squirrel throws an acorn from the top of an 18 foot tall tree. The acorn reaches a height of 18.36 feet above
the ground after 0.2 seconds and a height of 7 feet above the ground after 1 second.Write a quadratic function to represent the situation.

Answers

Answer 1

Now we have the values of h0 and v, so we can write the quadratic function that represents the situation: h(t) = -16t^2 - 0.1125t + 18

What is Quadratic function ?

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and x is the variable. The term "quadratic" comes from the fact that the highest degree of the variable x in the function is 2, making it a second-degree polynomial.

Let's use the equation of motion for a free-falling object to model the acorn's motion:

h(t) = -16t^2 + vt + h0

where:

h(t) is the height of the acorn at time t

t is the time in seconds

v is the initial vertical velocity (upwards or downwards)

h0 is the initial height of the acorn

We know that the acorn is thrown from the top of an 18-foot tree, so its initial height is h0 = 18 feet. We also know that after 0.2 seconds, the acorn reaches a height of 18.36 feet above the ground, so:

h(0.2) = 18.36

-16(0.2)^2 + v(0.2) + 18 = 18.36

Simplifying the equation, we get:

-3.2v + 18 = 18.36

-3.2v = 0.36

v = -0.1125

Therefore, the initial vertical velocity of the acorn is v = -0.1125 feet/second (negative because it is moving downwards).

Now we need to find the height of the acorn after 1 second. Using the same equation of motion:

h(1) = -16(1)^2 + v(1) + 18

We know that the height of the acorn after 1 second is 7 feet above the ground, so:

-16 + v + 18 = 7

v = -5

the initial vertical velocity of the acorn is v = -5 feet/second (negative because it is moving downwards).

This is the quadratic function that models the height of the acorn at any time t in seconds, where h(t) is in feet.

Therefore, Now we have the values of h0 and v, so we can write the quadratic function that represents the situation h(t) = -16t^2 - 0.1125t + 18

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Related Questions

What happens when a distribution is skewed to the right?

Answers

Answer:

Step-by-step explanation:

A distribution is said to be skewed to the right (also known as positively skewed) if it has a longer tail on the positive side of the mean or median, indicating that the majority of the data values are on the lower end and there are a few large values on the higher end. This results in a mean that is larger than the median.

In other words, the right skew occurs when the tail of the distribution is located to the right side of the peak, which pulls the mean to the right as well. The presence of outliers or extreme values on the right side of the distribution can cause right skew.

Right-skewed distributions are common in data sets that represent measurements or quantities that have a minimum value of zero or a natural lower limit, but can increase without bound, such as income, wealth, and height.

In summary, when a distribution is skewed to the right, it has a higher mean and lower median compared to a symmetrical distribution, and the majority of the data is concentrated on the left side.

Does someone mind helping me with this problem? Thanks!

Answers

By evaluating the linear equation we can see that the complete table is:

x|  -4   -2  0  2  4

y| 17    13  9   5  1

How to compete the table?

Here we have a linear function:

y = -2x + 9

And we want to complete the given table, to do so, we just need to evaluate the linear function in the given values of x.

if x = -2

y = -2*-2 + 9 = 4 + 9 = 13

if x = 0

y = -2*0 + 9 = 9

if x = 2

y = -2*2 + 9 = 5

if x = 4

y = -2*4 +9 = 1

Then the complete table is:

x|  -4   -2  0  2  4

y| 17    13  9   5  1

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please help

question 10!

Answers

The note Micah made for the test on right triangles is correct by the Pythagoras rule.

What is the Pythagoras rule?

