Which of these relations is a function?

The structure of the coordinates associated with specific radian measurements on the unit circle follows a distinct pattern. The x and y coordinates represents the cosine and sine values of the angle, respectively.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a Cartesian coordinate system.

It is commonly used in trigonometry to relate angles to the coordinates on the circle.

When we measure an angle in radians on the unit circle, we can associate specific coordinates with that angle.

The x-coordinate of a point on the unit circle represents the cosine value of the angle, while the y-coordinate represents the sine value of the angle.

These coordinates follow a pattern based on the radian measurement.

For example, when the angle is 0 radians (or 0 degrees), the corresponding point on the unit circle is (1, 0), where the x-coordinate is 1 (cosine of 0) and the y-coordinate is 0 (sine of 0).

As the angle increases, the coordinates change accordingly. For instance, when the angle is π/2 radians (or 90 degrees), the point on the unit circle is (0, 1), where the x-coordinate is 0 (cosine of π/2) and the y-coordinate is 1 (sine of π/2).

This pattern continues as the angle increases or decreases, and the coordinates on the unit circle change accordingly.

By using trigonometric functions, we can determine the cosine and sine values of any given angle and associate them with the appropriate coordinates on the unit circle.

In summary, the structure of the coordinates associated with specific radian measurements on the unit circle follows a pattern where the x-coordinate represents the cosine value of the angle, and the y-coordinate represents the sine value of the angle.

Together, these coordinates create points on the unit circle that correspond to the given radian measurement.

Learn more about Cartesian coordinate system here:

https://brainly.com/question/4726772

#SPJ11

The five steps to solving inequalities are:

To solve an inequality, one must isolate the inequality symbol, simplify the inequality, graph the inequality on a number line, make a sign analysis of the inequality, and find the solution set of the inequality.

Learn more about inequalities at: https://brainly.com/question/24372553

#SPJ4

you can reduce it to factors of degree 2 or less).

The two dice do not need to be identical. If it is possible, do it. If it is not possible, prove that it is not possible.

Some hints I got were to try to construct a pair of nonstandard dice such that the generating function for their sum matches the corresponding g.f. for a pair of standard dice and to note that the g.f. for a pair of standard dice can be factored quite a bit (you can reduce it to factors of degree 2 or less).

Learn more about Dice here:

https://brainly.com/question/2264527

#SPJ4

Using the empirical rule, we know that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

In this case, the mean is 56 and the standard deviation is 7. To find the number of phone calls between 35 and 77, we need to find how many standard deviations away from the mean these values are.

For 35: (35-56)/7 = -3

For 77: (77-56)/7 = 3

So the range we are interested in is 3 standard deviations below the mean to 3 standard deviations above the mean. Using the empirical rule, we know that approximately 99.7% of the data falls within this range.

Therefore, the approximate percentage of daily phone calls numbering between 35 and 77 is 99.7%.

Learn more about standard deviation here:

brainly.com/question/23907081

#SPJ11

Answer:

-48

Step-by-step explanation:

Answer:

\(-48\)

Step-by-step explanation:

\(--------------------------------------------\)

\(1\cdot-6\) = \(-6\)

\(2\cdot-6\) = \(-12\)

\(3\cdot-6\) = \(-18\)

\(4\cdot-6\) = \(-24\)

\(5\cdot-6\) = \(-30\)

\(6\cdot-6\) = \(-36\)

\(7\cdot-6\) = \(-42\)

\(8\cdot-6\) = \(-48\)

\(Answer\) ↑

\(--------------------------------------------\)

Hope this helps! <3

\(--------------------------------------------\)

Answer:

1. 10 x 12 = 120      2. 4 (48/12)

40% of Damien’s marbles are 6/5 or 1.2.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Damien has three marbles.

40% of Damien’s marbles are blue.

That means,

40% of 3 blue marbles.

So, using the percentage formula,

40% of 3,

= 40 x 3/100

= 120/100

= 12/10

= 6/5

= 1.2

Therefore, 1.2 marbles are blue.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ1

Answer:

A. I and II, only

Step-by-step explanation:

y = x

Switch variables.

x = y

y = 1/x

Switch variables.

x = 1/y

1/x = y

y = x²

Switch variables.

x = y²

±√x = y

y = x³

Switch variables.

x = y³

∛x = y

Answer:

x >4

Step-by-step explanation:

2x + 2 > 10

Subtract 2

2x+2-2> 10-2

2x > 8

Divide by 2

2x/2 > 8/2

x >4

Answer:

A, x>4

Step-by-step explanation:

Solve this like any other two step equations

2x + 2 > 10

Subtract 2 on each side

Now it becomes 2x > 8

Then divide 2'on each side

8/2=4

Therefore your answer is x>4

Which is answer A

Hope this helps!

