Answers
The best option regarding the solutions of the trigonometric equation 2sin(θ) + 1 = 0 in this problem is given as follows:
d. θ = 330º + 360ºn, θ = 210 + 360ºn.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
2sin(θ) + 1 = 0
Then, isolating the sine, we have that:
2sin(θ) = -1
sin(θ) = -1/2.
The values of theta for which the sine is of negative 1/2 are given as follows:
θ = 210º, θ = 330º.
(as the sine is negative for the third and fourth quadrant, hence we have to find the equivalent angle to 30º in each of these quadrants).
One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option d is correct.
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Related Questions
Find the area of the largest rectangle that can be inscribed in the ellipse x2 / a2 + y2 / b2 = 1.
Answers
The maximum area of the rectangle inside the ellipse is 2ab.
Given that,
Ellipse = x2 / a2 + y2 / b2 = 1
we know the general coordinates of any point in an ellipse of the equation
x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)
So, we take general vertices of rectangles as
(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)
So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ
So, its area will be ab4sinθcosθ (Length x Breadth)
Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A
Now A=2absin2θ
Now as the area is the maximum given in the question, we have to differentiate it with respect to θ
dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)
Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ = π / 2 and θ=π / 4
So now we to put θ=π / 4 in the equation of area which is A=2absin2θ
We get as A=2absin2π / 4=2absinπ / 2=2ab
Hence the max area of the rectangle inside the ellipse is 2ab.
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Olving ytem of linear equation in two variable
1. 4x8y=24 2. 2xy=19 3. 3x2y=15
4x2y=12 x-y=11 x2y=10
Answers
The solution of this system of linear equations is x=3, y=-5.
To solve this system of linear equations, you can use various methods such as substitution, elimination, or matrices. Here is one way to solve using the substitution method:
From equation 2, we can find the value of x in terms of y: x = (11+y)/2Substitute this value of x into equations 1 and 3:4((11+y)/2) + 8y = 24
3((11+y)/2) + 2y = 15
Solve for y in the first equation: 8y = 24 - 44 = -20y = -5
Substitute this value of y back into equation 2 to find x:x = (11 + (-5))/2
x = 3
Substitute the values of x and y back into the original equations to check if they are correct:4(3) + 8(-5) = 24
3(3) + 2(-5) = 15
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The question is -
Solving a system of linear equations in two variables,
4x + 8y = 242x - y = 113x + 2y = 15Ivan is a software salesman. His base salary is $2400, and he makes an additional $110 for every copy of History is Fun he sells.
Let P represent his total pay (in dollars), and let N represent the number of coples of History is Fun he sells. Write an equation relating P to N. Then use this
equation to find his total pay if he sells 24 coples of History is Fun.
Answers
The total pay when he sells 24 copies of Math exists Fun should be 3760.
What is meant by equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. A mathematical equation is a statement with two equal sides and an equal sign in between.
Numerical constants, symbolic names, mathematical operators, functions, and conditional expressions can all be found in expressions in some combination.
Calculation of the equation and the total pay:
His base salary is $2400, and he makes an additional $110 for every copy of Math is Fun he sells.
Here P means the total pay
So, here the equation be p = 2400 + 110 n
substitute the values in the above equation, we get
Now the total pay be
p = 2400 + 110(24)
simplifying the above equation, we get
= 2,400 + 2640
= 5040
The equation that should be related P to N should be considered as the 2400 + 110n.
Therefore, the total pay when he sells 24 copies of Math is Fun should be 5040.
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The total pay when he sells 24 copies of Math exists Fun should be 3760.
What is meant by equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. A mathematical equation is a statement with two equal sides and an equal sign in between.
Numerical constants, symbolic names, mathematical operators, functions, and conditional expressions can all be found in expressions in some combination.
Calculation of the equation and the total pay:
His base salary is $2400, and he makes an additional $110 for every copy of Math is Fun he sells.
Here P means the total pay
So, here the equation be p = 2400 + 110 n
substitute the values in the above equation, we get
Now the total pay be
p = 2400 + 110(24)
simplifying the above equation, we get
= 2,400 + 2640
= 5040
The equation that should be related P to N should be considered as the 2400 + 110n.
