Use the proportion d / 180° = r radians/πradians . Find the equivalent degree measure or radian measure 270°

To simplify the expression ³√(-5) * ³√(-25), we start by simplifying each cube root individually.  The cube root of -5 can be expressed as -∛5, where the negative sign is included to indicate that the result is a negative number. Similarly, the cube root of -25 can be written as -∛25.

Next, we can multiply these simplified exprsssions together. When we multiply -∛5 by -∛25, we get -∛(5 * 25) = -∛125.  Now, let's simplify the cube root of 125. The cube root of 125 is 5, since 5 * 5 * 5 = 125. However, since we have a negative sign in front, the final simplified result is -5. Therefore, the expression ³√(-5) * ³√(-25) simplifies to -5. This means that the product of the cube roots of -5 and -25 is equal to -5.

Learn more about simplified cube roots here: brainly.com/question/32030723

#SPJ11

The sequences pattern observed in the ratio column for the given set of numbers {3, 9, 27, 81} is that each term is obtained by multiplying the previous term by 3.

The pattern observed in the ratio column is a constant ratio of 3. Each term in the set is obtained by multiplying the previous term by 3.

Starting with the first term, 3, we can calculate the ratio between each pair of consecutive terms. The ratio between 9 and 3 is 9/3 = 3. Similarly, the ratio between 27 and 9 is 27/9 = 3, and the ratio between 81 and 27 is 81/27 = 3.

This constant ratio of 3 indicates that each term in the set is obtained by multiplying the previous term by 3. This pattern continues as we extend the sequence. For example, the next term in the sequence would be 81 * 3 = 243, and the subsequent term would be 243 * 3 = 729, and so on.

Therefore, the pattern observed in the ratio column is that each term in the set {3, 9, 27, 81} is obtained by multiplying the previous term by 3.

In conclusion, the ratio column reveals a constant ratio of 3 between each consecutive pair of terms in the given set. Each term is obtained by multiplying the previous term by 3.

Learn more about  sequences and ratios here:

https://brainly.com/question/29018365

#SPJ4

Question: As the number of terms gets greater, what pattern do you notice in the ratio column?

{3, 9, 27, 81}

To represent the system of equations 3x + 2y = 16 and y = 5 in matrix form, we can write the augmented matrix [A|B], where A represents the coefficients of x and y, and B represents the constants on the right-hand side of the equations.

The system can be written as:

3x + 2y = 16

   y = 5

In matrix form, the system can be represented as:

| 3   2 |  | x |  =  | 16 |

| 0   1 |  | y |     |  5 |

The matrix on the left side represents the coefficients of x and y, and the matrix on the right side represents the constants.

Visit here to learn more about matrix brainly.com/question/28180105

#SPJ11

The statement "If two lines intersect to form congruent adjacent angles, then the lines are perpendicular" is sometimes true.

Explanation:

When two lines intersect, they form two pairs of adjacent angles. If these adjacent angles are congruent (i.e., have the same measure), it is possible for the lines to be perpendicular. In this case, the statement is true.

However, it is also possible for the lines to intersect and form congruent adjacent angles without being perpendicular. This occurs when the lines are not perpendicular but are instead parallel or at an angle other than 90 degrees. In these cases, the statement is false.

Therefore, the statement is sometimes true, depending on the specific configuration of the intersecting lines.

To learn more about conditional statements click :

https://brainly.com/question/18152035

#SPJ4

The correct option is: The experimental probability of choosing a heart is 1/16 greater than the theoretical probability of choosing a heart.

Here, we have,

To compare the experimental probability and the theoretical probability of choosing a heart, we need to calculate both probabilities.

Experimental probability is determined by the number of favorable outcomes (in this case, the number of times Rochelle chose a heart) divided by the total number of outcomes (the total number of times Rochelle chose a card).