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

so by Pythagoras rule we can write:

For the first right triangle;

(x/√2)² + (x/√2)² = x²...(1)

from the left hand side of equation (1): (x/√2)² + (x/√2)²

x²/2 + x²/2

2(x²)/2 = x² {the right hand side of equation (1)}

and for the second right triangle;

(x√3/2)² + (x/2)² = x²...(2)

from the left hand side of equation (2): (x√3/2)² + (x/2)²

x²(3)/4 + x²/4

3x²/4 + x²/4

(3x² + x²)/4

4x²/4 = x² {the right hand side of equation (2)}

Therefore by Pythagoras rule the note Micah made for the test on right triangles is correct

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what is 3/4+1/2 answer

Answers

To add 3/4 and 1/2, you need to find a common denominator. One way to do this is to multiply the denominators together:

3/4 + 1/2 = (3/4)(2/2) + (1/2)(4/4)

This gives:

3/4 + 1/2 = 6/8 + 4/8

Now that the denominators are the same, you can add the numerators:

6/8 + 4/8 = 10/8

The answer can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:

10/8 = (10/2)/(8/2) = 5/4

Therefore, 3/4 + 1/2 = 5/4.

[tex]\huge\text{Hey there!}[/tex]


[tex]\mathsf{\dfrac{3}{4} + \dfrac{1}{2}}[/tex]

[tex]\mathsf{= \dfrac{3}{4} + \dfrac{1\times2}{2\times2}}[/tex]

[tex]\mathsf{= \dfrac{3}{4} + \dfrac{2}{4}}[/tex]

[tex]\mathsf{= \dfrac{3 + 2}{4 + 0}}[/tex]

[tex]\mathsf{= \dfrac{5}{4}}[/tex]

[tex]\mathsf{= 1 \dfrac{1}{4}}[/tex]


[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{5}{4}\ or \ 1 \dfrac{1}{4}}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]


~[tex]\frak{Amphitrite1040:)}[/tex]

can you help me with this question

Answers

Answer:

No, Tony should have rounded up to 38.

Step-by-step explanation:

Tony solved the inequality correctly; however, he rounded incorrectly.

8c+200≥500

Subtract 200 from both sides

8c≥300

Divide each side by 8

c≥37.5

Tony cannot wash 37.5 cars, because in the context it is impossible to wash half of a car. We round the answer up because rounding down would give us a value less than $500 (the inequality is greater than or equal to).

Therefore, the answer is 38. Tony is incorrect.

Write the word sentence as an inequality. Then solve the inequality.
225 is no less than 3/4 times a number w .
An inequality that represents this word sentence is.
The solution is

Answers

3/4w <= 225
Multiplying both sides by 4/3 to isolate w:
w >= (225 * 4)/3
w >= 300

So, the solution is w >= 300. That means that the number w has to be equal to or greater than 300 in order to satisfy the inequality.

Answer:

Like the other solver, I believe they are correct because I arrived at the same solution:

3/4w <= 225

Multiplying both sides by 4/3 to isolate w:

w >= (225 * 4)/3

w >= 300

Solution is w >= 300. In order to meet the inequality, the value of w must be equal to or larger than 300.

Ruby says that a quadrilateral is a square if and only if it is a rectangle. Is this a true biconditional statement?.

Answers

The statement "a quadrilateral is a square if and only if it is a rectangle" made by Ruby is a true biconditional statement in mathematical terms.

A quadrilateral is a four-sided shape that can have different properties based on its sides and angles.

Ruby says that a quadrilateral is a square if and only if it is a rectangle. This statement can be written as:

(Q is a square) if and only if (Q is a rectangle)

To understand if this statement is a true biconditional statement, we need to examine the definition of a square and a rectangle and how they relate to each other.

A square is a type of quadrilateral where all four sides are equal in length and all four angles are equal (90 degrees). In other words, a square is a rectangle that has four equal sides.

A rectangle is a type of quadrilateral where all four angles are equal to 90 degrees. This means that the opposite sides are parallel and equal in length.

Based on the definitions, we can conclude that the statement "a quadrilateral is a square if and only if it is a rectangle" is a true biconditional statement.

This means that if a quadrilateral is a square, it is also a rectangle and vice versa. If a quadrilateral is not a square, it cannot be a rectangle.

