The solution to the inequality 2x + 7 > 27 is x > 10
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
2x + 7 > 27
Subtract 7 from both sides of the inequality
So, we have
2x > 20
Divide both sides by 2
x > 10
Hence, the solution to the inequality 2x + 7 > 27 is x > 10
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Rolling two sixes in a row on a number cube is independent or dependent
Rolling two sixes in a row on a number cube (a fair six-sided die) is an independent event. The outcome of one roll does not affect the outcome of the subsequent roll. Each roll of the number cube is an independent trial, and the probability of rolling a six on each trial is always 1/6, regardless of the previous outcome.
What is (fg)(x)?
f(x)=2x
g(x)=2x2+3x
Write your answer as a polynomial or a rational function in simplest form
Given statement Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.
To find (fg)(x), we need to first find the product of f(x) and g(x) and simplify the expression.
f(x) = 2x
g(x) = [tex]2x^2[/tex] + 3x
To find (fg)(x), we substitute g(x) into f(x):
(fg)(x) = f(g(x)) = f([tex]2x^2[/tex] + 3x)
Now we substitute f(x) = 2x into the expression above:
(fg)(x) = 2([tex]2x^2[/tex] + 3x)
Distribute the 2:
(fg)(x) = [tex]4x^2[/tex] + 6x
So, (fg)(x) = [tex]4x^2[/tex] + 6x.
Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Fill in the banks if you had this question before!!
An equation for the total cars and trucks for dealership A is: x + y = 164.
An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.
The number of cars that dealership A sold is: 98 cars.
The number of trucks that dealership B sold is: 66 trucks.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of cars sold.Let the variable y represent the number of trucks sold.Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;
x + y = 164.
Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;
2x + 0.5y = 229.
By solving the systems of linear equations simultaneously, we have:
2x + 0.5(164 - x) = 229
1.5x + 82 = 229
x = 98 cars.
For the y-value, we have;
2(98) + 0.5y = 229
0.5y = 229 - 196
y = 33/0.5
y = 66 trucks.
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What’s the answer please
Answer:
40
Step-by-step explanation:
plugging in a and b will get us:
[tex]2^{2} + 6^{2} = c^{2}[/tex]
4 + 36 = [tex]c^{2}[/tex]
40 = [tex]c^{2}[/tex]
c= [tex]\sqrt{40\\[/tex]
I NEED YOUR HELP! PLEASE HELP! I WILL MARK YOU BRAINLIEST!!!!!!!!!!Andrea has 533.8 cm 3 of modeling clay. She plans to use 8.4 cm 3 to form a right pentagonal prism. She will also make a second prism that is a dialation of the first prism with a scale factor of 4. Does Andrea have enough modeling clay for both prisms? Determine the amount of clay that andrea has left over or is short.
If the height (h) of the prism is less than or equal to 0.978 cm, then Andrea has enough modeling clay for both prisms. If the height exceeds 0.978 cm, she will be short of modeling clay.
Let's calculate the volumes of both prisms:
Volume of the first prism: V1 = (8.4 cm²) × h
Volume of the second prism: V2 = (16 × 8.4 cm²)×(4h)
= 537.6 cm³ h
We know that Andrea has 533.8 cm³ of modeling clay.
To determine if she has enough clay for both prisms, we need to compare the total volume of the prisms to the amount of clay she has:
Total Volume = V1 + V2 = (8.4 cm²) × h + (537.6 cm³ × h)
Total Volume = (546 cm²) × h
Now we can set up the equation:
Total Volume ≤ Amount of Clay
(546 cm²) × h ≤ 533.8 cm³
Solving for h:
h ≤ 533.8 cm³ / (546 cm²)
h ≤ 0.978 cm
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A student takes a subway to a public library. The table shows the distance d (in miles) the student travels in t minutes. Determine whether the data can be modeled by a linear, exponential, or a quadratic function and then select a function rule to model the situation.
t
d
1
0.83
2
1.66
3
2.49
4
3.32
5
4.15
The linear function that models the situation is given as follows:
d = 0.85t.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The constant ratio for this problem is given as follows:
k = 0.83, as each division of d by t has a result of 0.83.
Hence the equation is given as follows:
d = 0.83t.
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1) Complete one drawing of each regular polygon: equilateral triangle, square, and regular hexagon, following the animations.
2) Create a design based on one of the 3 polygons.
3) Write a description of your design. Include the following information:
How many lines of symmetry does the design have?