Given the data provided:

Clubs: 29

Spades: 13

Hearts: 15

Diamonds: 23

The experimental probability of choosing a heart is:

P(Heart) = (Number of times Rochelle chose a heart) / (Total number of times Rochelle chose a card)

= 15 / (29 + 13 + 15 + 23)

= 15 / 80

= 3/16

The theoretical probability of choosing a heart can be calculated based on the assumption that all suits have an equal number of cards (since it is mentioned that each suit has an equal number of cards in a standard deck). There are 52 cards in total, and 1/4 of them are hearts (since there are four suits in total).

The theoretical probability of choosing a heart is:

P(Heart) = Number of hearts / Total number of cards

= (1/4) * 52

= 13

Comparing the two probabilities, we have:

Experimental probability of choosing a heart: 3/16

Theoretical probability of choosing a heart: 13

To determine how they compare, we can calculate the difference between the theoretical and experimental probabilities.

Difference = Theoretical probability - Experimental probability

= 13 - 3/16

To make a comparison, we need to simplify the expression:

Difference = (208/16) - (3/16)

= 205/16

Therefore, the experimental probability of choosing a heart is 205/16 greater than the theoretical probability of choosing a heart.

The correct option is: The experimental probability of choosing a heart is 1/16 greater than the theoretical probability of choosing a heart.

To learn more on probability click:

brainly.com/question/11234923

#SPJ4

complete question:

A standard deck of 52 cards contains four suits: clubs, spades, hearts, and diamonds. Each deck contains an equal number of cards in each suit. Rochelle chooses a card from the deck, records the suit, and replaces the card. Her results are shown in the table.

Clubs 29, Spades 13, Hearts 15, Diamonds 23

How does the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart?

The theoretical probability of choosing a heart is 1\16 greater than the experimental probability of choosing a heart.

The experimental probability of choosing a heart is 1\16 greater than the theoretical probability of choosing a heart.

The theoretical probability of choosing a heart is 1\26 greater than the experimental probability of choosing a heart.

The experimental probability of choosing a heart is 1\26 greater than the theoretical probability of choosing a heart.

Answer:

A. y = -5/2x - 5

Step-by-step explanation:

To find the equation of the line that is perpendicular to y = (2/5)x + 1, we need to determine the negative reciprocal of the slope of the given line.

The given line has a slope of 2/5. The negative reciprocal of 2/5 is -5/2.

Now, we can use the point-slope form of a linear equation to find the equation of the line that passes through the point (-10, 20) with a slope of -5/2:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Plugging in the values, we get:

y - 20 = (-5/2)(x - (-10))

y - 20 = (-5/2)(x + 10)

y - 20 = (-5/2)x - 25

y = (-5/2)x - 5

Therefore, the equation that represents the line perpendicular to y = (2/5)x + 1 and passes through (-10, 20) is:

A. y = -5/2x - 5

In this case, I will consider the relationship between a person's age and their income. I believe that income is more likely to have a higher standard deviation compared to age.

1. Economic Factors: Income is influenced by economic factors such as job market conditions, economic growth, and industry trends. These factors can fluctuate over time, leading to variations in income levels. On the other hand, age progresses in a more predictable manner.

2. Career Development: Income is strongly influenced by career development, including promotions, job changes, and salary negotiations. These factors introduce a level of unpredictability, as individuals may experience significant income changes at different stages of their careers. Age, although related to career progression, follows a relatively more predictable pattern.

3. Individual Choices: Income can also be influenced by individual choices such as entrepreneurship, investment decisions, and career changes. These choices introduce a higher level of variability as they depend on personal circumstances, risk appetite, and market conditions. Age, in contrast, progresses in a more linear and predictable manner.

Considering these reasons, it is reasonable to expect that income would have a higher standard deviation compared to age. Income is influenced by various external and personal factors that can result in significant fluctuations, making it less predictable compared to the relatively more stable progression of age.

Learn more about standard deviation visit:

brainly.com/question/13498201

#SPJ11

The central tendency of the data set is given by mean of the set and the value of mean is 12.6 .

Given,

Data set : 1,3,3,3,4,10,20,30,40 .

Here,

To calculate the central tendency of the data set firstly calculate the mean of the data set .