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A rectangle with side lengths y and z has perimeter 2y+2z. Elizabeth bought a rectangular painting of the seashore and wants to decorate the edges with sky-blue ribbon. The painting is 2 feet long and 1.5 feet wide.
What is the perimeter of the painting?

Answers

The  perimeter of the painting 7 feet.

What is Perimeter?

Perimeter is the distance around the edge of a shape. To find the perimeter by adding up the side lengths of various shapes.

Given:

A rectangle with side lengths y and z has perimeter 2y+2z.

Elizabeth bought a rectangular painting whose length = 2 ft and width = 1.5 ft.

So, the  perimeter of the painting

= 2l+ 2w

= 2(2)+ 2(1.5)

= 4 + 3

= 7 feet

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Which statements are true about the median? Check all that apply.

1. Put the values in numerical order before trying to find the median.

2. Median is a number that is much lower or much higher than the rest of the numbers.

3. The median is always greatly impacted by outliers.

4. The median is the number in the middle of an ordered set of values.

5. The median must be calculated by finding the mean of the two middle points when
there is an even number of data points.

Answers

Look I’m the comments

A standard volleyball court is in the shape of a rectangle. It has an area of 2100 square feet. If the length of the court is 22.4 feet, then what will be the height?

Answers

Answer: The height of the  court is 93.75 feet.

Step-by-step explanation:

We know that the area of a rectangle is given by :-

Area = length x width/height                                 (1)

Given : A standard-size volleyball court has an area of 2,100 square feet.

The length of the court is 22.4 feet.

To find : The width of the court.

According to (1) , we have

[tex]2100=22.4*height[/tex]

Then,

[tex]Height=\frac{2100}{22.4} =93.75[/tex]

Hence, the height of the  court is 93.75 feet.

Show that the quadrilateral with the vertices $H(1,\ 9),\ J(4,\ 2),\ K(5,\ 2),\ L(8,\ 9)$H(1, 9), J(4, 2), K(5, 2), L(8, 9)​ is a trapezoid. Then decide whether it is isosceles.

Answers

The midpoints of the given quadrilateral, AB = CD and AD = BC, are equal.

What is meant by quadrilateral vertices?Vertices are the angular intersections of two sides or edges. The four vertices of a quadrilateral are A, B, C, and D. (iii)Angles. A quadrilateral's angle is the inclination between its two sides.A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. Four non-collinear points are joined to create it. Quadrilaterals' interior angles add up to a constant 360 degrees.A polygon's vertex is a point where the sides or edges of the object or two rays or line segments meet. Vertices is the plural of a vertex.

Let P represent the quadrilateral's vertices (-4,2) Q (2,6): Let A, B, C, and D be the midpoints of P(-4,2) and Q. R(8,5) and S (9,-7) (2,6)

Consequently, A's coordinates are

[tex]$\left(\frac{-4+2}{2}, \frac{2+6}{2}\right)=\left(\frac{-2}{2}, \frac{8}{2}\right)=(-1,4)$[/tex]

Coordinates of B are

[tex]$\left(\frac{2+8}{2}, \frac{6+5}{2}\right)=\left(\frac{10}{2}, \frac{11}{2}\right)=\left(5, \frac{11}{2}\right)[/tex]

Coordinates of c are

[tex]$\left(\frac{8+9}{2}, \frac{5-7}{2}\right)=\left(\frac{17}{2}, \frac{-2}{2}\right)=\left(\frac{17}{2},-1\right)[/tex]

coordinates of D are [tex]$\left(\frac{9-4}{2}, \frac{7+2}{2}\right)=\left(\frac{5}{2}, \frac{-5}{2}\right)$[/tex]

Distance between A and B

[tex]$& d(A, B)=\sqrt{(-1-5)^2+\left(4-\frac{11}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]

Simplify,

[tex]$& d(C, D)=\sqrt{\left(\frac{17}{2}-\frac{5}{2}\right)^2+\left(-1+\frac{5}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]

Then,

[tex]$& d(A, D)=\sqrt{\left(-1-\frac{5}{2}\right)^2+\left(4+\frac{5}{2}\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}} \\[/tex]

We get,

[tex]$& d(B, C)=\sqrt{\left(5-\frac{17}{2}\right)^2+\left(\frac{11}{2}+1\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}}[/tex]

As a result, the given quadrilateral's midpoints, AB = CD and AD = BC, are equal.