How many degrees does the design need to be rotated to match itself? (Hint: See the polygons at the start of the lesson.)
How did you decide to color your design?
What patterns do you see in your design?
The description of the image is one that has a four-horned star. The description is as follows:
It comprises of four equilateral triangles and One Square.
Next,
The image or shape has twelve (12) symmetrical lines.
Next,
It must be rotated 90° (clockwise or anticlockwise) in order for the image to match itself.
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Help pls i don't understand
ΔFSH ≅ ΔFSI by the rule of angle-angle-side theorem, or AAS.
What is Angle- Angle - Side theorem?The angle-angle-side theorem, or AAS, tells us that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.
If we consider triangle FSH and triangle FSI, we will observe the following;
angle HFS = angle IFSangle FSH = angle FSIlength HS = length SISo based on the angle-angle-side theorem, or AAS, we can see that triangle FSH is congruent to triangle FSI.
Thus, our answer will be; ΔFSH ≅ ΔFSI by the rule of angle-angle-side theorem, or AAS.
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A number n minus the sum of the number and eight
The algebraic expression for the sentence in this problem is given as follows:
n - (x + 8).
How to obtain the algebraic expression for the sentence?The sentence in this problem is given as follows:
"A number n minus the sum of the number and eight".
The sum of an unknown number x and eight is given as follows:
x + 8.
The subtraction of the number n by the expression is given as follows:
n - (x + 8).
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Graph the image of this quadrilateral after a dilation with a scale factor of 2 centered at the origin. Use the polygon tool to graph the quadrilateral.
The new coordinates of the quadrilateral ABCD after the dilation is:
A' = (-6, 6)
B' = (-8, -4)
C' = (4, -8)
D' = (0, 0)
We have,
To find the coordinates of the new quadrilateral after a dilation with a scale factor of 2 centered at the origin, we multiply the x and y coordinates of each point by the scale factor.
Given the original coordinates of the quadrilateral ABCD:
A = (-3, 3)
B = (-4, -2)
C = (2, -4)
D = (0, 0)
To dilate the coordinates with a scale factor of 2, we multiply each coordinate by 2:
A' = 2 x (-3, 3) = (-6, 6)
B' = 2 x (-4, -2) = (-8, -4)
C' = 2 x (2, -4) = (4, -8)
D' = 2 x (0, 0) = (0, 0)
Thus,
The new coordinates of the quadrilateral ABCD after the dilation is:
A' = (-6, 6)
B' = (-8, -4)
C' = (4, -8)
D' = (0, 0)
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What is the meaning of "definition of finiteness uses the notion of a natural number"?
Answer:
Look Below
Step-by-step explanation:
The statement "definition of finiteness uses the notion of a natural number" means that when defining what it means for a set or collection to be finite, the concept of a natural number is employed.
In mathematics, a set is said to be finite if it can be put into a one-to-one correspondence with a specific subset of the natural numbers. This subset typically starts with the number 1 and includes a finite sequence of consecutive natural numbers, depending on the size of the set.
For example, consider a set A with three elements: A = {a, b, c}. To show that A is finite, we can establish a one-to-one correspondence between the elements of A and the set {1, 2, 3} as follows: a ↔ 1, b ↔ 2, c ↔ 3. This mapping shows that each element of A corresponds to a unique natural number, and vice versa. Since there is a bijection (a one-to-one correspondence) between the elements of A and a subset of the natural numbers, we conclude that A is finite.
Thus, in the definition of finiteness, the notion of a natural number is used to provide a precise and rigorous characterization of what it means for a set to be finite. It allows us to establish a clear distinction between finite sets and infinite sets, which do not have a one-to-one correspondence with any subset of the natural numbers.
is 72 and has an IRA with a fair market value of
Use
Table
45 to determine her required minimum distribution. b) What penalty would she incur if she failed to take the
distribution? c) What penalty would she have paid if she had made an early withdrawal of $10,000 to take a
vacation?
May Kawasaki's required minimum distribution (RMD) is $3,808. This is calculated by dividing her IRA balance of $98,000 by the distribution period of 26.2, which is found in the Uniform Life Table on page 45 for a 72-year-old.
How to explain the informationb) If May Kawasaki fails to take her RMD, she will incur a 50% penalty on the amount she should have withdrawn. In this case, the penalty would be $1,904.
c) If May Kawasaki had made an early withdrawal of $10,000 to take a vacation, she would have paid a 10% penalty on the amount withdrawn. In this case, the penalty would have been $1,000.