So,

Mean = Sum of all the observation in the data set / Number of observations in the data set

So,

Mean = 1+3+3+3+4+10+20+30+40/9

Mean = 114/9

Mean = 12 .6

Thus the mean of the data set is 12.6 .

Therefore mean represents the central tendency of the data correctly .

Know more about central tendency ,

https://brainly.com/question/32289907

#SPJ4

The correct assumption to initiate an indirect proof is "∠S is an acute angle."option C

In order to start an indirect proof of the statement "Angle S is not an obtuse angle," we would need to assume that option C is true, which states "∠S is an acute angle."

An indirect proof, also known as a proof by contradiction, involves assuming the negation of the statement and then arriving at a contradiction. In this case, if we assume that ∠S is an obtuse angle (option B), we would be directly assuming the statement we are trying to prove false.

This assumption would not lead us to a contradiction and would not allow us to complete an indirect proof.

On the other hand, assuming that ∠S is an acute angle (option C) sets up a potential contradiction since the original statement claims that ∠S is not an obtuse angle.

If we can show that assuming ∠S is an acute angle leads to a contradiction, we can conclude that ∠S is not an obtuse angle, which is what we want to prove.

Therefore, the correct assumption to start an indirect proof of the statement is option C, "∠S is an acute angle."

For more question on acute angle visit:

https://brainly.com/question/6979153

#SPJ8

Answer:

Part 1:

Part 2:504

Step-by-step explanation:

part 1 multiply 144 by 4 then divide by 12 = 84

and multiply 42 by 4 then divide by 12 =48

part 2 144 times 42 divided by 12 = 504

The equation of the tangent line to the Witch of Agnesi at a given point (x0, y0) is:  [tex]\(y - y_0 = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}(x - x_0)\)[/tex]

The tangent lines to the curve called the Witch of Agnesi at a given point can be determined by finding the derivative of the curve and evaluating it at that point.

To find the equation of a tangent line, we need the derivative of the curve. The equation of the Witch of Agnesi is given by:

[tex]y = \frac{8a^3}{x^2 + 4a^2}[/tex]

where 'a' is a constant that determines the shape of the curve.

Taking the derivative of y with respect to x, we can find the slope of the tangent line:

[tex]\frac{dy}{dx} = \frac{-64a^3x}{(x^2 + 4a^2)^2}[/tex]

Let's assume we want to find the tangent lines at the point (x0, y0). We can substitute these coordinates into the derivative expression:

[tex]\frac{dy}{dx}\Bigr|_{x=x_0} = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}[/tex]

This gives us the slope of the tangent line at the point (x0, y0).

Now, using the point-slope form of a line, we can write the equation of the tangent line:

[tex]y - y_0 = \frac{dy}{dx}\Bigr|_{x=x_0}(x - x_0)[/tex]

Substituting the values we obtained earlier, the equation of the tangent line becomes:

[tex]y - y_0 = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}(x - x_0)[/tex]

This equation represents the tangent line to the Witch of Agnesi at the point (x0, y0).

To know more about the Witch of Agnesi, refer here:

https://brainly.com/question/33614999#

#SPJ11

The arithmetic mean is commonly used as a measure of central tendency because it is intuitive, easy to calculate, and suitable for most data types.

The arithmetic mean, or simply the mean, is the sum of all data values divided by the number of values. It is commonly used as a measure of central tendency because it is intuitive and easy to calculate. However, the mean can be influenced by extreme values, known as outliers, which may distort its interpretation. In contrast, the geometric mean is useful for dealing with multiplicative quantities, such as growth rates or ratios, but it is less commonly used as a measure of central tendency.

To calculate the population standard deviation and variance, assuming equal weights, you first find the mean of the data set. Then, for each data point, subtract the mean and square the result. Sum up all the squared differences, divide by the total number of data points, and take the square root to obtain the standard deviation. Variance is obtained by taking the average of the squared differences from the mean, without taking the square root.

