The midpoints of the three sides of a triangle are P(-7; -2), Q(-1; 9) and R(5; -3).
Calculate the area of the circumscribed circle of the triangle.

dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.

To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.

Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

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At this point, the vector "intvector" will contain all of the integers read from input minus five.

int x = 0;

vector<int> intvector;

while (x != 0)

{

   cin >> x;

   intvector.push_back(x - 5);

}

First, we create a variable to store the integer from input, "x", and a vector to store the integers minus five, "intvector". Then, we create a while loop that runs until the value of "x" is equal to zero. Inside the loop, we read an integer from input and store the value in "x". Then, we subtract five from "x" and add the resulting value to the vector "intvector". This loop will run until the value of "x" is equal to zero.  At this point, the vector "intvector" will contain all of the integers read from input minus five.

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The total number of brothers and sisters in the family can be represented by the equation 4x + 2.

Number of brothers and sisters mike has = x

Number of brothers and sisters Emily has = 3x

Mike = 1 brother

Emily= 1 sister

Total boys and girls are there in this family = Number of brothers and sisters mike has + Number of brothers and sisters Emily has + Mike + Emily

= x + 3x + 1 + 1

= 4x + 2

Hence, there are 4x + 2 boys and girls in the family including mike and Emily.

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A graph of the inequality 3x - 2y > 4 is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In this exercise, we would use an online graphing calculator to plot the given inequality 3x - 2y > 4 as shown on the graph attached below. Based on the graph (see attachment), we can logically deduce that the solution to the given inequality is the shaded region.

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The solutions to the equations of the triangle is given by x = 86 and the value of y = 56

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ABC

Now , the equation is

3x - 5y = -22   be equation (1)

Now , the measure of ∠A = ( y - 18 )°

The measure of ∠B = y°

The measure of ∠C = x°

Now , for a triangle

∠A + ∠B + ∠C = 180°

Substituting the values in the equation , we get

y - 18 + y + x = 180

On simplifying the equation , we get

2y + x = 198   be equation (2)

Multiply equation (2) by -3 , we get

-6y - 3x = -594   be equation (3)

Adding equation (3) and equation (1) , we get

-5y - 6y = -594 - 22

-11y = -616

Divide by -11 on both sides of the equation , we get

y = 56

Substitute the value of y in equation (2) , we get

2 ( 56 ) + x = 198

x + 112 = 198

Subtracting 112 on both sides of the equation , we get

x = 86

Hence , the solution to the equation is ( 86 , 56 )

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The trigonometric ratios and the graph of the periodic function indicates that we get;

1. sin(θ) = -√(13)/7, csc(θ) = -7·√(13)/13

cos(θ) = 6/7, sec(θ) = 1 1/6

tan(θ) = -√(13)/6, cot(θ) = -6·√(13)/13

2. Vertical shift = 4

Amplitude = 3

Period = 6

Equation; y = 3·sin((π/3)·(x - 1.5)) + 4

A periodic function is one in which the values of the function are repeated at regular intervals. Trigonometric functions, such as sinusoidal functions are periodic functions.

1. sin(θ) = -√(13)/7

csc(θ) = 1/sin(θ), therefore;

csc(θ) = 1/(-√(13)/7) = -7/√(13) = -7·√(13)/13

csc(θ) = -7·√(13)/13

sin(θ) = Opposite/Hypotenuse

3·π/2 < θ < 2·π, therefore, θ is in quadrant IV

Making use of the proportional or comparative dimensions of the corresponding lengths in a unit circle, we get;

Relative length of the hypotenuse = 7 units

Relative length of the opposite side = -√(13)

The Pythagorean Theorem, indicates that the adjacent side can be found as follows;

Length of the adjacent side = √(7² - 13) = 6

cos(θ) = Adjacent/Hypotenuse

Therefore;

sec(θ) = 1/cos(θ), therefore;

sec(θ) = 1/(6/7) = 7/6 = 1 1/6

tan(θ) = sin(θ)/cos(θ)

Therefore; tan(θ) = (-√(13)/7)/(6/7) = -√(13)/6

cot(θ) = 1/tan(θ), therefore;

cot(θ) = 1/(-√(13)/6) = -6/√(13) = -6·√(13)/13

cot(θ) -6·√(13)/13

2. The vertical shift is the vertical displacement of the midline above the x-axis, which can be found as follows;

The location of the midline = (Peak value + Minimum point)/2

Therefore, the location of the midline = (7 + 1)/2 = 4

The period = 1/Frequency

The frequency = Number of cycles per second

The graph indicates that in 1 unit, the cycle completed = 1/6

Therefore; Frequency = 1/6

Period = 1/(1/6) = 6

The amplitude is the the distance from the peak to the midline, therefore;

The equation of the form of a sinusoidal function; y = A·sin(B·(x + C)) + D, indicates that we get;

A = The amplitude = 3

Period = 2·π/B, therefore;

6 = 2·π/B

B = 2·π/6 = π/3

D = The vertical shift = 4

When x = 0, y = 7 = Highest value, therefore;

sin((π/3)·(0 + C)) = sin(π/2)

π·C/3 = π/2

C/3 = 1/2

C = 3 × 1/2 = 3/2 = 1.5

The equation is therefore;

A vertical reflection of a function, f(x) is -f(x). The leading coefficient of the equation is positive, therefore, there are no vertical reflection or flip

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Answer:

[tex] \color{grey}{ \boxed{\sf x < \frac{1}{2} }}[/tex]

Solve..

Let's solve your inequality step-by-step.

[tex] \sf{3(6x+10)<39} [/tex]

Step 1: Simplify both sides of the inequality.

