how to find the zeros and multiplicity of a polynomial

Answer: In an equilateral triangle, the hypotenuse and its opposite side are equal

By the way, I am human. There is too many bot answers.

The values for sine and cosine are equal at 45 degrees because they are related to the right triangle formed by the angle.

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.

When the angle is 45 degrees, the triangle formed is a 45-45-90 triangle, this is a special triangle in which all the angles are 45 degrees and all the sides are in the ratio of 1:1:√2.

In this triangle, the hypotenuse is √2 times the length of either leg. So, the sine of 45 degrees is opposite/hypotenuse = (1/√2) and the cosine of 45 degrees is adjacent/hypotenuse = (1/√2). Since the opposite and adjacent sides are of the same length in the 45-45-90 triangle, the sine and cosine of 45 degrees are equal.

So, sine 45 = cosine 45 = 1/√2.

The cost of plan A is represented by the equation:

Cost A = 40 + 0.02x

where x is the number of minutes of calls.

The cost of plan B is represented by the equation:

Cost B = 0.18x

To find the point where the two plans cost the same, we can set the two equations equal to each other and solve for x:

40 + 0.02x = 0.18x

40 = 0.16x

x = 250

So when the customer makes 250 minutes of calls, the cost of the two plans will be the same.

The cost of plan A will be 40 + 0.02250 = $50 and the cost of plan B will be 0.18250 = $45

So when the customer makes 250 minutes of calls, Plan A and Plan B cost the same amount of money.

Equation for m< 1 (x - 9)° and m <2 =(8x)° is <1 = 168 <2 = 12

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

When one side of an equation equals the other, it is said to be an equation. For instance, in this case, we know that 4 + 4 = 8 and 10 - 2 = 8, which means that this equation is correct.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10.

To start, you must find x.

8x + x -9 = 180

9x -9 = 180

9x = 189

x = 21

Now, change both angles' x values to 21.

8(21) = 168

(21) - 9 = 12

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Answer:

15 boys

Step-by-step explanation:

We know

A group has 20 children

25% girls

25% = 0.25

20 times 0.25 = 5 girls

20 - 5 = 15 boys

So, there are 15 boys

The slope of the given graph is m = -1, and the y-intercept is y = 1.

A line's slope reveals its inclination and direction. Without actually using a compass, determining the slope of lines in a coordinate plane can aid in determining whether the lines are parallel, perpendicular, or have no relation at all.

Any two different points on a line may be used to derive the slope of that line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line equation.

Consider each box of the graph as 1 unit.

So, from the graph, at x = 0

y = 1

So, this is the y-intercept of the line.

Consider any two points

(x₁, y₁) = (0, 1)

(x₂, y₂) = (1, 0)

The slope is given by the slope formula as

m = (y₂ - y₁)/(x₂ - x₁)

= (0 - 1)/(1 - 0)

= -1

The slope of the graph is m = -1.

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Answer:

ans is= Rs.2925. . . . . . .

One binomial's terms are multiplied by the other binomial's terms. The algebraic total of these products is then calculated after this step. We employ a technique called the FOIL method to multiply binomials.

Therefore, the order in which the terms are multiplied in this order is FOIL (First Outer Inner Last).

An algebraic expression with two terms joined by a plus or minus sign is known as a binomial. Binomial multiplication is comparable to multiplying two whole numbers or fractions. Utilising the distributive property of multiplication twice is one way to multiply binomials.

The letters in the acronym FOIL stand for First, Outer, Inner, and Last. Since only binomials may be multiplied using this approach, it cannot be used to multiply all polynomials. The FOIL formula has the following general form: (a + b) (c + d) = ac + ad + bc + bd.

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Answer:

Randy

Step-by-step explanation:

Randy:  2 runs / 3 innings = 0.67

Felix:  4 runs / 5 innings = 0.80

Johan:  5 runs / 7 innings = 0.71

You get the "Array indices must be positive integers or logical values" error when using the "angle" function because you are trying to use a non-numeric or non-logical value as an index.

The "angle" function in MATLAB is used to find the phase angle of a complex number. When you are trying to use the function, you are probably passing in a variable or expression that is not a numeric or logical value.

In MATLAB, array indices must be positive integers or logical values. When you try to use a non-numeric or non-logical value as an index, you will get the "Array indices must be positive integers or logical values" error.

This means that you need to make sure that the variable or expression you are passing into the "angle" function is a numeric or logical value before using it as an index.