It is a parallel gramme as a result.

The complete question is :

A quadrilateral has the vertices at the point (−4,2),(2,6),(8,5) and (9,−7). Show that the mid-point of the sides of this quadrilateral are the vertices of a parallelogram.

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Independent Practice
Graph the following function. Then, write the domain and range.
f(x)=3*
*HINT: Make a table first

Answers

Based on the graph of this exponential function, the domain and range are as follows;

Domain = {-∞, ∞}.

Range = {0, ∞}.

What is a domain?

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞}.

Range = {0, ∞} or {y|y > 0}.

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Find two consecutive whole numbers that \sqrt(139) lies between.

Answers

Answer:

11 and 12

Step-by-step explanation:

11^2<139

but

12^2>139

therefore

it lies between 11 and 12

Please help me I’ll give you the best rating nO lie Trust

Answers

The distance the cyclist travelled during the time are as follows;

4 meters, 18 m and 45 etc.

What is speed?

Speed can be calculated as the ratio of distance traveled to the time taken

Distance = speed x time

Distance = 5 x 0.8

= 4 meters

Distance = 10 x 1.8

= 18 meters

Distance = 15 x 3

= 45 meters.

Here Segment shows as time is increasing, distance is also increasing. Which means the cyclist is moving forward at a speed.

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A triangle has vertices on a coordinate grid at

J(-7,−7) K(−7,3) and L(−1,3)
What is the length, in units, of JK ?

Answers

The requried measure of length JK on the coordinate plane is 10 units.

How to calculate the length between two points (x₁, y₁) and (x₂, y₂)?

The distance between two points on the coordinate plane can be evaluated by the distance formula as,
D = √((x₂ - x₁)^2 + (y₂ - y₁)²)

Here,
The coordinates of the two points J(-7, -7) and K(-7, 3) suggest that they lie on a vertical line, where the x-coordinate is constant (-7) and only the y-coordinate changes. The distance between these points is equal to the difference in their y-coordinates.
Therefore, the length of JK is,
JK = |y-coordinate of K - y-coordinate of J|
    = |3 - (-7)| = |3 + 7| = 10

So, the length of JK is 10 units.

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Use the rules of equations and Inverse operations to solve the equation.
3x² = 48
04
0 +4
0 -4
0+2

Answers

Answer:

Below

Step-by-step explanation:

3 x^2 = 48      divide both sides of the equation by 3 to get

x^2 = 16         Now, sqrt both sides

x = + 4  or  -4

Custom Castings, Inc. pays its employees on a piece-rate basis of $1.28 for each acceptable piece produced. What gross pay was earned by an employee whose production of 483 pieces included 9 pieces
that did not pass inspection?

Answers

To find the gross pay earned by the employee, we need to first calculate the number of acceptable pieces that the employee produced.

The total number of pieces produced by the employee is 483, but 9 of those pieces did not pass inspection. Therefore, the number of acceptable pieces produced by the employee is:

483 - 9 = 474

Now we can calculate the gross pay earned by the employee by multiplying the number of acceptable pieces produced by the piece rate of $1.28:

Gross pay = 474 x $1.28
Gross pay = $606.72

Therefore, the employee earned a gross pay of $606.72.

The change in the number of students at a high school in Naples was the same from 2007 to 2013 as it was from 2013 to 2019.

Which type of function best models the data?

Answers

Answer: The type of function that best models the data would depend on the actual change in the number of students and the specific data points for each year. However, if the change in the number of students was the same for each time period, a linear function would be a good candidate for modeling the data. This function would have the form y = mx + b, where m represents the rate of change (the change in the number of students over a certain time period) and b is the y-intercept (the number of students at the starting year).