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1. May Kawasaki is 72 and has an IRA with a fair market value of $98,000. a) Use the Uniform Life Table on p. 45 to determine her required minimum distribution. b) What penalty would she incur if she failed to take the distribution? c) What penalty would she have paid if she had made an early withdrawal of $10,000 to take a vacation?
Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than once. y = 3x - 1 2y - 6x = 4 2y = -x + 6 4y + 2x = 12 y = 2x + 3 x+y = -9 inconsistent consistent independent dependent
y = 3x - 1: consistent, independent
2y - 6x = 4: consistent, independent
2y = -x + 6: consistent, independent
4y + 2x = 12: consistent, independent
y = 2x + 3: consistent, independent
x + y = -9: consistent, dependent
y = 3x - 1 and 2y = -x + 6: inconsistent
Let's match each system on the left with the appropriate words that describe the system on the right:
y = 3x - 1: consistent, independent
This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
2y - 6x = 4: consistent, independent
Similar to the first system, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
2y = -x + 6: consistent, independent
This system also represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
4y + 2x = 12: consistent, independent
Like the previous systems, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
y = 2x + 3: consistent, independent
This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
x + y = -9: consistent, dependent
This system represents a linear equation with infinitely many solutions. The equations are multiples of each other, meaning they represent the same line. Therefore, any point on the line satisfies both equations.
y = 3x - 1 and 2y = -x + 6: inconsistent
This system represents inconsistent equations that do not have a common solution. The lines represented by the equations are parallel and do not intersect.
To summarize the matches:
y = 3x - 1: consistent, independent
2y - 6x = 4: consistent, independent
2y = -x + 6: consistent, independent
4y + 2x = 12: consistent, independent
y = 2x + 3: consistent, independent
x + y = -9: consistent, dependent
y = 3x - 1 and 2y = -x + 6: inconsistent
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In circle S with m/RST = 84 and RS = 8 units, find the length of arc RT. Round
to the nearest hundredth.
The length of the arc RT is 11.72 units.
What is an arc?An arc is defined as a portion of the boundary of a circle or a curve.
To calculate the length of the arc RT, we use the formula below
Formula:
L = 2πr∅/360.................. Equation 1Where:
L = Length of an arcr = Radius of the circle∅ = Angle subtends at the center of the circle by the arcFrom the question,
Given:
r = 8 units∅ = 84°π = 3.14Substitute these values into equation 1
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A shelf has different sizes of bottles of laundry detergent this line plot shows the number of cups of laundry detergent in each bottle Natalie buys a bottle of the size of laundry detergent that has 4 bottles on the shelf she uses 1/8 cup for each load of laundry she does how many loads of laundry can Natalie do with her bottle of laundry detergent
Using the division operation , Natalie can do 64 loads of laundry with her bottle of detergent.
From the line plot , the detergent with 4 bottles has 8 cups in it.
Fraction of cup used per laundry = 1/8
Total cups of detergent in bottle = 8
Number of laundry Natalie can do :
(Total cups of detergent in bottle / Fraction of cup used per laundry )
Number of loads of laundry that can be done :
= 8 / (1/8)
= 8 × 8/1
= 64
Therefore, Natalie can do 64 loads of laundry with her bottle of detergent.
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Which data set could be represented by
the box plot shown below?
H
0 2 4 6 8
Choose 1 answer:
A
Creating box plots
B
C
D
10 12 14 16 18 20
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
The given box plot represented by the data sets in option A and B.
From the given box plot, we have
Minimum value = 3
Maximum value = 18
First quartile (Q1) = 7
Third quartile (Q3) = 13
Median = 10
Option A:
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
Median = 12
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option B:
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Option C:
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option D:
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Therefore, the correct options are B and D.
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Susan bought a 1 kilogram bag of grapes. On the way home, she ate 125 grams of the grapes. How many grams of grapes does Susan have left? use math language and symbols to explain how you used the correct measurement units to solve the problem.
Susan has 875 grams of grapes left.
1. Susan bought a 1 kilogram bag of grapes, which is equivalent to 1000 grams (since there are 1000 grams in a kilogram).
2. Susan ate 125 grams of the grapes on her way home.
3. To find out how many grams of grapes Susan has left, we need to subtract the amount she ate from the initial weight of the bag. Therefore, we subtract 125 grams from 1000 grams.