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Complete question:

Why do I get "Array indices must be positive integers or logical values" error when using "angle" function?

The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed.

[tex]y=a(x-hx)^{2} + k[/tex]  the answer is F(x) = [tex]4x^{2} -1[/tex]

What is meant by graph?

We are given a function:

G(x)=[tex]x^{2}[/tex]

The graph of G([tex]x[/tex]) is also shown in the given question figure.

It is a parabola with vertex at (0,0).

Sign of [tex]x^{2}[/tex] is positive, that is why the parabola opens up.

General equation of parabola is given as:

[tex]y=a(x-hx)^{2} + k[/tex]

Here, in G(x), a = 1

Vertex (h,k) is (0,0).

As seen from the question figure,

The graph of F(x) opens down that is why it will have:

Sign of [tex]x^{2}[/tex] as negative. i.e. a = -1

And vertex is at (0,-5)

Putting the values of a and vertex coordinates,

[tex]y= -1 (x-0x)^{2} + (-5)[/tex]

Hence, the equation of parabola will become:

[tex]y=-x^{2} -5x[/tex]

The correct answer is:

F(x) =[tex]y=4x^{2} -1[/tex]

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0.5 is equivalent to the fraction 1/2.

What is a fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

We are given 0.5 which is to be converted into a fraction.

So, for this we will take 0.5 as the numerator and 1 as the denominator because anything divided by 1 is the number itself.

Thus, we get

⇒0.5/1

Now, we will multiply both numerator and denominator by 10.

From this, we get

⇒(0.5*10)/(1*10)

⇒5/10

Now, we will reduce the fraction to the lowest form by dividing both numerator and denominator by 5.

From this, we get the fraction as 1/2.

Hence, 0.5 is equivalent to the fraction 1/2.

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A BAR graph would be most suitable for displaying the given data.

The visual representation of numerical data is a graph. Graphs offer a visual means of presenting complicated data and demonstrating the link between various variables or data sets. Graphs are a fantastic tool for highlighting patterns and connections in data.

Given data, The number of pets in each student's household.

Stem-and-leaf plot:

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. As data are gathered, they are organised using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf.

Thus it is not suitable for given data.

Line graph:

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time. Line graphs are frequently used in finance to show the historical price movement of an asset or instrument.

Since, we have similar but Discrete with three variables in our data thus this graph is also not suitable.

Bar graph:

A bar graph (also known as a bar chart or bar diagram) is a visual tool that uses bars to compare data among categories. A bar graph may run horizontally or vertically.

Since we need to compare the data thus, bar graph is most suitable for the giving condition.

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We would expect about 16 people in a sample of 800 people to be redheads, give or take some random variation.

What is probability ?

Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. Probability can be expressed as a fraction, decimal, or percentage. For example, a probability of 0.5 is the same as a probability of 1/2 or 50%.

The probability of an event can be calculated by counting the number of favorable outcomes and dividing by the total number of possible outcomes.

If 2% of the population has red hair, we can expect 2 out of every 100 people in the population to be redheads. To find out how many redheads we would expect in a sample of 800 people, we can use this proportion and multiply it by the number of people in the sample.

2/100 * 800 = 16

So, we would expect about 16 people in a sample of 800 people to be redheads, give or take some random variation.

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Chance is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes the impossibility of an occurrence and 1 denotes its certainty. It is possible to represent probability as an integer, decimal, or percentage. A probability of 0.5, for instance, is equivalent to a possibility of 1/2 or 50%.

By counting the favorable outcomes and dividing by the total number of potential outcomes, one can determine the probability of an occurrence.

We can anticipate that 2 out of every 100 people in the community will have red hair if red hair makes up 2% of the population. We can calculate the proportion of redheads we would anticipate in an 800-person group by

Slope of the line that contains the points (13, -2) and (3,-2) is 0.

What is Slope of line?

The increase divided by the run is the slope. By examining the rise and run, you can infer the slope of a line from its graph. A line has the property that its slope remains constant throughout. Therefore, you may determine the slope by selecting any two points along the line's graph.

By definition, the slope or gradient of a line describes its steepness, incline, or grade.

m = y2 - y1/x2 - x1

Given ;

x1 =13, x2 = 3, y1 = -2, y2 = -2

ΔX = x2-x1

ΔX = 3 - 13

ΔX = -10

Now, calculating ΔY ;

ΔY = y2 - y1

ΔY =-2 - (-2)

ΔY = 0

Hence, Slope of the line is ;

Slope(m) = ΔY/ΔX

Slope(m)= 0/-10

Slope (m) = 0

Therefore , Slope of the line that contains the points (13, -2) and (3,-2) is 0.

