallons

Step-by-step explanation:

there are four quarts in one gallon. so, to convert 312 quarts to gallons you must divide by 4. The answer is 78 gallons.

I think the answer is 78

Two parallel lines l and m are cut by a transversal t. If the interior angles of the same side of t are (2x−8)∘ and (3x−7)∘, find the measure of each of these angles.

Answers

Step-by-step explanation:

When two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. This means that their measures add up to 180 degrees.

In this case, the two interior angles on the same side of the transversal 't' are (2x-8) degrees and (3x-7) degrees. Since these angles are supplementary, we can write the equation (2x-8) + (3x-7) = 180.

Solving this equation for x, we get:

(2x-8) + (3x-7) = 180

5x - 15 = 180

5x = 195

x = 39

Substituting this value of x into the expressions for the two interior angles, we find that their measures are:

(2x-8) = (2*39 - 8) = 70 degrees

(3x-7) = (3*39 - 7) = 110 degrees

So, the measure of each of these angles is 70 degrees and 110 degrees.

The two cones are similar. The smaller cone has a

surface area of 11. 74 inches

Complete the last step to determine the surface area of

the larger cone

3. 5 in.

1. The scale factor of the larger to the smaller is

Sor

2. The surface area will change by the square of the

scale factor, which is

3. Let the surface area of the larger cone be x.

Then, the proportion is = 11

4. Solve for x and round to the nearest hundredth.

The surface area of the larger cone is about

inches

Answers

The surface area of the larger cone is about 41.09 square inches.

To determine the surface area of the larger cone, we can set up a proportion based on the scale factor between the two cones. Let's call the scale factor "k".

From the given information, we know that the surface area of the smaller cone is 11.74 square inches and the surface area of the larger cone is unknown (let's call it "x" square inches).

Using the scale factor, we can write the proportion:

(11.74 / x) = (3.5 / 3.5)

Simplifying the proportion, we have:

11.74 = (x / 3.5)

To find the value of "x", we can cross-multiply:

x = 11.74 * 3.5

x ≈ 41.09

The surface area of the larger cone is approximately 41.09 square inches, rounded to the closest hundredth.

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if each square on the grid represents 400m squared, how many miles will your family travel in total

Answers

The family will travel approximately 0.0037075 miles in Total.

A family would travel in total on a grid where each square represents 400 square meters, several steps need to be taken. First, we need to determine the area covered by the family.

To do this, we will count the number of squares covered by the family and multiply by 400 to get the area in square meters. Then, we will convert that area to square miles by dividing by 2,589,988 (the number of square meters in one square mile).

Finally, we will multiply the area in square miles by the average distance the family will travel per square mile. Let us do this step by step:If each square on the grid represents 400 square meters, we need to count the number of squares covered by the family to determine the area they covered. From the grid, it can be seen that the family covered 12 squares. Therefore, the area covered by the family is 12 × 400 = 4800 square meters.

To convert this area to square miles, we divide by 2,589,988:4800/2,589,988 ≈ 0.00185375 square miles. Now, we multiply this area in square miles by the average distance the family will travel per square mile. Let's assume the family walks 2 miles per square mile. Therefore, the total distance they will travel is 0.00185375 × 2 = 0.0037075 miles.

Therefore, the family will travel approximately 0.0037075 miles in total.

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Explain the characteristics of authoritarianism and identify two central Asian countries that have this type of government.

Answers

Answer:

Authoritarianism is a form of government in which the rulers, that is, those who exercise the political functions of the nation, carry out their tasks in an autocratic and centralized manner. Thus, they do not limit their power but, on the contrary, cling to it, at the expense of citizens' rights. A clear example of authoritarian governments that rule in Central Asian countries are Turkmenistan and Turkey.

Answer:

. . A clear example of authoritarian governments that rule in Central Asian countries are Turkmenistan and Turkey Thus, they do not limit their power but, on the contrary, cling to it, at the expense of citizens' rights Authoritarianism is a form of government in which the rulers, that is, those who exercise the political functions of the nation, carry out their tasks in an autocratic and centralized manner

A cylindrical tank holds 352 cu. ft. of water. The height of the tank is 7 ft. Find the
radius of the tank.
pls help me thx and show your work

Answers

Answer:

0.3334 ft

Step-by-step explanation:

Measure the height and radius of the tank. The radius is the distance from the center of the tank to its outer edge. Another way to find the radius is to divide the diameter, or width, by two. Square the radius by multiplying the radius times itself and then multiply it by 3.1416, which is the constant pi.

Given height and volume: r = √(V / (π * h)),Given height and lateral area: r = A_l / (2 * π * h),Given height and total area: r = (√(h² + 2 * A / π) - h) / 2,Given height and diagonal: r = √(h² + d²) / 2,Given height and surface-area-to-volume ratio: r = 2 * h / (h * SA:V - 2),Given volume and lateral area: r = 2 * V / A_l,Given base area: r = √(A_b / (2 * π)),Given lateral area and total area: r = √((A - A_l) / (2 * π)).