The requried area of the composite figure is given as 180 ft³.

Surface area is defined as the measure of a region or surface is called as surface area.

Here,
from the figure,
Surface area is given as,
Area = area of the lower rectangle + 2[area of the triangle] + area of the middle rectangle
Area = 6 × 6 + 2 × 1/2 ×(6×6) + 18 × 6

Area = 36 + 36 + 108
Area = 180 ft²

Thus, the requried area of the composite figure is given as 180 ft³.

Learn more about the surface area here: https://brainly.com/question/2835293

#SPJ1

Answer:

the solution points for the system of equations are (3, 25) and (-7/2, -7).

Step-by-step explanation:

We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:

Substitute y = 2x^2 + 5x - 10 into the second equation:

4x - (2x^2 + 5x - 10) = -11

Simplifying the left side of the equation:

4x - 2x^2 - 5x + 10 = -11

Rearranging the terms:

2x^2 - x + 21 = 0

Using the quadratic formula:

x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)

x = (1 ± sqrt(169)) / 4

x = (1 ± 13) / 4

Simplifying:

x = 3 or x = -7/2

Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:

For x = 3:

y = 2(3)^2 + 5(3) - 10 = 25

So one solution point is (3, 25).

For x = -7/2:

y = 4(-7/2) + 11 = -7

So the other solution point is (-7/2, -7).

Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).

Each child gets =7×8=56crayoms

Total boxes

Round to next whole as we can't have depict

Answer:

5 boxes

Step-by-step explanation:

There are 12 crayons in one box.

So,8×7=56

56crayons

Then divide 56 and 12

56 ÷12 =4.66

Round of 4.66 and u will get 5

So,the answer is 5 boxes

Answer:

ohh this is little bit hard

Step-by-step explanation:

Answer:

-3p

Step-by-step explanation:

Answer:

-3p

Step-by-step explanation:

5p - 4p = 1p - 4p = -3p

Answer:

-1/2

Step-by-step explanation:

y2-y1/x2-x1

3-(-2)/ -3-7

5/-10

= -1/2

Answer:

9/25

Step-by-step explanation:

36/100 = 9/25

Answer:

Finn is correct

Step-by-step explanation:

When a figure is dilated to create a larger image, the scale factor will be greater than one, but just because a number is a fraction doesn't necessarily mean that it is less than one. For example, the scale factor could have been 5/4 and that is just as possible as any other whole number. (Even so, it depends on what you're learning. Sometimes when teachers introduce fractions they define it as a number smaller than one, but you can always use the 5/4 example to explain your answer if this is the case for you)

i hope this answer helped you! please lmk if i made a mistake :)

Answer:

About 10.4 cm

Step-by-step explanation:

By the Law Of Sines:

\(\dfrac{6}{\sin 30}=\dfrac{b}{\sin 120} \\\\\\b=\dfrac{6}{\sin 30}\cdot \sin 120\approx 10.4\text{ cm}\)

Hope this helps!

The value of b for the triangle will be equal to 10.5.

According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

The value of 'b' will be calculated as,

6 / sin 30 = b / sin 120

b = ( 6 / sin 30 ) x sin 120

b = 10.5

To know more about the sine rule follow

https://brainly.com/question/25942833

#SPJ2

Answer:

x = 27°

Step-by-step explanation:

Given the lines are parallel you have a pair of same-side interior angles and these angles = 180°

x + 72 + 3x = 180

4x + 72 = 180

4x = 108

x  = 108/4

x = 27°

The value of x will be 27 degree

Given the lines are parallel you have a pair of same-side interior angles and these angles = 180°

x + 72 + 3x = 180

4x + 72 = 180

4x = 108

x  = 108/4

x = 27°

The value of x will be 27 degree

To learn more about the angles of parallel lines refer to:

https://brainly.com/question/24607467

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

Learn more about inequalities here:

https://brainly.com/question/11613554

#SPJ1

Answer:

3/8

Step-by-step explanation:

The kites are similar, so the scale is 24/64 = 3/8.  This is also the ratio between corresponding side lengths.