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The total reports during the year is 15.

percentage, a relative value indicating hundredth parts of any quantity.

Given that tanik turns in his third report. his teacher says 20% of his reports for the year are done.

We have to find the number of research reports will Tanik complete during the school year.

Let the number of reports be = x

As mentioned, when Tanik submitted his 3rd report, he had completed 20% of the reports so

20/100×x=3

0.2x=3

Divide both sides by 0.2

x=15

Hence,  the total reports during the year is 15.

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Answer:

answer is 114 I have confirmed it

Its slope is 0, which indicates that it is a horizontal line, and its

y-intercept is −3.

When an equation of a line has only one variable, the resulting graph is a horizontal or a vertical line.

The graph of the line  x=a

, where  a is a constant, is a vertical line that passes through the point  (a,0) . Every point on this line has the x-coordinate equal to a, regardless of the y-coordinate.

The graph of the line  y=b , where  b  is a constant, is a horizontal line that passes through the point  (0,b) . Every point on this line has the y-coordinate equal to b, regardless of the x-coordinate.

We can write

y=−3

as

y=0x−3

So, its slope is 0, which indicates that it is a horizontal line, and its

y-intercept is −3. Hence, its graph looks like

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The correct option is 'The domain of both functions is all real numbers'.Option A

Generally, functions are f(x) = 5x and g(x) =5x

Since the domain of f(x) is, D= { x : x belongs to all real numbers.}

Therefore, the set of all real numbers constitutes the domain of f(x).

Due to the fact that f(x) and g(x) both return the same result,

Therefore, the set of real numbers is likewise included in the domain of g(x).

Now, the range of f(x) is , R=  { 5x : x belongs to all real numbers.}

As a result, the set of possible values for f(x) includes only real numbers.

In addition, the range of g(x) includes all real values.

Given what has been said so far, it is clear that only choice (1) should be considered accurate.

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CQ

Keshawn is asked to compare and contrast the domain and range for the two functions.

f(x) = 5x

g(x) = 5x

Which statements could he include in his explanation? Check all that apply.

1. The domain of both functions is all real numbers.

2. The domain of f(x) is x > 5.

3. The domain of g(x) is x > 5.

4. The range of both functions is y > 5.

5. The range of f(x) is y > 0.

6. The range of g(x) is y > 0.

The point (-4, 2) be located in second quadrant. Due to the fact that x is negative and y is positive.

The coordinate system's two axes, the x-axis and the y-axis, define a region is called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle.

These areas include coordinates, or positive and negative values of the x- and y-axes. The position of a point in a quadrant is indicated by the coordinates.

The first quadrant is located in the graph's upper right-hand corner. Both the x and y values in this quadrant are positive.

The second quadrant is located in the graph's upper left corner. The value of y is positive in this quadrant while the value of x is negative.

The third quadrant is located in the graph's lower left-hand corner. It includes both the negative values of x and y.

Fourth Quadrant, the final quadrant has a positive x value and a negative y value, and it is located in the lower right corner.

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The complete question is:

What quadrant will the point (-4, 2) be located in?

By using exponential growth formula we get 5531 fish in the pond after 6 months.

To find the number of fish in the pond after 6 months, we can use the formula for exponential growth:

N(t) = N0 * [tex](1 + r)^{t}[/tex]

where N(t) is the number of fish at time t (in this case, after 6 months), N0 is the initial number of fish (7), and r is the growth rate (2.9 fish per month).

We can substitute these values into the formula and solve for N(6):

N(6) = 7 * [tex](1 + 2.9)^{6}[/tex]

N(6) = 7 * [tex](3.9)^{6}[/tex]

Using the calculator, we get N(6) = 7 * 791.64 = 5530.5

Rounding up to the nearest whole fish, we get 5531 fish in the pond after 6 months.

Note: The exponential model assumes that the growth rate is constant over time and that the pond has unlimited resources to sustain the fish population.

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The simplification of the expression is [tex]\frac{7}{5}[/tex].