Standard deviation measures the average distance between each data point and the mean. A larger standard deviation indicates a greater spread or variability in the data. Variance is similar to standard deviation but lacks the square root, so it represents the average of the squared differences. These measures are commonly used in statistical analysis to describe the dispersion of data points, assess the uncertainty or variability in a sample or population, and make comparisons between different data sets. They play a crucial role in hypothesis testing, confidence intervals, and inferential statistics.

Learn more about arithmetic here:

https://brainly.com/question/15196910

#SPJ11

Scalar multiplication on matrices involves multiplying each element of the matrix by a constant value. In applications, it can be used to scale payoffs in a game or adjust the relative values of outcomes.

To perform scalar multiplication on matrices, you simply multiply each element of the matrix by the scalar value. Scalar multiplication allows you to scale the matrix by multiplying all its entries by a constant value. Here's an example to illustrate the concept:

Suppose we have the following matrix:

A = [1 2 3]

   [4 5 6]

   [7 8 9]

And we want to multiply it by a scalar value of 2. To do this, we multiply each element of the matrix by 2:

2A = [2*1 2*2 2*3]

        [2*4 2*5 2*6]

        [2*7 2*8 2*9]

    = [2 4 6]

        [8 10 12]

        [14 16 18]

So, 2A is the resulting matrix after scalar multiplication.

In the context of applications, let's consider a scenario where we have a matrix representing the payoffs in a game, and we want to double all the payoffs. We can achieve this by multiplying the matrix by a scalar value of 2. The scalar multiplication will scale all the payoffs by a factor of 2, effectively doubling them.

This operation can be useful when analyzing game theory models or conducting simulations. By scaling the payoffs, you can evaluate the impact of changing the relative values of different outcomes in a game or analyze the effects of increasing or decreasing the rewards or penalties involved.

Remember that scalar multiplication only affects the magnitude of the entries in the matrix and does not change the matrix's structure or dimensions.

To learn more about matrix  Click Here: brainly.com/question/29132693

#SPJ11

Answer:

x = 6

Step-by-step explanation:

since line m bisects CW at point T , then

CT = TW = 3x + 2

and

CT + TW = CW

3x + 2 + 3x + 2 = 40

6x + 4 = 40 ( subtract 4 from both sides )

6x = 36 ( divide both sides by 6 )

x = 6

Answer:

Step-by-step explanation:

To find the value of x, we can use the property of a bisector that divides a line segment into two equal parts. Therefore, CT = TW.

Given that CW = 40 and TW = 3x + 2, we can substitute TW with CT to get:

CT = TW

CT = 3x + 2

We also know that CW = CT + TW, so we can substitute the values of CT and TW to get:

CW = CT + TW

40 = CT + (3x + 2)

38 = CT + 3x

38 - 3x = CT

Since line m bisects CW at point T, we know that CT = TW. Substituting this into the equation above, we get:

38 - 3x = TW

38 - 3x = 3x + 2

36 = 6x

x = 6

A. To determine whether the variances are equal, conduct a right-tail test using appropriate statistical methods.

B. To test the equality of variances, we can use a right-tail test, also known as a folded test.

This test compares the variances of two samples to assess whether they are statistically different or not.

Here are the steps to conduct the right-tail test for equal variances:

1. State the null and alternative hypotheses:

  - Null hypothesis (H0): The variances of the two samples are equal.

  - Alternative hypothesis (H1): The variances of the two samples are not equal.

2. Choose an appropriate significance level (e.g., α = 0.05) to determine the critical value.

3. Calculate the test statistic.

There are different tests available, such as the F-test or Bartlett's test, depending on the nature of the data and assumptions.

The test statistic measures the ratio of the variances and follows a specific distribution under the null hypothesis.

4. Determine the critical value corresponding to the chosen significance level.

This critical value helps determine whether to reject or fail to reject the null hypothesis.

5. Compare the test statistic with the critical value.

If the test statistic exceeds the critical value, we reject the null hypothesis, indicating that the variances are significantly different.

If the test statistic does not exceed the critical value, we fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude a significant difference in variances.

By following these steps and conducting the appropriate test, you can determine whether the variances of the samples are equal or not.