Gilbert's weekly pay in dollars, D. can be represented by the function D = 13.5h, where h represents the number of hours
he works during a week.

Answers

Answer:

she will have 27,216 dollars after 12 week

27,216 per week

Step-by-step explanation:

12 week has (12*7*24)=2,016 hours

D = 13.5h    D = 13.5*(2,016 )=27,216

f ( x ) = − x 2 − 12 Find f ( − 3 )

Answers

Answer:

f(-3)=-21

Step-by-step explanation:

f(x)=-x2-12

f(-3)=-(-3)2-12

f(-3)=-9-12

f(-3)=-21

Answer:

-3

Step-by-step explanation:

x=-3 substitute in the equation

+3 squared-12=-3

-2+ 3(1-4)-2 what to do ???​

Answers

Answer:

-13

Step-by-step explanation:

−2+3(1−4)−2

=−2+(3)(−3)−2

=−2+−9−2

=−11−2

=−13

Step-by-step explanation:

Is this ok

If its correct, please don't forget to like and mark me

A loan of R 180 000, granted at 15,6% p.a. compounded monthly, is amortised by means of regular equal monthly payments of R 6 300 and a final payment F (F < R 6 300) made one month after the last equal payment of R 6 300. If the first payment is made one month after the loan is granted, then the final payment F , (to the nearest cent)

Answers

The final payment F, made one month after the last equal payment, for a loan of R 180,000 at an interest rate of 15.6% p.a. compounded monthly with regular equal monthly payments of R 6,300, is R 6,345.94 (to the nearest cent).

To calculate the final payment F, we need to determine the remaining balance after the last equal payment of R 6,300. We can consider it as the present value of the remaining debt, including one month of interest.

First, we calculate the monthly interest rate by dividing the annual interest rate by 12:

r = 15.6% / 12 = 0.013

Next, we calculate the remaining balance as the present value of the remaining debt after the last equal payment:

Remaining balance = R 180,000 * (1 + r)^(n_remaining) - R 6,300

Where: n_remaining = Number of remaining months after the last equal payment (1 month)

Remaining balance = 180,000 * (1 + 0.013)^1 - 6,300 = R 180,000 * 1.013 - 6,300 = R 180,000 * 1.013 - 6,300 = R 182,340

Finally, we subtract the remaining balance from the final payment to determine the value of F:

F = Remaining balance - R 6,300 = R 182,340 - 6,300 = R 6,345.94 (to the nearest cent)

Therefore, the final payment F, made one month after the last equal payment, is R 6,345.94 (to the nearest cent).

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if two samples are selected from the same population, under what circumstances are the two samples guaranteed to have exactly the same t statistic?

Answers

If two samples are selected from same population, then two samples are  guaranteed to have exactly same t-statistic is (d) If samples are same-size and have same-mean and have same-variance.

If two samples are selected from the same population and have the same size, same mean, and same variance, the t statistic calculated for both samples will be exactly the same.

The t statistic is computed using the sample means, sample variances, and sample sizes. When these values are identical for both samples, the calculations for the t-statistic will yield the same result.

This scenario ensures that the t-statistic, which is used for hypothesis testing or constructing confidence intervals, will be consistent across the two samples.

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

If two samples are selected from the same population, under what circumstances are the two samples guaranteed to have exactly the same t statistic?

(a) If the samples are the same size and have the same variance.

(b) If the samples are the same size and have the same mean.

(c) If the samples have the same mean and the same variance.

(d) If the samples are the same size and have the same mean and have the same variance.

*Will mark brainliest* Can someone explain this to me?

Answers

251.33
Is right
Hope that helped XD

A fair coin is tossed five times. The event "A = getting all heads" has probability = 1/32. (a) Describe in words what the event AC is. At least one tail occurs in the five flips. At least four tails occur in the five flips. At least four heads occur in the five flips. Getting all tails. At least one head occurs in the five flips. (b) What is the probability of AC? (Enter your answer as a fraction.)

Answers

The event AC describes the scenario in which at least one tail occurs in the five coin flips.The probability of AC is 31/32.

(a) In words, the event AC describes the scenario in which at least one tail occurs in the five coin flips.

Event AC can also be written as {HTTTT, THTTT, TTHTT, TTTHT, TTTTH, HTTTH, HHTTT, THHTT, TTHHT, TTTHH, HTTHH, HHTTH, THHHT, TTHHH, HTHTT, HHTHT, THHTH, HTTHT, THTHT, HTTH, THTTH, TTHTH, TTHHT, THTHH, HTTHH, THHTH, HTHHT, HHTHH, THHH, TTHH, THTH, HTTH, HHTH, THHT}.

(b) The probability of AC can be calculated as follows:

There are two possible outcomes of each coin flip: heads or tails.

Since the coin is fair, both outcomes are equally likely.