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is

=> 1 + [tex]\frac{1}{1+\frac{1}{1+\frac{1}{2} } }[/tex]

=> 1 + [tex]\frac{1}{1+\frac{1}{\frac{2+1}{2} } }[/tex]

=> 1 + [tex]\frac{1}{1+\frac{1}{\frac{3}{2} } }[/tex]

=> 1 + [tex]\frac{1}{1+\frac{3}{2} }[/tex]

=> 1 + [tex]\frac{1}{\frac{2+3}{2} }[/tex]

=> 1 + [tex]\frac{1}{\frac{5}{2} }[/tex]

=> [tex]1+\frac{2}{5}[/tex]

=> [tex]\frac{5+2}{5}[/tex]

=> [tex]\frac{7}{5}[/tex]

Hence the simplification of the expression is [tex]\frac{7}{5}[/tex].

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To find the number of solutions to given equation by comparing the coefficients of the variables of the equations.

We know that a solution of an equation is a value that satisfies given equation.

We can find the number of solutions to given equation by comparing the coefficients of the variables of the equations.

There are three types of solutions to the set of linear equations:    Unique Solution: The linear equation in one variable (equation of the form ax + b = 0) always has a unique solution.    

No Solution: When the graphs of the linear equations represents parallel lines, then the system of linear equations has no solution.

Infinitely Many Solution: if the system of equations represent coincident lines, and they have the same y-intercept, then the system of equations has infinitely many solutions.

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The form of function is a logarithmic function. either "y equals the log of x, base b" or "y equals the log, base b, of x."

What is logarithmic function?

An exponential function's inverse is a logarithmic function. An exponential function's basis is the same as that of a log function. Exponents include logarithms. f(x) = bx is the formula for the exponential function. f(x) = log base b of x is how the logarithmic function is expressed.

The expression "y equals the log of x, base b" or "y equals the log, base b, of x" is the definition of a logarithmic function. In both cases, b > 0, b 1, and x > 0. There are no limitations on y. logarithm, the exponent or power that a base must be increased to in order to get a specific number. If bx = n, then mathematically, x is the base-b logarithm of n.

Determine the logarithmic function of the provided graph by using the provided points in the following manner:

[tex]f(x) = log_a(x-h)[/tex]

Create two equations by substituting the provided points (3/2, 1) and (3, -1) into the formula:

[tex]log_a(\frac{3}{2}-h) = 1[/tex]

[tex]log_a({3}-h) = -1[/tex]

To isolate a, use the log law and rearrange each equation:

[tex]log_a(\frac{3}{2}-h) = 1[/tex]

⇒ [tex]a^1 = (\frac{3}{2}-h)[/tex]

⇒1/a = 3 - h

⇒ a = 1/ [tex]\frac{3}{2}[/tex] - h  ....................................(1)

[tex]log_a({3}-h) = -1[/tex]

⇒[tex]a^{-1} = ({3}-h)[/tex]

⇒ 1/a = 3-h

⇒ a = 1/3-h ..............................................(2)

Solve for h:

⇒ 3/2 - h = 1/3-h

⇒ 3-2h/2 = 1/3-h

⇒ 9 - 9h + 2h^2 = 2

⇒(2h-7)(h-1) = 0

⇒ h = 7/2, 1

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The substitution method is a powerful tool used to solve systems of linear equations with three variables. Beginning with one of the equations for one of the variables, utilise the substitution method.

This will give you an expression for that variable in terms of the other two. Then, substitute this expression into the other equations and solve for the remaining variables.

Consider, for example, a set of linear equations involving the variables x, y, and z:

x + y + z = 13

2x + 4y - z = 6

3x - 2y + 3z = 11

Start by solving the first equation for x in order to apply the substitution method here:

x = 13 - y - z

Now solve for y and z by substituting this expression into the previous two equations:

2(13 - y - z) + 4y - z = 6

39 - 2y + 3z = 6

3(13 - y - z) - 2y + 3z = 11

39 - 5y + 6z = 11

Subtract 39 from both sides of each equation, then solve for y and z using elimination or another method. Once you have found values for both variables, plug them into the original expression for x to find its value.

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Divide the population standard deviation () by the square root of the sample size (n) to obtain the standard deviation of the sample mean (X).

The sample mean is normally distributed, with mean X= and standard deviation X=/n, where n is the sample size, for samples of any size taken from a population that is normally distributed.

The standard deviation of the population divided by the square root of the sample size is equal to the standard deviation of the sampling distribution of means.

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The size of the angle marked y correct to three significant figures is 26.6°.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given is a right angled triangle.

