why is tan(theta) equal to tan(theta + 2pi)

Answer: 9%

Step-by-step explanation:

What is Vector field?

A vector field is a function that associates a vector to every point in a given space, commonly used in calculus and physics to model physical phenomena.

According toh the given information:

To sketch the vector field F(x, y) = (\(Y_{i} +X_{j}\))/ sqrt(x² + y²), we can first analyze the behavior of the vector field at various points in the xy-plane.

Let's consider a few points:

1) At the origin (0,0), the denominator of the expression for F is undefined, so the vector field is not defined at this point.

2) Along the x-axis (y = 0), F(x,0) = xj / |x|, which means that the vectors point horizontally to the left for negative values of x and horizontally to the right for positive values of x.

3) Along the y-axis (x = 0), F(0,y) = yi / |y|, which means that the vectors point vertically upwards for positive values of y and vertically downwards for negative values of y.

4) At points away from the origin, we can analyze the direction of the vectors by considering the value of the expression \(Y_{i} +X_{j}\) . If y is positive, then the vector will point upwards (in the positive y direction) and if y is negative, the vector will point downwards (in the negative y direction). Similarly, if x is positive, the vector will point towards the right (in the positive x direction) and if x is negative, the vector will point towards the left (in the negative x direction). The magnitude of the vectors decreases as we move away from the origin, because the denominator of the expression for F increases.

Based on this analysis, we can sketch the vector field.

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Using the vector end points the slope of the vector field is plotted.

The steps below are used to create a vector field:

a) Convert the supplied function to vector notation (also known as vector components form).

b) Define some arbitrary vector space points.

c) Apply the provided function to each of these points to determine the vector values.

d) Assess the arbitrary points as the absolute starting position and the arbitrary points plus vector values as the absolute finishing point.

Draw each of the aforementioned vectors such that it begins at the aforementioned starting point and finishes at the aforementioned computed finishing point.

For the given vector field we evaluate the function at different coordinates such as (0, 1), (0, -1), (1, 0), (-1, 0).

For f(0, 1) we have <1, 1>

For (1, 0) = <1, 1>

For (-1, 0) = <-1, -1>

Using the vector end points the slope of the vector field is plotted.

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Answer:

nearest percentage=64%

Step-by-step explanation:

math

The Standard Error of mean is 217.71 .

The critical value , Z꜀= 1.96 < Z , it is then concluded that the null hypothesis is rejected.

Hence, we can say that the the mean earnings of men in the General Social Survey is not representative of the earnings of the entire U.S. male population.

We have given that

A researcher working with the General Social Survey (GSS) on a project focusing on income and health.

Sample size, N = 1500

Sample mean , X-bar =$31,607

male population mean , μ = $33,405

Standard deviations, σ = $8,432

Std. error of mean , S.E = σ /√N

= 8432/√1500

= 217.71

Consider null and alternative hypothesis as

H₀ : μ = 33405

Hₐ : μ not equal to 33,405

Rejection region: Based on information provided the significance level,alpha = 0.05 and the critical value for two tailed test , Z꜀ = 1.96.

The rejection region for two tailed test R is

{ z : |z|> 1.96}.

Test Statistic:

Z- statistic test formula,

Z = (X-bar - u)/std. error

=> Z = ( 31,607 - 33,405)/217.71

=> Z = - 8.259

Decision: Since, it is observed that |z| = 8.259 > Z꜀ = 1.96 , it is concluded that Null hypothesis is rejected .

Conclusion: It is concluded that Null hypothesis H₀ is rejected. So there is sufficient evidence to support the claim that the population mean ,u is different from 33,405 at α = 0.05 significance level.

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.

To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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Answer:

I think it is 15.708. sry if i am wrong

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

hope it helps

Answer: A linear equation in two variables can be described as a linear relationship between x and y, that is, two variables in which the value of one of them (usually y) depends on the value of the other one (usually x). In this case, x is the independent variable, and y depends on it, so y is called the dependent variable.

Three types of infinitives in Spanish are the word that ends with the letters -er , -ar, and -ir.

Explanation:

Infinitive : In general sense infinitive represent the action or the purpose.

Infinitive in Spanish are generally non -conjugated verbs and they are ending with -er , -ar , -ir.

Basically infinitive in Spanish classified into three groups.

-er : Aprender meaning camping.

-ar : Acampar meaning Camping and so on.

Therefore, the three types of Spanish infinitives are word ends with -er , -ar, and -ir.

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The function with an amplitude of 3 and a phase shift of π/2 is h(x) = 3 cos (2x - π/2) + 3.

The amplitude of a function is the distance between the maximum and minimum values of the function, divided by 2. The phase shift of a function is the horizontal shift of the function from the standard position,

(y = cos(x) or y = sin(x)).
To find the function with an amplitude of 3 and a phase shift of π/2, we need to look for a function that has a coefficient of 3 on the cosine term and a horizontal shift of π/2.
Looking at the given options, we can eliminate option a) because it has a coefficient of -3 on the cosine term, which means that its amplitude is 3 but it is inverted.