Therefore, the total pay when he sells 24 copies of Math is Fun should be 5040.
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The KOT club has 5 pledges. They will send at least 2 and no more than 4 pledges to work at Goodwill on Helping-Out Day. In how many ways can this be done?
Answers
Answer:
The KOT club has 5 pledges and can send between 2 and 4 pledges to work at Goodwill on Helping-Out Day. This can be done in 10 different ways
Step-by-step explanation:
What is −30y − 15 if y is 7?
Answers
So, the value of −30y − 15 when y is equal to 7 is −225.
Answer:
-225
Step-by-step explanation:
-30*7=-210
-210-15=-225
please give brainliest
What are examples of perfect square Trinomials?
Answers
Example of perfect square trinomial is: x² + 6x + 9 it is expressed as
(x + 3)²
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Example:
x² + 6x + 9
= x² + 3x + 3x + 9
= (x +3) (x + 3)
= (x + 3)²
so, this is a perfect square trinomial.
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Evaluate a+4a+4a, plus, 4 when a=7a=7a, equals, 7
Answers
The evaluation of the expression a + 4 when a = 7 is 11
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
Expression: a + 4
Value a = 7
Substitute the known values in the above equation, so, we have the following representation
a + 4 = 7 + 4
Evaluate the like terms in the equation
So, we have the following representation
a + 4 = 11
Using the above as a guide, we have the following:
The solution is 11
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What additional information would be necessary to determine sin a without using the Pythagorean theorem explain brainly?
Answers
The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem.
In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulae.
In order to determine sin a without using the Pythagorean theorem, we will need to have the value of the opposite side and angle. Sin (a) = opposite / hypotenuseHere, the hypotenuse is not given, so we will need to have the value of the opposite side and angle (a) in order to determine sin a without using the Pythagorean theorem.
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Jai is 1. 45 meters tall. At 11 a. M. , he measures the length of a tree's shadow to be 39. 55 meters. He stands 34. 1 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter
Answers
The height of the tree to the nearest hundredth of a meter is 10.5 meters.
The length of Jai's shadow = length of tree's shadow - distance of standing of Jai
Length of Jai's shadow = 39.55 - 34.1
Performing subtraction on Right Hand Side of the equation
Length of Jai's shadow = 5.45 meters
Tan theta = height of tree/length of shadow = height of Jai/length of his shadow
height of tree/39.55 = 1.45/5.45
Keep the values in formula
Height of tree = 39.55×1.45/5.45
Performing multiplication
Height of tree = 57.35/5.45
Performing division
Height of tree = 10.5 meters
Thus, the height of tree is 10.5 meters.
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Out of 30 students surveyed, 17 have a dog. based on these results, predict how many of the 300 students in the school have a dog?
Answers
1. Use the proportion 17/30 = x/300 to find the answer
2. Cross multiply
30x = 5100, which can also be written as 3x = 510 because they both have at least 1 zero and 0/0 cancels out.
3. Divide both sides by 3 to get the variable alone
X = 3x/3 = 510/3
4. Simplify
X = 170
Santiago has 5 11/16 cups of dough to make dumpling. If he uses 13/16 cups of dough for each dumplings how many dumplings can santiago make?
Answers
Santiago can make 7 dumplings
To find out how many dumplings Santiago can make, we need to divide the total amount of dough (5 11/16 cups) by the amount of dough used per dumpling (13/16 cups).
To do this, we can first convert the fractions to have a common denominator. In this case, the denominator of 13/16 is 16, so we can convert 5 11/16 to have a denominator of 16 as well:
5 11/16 = (5 * 16) + 11/16 = 80 + 11/16
Now we can divide:
(80 + 11/16) ÷ (13/16) = (80 + 11) ÷ 13 = 91 ÷ 13
So Santiago can make 91/13 dumplings. This can be simplified further to 7 dumplings. So Santiago can make 7 dumplings with 5 11/16 cups of dough.