Step-by-step explanation:

Learn what an identity matrix is and about its role in matrix multiplication. ... How do you find the multiplicative inverse of a given matrix?

Answers

Answer:

See below

Step-by-step explanation:

[tex]I_1=[1],\, I_2=\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right],\,I_3=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right],\,...[/tex] and so on are examples of identity matrices.

The multiplicative inverse of a 2x2 matrix is [tex]\displaystyle A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex] where ad-bc represents the determinant. Multiplying this with the original matrix will produce the identity matrix as described previously. Usually, you'll mostly deal with 2x2 matrices when it comes to this topic, but don't worry too much.

From 1995 to 2005, the tuition at a college increases by about 7% per year. If this trend continues......
a. Write an exponential growth function that models the tuition over time.

b. What will the tuition be in 2020?

c. What was the tuition be in 1995?

d. What was the tuition in 2011?

Answers

a) An exponential growth function that models the tuition which increased from 1995 to 2005 by 7% annually, is y = 8,000 (1.07)^t.

b) If the trend of annual increase in tuition continues, the tuition in 2020 will be $43,419.20.

c) The tuition in 1995 was $8,000.

d)  If the trend of annual increase in tuition continues, the tuition in 2011 will be $23,617.28.

What is an exponential growth function?

An exponential growth function is one of the two types of exponential functions.

The exponential growth function is marked by an increasing constant rate and modeled as f(x ) = a (1 + r)^x , where r is the growth rate.

The other exponential function is known as an exponential decay function because it shows a constant rate of decrease.

The tuition in 1995, y = $8,000

Annual increase = 7% = 0.07

Time from 1995 = t

Time from 1995 to 2020 = 25 years

Time from 1995 to 2011 = 16 years

Exponential function:

y = 8,000 x (1 + 7%)^t

y = 8,000(1.07)^t

When t = 25 years, y = 8,000 x (1.07)^25 = 8,000 x 5.4274 = $43,419.20

When t = 16 years, y = 8,000 x (1.07)^16 = 8,000 x 2.95216 = $23,617.28

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Question Completion:

Tuition in 1995 = $8,000

Determine the equation of the circle graphed below

Answers

The equation of the circle graphed is given as follows:

(x + 3)² + (y - 4)² = 41.

What is the equation of a circle?

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The center in this problem has the coordinates given as follows:

(-3,4).

Hence:

(x + 3)² + (y - 4)² = r².

x = -1 and y = 9 is a point on the circumference of the circle, hence the radius of the circle is obtained as follows:

r² = (-1 + 3)² + (9 - 4)²

r² = 41.

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what is (fxg)(x)

f(x)=x^3-4x+2
g(x)=x^2+2

Answers

Answer: x^6+6x^4+8x^2+2

Step-by-step explanation:

Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in

(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2

I need help with this please and thank you.

Answers

The standard form of the Polynomial would be [tex]x^{4}[/tex]  -x³ /2 -8

What is polynomial?

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial.

We must consider each term's degree in order to write any polynomial in standard form.

Given the polynomial -8 -x³ /2 -xx³ with the highest degree comes first, followed by x raise to power 4, and then the constant, -8, comes last.

Thus, we would have:

[tex]x^{4}[/tex]  -x³ /2 -8

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Which one of these ordered pairs show a combination of 12 coins from the graph?



Which one of these ordered pairs show a combination of 12 coins from the graph?


(10, 2)

(5, 5)

(10, 5)

(10, 10)

Answers

The ordered pair that show a combination of 12 coins from the graph is (10, 2)

How to determine the ordered pair

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

The graph

The purple line represents the combination of 12 coine

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

The equation is

x + y = 12

From the list of options, we have

(10, 2): 10 + 2 = 12

Hence, the ordered pair is (10, 2)


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Assume that we have two events, A and B; that are mutually exclusive Assume further that we know P(A) = 0.30 and P(B) = 0.70. If an amount zero, enter "0". What is P(AnB)? What is P(AIB)? student in statistics argues that the concepts of mutually exclusive events and independent events are really the same_ and that if events are mutually exclusive they must be independent; Do You agree with this statement? Use the probability information in this problem to justify your answer. Select your answer because P(AIB) Select your answer P(A). What genera conclusion would You make about mutually exclusive and independent events given the results of this problem?