Option b) has a coefficient of 3 on the cosine term but it has a phase shift of -π/2, which means it is shifted to the left instead of to the right. Option d) has a phase shift of π/2, but it has a coefficient of -2 on the cosine term, which means its amplitude is 2 and not 3.
A*cos(B( x - C)) + D

Where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

f(x) = -3 cos(2x - π) + 4

Amplitude: |-3| = 3

Phase shift: π (not π/2) b) g(x) = 3cos(2x + π) -1

Amplitude: |3| = 3

Phase shift: -π (not π/2) c) h(x) = 3 cos (2x - π/2) + 3

Amplitude: |3| = 3

Phase shift: π/2 d) j(x) = -2cos(2x + π/2) + 3200

Amplitude: |-2| = 2 (not 3)

Phase shift: -π/2
Therefore, the only option left is c) h(x) = 3 cos (2x - π/2) + 3. This function has a coefficient of 3 on the cosine term and a horizontal shift of π/2, which means it has an amplitude of 3 and a phase shift of π/2.
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Answer:

A lot

Step-by-step explanation:

According to the estimate provided by the building contractor, an office building of 55,000 square feet would require 919 Ethernet connections.

The given estimate states that 9 Ethernet connections are needed for every 700 square feet of office space. To determine the number of Ethernet connections required for an office building of 55,000 square feet, we need to calculate the ratio of the office space to the Ethernet connections.

First, we divide the total office space by the space required per Ethernet connection: 55,000 square feet / 700 square feet/connection = 78.57 connections.

Since we cannot have a fractional number of connections, we round this value to the nearest whole number, which gives us 79 connections. Therefore, an office building of 55,000 square feet would require 79 Ethernet connections according to this calculation.

However, the closest answer option provided is 919 Ethernet connections. This implies that there may be additional factors or specifications involved in the contractor's estimate that are not mentioned in the question. Without further information, it is unclear why the estimate differs from the calculated result.

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Answer:B

Step-by-step explanation:

Answer:

13y

Step-by-step explanation:

1y-14y

13y

The sum of 13y

Answer:

  3x +4y = 25

Step-by-step explanation:

You want the equation of the tangent to the graph of x² +y² = 25 at the point (3, 4).

The given equation is that of a circle of radius 5 centered at the origin. For some point (x, y) on the circle, the radius to that point will have a slope of m = y/x. This means the tangent will have a slope of ...

  -1/m = -1/(y/x) = -x/y

For the given point, the slope of the tangent is -3/4.

The y-intercept in the slope-intercept form equation for a line is 'b'. We can solve for that ...

  y = mx +b

  b = y - mx

For (x, y) = (3, 4) and m = -3/4, the y-intercept is ...

  b = 4 -(-3/4)·3 = 4 +9/4 = 25/4

Using the values of m and b we found, the slope-intercept form equation for the tangent is ...

  y = -3/4x +25/4

In standard form, the equation becomes ...

  4y = -3x +25

  3x +4y = 25

__

Additional comment

If you work through this process for point (a, b) on the circle of radius r centered at the origin, you find the equation of the tangent at that point is ...

  ax +by = r²

If the center of the circle is at (h, k), then the equation will be the same thing translated to the new center:

  (a -h)(x -h) +(b -k)(y -k) = r²

<95141404393>

Answer: 13

Step-by-step explanation:

Using exponential function, the rent of the apartment during the 8th year of living in the apartment would be approximately $2765.5.

What is an exponential function?

The formula for an exponential function is \(f(x) = a^x\), where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To solve this problem using an exponential function, we can use the formula -

\(y = a \times (1 + r)^t\)

where -

y is the final value we want to find (in this case, the rent in the 8th year)

a is the initial value (in this case, the rent in the first year, which is $1200)

r is the growth rate per period (in this case, 11% per year, or 0.11)

t is the number of periods (in this case, 8 years)

Plugging in the values in the equation, we get -

\(y = 1200 \times (1 + 0.11)^8\)

y = 1200 × 2.30453777

y = 2765.44532

Rounding to the nearest tenth, we get -

y ≈ $2765.5

Therefore, the rent of the apartment value is obtained as $2765.5.

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Answer:

180

Step-by-step explanation:

Pentagon has a total interior angle of 540 degrees.

Hexagon has a total interior angle of 720 degrees.

720-540 = 180

Answer:

the topmost one maybe?

Step-by-step explanation:

I'm guessing since X & Y are negative, (it's written X,Y,Z, right?)

The point would be reducing on the X&Y axes, an since Z is positive, it would increase on the Z axis

The point C( -2,-1, 2) is represented by option 4 in the three dimensional space

Let (x, y , z) be any point in the three dimension then x represents x-coordinate, y represent y-coordinate and z represent z- coordinate

The point C( -2, -1. 2) represent point with x = -2 , y = -1  and z = 2

(-2,-1) is point with x= -2 and y = -1 represent  is marked in the the x y plane in fourth quadrant and z =2 means that this (-2,-1 ) is taken 2 units up in the perpendicular direction of positive z- axis as shown in the attached figure.

