Compute the Fourier coefficients and write the Fourier series in the complex and real forms. Thank you!
(d) f(x) = x2 on [0, 1], and extended to R by 7-periodicity.
1

Answer:

Step-by-step explanation:

You keep the same slope since it's supposed to be parallel. But first you need to write it in slope intercept form. So the y can't have a number in front of it, so you must divided everything after the equal sign by the 3. So the equation becomes y=2/3x−1. Now you plug in the points to find a parallel equation using point slope form y−(4)=(23)(x−(−3)). Then you solve that and you get y=2/3x+6.

Answer:

c. 137°

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Try D first because it is the simplest.

Randomly, I tried 5*-59.

It gives -295. That is not correct numerically because the given y value is -471

A is numerically impossible. You can estimate it by saying 176 - 59 = something much different than - 235

B doesn't work either. -59*5 - 235 = -530 which is not the answer given.

C better work -59*5 - 176 = -471 which is correct.

Answer:

let the candies be 2x and 3x then 2x+3x=35

x=7, no. of red candies=14 and yellow=21

now, 14-2=12 and 21+1=22

thus the new ratio will be 12:22 or 6:11.

S" > 0 indicates that the rate of change of sales is increasing.

What is rate?

A rate is a measure of the amount of change of one quantity with respect to another quantity, typically expressed as a ratio.

The derivative of a function represents its rate of change at a particular point. In this case, S represents the monthly sales of Bluetooth headphones, and its derivative S' represents the rate of change of sales. If S' is increasing, it means that the rate of change of sales is getting larger over time.

Mathematically, this means that the second derivative S" (which represents the rate of change of the rate of change) is positive, since an increasing slope of the original function (S') corresponds to a positive value for the second derivative.

Therefore, S" > 0 indicates that the rate of change of sales is increasing.

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45 |   45 divided by 5 = 9    

So i think if we do the same for 70 we will get the length

70| 70 divided by 5 = 14

So the length = 14

--If I'm incorrect please correct me

Using the difference, the height of stack increased per cup is 0.5 centimeters.

The graph of the question is given below:

In the given question we have to find the how much does each cup after the first add to the height of the stack.

From the graph we can see that when there have 3 cups then the height of the stake is 5.5. When there have 8 cups then the height of the stack is 8.

So the incresed cup = 8-3 = 5

Incresed height of the stack = 8-5.5 =2.5

So the height of stack increased per cup = increased height/increased cup

the height of stack increased per cup = 2.5/5

the height of stack increased per cup =0.5

Hence, the height of stack increased per cup is 0.5 centimeters.

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A confounding variable that could make the manager's conclusion inappropriate is the amount of exercise the members participate in. The manager did not take into account whether or not those who participated in the dietary program also participated in a higher amount of exercise than those who did not participate in the program.

It is possible that members who participated in the dietary program also participated in a higher amount of exercise than those who did not participate in the program, resulting in increased weight loss. This would mean that it was not the dietary program alone that caused the weight loss, but rather the combination of the dietary program and the additional exercise. Therefore, the manager's conclusion that the dietary program caused the increased weight loss is inappropriate without taking into account the amount of exercise the members participated in.

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The area of the sector is 397.995 m²

For a sector in a circle of radius R, defined by an angle θ, the area is given by the formula:

A = (θ/360)*3.14*R²

Here we know that the radius of the circle is 13 meters, and the angle is 270 degrees.

Then replacing that in the formula for the area we will get:

A = (270/360)*3.14*(13m)²

A = 397.995 m²

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Answer:

118 .........................

Answer:

????????????????????

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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The true statements are:

The greatest common factor of 20 and 30 is 10.

The least common multiple of 20 and 30 is 60.

The common factor is 2.

Consider the numbers 20 and 30,

The factors of 20 are 1, 2, 3, 4, 5, 10, and 20.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

The common factors are 1, 2, 3, 5, 6, 10 and hence the greatest common factors are 10.

And, 2 is a common factor.

The multiples of 20 are 20, 40, 60, 80, 100, ....

The multiples of 30 are 30, 60, 90, 120, ...

Therefore, the least common multiple is 60.

The GCF and LCM of 20 and 30 are 10 and 60 respectively. The common factor is 2.

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Answer:The slope is m= 1/2

(0,-2) & (2,-1)

Step-by-step explanation:

(0,-2) & (2,-1)

m=y²-y¹/x²-x¹

m=(-1)-(-2)/2-0

m=1/2

The approximate intensity of the earthquake is (b) 63096

From the question, we have the following parameters that can be used in our computation:

M = log(I)

When the magnitude is 4.8

We have the following representation

M = 4.8

Substitute the known values in the above equation, so, we have the following representation

log(I) = 4.8

Take the antilog of both sides

I = 63095.734448

Approximate

I = 63096

Hence, the intensity is 63096

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Answer:

B

Step-by-step explanation:

Answer: yes, Rachelle is correct.

Step-by-step explanation:

first, if you're moving left, you're subtracting from the x value.

4-4=0

next, if you're moving down then you're subtracting from the y value.

2-2=0

if you subtract more than the given numbers, like said in the problem, you would have coordinates like (-1,-1) or (-3,-4)

therefore, you would be in the third quadrant.

Answer:

Undefined

Step-by-step explanation:

Given that the equation \(x=-4\) is a vertical line that intersects the x-axis at \(x=-4\), there is only a change in \(y\), but no change in \(x\). Thus, the rate of change is undefined since you cannot divide by 0.