\(4\sin^2 x - 3 = 3 \sin x\\\\\implies 4\sin^2 x -3 \sin x -3 =0\\\\\implies 4u^2 -3u -3 =0~~~~~~~~~~~~~~;[\text{Set} ~ \sin x = u]\\\\\implies u = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 4 \cdot (-3)}}{2(4)}~~~~~~;[\text{Apply quadratic formula}]\\\\\\\implies u = \dfrac{3\pm\sqrt{57}}8\\\\\implies \sin x = \dfrac{3\pm\sqrt{57}}8~~~~~~;[\text{Substitute back}~ u = \sin x]\\\\\text{Now,}\\\\\sin x = \dfrac{3+\sqrt{57}}8\\\\\text{No solution for}~ x\in \mathbb{R} ~\text{Since}~ -1\leq \sin x \leq 1\\\)

\(\sin x = \dfrac{3 - \sqrt{57}}8\\\\\implies x = n\pi + (-1)^n \sin^{-1} \left(\dfrac{3-\sqrt{57}}8\right)\\\\\\\text{ When n = 1,2 and}~ [0,2\pi]},\\\\\\x= \pi - \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)~ \text{and} ~x = 2\pi + \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)\\\\\text{In decimal,}\\\\x= 3.75~~~~ \text{and}~~~ x =5.68\)

Answer:

(0,4)

Step-by-step explanation:

When you are finding the y-intercept, the x = 0

y = -2x + 4

y = -2(0) + 4

  = 0 + 4

y = 4

Meaning y = (0,4)

\(\sf{\underline{Given:-}\)

   \(~~~~~~~\bigstar\overbrace{The~equation~of~the~line}}\)

\(\sf{\underline{To~find:-}}\)

\(\bigstar{\overbrace{The~y-intercept~of~the~line}}\\\sf{\underline{Solution:-}}\)

Since the equation is written in slope-intercept form (y=mx+b), then we just look at the b term, which stands for the y-intercept.

Notice that the y-intercept is a constant...

Hence, the y-intercept of the line is

\(\bigstar{\boxed{\pmb{4}}}\)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

The equation x^2 - 14x + 24 = 0 can be solved to find the roots. The roots of the equation are x1 = 2 and x2 = 12.

To find the roots of the equation x^2 - 14x + 24 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the roots can be calculated using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -14, and c = 24. Plugging these values into the quadratic formula, we get:

x = (-(-14) ± √((-14)^2 - 4(1)(24))) / (2(1))

= (14 ± √(196 - 96)) / 2

= (14 ± √100) / 2

= (14 ± 10) / 2

This gives us two solutions:

x1 = (14 + 10) / 2 = 24 / 2 = 12

x2 = (14 - 10) / 2 = 4 / 2 = 2

Therefore, the roots of the equation x^2 - 14x + 24 = 0 are x1 = 2 and x2 = 12.

To learn more about quadratic click here:

brainly.com/question/22364785

#SPJ11

The system of linear equation that represent this problem is

6x + 10y = 900

10x + 4y = 1220

Let's represent the number of CDs Roberto bought as x and the number of magazines as y

The problem states the following information:

Using the variables;  x and y as given;

1. Roberto bought 6 CDs and 10 magazines for $900.00 pesos. This can be represented as the equation:

  6x + 10y = 900

2. María bought 10 CDs and 4 magazines for $1,220.00 pesos. This can be represented as the equation:

  10x + 4y = 1220

So, the system of equations representing the problem is:

6x + 10y = 900

10x + 4y = 1220

learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

Translation: Roberto bought 6 cd's and 10 magazines for $900.00 pesos; In the same store, her friend María bought 10 CDs and 4

magazines at $1,220.00 pesos. What is the system of equations with two unknowns that represents the problem?

The statement z + z is a real number is true, and it simplifies to 2a, where a is the real part of the complex number z.

To show that z + z is a real number, we need to use the definition of complex conjugates and simplify the expression.

Given z = a + bi, the complex conjugate of z is denoted as z* and is defined as z* = a - bi.

Now, let's compute z + z*:

z + z* = (a + bi) + (a - bi)

Using the distributive property, we can simplify the expression:

z + z* = a + a + bi - bi

Combining like terms, we get:

z + z* = 2a + 0i

Since the imaginary part of the expression is zero (0i), we can conclude that z + z* is a real number, specifically 2a.

know more about real number here;

https://brainly.com/question/17019115

#SPJ11

Answer:

both

Step-by-step explanation:

you can solve this problem with substitution:

5(0) + 12(5) = 60

0 + 60 = 60 is true, therefore the first ordered pair is a solution

the second ordered pair is:

2, 25/6

therefore:

5(2) + 12(25/6) = 60

10 + 50 = 60

10 + 50 = 60 is true, therefore the second ordered pair is also a solution.

in conclusion, both of the ordered pairs are solutions.