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Is parallel processing always faster?
Answers
Only when each iteration is sufficiently time-consuming in terms of CPU usage does parallel programming become more effective.
Parallel processing: What is it?The term "parallel processing" is used to deliver simultaneous data-processing activities, which is utilized to increase the computing performance of computer systems. Additionally, a parallel processing system has the ability to process input concurrently for quicker execution times.
As an illustration, when an instruction is being carried out in an ALU, the following instruction may be read from memory. The system may be equipped with two or more ALUs and be able to carry out multiple instructions at once.
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Which one of these is correct? Could you explain
Answers
Quadratic Standard Form:
ax²+bx+c=0
Replace = sign with <:
ax²+bx+c<0
So, we want to get 0 on the right side of the inequality to be in standard form.
To do this, we’ll add 18 to both sides:
x²-9x+18<0
This cancels out the -18 on the right, making it 0 because -18+18=0, and of course to keep the equation equal, we must add 18 to the left side as well.
Now, let’s understand the inequality. In standard form, a quadratic is equal to 0 to find the zeros. This is so that we can find what x-values will produce an output (y-value) of 0, as a y-value of 0 means no vertical change. It shows what x-values intercept the x-axis, which are the zeros (or roots) of the quadratic. Therefore, this inequality means: what x-values are less than 0, or go below the x-axis. To find this, we will factor the quadratic to see what x-values produce y-values less than 0.
Factor:
We know that -3-6=-9 and -3•-6=18
(x-3)(x-6)<0
So, the zeros of the function are x=3, 6. However, for x-values 3 and 6, the output is 0 since these values are x-intercepts. The inequality states less than 0, so we need look at x-values that produce a negative output.
So, if x=3, 6, then x>3 and x<6. Let’s look at the graph:
help i cant solve it
Answers
Answer:
Step-by-step explanation:
We have,
x = 3y - 3 ---> x - 3y = -3 ------(1)
5x + 4y = 23 -----(2)
Multiplying eq. (1) by 5:
5x - 15y = -15 ------(3)
5x + 4y = 23
Subtracting (1) from (3):
-19y = - 38
y = 2
therefore, x - 6 = -3
x = 3
For triangle ABC use the Triangle Proportionality Theorem to solve for x
1. what is the value of x?
2. What is the perimeter of triangle ABC?
show ALL work-- PLEASE HELP!
Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
The two triangles in the shown figure are similar, therefore conclusion can be made that :
Ratio of its it's corresponding sides is equal.
[tex]\qquad \sf \dashrightarrow \: \dfrac{2x - 4 + 6}{6} = \dfrac{24}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2x + 2}{6} = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x + 2 = 6 \times 6[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x + 2 = 36[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 36 - 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 34[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 17[/tex]
Therefore, The value of x is " 17 "
Now, the measure of side BC is :
[tex]\qquad \sf \dashrightarrow \: 2x - 4[/tex]
[tex]\qquad \sf \dashrightarrow \:2 (17) - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: 34 - 4[/tex]
[tex]\qquad \sf \dashrightarrow \: 30 \: \: units[/tex]
So, its perimeter will be :
[tex]\qquad \sf \dashrightarrow \: p = AB + AB + BC [/tex]
[tex]\qquad \sf \dashrightarrow \: p = 24 + 26 + 30[/tex]
[tex]\qquad \sf \dashrightarrow \: p = 80 \: \: units[/tex]
Answer:
1) x = 17,2) P = 86 units.------------------------------------
Part 1According to Triangle Proportionality Theorem we have the following equal proportions:
(24 - 4)/4 = (2x - 4)/620/4 = (x - 2)/35 = (x - 2)/3x - 2 = 5*3x - 2 = 15x = 17Part 2The missing side is:
BC = 6 + 5*6 = 6 + 30 = 36 unitsThe perimeter is:
P = 24 + 36 + 26 = 86 unitswe roll a fair 6 sided die 5 times. what is the probability that we get a one or a two in exactly 3 of the 5 rolls
Answers
The probability is 5/32.
Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
To roll exactly 4 odds out of 5 rolls is [tex](\frac{1}{2} )^{4}\frac{1}{2}[/tex] where the odds are 1, 3, and 5 for 3/6=1/2 and the other 1/2 is the probability of rolling an even since we want exactly 4 odds.
Since there are 5 dice being rolled there are 5 ways to order them.
So the probability is 5/32.
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The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
Ponies
3
Rabbits
8
Sheep
6
0/1
Write the ratio of ponies and goats to rabbits and
sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, if
possible.
Answers
Answer:
3/7
Step-by-step explanation:
3 ponies + 3 goats = 6 total
8 rabbit + 6 sheep = 14 total
6/14 simplified is 3/7.
A sequence begins with 2. Each term is calculated by multiplying the previous term by −1, then subtracting 3.
Which answer correctly represents the sequence described?
a) {2,−5,2,−5,…}
b) 2,−5,2,−5,…
c) 0,−3,0,−3,…
d) {0,−3,0,−3,…}
Answers
The sequence is going to be {2,−5,2,−5,…}. Since we can see that options A and B are one and the same, the correct answer is options A and B.
A sequence is a successive arrangement of two or more things that are constructed on the basis of a given formula.
Here, the first term is = 2
Each previous term has been multiplied by = -1
And then, it has been subtracted by = 3
So, following the formula given, we conclude that the second value will be = 2×(-1)-3 = -5
Similarly, the formula is going to be applied to the second term now which is -5, and then the third term is going to be = -5×(-1)-3 = 2
In this fashion, we can make the sequence. Options A and B is the correct answer.
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Combine like terms to simplify this expression:
8 + 7y + 2y + 4
Answers
Answer: The resulting expression is 8+9y+4, which simplifies to 12+9y.
Step-by-step explanation: To combine like terms, we add the coefficients of the terms that are the same. In this expression, the like terms are 2y and 7y. Their coefficients are 2 and 7, respectively, so when we add them we get 2+7=9. The resulting expression is 8+9y+4, which simplifies to 12+9y.
What is the coefficient of XY in 7xy?
Answers
The coefficient of XY in 7xy is 7
Any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value is known as a coefficient in mathematics. In some phrases, a letter might be substituted for the usual number. For example, x is the variable and a and b are the coefficients in the formula: ax2 + bx + c.
What is a coefficient?
A coefficient is a quantity or number that is coupled with a variable. Frequently, an integer is multiplied by the variable and written next to it. The variables that don't have a corresponding number are presumed to have a coefficient of 1.
Seven is the coefficient of XY in 7xy.
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PLEASE HELP. I'LL DO ANYTHING THAT'LL BENEFIT YOU.
Answers
If you double the amount of fluid ounces, the amount of cups also double
There is a proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.
The cost of renting equipment is sometimes proportional; because, it depends on whether the equipment has a rental fee and charge per hour or just a charge per hour. Option A.The cost of mailing a letter is proportional to the weight. The cost of mailing a 6-ounce letter is $2.82. Option BThe donation is proportional to the dinner bill
The donation for a dinner bill of $50 is $9
How to determine proportional relationship?If there are 8 fluid ounces in one cup
8 : 1 = 16 : x
8/1 = 16/x
8 × x = 16 × 1
8x = 16
x = 16/8
x = 2
The difference between weight = 1
The difference between cost = $0.68 - $0.47
= $0.21
$0.89 - $0.68
= $0.21
$1.10 - $0.89
= $0.21
Cost of mailing 6-ounce letter
1 : 0.47 = 6 : x
1/0.47 = 6/x
1 × x = 6 × 0.47
x = $2.82
The donation for a dinner bill $50 is
Dinner bill : donation
25 : 4.50 = 50 : x
25/4.50 = 50/x
25 × x = 50 × 4.50
25x = 225
x = 225/25
x =$ 9
Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.
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33
Problem 2
m, p, and z represent the lengths of the three sides of this right triangle.
m
i
Z
Р
Select all the equations that represent the relationship between m, p, and z.