Answer:

Ordinary least squares

Step-by-step explanation:

The ordinary least squares means the estimations that done for parameters in a regression model by lowering the sum of the square residuals. It also predicted the coefficient of the regression equation that generate the actual and the expected values of the dependent variable is known as ordinary least squares

Therefore the above represent the answer

One drink of an alcoholic beverage contains approximately 100 to 150Kcal. That is option D

An alcoholic beverage is a type of beverage that contains ethanol which is also a type of alcohol.

The three main types of alcoholic beverage are beer, wine and spirits.

Alcoholic drinks contain a lot of kilojoules and have no nutritional benefits

One drink of an alcoholic beverage contains approximately 100 to 150Kcal.

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Answer:

Step-by-step explanation:

In a right triangle, the sides forming the right angle also determine the angle opposite one of the sides.

Tan(29) =26/x                Multiply both sides by x

x tan(29) = 26                 Divide by tan(29)

x = 26/tan(29)                Find tan(29)

x = 26/0.5543                Divide

x= 46.9

The following are the variables that could be of interest to generate environmental data: Pollution levels: Pollution levels are a measure of the degree to which the air is contaminated.

Contaminants in the air, such as particulate matter and toxic gases, can be hazardous to human health and the environment, and monitoring them can provide valuable data on air quality.Air quality: Air quality refers to the level of pollution in the air. This could include measurements of various pollutants, such as nitrogen dioxide, sulfur dioxide, and particulate matter. This data can be gathered by a variety of sensors, including gas analyzers, particle counters, and spectrometers.Ozone concentration: Ozone concentration refers to the amount of ozone in the air. Ozone is a powerful oxidant that can have both beneficial and harmful effects on human health and the environment. Storm intensity: Storm intensity refers to the severity of a storm.

This could include measurements of wind speed, rainfall, and lightning activity. Data on storm intensity can be gathered using weather stations, Doppler radar, and lightning detection systems.Vegetation density: Vegetation density is a measure of how much plant life is present in a given area. This data can be used to monitor changes in ecosystems over time and to assess the impact of human activities on the environment. Vegetation density can be measured using satellite imagery, ground-based surveys, and remote sensing technologies.Earthquake intensity: Earthquake intensity refers to the strength of an earthquake. This could include measurements of ground motion, ground acceleration, and ground displacement. Data on earthquake intensity can be gathered using seismometers and other ground-based sensors. Wildlife diversity can be measured using a variety of techniques, including surveys, camera traps, and acoustic monitoring.

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Answer:

C. five samples.

Step-by-step explanation:

The solution of the values of the triangle are

sin A ≈ 0.29

cos A ≈ 0.29

sin 8 ≈ 0.29

cos 8 = 1

Finding sin A:

The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle (in this case, side b) to the length of the hypotenuse (in this case, side a). Therefore, sin A = b/a. Substituting the given values, we have sin A = 5.69/19.45 ≈ 0.2937 (rounded to the nearest hundredth).

Finding cos A:

The cosine of an angle in a right triangle is defined as the ratio of the length of the side adjacent to the angle (in this case, side b) to the length of the hypotenuse (in this case, side a). Therefore, cos A = b/a. Substituting the given values, we have cos A = 5.69/19.45 ≈ 0.2927 (rounded to the nearest hundredth).

Finding sin 8:

To find the sine of angle 8, we first need to determine the value of angle 8. In a right triangle, the sum of the angles is always 180 degrees. Since angle C is 90 degrees, we have angle A + angle B = 180 - 90 = 90 degrees. Therefore, angle B = 90 - angle A = 90 - 8 = 82 degrees.

Now, we can find sin 8 by considering the ratios of the sides in the right triangle with angle 8. The sine of angle 8 is defined as the ratio of the length of the side opposite angle 8 to the length of the hypotenuse. Using the given side lengths, we have sin 8 = b/a. Substituting the values, we get sin 8 = 5.69/19.45 ≈ 0.2937 (rounded to the nearest hundredth).

Finding cos 8:

Similarly, to find the cosine of angle 8, we can use the definition of cosine in a right triangle. The cosine of angle 8 is the ratio of the length of the side adjacent to angle 8 to the length of the hypotenuse. Therefore, cos 8 = a/a. Substituting the given values, we have cos 8 = 19.45/19.45 = 1.

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To the correct number of significant figures, the area of the rectangle is 1.723 m². The correct answer is an option (C).

As per the question, we have:

The length of the rectangle = 3.24 m

The width of the rectangle = 0.532 m

To find the area of the rectangle, we can use the formula:

Area of the rectangle = length x height

Substituting the given values, we get:

Area of the rectangle = 3.24 m × 0.532 m

Area of the rectangle = 1.72368 m²

To the correct number of significant figures, the area of the rectangle is 1.723 m².

Therefore, the correct answer is an option (C).

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Answer:

  a) 45/4

  b) 3

  c) 12

  d) 24

  e) no; rate of change varies

Step-by-step explanation:

The average rate of change on interval [a, b] is given by ...

  m = (f(b) -f(a))/(b -a)

The function values are read from the table.

__

a) m = (f(4) -f(0))/(4 -0) = (48 -3)/(4 -0) = 45/4

b) m = (f(1) -f(0))/(1 -0) = (6 -3)/(1 -0) = 3

c) m = (f(3) -f(2))/(3 -2) = (24 -12)/(3 -2) = 12

d) m = (f(4) -f(3))/(4 -3) = (48 -24)/(4 -3) = 24

e) Not a linear function. The rate of change is not constant.

Answer:

50 miles per hour, 150 miles

Step-by-step explanation:

To find miles per hour , divide 80 by 1.6 This is 50

Thus, 80km/hr = 50 miles / hour

Also if the car travels 50 miles an hour, then in 3 hours it goes 50 x 3 = 150 miles.

Hope this helps