The Laplace Transform of f(x) is:

\boxed{F(s) = \frac{3e^{-3s}}{s} - \frac{e^{-3s}}{s^2} + \frac{1}{s^2}}

Laplace Transform of the given function using the appropriate formula is as follows:

1. f(x)= ⎩
⎨
⎧
​
2,
−1,
3,
​
0≤x<3
3≤x<5
x≥5
​
We have the Laplace Transform formula:

F(s) = L(f(x)) = \int_{0}^{\infty} e^{-sx} f(x) dx

Therefore, we will find the Laplace Transform for all three intervals separately as follows:

For 0 ≤ x < 3, f(x) = 2

So,\begin{aligned} F(s) &= \int_{0}^{3} e^{-sx} (2) dx \\ &= 2\left[\frac{e^{-sx}}{-s}\right]_{0}^{3} \\ &= 2\left[\frac{e^{-3s}}{-s} - \frac{e^{-0}}{-s}\right] \\ &= \frac{2}{s}\left(1 - e^{-3s}\right) \end{aligned}

For 3 ≤ x < 5, f(x) = -1

So,\begin{aligned} F(s) &= \int_{3}^{5} e^{-sx} (-1) dx \\ &= \left[\frac{e^{-sx}}{-s}\right]_{3}^{5} \\ &= \frac{e^{-3s}}{s} - \frac{e^{-5s}}{s} \end{aligned}

For x ≥ 5, f(x) = 3

So,\begin{aligned} F(s) &= \int_{5}^{\infty} e^{-sx} (3) dx \\ &= \left[\frac{e^{-sx}}{-s}\right]_{5}^{\infty} \\ &= \frac{e^{-5s}}{s} \end{aligned}

Therefore, the Laplace Transform of f(x) is:

\boxed{F(s) = \frac{2}{s}\left(1 - e^{-3s}\right) + \frac{e^{-3s}}{s} - \frac{e^{-5s}}{s}}

2. f(x)= ⎩
⎨
⎧
​
0,
1,
0,
1,
​
0≤x<1
1≤x<2
2≤x<3
x≥3
​
We have the Laplace Transform formula:

F(s) = L(f(x)) = \int_{0}^{\infty} e^{-sx} f(x) dx

Therefore, we will find the Laplace Transform for all four intervals separately as follows:

For 0 ≤ x < 1, f(x) = 0

So,\begin{aligned} F(s) &= \int_{0}^{1} e^{-sx} (0) dx \\ &= 0 \end{aligned}

For 1 ≤ x < 2, f(x) = 1

So,\begin{aligned} F(s) &= \int_{1}^{2} e^{-sx} (1) dx \\ &= \left[\frac{e^{-sx}}{-s}\right]_{1}^{2} \\ &= \frac{e^{-s}}{s} - \frac{e^{-2s}}{s} \end{aligned}

For 2 ≤ x < 3, f(x) = 0

So,\begin{aligned} F(s) &= \int_{2}^{3} e^{-sx} (0) dx \\ &= 0 \end{aligned}

For x ≥ 3, f(x) = 1

So,\begin{aligned} F(s) &= \int_{3}^{\infty} e^{-sx} (1) dx \\ &= \left[\frac{e^{-sx}}{-s}\right]_{3}^{\infty} \\ &= \frac{e^{-3s}}{s} \end{aligned}

Therefore, the Laplace Transform of f(x) is:

\boxed{F(s) = \frac{e^{-s}}{s} - \frac{e^{-2s}}{s} + \frac{e^{-3s}}{s}}

3. f(x)={ x,
3,
​
0≤x<3
x≥3
​
We have the Laplace Transform formula:

F(s) = L(f(x)) = \int_{0}^{\infty} e^{-sx} f(x) dx

Therefore, we will find the Laplace Transform for both intervals separately as follows:

For 0 ≤ x < 3, f(x) = x

So,\begin{aligned} F(s) &= \int_{0}^{3} e^{-sx} (x) dx \\ &= \left[\frac{xe^{-sx}}{-s}\right]_{0}^{3} - \int_{0}^{3} \left(\frac{e^{-sx}}{-s}\right) dx \\ &= \frac{3e^{-3s}}{s} - \left[\frac{e^{-sx}}{s^2}\right]_{0}^{3} \\ &= \frac{3e^{-3s}}{s} - \frac{e^{-3s}}{s^2} + \frac{1}{s^2} \end{aligned}

For x ≥ 3, f(x) = 3

So,\begin{aligned} F(s) &= \int_{3}^{\infty} e^{-sx} (3) dx \\ &= \left[\frac{3e^{-sx}}{-s}\right]_{3}^{\infty} \\ &= \frac{3e^{-3s}}{s} \end{aligned}

Therefore, the Laplace Transform of f(x) is:

\boxed{F(s) = \frac{3e^{-3s}}{s} - \frac{e^{-3s}}{s^2} + \frac{1}{s^2}}

learn more about Laplace Transform on:

https://brainly.com/question/29583725

#SPJ11

Answer:

People are more likely to avoid approaching difficult situations as they fear failure or looking bad to others if they get it wrong. They lack the point of view of being looked upon as brave for attempting something that others avoid.