Learn more about  null and alternative hypotheses:

brainly.com/question/33444525

#SPJ11

The components on the x-y plane is 7 k N. The magnitude and the coordination of the directions are α = 48.49° , β = 123.84° and Y = 60°.

F = 8.08KN

on the x-y plane the F components can be written as,

F(x , y) = 7k

F x = 7k cos 40° = 5.36 k N and,

F y =7k sin 40° = -4.5k

F cos 30° = 7k

F = 8.08 k N

also,

F = F sin 30° = 4.04k N

hence,

The magnitude and the coordination of the directions are α = 48.49° , β = 123.84° and Y = 60°.

To learn more about directions:

https://brainly.com/question/28108225

#SPJ4

The question is -

Determine the magnitude and coordinate direction angles of the force F acting on the support. The component of F in the x-y plane is 7 k N.

Answer:

yes

Step-by-step explanation:

The simplified form of -√200 is -10√2.

Here, we have,

To simplify the radical expression -√200, we can factor 200 into its prime factors and then simplify the square root.

The prime factorization of 200 is:

200 = 2 × 2 × 2 × 5 × 5 = 2³ × 5²

Now, let's simplify the square root using the property of radicals:

-√200 = -√(2³ × 5²)

Since the square root of a product is equal to the product of the square roots, we can simplify further:

-√(2³ × 5²) = -√(2³) × √(5²)

The square root of 2³ is √(2 × 2 × 2) = 2√2, and the square root of 5² is 5.

Putting it all together:

-√200

= -√(2³) × √(5²)

= -2√2 × 5

= -10√2

Therefore, the simplified form of -√200 is -10√2.

To learn more on square root click:

brainly.com/question/29286039

#SPJ4

The student's errors are (41)² or (√41)² instead of 41, similarly,  (29)² or (√29)² instead of 29.

The correct equation in standard form of the ellipse x²/b² + y²/a² = 1.

The standard equation of an ellipse is x² a² + y² b² = 1.

x² a² + y² b² = 1. this equation defines an ellipse centered at the origin.

If a > b , a > b , the ellipse is stretched further in the horizontal direction, and if b > a , b > a , the ellipse is stretched further in the vertical direction

A student claims that an equation of the ellipse shown is x²/41 + y²/29 = 1.

The standard equation of an ellipse is x² a² + y² b² = 1.

If we divide by a² * b²,

The final equation is

x²/b² + y²/a² = 1.

If compare with  x²/41 + y²/29 = 1.

We find that,

So, the student's errors are (41)² or (√41)² instead of 41, similarly,  (29)² or (√29)² instead of 29.

Therefore, the correct equation in standard form of the ellipse x²/b² + y²/a² = 1.

Learn more about ellipse here:

https://brainly.com/question/11636069

#SPJ4

To calculate the time it takes for Sam to meet Leona, we divide the distance Leona has covered (2.5 miles) by the relative speed of Sam and Leona (1 mile per hour). This gives us 2.5 miles / 1 mile per hour = 2.5 hours. It will take Sam 5 hours to meet Leona.

To explain further, let's analyze the situation. Leona walks at a rate of 5 miles per hour, while Sam walks at a rate of 6 miles per hour. We are given that Sam starts half an hour after Leona. Since they start from the same place and walk in a straight line, we can determine the time it takes for them to meet.

In the time it takes Sam to start walking, Leona has already covered a certain distance. We can calculate this distance by multiplying Leona's walking rate (5 miles per hour) by the time she walks before Sam starts (0.5 hours). The distance covered by Leona is therefore 5 miles per hour * 0.5 hours = 2.5 miles.

Once Sam starts walking, he is moving at a faster rate than Leona. The relative speed between them is the difference between their walking rates, which is 6 miles per hour - 5 miles per hour = 1 mile per hour.

To calculate the time it takes for Sam to meet Leona, we divide the distance Leona has covered (2.5 miles) by the relative speed of Sam and Leona (1 mile per hour). This gives us 2.5 miles / 1 mile per hour = 2.5 hours.

Therefore, it will take Sam 2.5 hours to meet Leona.