1000 grams - 125 grams = 875 grams
4. Thus, Susan has 875 grams of grapes left.
measurement units:
In this problem, we used grams as the measurement unit. Grams are commonly used to measure the weight of small objects like grapes. Since the problem stated that Susan bought a 1 kilogram bag of grapes, it was necessary to convert the kilogram measurement to grams.
This conversion was done by multiplying the kilogram value by 1000 (1 kilogram = 1000 grams). By using the correct measurement units, we were able to accurately calculate the amount of grapes Susan had left after eating a portion.
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7+(2x4)-8÷(12-6)x(6÷2)
Answer:
11
Step-by-step explanation:
Remember PEMDAS
7+(2x4)-8÷(12-6)x(6÷2)
7 + 8 - 8 : 6 × 3 =
7 + 8 - 8/6 × 3 =
7 + 8 - 4 =
11
Find the number that belongs
in the green box.
37⁰
64°
[?]
30
Round your answer to the nearest tenth.
Answer:
? ≈ 20.1
Step-by-step explanation:
using the Sine rule in the triangle
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex]
with a = ? , b = 30 , ∠ A = 37° , ∠ B = 64° , then
[tex]\frac{?}{sin37}[/tex] = [tex]\frac{30}{sin64}[/tex] ( cross- multiply )
? × sin64° = 30 × sin37° ( divide both sides by sin64° )
? = [tex]\frac{30sin37}{sin64}[/tex] ≈ 20.1 ( to the nearest tenth )
The roof gable on Charlene's house has two
equal sides. One angle measures 110.4°. The
other two angles are equal to each other.
Estimate the measure of each of the other
two angles.
Each of the other two angles in the roof gable measures approximately 34.8°.
How to calculate the valueIf the roof gable on Charlene's house has two equal sides, and one angle measures 110.4°, we can determine the measure of each of the other two angles by using the fact that the sum of the angles in a triangle is always 180°.
Let's denote the measure of the other two angles as x.
Since the two equal sides of the gable form an isosceles triangle, the two angles opposite those sides are equal.
Therefore, we have:
x + x + 110.4° = 180°
Combining like terms:
2x + 110.4° = 180°
Now, let's solve for x:
2x = 180° - 110.4°
2x = 69.6°
x = 69.6° / 2
x = 34.8°
Therefore, each of the other two angles in the roof gable measures approximately 34.8°.
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Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.” Here is a dot plot of their responses.
in the dot plot given, A rating of 6 is not a good description of the center of this data set because it does not accurately represent the most common or typical response.
How is this so?
To determine the center of data set, we typically look for the measure of central tendency, such as the mean, median, or mode.
From the dot plot, we can observe that the mode is at the rating of 10, with six students giving this highest rating. In contrast, the rating of 6 has only two students, making it less representative of the center.
Therefore, a rating of 6 does not accurately capture the overall sentiment or the central tendency of the data set.
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Full Question:
Please see the attached.
Answer Question 11 please
Answer:
increasing exponential function.
Step-by-step explanation:
We can see from the table that the function is not increasing by the same amount as it goes up by 1 in x, so it is not linear.
It must be exponential.
It is increasing at it increases in x, so it is an increasing exponential function.
Calculate the unshaded portion of the figure
Answer:
Approx 8.47 [tex]m^2[/tex]
Step-by-step explanation:
First, find the area of the entire figure. Which can be found by multiplying the two sides of the square by each other= [tex]6*6=36m^2[/tex]
Now, ignore the square and just focus on the pentagon and finding the area of that. The formula for the area of a pentagon is [tex]A=1/2Apothem*Perimeter[/tex]
In order to find the apothem, you can make a mini triangle and use trig (Tangent) to find the height (apothem) of the triangle. Then, you take the side length of the base of the pentagon which is 4 and then you multiply it by the number of sides (5) to get 20. Then, by plugging it into our formula, you use the apothem*10 (divided by 2) and you get the area, and then you just subtract that from 36.
A vet records the weight of all the dogs she has seen in the last week the data is recorded bellow in pounds. 61, 10, 32, 19, 22, 22, 29, 36, 14, 49, 3 What is the mean Median, mode, standard deviation, and the outlier (if any)?