Answers
On solving the provided question, we can say that since it it is right angled triangle so the relation that be formed is [tex]m^2 = p^2 + z^2[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
since it it is right angled triangle
so the relation that be formed is
[tex]m^2 = p^2 + z^2[/tex]
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Find the domain and range of the function graphed below. PLEASE SHOW YOUR WORK!!
Answers
The domain and range of the function on the graph are:
D: [-2, 1)R: [0, 4]How to find the domain and range of the function below?Remember that for any function y = f(x), we define the domain as the set of possible inputs (possible values of x) and the range is the set of the possible outputs of the function (possible values of y).
To find the domain we need to look at the horizontal axis. The minimum is at x = -2 with a colored circle, so x = -2 belongs to the domain.
The largest value is at x = 1, now with an open circle, then this value does not belong to the domain. Thus the domain is:
D: [-2, 1)
For the range we need to look at the vertical axis, the minimum is at zero and the maximum at 4, then the range is:
R: [0, 4]
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Gwen scans a photo that is 4inches wide by 6 inches long into her computer. If she scales the length down to 3inches how wide should the similar photo be?
Answers
The similar photo should be 4.5 inches wide.
What is scale factor?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor. It also tells by how many times is {y} greater than {x}.
Given is that Gwen scans a photo that is 4 inches wide by 6 inches long into her computer. Now, she scales the length down to 3 inches.
We can write -
y₁/x₁ = y₂/x₂
6/4 = 3/x₂
x₂ = 6 x 3/4
x₂ = 6 x 0.75
x₂ = 4.5
Therefore, the similar photo should be 4.5 inches wide.
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PLEASE HELP ASAP. I WILL GIVE BRAINLIEST!!!
Which of the following is not an expression
A. 7 - 5x
B. 2 + 3x = 8
C. x/2 + 1
D. 2x + 6
Answers
Answer:
B) 2 + 3x = 8
Step-by-step explanation:
Option B is not an expression as expressions do not have equal signs.
Solve the simultaneous equations
xy=-16
y=x+8
Answers
Answer:
x = 4, y = 12
Step-by-step explanation:
xy = -16
y = x + 8
substitute y = x + 8 into xy = -16
x(x + 8) = -16
x^2 +8x + 16 = 0
x = 4
sub x = 4 into y = x + 8
y = 4 + 8
y = 12
Find the measure of the given angle. Round to the nearest degree.
(O
6
?
13
Answers
15 degrees by eye i think
I need help with question 9. It’s all about functuons
Answers
Answer:
gay
Step-by-step explanation:
gayayayayayayaydyfyfaygaygagya
A bookcase is 3 feet high and 3 feet wide. Two braces are going to be built to diagonally cross the back of the case. How long is the piece of wood that is needed to build each brace?
Answers
The length of each piece of wood needed to build each brace of the bookcase will be 4.24 feet.
Based on the dimensions, the shape of bookcase is square. So the diagonal of the bookcase will be calculated from the formula -
Diagonal = ✓side² + side²
Keep the values in formula to find the value of diagonal
Diagonal = ✓ 3² + 3²
Taking square on Right Hand Side of the equation
Diagonal = ✓9 + 9
Performing addition on Right Hand Side of the equation
Diagonal = ✓ 18
Finding square root on Right Hand Side of the equation
Diagonal = 4.24 feet
Thus, each diagonal will be 4.24 feet.
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How do you plot a coordinate plane?
Answers
We can plot in the coordinate plane if an ordered pair is known to us.
What is coordinate plane?The space or plane in where location of points is represented by a pair of numerical terms with respect to some reference lines or reference direction is called coordinate plane.
How do we plot a coordinate plane?
let we have some pair of numerical terms such as A (4, 9) and B (6, 10)
that is needed to plot in the coordinate plane.
At first, we will plot the point A (4, 9)
we will start from the origin and move horizontally along the direction of X axis up to 4 unit. In the next, start again and move up vertically in the direction of y axis up to 9 unit. And we will draw a point at the final location.
By the same way, we can plot the point B.
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