Learn more about distance here : brainly.com/question/15172156

#SPJ11

The level of measurement that would be applied when doing a survey on the average American's shoe size is ordinal.

Ordinal scales are measurements that can be ordered from smallest to largest, but the intervals between the measurements do not have meaning. In the case of shoe size, we can order the different sizes from smallest to largest, but we cannot say that a size 10 shoe is twice as big as a size 5 shoe.

For example, we could say that the average American shoe size is 9, but we could not say that the average American's foot is 9 inches long. This is because there is no one-to-one correspondence between shoe size and foot length.

A person with a size 9 shoe could have a foot that is 9 inches long, but they could also have a foot that is 8.5 inches long or 9.5 inches long. The only thing that we know for sure is that the person's foot is larger than a size 8 shoe and smaller than a size 10 shoe.

To learn more about Ordinal scales click here : brainly.com/question/28538964

#SPJ11

The angles that form linear pairs are ∠SRT and ∠TRU, and ∠VRW and ∠WRS. These pairs of angles are adjacent and their measures add up to 180 degrees, making them linear pairs.

To determine which angles are linear pairs, we need to identify pairs of adjacent angles whose measures add up to 180 degrees. Based on the given angles, ∠SRT and ∠TRU form a linear pair because they are adjacent and their measures add up to 180 degrees.

Similarly, ∠VRW and ∠WRS also form a linear pair because they are adjacent and their measures add up to 180 degrees. On the other hand, the remaining angle pairs, ∠SRT and ∠TRV, ∠VRU and ∠URS, and ∠URW and ∠WRS, do not meet the criteria for being linear pairs since their measures do not add up to 180 degrees.

Learn more about Linear pairs here :

brainly.com/question/1757859

#SPJ11

After translation, the new vertices of the triangle is D'(-4, -1), E'(0, -1) and F'(-4, 3)

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the translation equation:

(x , y) ⇒ (x - 4, y - 5)

This means the triangle was translated 4 units left and 5 units down.

The vertices of the triangle is D(0, 3), E(4, 3) and F(0, 7). After translation, the new points is:

D'(-4, -1), E'(0, -1) and F'(-4, 3)

Find out more on equation at: https://brainly.com/question/29797709

#SPJ1

The correct representation of the combined function is h(x) = 22x - 3, x ≥ 0.

The combined function obtained by dividing f(x) = 2x by g(x) = 2 - x³ is represented by h(x) = 22x - 3, x ≥ 0.

In this case, the division of f(x) by g(x) results in a polynomial function. Since the domain restriction given by x ≥ 0 applies to both f(x) and g(x), it also applies to the combined function h(x). Therefore, h(x) = 22x - 3 is valid only for x values greater than or equal to 0.

Thus, the correct representation of the combined function is h(x) = 22x - 3, x ≥ 0.

Learn more about function from

https://brainly.com/question/11624077

#SPJ11

The difference between -28 and -14 is -14. When subtracting -14 from -28, the result is -14.

When finding the difference between two numbers, you subtract the smaller number from the larger number. In this case, we have -28 and -14.

To find the difference between -28 and -14, we subtract -14 from -28:

-28 - (-14)

When subtracting a negative number, it is equivalent to adding the positive value. So, we can rewrite the expression as:

-28 + 14

Now, performing the addition:

-28 + 14 = -14

Therefore, the difference between -28 and -14 is -14.

To learn more about numbers  Click Here: brainly.com/question/24908711

#SPJ11

Using the multiplication Principle of indices, the equivalent expression is [tex]2^{5+x}[/tex] and 32 * [tex]2^{x}[/tex]

According to indices values with the same base and bounded by the multiplication operator would be added.

Therefore, to simplify the given expression :

Therefore, We would sum the powers and use a single base as [tex]2^{5+x}[/tex]

Learn more on indices : https://brainly.com/question/170984

#SPJ1

The equivalent expressions are;

2⁵⁺ˣ

32. 2ˣ

Options B and D

First, we need to know that index forms are defined as mathematical forms used in the representation of numbers or values that are too large or too small.