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Answer:

A. 2 x 3=6  B. 6 x 2=12

Step-by-step explanation:

so you multiply 2 and 3 and it make 6 and then you multiply 6 and 2 and it makes 12.

The average commute for 95% of the students is between 19.0 and 4.2 miles.

The average distance is 19 miles.

Therefore, the standard deviation is 4.2 miles.

A) 2.7 = 19 - a(4.2)

where;

a deviates from the mean by a certain number of standard deviations. Thus;

a = (19 - 2.7) ÷ 4.2

a = 3

In a normal distribution, 3 standard deviations from the mean indicate that 95% of the data falls within that range.

B) The data are 2 standard deviations apart from the mean at the 95% confidence level. Thus;

CI = 19 ± 2(4.2)

CI = (18 - 10.2) OR (18 + 10.2)

CI = (7.8, 28.2)

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The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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The values of these coefficients to set up the appropriate form of the particular solution is  A cos(x) + B sin(x) + C cos(3x) + D sin(3x)

The correct option is:   Yp = A cos(x) + B sin(x) + C cos(3x) + D sin(3x)

To set up the appropriate form of a particular solution for the given differential equation, we need to first determine the type of the forcing function. The forcing function in this case is 5sinx + 5cos3x, which is a combination of sine and cosine functions with different frequencies. Therefore, the appropriate form of the particular solution would be a combination of sine and cosine functions with coefficients that need to be determined.
The general form of the particular solution can be written as:
yp = A cos(x) + B sin(x) + C cos(3x) + D sin(3x)
Here, A, B, C, and D are the coefficients that need to be determined using the method of undetermined coefficients or variation of parameters. We do not need to determine the values of these coefficients to set up the appropriate form of the particular solution.
Therefore, the correct option is:
D. Yp = A cos(x) + B sin(x) + C cos(3x) + D sin(3x)

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The appropriate form of a particular solution for a differential equation is the form of the solution that matches the form of the non-homogeneous term in the equation. In this case, the non-homogeneous term is 5sin(x) + 5cos(3x), which is a sum of trigonometric functions.

Therefore, the appropriate form of a particular solution would be a linear combination of trigonometric functions, as seen in options B and D. However, we cannot determine the values of the coefficients without further information. It is important to note that the choice of the appropriate form of a particular solution is crucial in finding the complete solution to a differential equation, as it allows us to separate the homogeneous and non-homogeneous parts and solve them separately.
To set up the appropriate form of a particular solution, yp, for the given differential equation y(4) + 10y'' + 9y = 5sinx + 5cos3x, you need to consider the terms on the right-hand side of the equation. Since the right-hand side contains sin(x) and cos(3x) terms, the particular solution should also include these trigonometric functions.

The appropriate form of a particular solution, yp, is: yp = A cos x + B sin x + C cos 3x + D sin 3x (option D). In this form, A, B, C, and D are coefficients to be determined later, and the solution contains the necessary trigonometric functions that match the right-hand side of the given differential equation.

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Based on the bearings of the direction and the distances given, the distance of point B from A is 1.62 km.  Point C's distance from A is 5.92 km east and 2.16 km south.

To find the distance from point B to point A, the Cos function should be used.

Point A's distance from B can be found as:

= Cos (143 - 90) x distance from point A

= Cos (53°) x 2.7

= 1.62 km

The distance of C from A eastward is:

= 1.62 + 4.3

= 5.92 km

As C is southward from point A, the function to be used is the Sin function.

The distance southward of c from A is:

= Sin(53°) x 2.7

= 2.16 km

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By the box plot, Field B has typically shorter plants as in Field A.

A box plot is a visual representation of the localization, dispersion, and skewness of a collection of numerical data through its quartiles.

The center "box" denotes the group's middle 50% of points. The inter-quartile range is the range of scores from the lower to higher quartile. The interquartile range encompasses the middle 50% of the scores. 75 percent of the scores are lower than the highest quartile.

When doing descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

For the field A the mean height of the sunflower is 9 feet

And for Field B the mean height of the sunflower is 7 feet.

The height distribution in Field A is smaller with range varying from 6 to 10 feet but the Field B has typically shorter plants as a whole as the mean height is 7 feet.

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Answer:

5

Step-by-step explanation:

Answer:

m=96

Step-by-step explanation:

Set up the equation:    m/8 = 12

Multiply each side by 8:  (the 8 on the left side cancels out) and you get left with m= 96

Answer:

Enlargement by ratio of 3, shift 2 units right, shift 4 units down

Step-by-step explanation:

There isn't really a way how to do this step by step, its just common sense

Feel free to ask my questions in the comments

Cindy gets (12-c) amount while others get 12 cookies.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

From the question, we are informed that Grandma baked 96 cookies

And there are 8 grandchildren available

To calculate the number of cookies each of them gets we have,

= 96 /8

= 12 cookies

This means each gets 12 cookies

But Cindy received fewer cookies with less C amount.

Therefore Cindy gets (12-c) amount while others get 12 cookies.

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Answer:

1 food

2 happines

3 live hood

4 help

5 income