Answer:
Mean: 27
Median: 22
Mode: 22
Standard deviation: 17
No outlier (61 might be one just check with people you know and see if they have an outlier or not)
Step-by-step explanation: Give a definition of mean, median, mode…and just add your answers.
What cumulative frequency should be used in solving the 28th percentile
The cumulative frequency to be used in solving the 28th percentile is 16.
What is cumulative frequency?Cumulative frequency is described as the total of a frequency and all frequencies in a frequency distribution until a certain defined class interval.
we add up the frequencies until we reach or exceed 28% of the total data set in order to find the cumulative frequency for the 28th percentile.
Total frequency = 4 + 9 + 16 + 10 + 9 + 2 = 50
28th percentile = (28/100) * Total frequency
28th percentile = (28/100) * 50 = 14
We start from the beginning of the distribution and add up the frequencies until we reach or exceed 14 so as to find the cumulative frequency.
In conclusion, and with reference to the given data set we notice that the cumulative frequency exceeds 14 at the 91-120 minute interval = 16.
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Can you factor 5v²-30v+70
Answer: Unfactorable
Step-by-step explanation:
5v^2-30v+70
5(v^2-6v+14)
You can't factor v^2-6v+14 with rational numbers
5. If a triangular figure is in the shape of an
isosceles right triangle, what is the measure
of each base angle?
Answer: each base angle in an isosceles right triangle measures 45 degrees.
Step-by-step explanation:
In an isosceles right triangle, two sides have equal lengths, and one angle is a right angle (90 degrees).
Since it is an isosceles triangle, the two base angles (the angles opposite the equal sides) must be congruent, meaning they have the same measure.
To find the measure of each base angle, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Let's denote the measure of each base angle as "x". Then, the sum of the three angles in the triangle can be expressed as:
x + x + 90 = 180
Simplifying the equation:
2x + 90 = 180
Subtracting 90 from both sides:
2x = 90
Dividing both sides by 2:
x = 45
Help with the following equation 8x²-6x-5=x
Answer:
[tex]8 {x}^{2} - 6x - 5 = x[/tex]
[tex]8 {x}^{2} - 7x - 5 = 0[/tex]
x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)
= (7 + √(49 + 160))/16
= (7 + √209)/16
= -.4661, 1.3411 (to 4 decimal places)
Can someone answer this please
Answer: N= 12
Step-by-step explanation: if you follow PEMDAS, you take (4^3)^4 and multiply 3*4 which is 12.
Because the base of 4^12=4^n is the same you leave it alone and N is equal to 12
Answer:
Hi
Please mark brainliest ❣️
Thanks
Suppose that point P is the point on the unit circle obtained by rotating the initial ray through θ° counterclockwise. What is the length of segment OP?
The length of segment OP, which represents the distance from the origin to point P on the unit circle, is always equal to 1.
To determine the length of segment OP on the unit circle, we need to use trigonometry. Let's break down the problem step by step:
Definition: The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.
Initial Ray: The initial ray is a line segment that starts from the origin (0, 0) and extends to a point on the unit circle. It forms an angle with the positive x-axis.
Rotation: We are rotating the initial ray counterclockwise by θ degrees. This means we are essentially finding a new point on the unit circle based on the angle θ.
Trigonometric Functions: The trigonometric functions sine (sin) and cosine (cos) are particularly useful for calculating the coordinates of points on the unit circle.
sin(θ) gives the y-coordinate of a point on the unit circle.
cos(θ) gives the x-coordinate of a point on the unit circle.
Coordinates of Point P: Since we are rotating the initial ray counterclockwise by θ degrees, the coordinates of point P on the unit circle can be obtained as follows:
x-coordinate of P: cos(θ)
y-coordinate of P: sin(θ)
Distance from the Origin (Length of Segment OP):
Using the coordinates of point P, we can calculate the distance between the origin (0, 0) and point P using the distance formula.
The distance formula states that for two points (x1, y1) and (x2, y2), the distance between them is given by:
d = √((x2 - x1)² + (y2 - y1)²)
In this case, point P has coordinates (cos(θ), sin(θ)), and the origin is (0, 0). Thus, the distance (length of segment OP) is:
d = √((cos(θ) - 0)² + (sin(θ) - 0)²)
= √(cos²(θ) + sin²(θ))
= √(1) [Using the trigonometric identity: sin²(θ) + cos²(θ) = 1]
= 1
Therefore, the length of segment OP, which represents the distance from the origin to point P on the unit circle, is always equal to 1.
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