Therefore, the probability of getting tails in one flip is 1/2, and the probability of getting heads in one flip is also 1/2.In order to find the probability of AC, we will use the complement rule:Prob(AC) = 1 - Prob(A)Prob(A) = 1/32Prob(AC) = 1 - 1/32Prob(AC) = 31/32

Therefore, the probability of AC is 31/32.

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Find the value of x. Round to the
nearest tenth.
X
37
6
X=
Enter

Answers

Answer:

x ≈ 4.5

Steps:

tan(37°) = 0.75..

tan(37°) = x/6

x/6 = 0.75..

x = 0.75.. × 6

x = 4.52.. ≈ 4.5

Answer:

The answer is 4.5

Step-by-step explanation:

x =4.5

Fill in 4.5

(PLZ I NEED HELP QUICLY) Angela lives in a remote area serviced by only two cell phone towers. Tower 1 is located 5 miles west and 2 miles south of her home and transmits a signal for 12 miles. Tower 2 is located 8 miles east and 7 miles north of her home and transmits a signal for 10 miles. Consider the location of Angela’s house to be (0, 0) on a coordinate grid. The system of inequalities represents this scenario.
Angela travels to a friend’s house, which is 4 miles east and 8 miles north of her house. Will Angela have cell phone service at her friend’s house?

A. Angela will not have any cell phone service.
B. Angela will have cell phone service from tower 1 only.
C. Angela will have cell phone service from tower 2 only.
D. will have cell phone service from both towers.

Answers

Angela will have cell phone service from tower 2 only , Option C is the answer.

What is an Inequality ?

An inequality is an algebraic expression connected to another algebraic expression with an inequality operator.

The two inequalities given are

(x+5)² + (y+2)² ≤ 144

(x-8)² +(y-7)²  ≤100

The inequalities are plotted on the graph

and the location of Angels's Friends ( 4 , 8) is also plotted

If this lies in the area of the Inequalities she will have signal.

At Angela's friends house she will have the signal of Tower 2 only.

Therefore Option C is the answer.

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Dada la recta L1:x+(m+2)y=n−5 pasa por el punto (1,2) y que es paralelo a la recta L2:3y=2x−4. Determine m+n .

Answers

Answer:

-1/2

Step-by-step explanation:

The point slope form of equation of a line is expressed as;

[tex]y - y_{0} = m(x-x_0)[/tex]

m is the slope

(x₀, y₀) is the point on the line

Given

(x₀, y₀) = (1, 2)

Given the equation 3y = 2x - 4

Rewrite the equation

y = 2/3x - 4/3

mx = 2/3x

m = 2/3

The slope is 2/3

Substitute the slope and the point into the formula above

[tex]y -y_0 =m(x-x_0)\\y - 2 = 2/3(x - 1)\\3(y-2) = 2(x-1)\\3y - 6 = 2x - 2\\Swap\\2x - 2 = 3y - 6\\2x - 3y = -6 + 2\\2x - 3y = -4\\x - 3/2 y = -4/2\\x - 3/2 y= -2[/tex]

Compare the expression to x+(m+2)y=n−5

m + 2 = -3/2

m = -3/2 - 2

m = -7/2

Similarly

n - 5 = -2

n = -2 + 5

n = 3

m + n = -7/2 + 3

m + n = -1/2

hence the sum of m and n is -1/2


I need help on this. ​

Answers

g = 2
:::::::::::::::::::

determine which rate should be used to complete the conversion: 12 gallons per hour to gallons per minute.
A. 1 hour per 60 minutes
B. 60 minutes per 1 hour

Answers

B.....................

Goods Neargo Bank hires salespeople to call potential customers to see if they'll open a new bank account. Suppose there's a 5% chance a call will result in a new bank account. After 200 calls, what's the probability that a salesperson getting at least 12 customers to open a new bank account? Use the binomial distribution function in Excel to answer this question

Answers

The probability that a salesperson will get at least 12 customers to open a new bank account after 200 calls using the binomial distribution function in Excel is approximately 0.9999.

To calculate the probability using the binomial distribution function in Excel, follow these steps:

1. Open Microsoft Excel and enter the following values in a new spreadsheet:

  - In cell A1, enter the number of trials (200).

  - In cell B1, enter the probability of success on a single trial (0.05).

  - In cell C1, enter the minimum number of successes needed (12).

2. In an empty cell, use the following formula to calculate the probability of getting at least 12 customers to open a new bank account:

  =1-BINOM.DIST.CUMULATIVE(C1-1, A1, B1, TRUE)

  This formula uses the BINOM.DIST.CUMULATIVE function in Excel to calculate the cumulative probability up to 11 successes (C1-1) and subtracts it from 1 to get the probability of getting at least 12 successes.

3. Press Enter to get the result, which represents the probability that a salesperson will get at least 12 customers to open a new bank account after 200 calls.

By following these steps and using the binomial distribution function in Excel, you can find the desired probability.

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