The rules of index forms are;

From the information given, we have that;

2⁵. 2ˣ

Now, add the bases, we have;

2⁵⁺ˣ

Learn more about index forms at: https://brainly.com/question/15361818

#SPJ1

The shortest distance between Caroline's and Mattie's houses can be found using the Pythagorean theorem.

By considering Caroline's northward walk of 6 blocks and then eastward walk of 8 blocks, the shortest distance can be calculated as 10 blocks.

To find the shortest distance between Caroline's and Mattie's houses, we can visualize their movements as forming a right triangle. Caroline walks north for 6 blocks and then turns east for 8 blocks, creating a right-angled triangle.

According to the Pythagorean theorem, the square of the hypotenuse (shortest distance) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we can calculate the shortest distance as follows: sqrt((6^2) + (8^2)) = sqrt(36 + 64) = sqrt(100) = 10 blocks. Therefore, the shortest distance between Caroline's and Mattie's houses is 10 blocks.

Learn more about  Pythagorean theorem here :

brainly.com/question/14930619

#SPJ11

The amplitude of the function is 1 and the period is 2

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

y = sin[θ + 2)

A sinusoidal function is represented as

f(x) = Asin(B(x + C)) + D

Where

Amplitude = A

Period = 2π/B

Using the above as a guide, we have the following:

Amplitude = 1

Period = 2π/1

Evaluate

Amplitude = 1

Period = 2π

Hence, the amplitude is 1 and the period is 2

Read more about sinusoidal function at

brainly.com/question/21286958

#SPJ4

For the factor x⁴ + 3x² - 4 = 0, we have the roots x = 2i, x = -2i, x = 1, and x = -1. To find the roots of the equation x⁵ + 3x³ - 4x = 0, we can factor out an x from the equation:

x(x⁴ + 3x² - 4) = 0

Now we have two factors: x and (x⁴ + 3x² - 4). We can solve for each factor separately to find the roots.

1. Factor: x = 0

When x = 0, the equation is satisfied. Therefore, x = 0 is one of the roots.

2. Factor: x⁴ + 3x² - 4 = 0

To find the roots of this quartic equation, we can substitute y = x²:

y² + 3y - 4 = 0

Now we have a quadratic equation in terms of y. We can factor it:

(y + 4)(y - 1) = 0

Setting each factor equal to zero, we get:

y + 4 = 0   -->   y = -4

y - 1 = 0   -->   y = 1

Substituting back y = x²:

For y = -4:

x² = -4   -->   x = ±2i

For y = 1:

x² = 1   -->   x = ±1

Therefore, for the factor x⁴ + 3x² - 4 = 0, we have the roots x = 2i, x = -2i, x = 1, and x = -1.

Combining all the roots, we have:

x = 0, x = 2i, x = -2i, x = 1, and x = -1.

Hence, these are all the roots of the equation x⁵ + 3x³ - 4x = 0.

Learn more about quadratic here:

brainly.com/question/22364785

#SPJ11

[tex]y[/tex] is the dependent variable and [tex]x[/tex] is the independent variable.

The given linear equation is [tex]y = 8x-2[/tex]
here, [tex]x[/tex] is the input and [tex]y[/tex] is the output

[tex]Y\\[/tex] gives different solutions, as the input is changed

i.e., when [tex]x[/tex] is changed, [tex]y[/tex] gives different answers. Which says that [tex]y\\[/tex] is dependent on [tex]x \\[/tex] where [tex]x[/tex] is independent

Eg:

1. When [tex]x =2[/tex]                    2. When [tex]x = 2\\[/tex]

[tex]y= 8(1)-2\\[/tex]                             [tex]y=8(2)-2\\[/tex]

   [tex]= 8-2\\[/tex]                                    [tex]= 16-2[/tex]

[tex]y=6\\[/tex]                                       [tex]y=14\\[/tex]

Thus, [tex]y[/tex] is the dependent variable and [tex]x[/tex] is the independent variable.

To learn more about dependent and independent variables:
https://brainly.com/question/31613543