Answers

P(A∩B) = 0 (the probability of both events occurring is zero).

P(A|B) = 0.

No. The student's argument that mutually exclusive events are independent is incorrect.

How to find P(AnB) and P(AIB) of the event?

If events A and B are mutually exclusive, then by definition they cannot occur at the same time.

Thus, P(A∩B) = 0 (the probability of both events occurring is zero).

Since events A and B are mutually exclusive, they cannot be independent. In fact, if two events are mutually exclusive, it means that the occurrence of one event precludes the occurrence of the other event, so they are completely dependent on each other.

To calculate P(A|B), we can use the formula:

P(A|B) = P(A∩B) / P(B)

Since P(A∩B) = 0 and P(B) = 0.70, we have:

P(A|B) = 0 / 0.70 = 0

This means that if we know event B has occurred (i.e., P(B) > 0), then the probability of event A occurring (i.e., P(A|B)) is zero. Therefore, events A and B are not independent.

The student's argument that mutually exclusive events are independent is incorrect. Mutually exclusive events are by definition dependent events.

In general, the concept of mutually exclusive events and the concept of independent events are not the same. Mutually exclusive events are dependent events, while independent events are events that do not depend on each other.

In this problem, the fact that events A and B are mutually exclusive means that they are dependent events, and this is reflected in the probability calculation for P(A|B), which is zero. Therefore, we can conclude that mutually exclusive events are not independent events.

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Question Progress
Homework Progress
19/48 Marks
The circle shown has a radius of 4 cm.
Not drawn
to scale
What is the length of the diameter of the circle?

Answers

The length of the diameter of the circle is 8 cm.

What is Diameter?

The diameter of a circle is the distance measured through its centre. The radius of a circle is the distance from the center to any point on the edge. The diameter is divided by the radius.

Given:

Radius = 4 cm

As, the radius is the point which starts from center  and reach to point on the surface of the Circle.

and, the Diamter is the two times of the radius.

So, Diameter = 2 x radius

D= 2 x 4

diameter = 8 cm

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May i get some help Fast please

Mr. Fernandez deposits $60,000 into an account that pays 2.5% annual interest compounded quarterly. What will be the balance after 20 years? Round to the nearest cent

Answers

:Answer: $90000

i = prt (interest = principle x rate x time)

i = 60000 x 0.025 x 20

i = $30000 interest

b = p + i (balance = principle + interest)

b = 60000 + 30000

b = $90000 balance

The freshman class at Arlington High school is made up of 480 female students. This represents 65% of the freshman class. How many total students are freshmen?

Answers

The number of freshmen that are students is 738

How to calculate the number of freshmen that are students?

Let y represent the number of students that are freshmen

The freshmen class is made up of 480 female students

This number represents 65% of the freshmen class

Therefore the total number of students that are freshmen can be calculated as follows

y × 65/100= 480

65y/100= 480

Cross multiply both sides

65y= 480 × 100

65y= 48000

y= 48000/65

y= 738.4

≅ 738

Hence 738 students are freshmen

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55/135 in simplest form

Answers

Answer:

11/27

Step-by-step explanation:

55/135 (divide by 5)

11/27

The answer to the problem is 11/27

Graph the angle -4pi/3 in standard position :)

Answers

The point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.

What is the unit circle?

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

The angle for this problem is given as follows:

-4pi/3.

Hence the sine and the cosine are given as follows:

sin(-4pi/3) = 0.866.cos(-4pi/3) = -0.5.

Hence the point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.

(the equation of the unit circle is x² + y² = 1).

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