By the definition of trigonometric functions,

Sin y = Opposite side / Hypotenuse

sin y = 31.4 / 70.2

sin y = 0.447

y = 26.57

  = 26.6

Hence the value of y is 26.6.

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The inequality equation for the measurements of the rectangular field must satisfy t<225.

If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.

Given that,

The length of the rectangle is 2t meters

the breadth of the rectangle is 50 meters

The perimeter of the rectangle is given by 2×(length+breadth)

Here the perimeter of the rectangle is less than 1km=1000meter

Forming an equation with the given data

2×(2t+50)<1000

2t+50< 1000/2

2t+50<500

2t<500-50

2t<450

t<450/2

t<225

Thus, The inequality equation for the measurements of the rectangular field must satisfy t<225.

Complete question: A rectangular field has these measurements kim walks around the edge of the field. she walks less than 1km. form and solve an equality to find the possible values of t when length of the field is 2t meters and breadth is 50 meters

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Spinning a spinner with three equal sections colored white, red, and blue yield the probability of having yellow color is B: '0%', i.e p (yellow) = 0%.

As in the given scenario where a spinner with white, red, and blue colors is rolled and is asked about determining the p(yellow). That is the probability of getting yellow at which the spinner stops. It is clearly written that the spinner has three sections of equal colors which are red, blue and white. And there is no section on the spinner with yellow color, so it is not possible to get yellow color over rolling of the spinner.

It means that 0% probability exists for yellow color.

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A perimeter is the length of a two-dimensional shape's boundary. It is sometimes described as the total length of the object's sides. The perimeter of that shape is equal to the algebraic sum of the lengths of its sides.

The term "two-dimensional shape" refers to any shape that is flat and has only two dimensions, i.e. length and breadth. Each polygon is a flat, 2-D figure that rests on a plane. Polygons, such as triangles, rectangles, and squares, are closed figures that are enclosed by a series of lines. The length or linear measure of these confined line segments is known as the polygon's perimeter (peri: around; metre: measure). Or to put it another way, it is the length of its borders. The centimetre (cm) or metre is its unit (m).

The whole distance that a rectangle's boundaries, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides. Since a rectangle's perimeter is a linear measurement, the unit will be in metres, centimetres, inches, feet, etc.

Perimeter of a rectangle = sum of four sides

= AB     +     BC        + CD       +   AD

= length + breadth + length + breadth

= 2 length + 2 breadth

Perimeter of a rectangle =   2 × (length + breadth)

The radius of the circle serves as one of the three variables in the perimeter of a circle formula, along with two constants. The formula for calculating a circle's circumference or perimeter is as follows:

Circumference of a circle is equal to 2πr.

where,

r = radius of the circle

D = diameter of the circle

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Answer:

  381 feet

Step-by-step explanation:

You are 220 ft from a tree whose top you see at a 60° angle of elevation. You want to know the height of the tree.

The tangent relation between sides of a right triangle is ...

  Tan = Opposite/Adjacent

where "opposite" and "adjacent" refer to the sides opposite and adjacent to the acute angle of interest.

Here, the 60° angle of elevation is adjacent to the 220 ft distance from the tree, and opposite the height of the tree. This means ...

  tan(60°) = height/(220 ft)

Multiplying by 220 ft, we find the height to be ...

  height = (220 ft)tan(60°) = 220√3 ft ≈ 381 ft

The tree is 381 feet tall.

__

Additional comment

The triangle that models this geometry is a 30°-60°-90° right triangle, one of the "special" right triangles that often shows up in geometry and trigonometry problems. Its side lengths have the ratio 1 : √3 : 2. Knowing this, you know the tree height is √3 times the distance from the tree:

  220√3 ft

Your calculator can tell you this is about 381 feet.

To find the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the distance from the tree) and the angle. The formula is:

Why is it referred to as a tangent function?

Tangent is derived from the Latin verb tangere, which means "to touch." A circle has one point where a line that is tangent to it intersects.

tangent(angle) = opposite / adjacent

In this case, the angle is 60 degrees, the opposite side is the height of the tree, and the adjacent side is the distance from the tree, which is 220 feet. So we can write:

tan(60) = height / 220

To find the height, we can divide both sides by the tangent of 60 degrees:

height = 220 * tan(60)

The exact value of the height of the tree is not possible to be obtained with the given information, the height of the tree is a number in the infinite set of real numbers.

We can use a calculator or a table of tangents to find an approximate value of the height.

It could be around 379.3 ft.

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