[tex] \sf{18x+30<39}[/tex]

Step 2: Subtract 30 from both sides.

[tex] \sf18x+30−30<39−30 \\ \sf18x<9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

Step 3: divide by 18

[tex] \sf{x <\frac{9}{18} = \frac{9 \times 1}{9 \times 2} } \\ \\ \sf x < \frac{1}{2} [/tex]

The time complexity of constructing a heap of n elements is no better than O(nlogn).

The correct statement is that heap sort functions in O(nlogn) time and a heap of n elements may be constructed in no better than O(nlogn) time.

Heap sort is an efficient sorting algorithm that uses a heap data structure to store the data elements. The heap is a complete binary tree structure where the root node is the largest element in the heap and each node contains a value that is less than or equal to its parent node. The heap is constructed in a bottom-up fashion, meaning that each leaf node is compared to its parent node and swapped if it is larger. This ensures that the root node is always the largest element in the heap.

The complexity of heap sort is O(nlogn), since the heap is constructed in O(n) time but the sorting operation requires O(nlogn) time. This is because, for each element in the heap, the sorting algorithm must compare it to its parent node and swap if necessary. Therefore, the overall time complexity of the algorithm is O(n) + O(nlogn) = O(nlogn).

The complexity of constructing a heap of n elements is also O(nlogn), since each element must be compared to its parent node and swapped if necessary. This process must be repeated for each element in the heap, so the time complexity is O(n) + O(nlogn) = O(nlogn). Therefore, the time complexity of constructing a heap of n elements is no better than O(nlogn).

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For two fair 6-sided diced that are rolled, the expected value of maximum (E(m)) is 3.5 and variance of maximum (Var(m)) is 2.91.

To find the expected value of the maximum of two dice rolls, we need to find the sum of the products of each maximum value and its probability of occurring.The maximum value of each combination of two dice rolls can range from 2 to 6, with the following probabilities:

Maximum of 2: 1/36

Maximum of 3: 2/36

Maximum of 4: 3/36

Maximum of 5: 4/36

Maximum of 6: 5/36

So the expected value (E(m)) can be calculated as:

E(m) = (2 × 1/36) + (3 × 2/36) + (4 × 3/36) + (5 × 4/36) + (6 × 5/36)

E(m) = 3.5

To find the variance of the maximum (Var(m)), we need to use the formula for variance of a discrete random variable:

Var(m) = E((m - E(m))²)

Var(m) = E((m - 3.5)²)

Var(m) = (2 - 3.5)² × 1/36 + (3 - 3.5)² × 2/36 + (4 - 3.5)² × 3/36 + (5 - 3.5)² × 4/36 + (6 - 3.5)² × 5/36

Var(m) = 2.91

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Answer.

Tha answer will be 6x/5 as a fraction

Step-by-step explanation:

As a decimal it is 1.2 cause

6/5=1 1/5= 1.2

Answer:

6/5x

Step-by-step explanation:

To find the equivalent expression, you need to simplify the expression (4/5x + 1) + (2/5x - 1) by combining like terms.

Starting with the first pair of terms:

(4/5x + 1) + (2/5x - 1)

= (4/5x) + (2/5x) + 1 - 1

= (6/5x) + 0

= 6/5x.

So, the equivalent expression for (4/5x + 1) + (2/5x - 1) is 6/5x.

The truth value of a statement can be determined by evaluating the statement in the context of the given universe of discourse.

3xVy(xy = 0): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be zero. This is impossible in the set of real numbers.

3x (x2 = -1): False. The statement is saying that for any x in the universe of discourse, the square of x must be -1. This is impossible in the set of real numbers.

3xVy 0(xy = 1): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be one. This is impossible in the set of real numbers.

VxSy((x + y = 2) A (2x - y = 1)): True. The statement is saying that for any x and y in the universe of discourse, the sum of x and y must be 2 and the difference between 2x and y must be 1. This is possible in the set of real numbers, so the statement is true.

Vx #03y(xy = 1): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be one. This is impossible in the set of real numbers.

3x(x2 = 2): False. The statement is saying that for any x in the universe of discourse, the square of x must be 2. This is impossible in the set of real numbers.

Vx3y(x2 = y): False. The statement is saying that for any x and y in the universe of discourse, the square of x must be equal to y. This is impossible in the set of real numbers.

Vx3y (x = y): True. The statement is saying that for any x and y in the universe of discourse, x must be equal to y. This is possible in the set of real numbers, so the statement is true.

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Thus, a vector function that represents the curve of intersection of the cone and the plane is: [tex]r(t) = tcos(t), 1 +\sqrt{ (1 - t^2)}, 1 -\sqrt{ (1 - t^2)}, tsin(t)[/tex]

The vector function that represents the curve of intersection of a cone and a plane can be found by equating the equation of the cone and the equation of the plane, and then solving for x and y in terms of z.

Given the cone  [tex]z = \sqrt{(x^2 + y^2)}[/tex]  and the plane  [tex]z = 1 + y[/tex] , we have:

[tex]\sqrt{(x^2 + y^2) }= 1 + y[/tex]

Squaring both sides, we get:

[tex]x^2 + y^2 = (1 + y)^2 = 1 + 2y + y^2[/tex]

Solving for y, we get:

[tex]x^2 + y^2 - 2y = 1[/tex]

[tex]y^2 - 2y + x^2 - 1 = 0[/tex]

Using the quadratic formula, we get:

[tex]y = 1 + \sqrt{(1 - x^2)} , 1 + \sqrt{(1 - x^2)}[/tex]

Thus, a vector function that represents the curve of intersection of the cone and the plane is:

[tex]r(t) = tcos(t), 1 +\sqrt{ (1 - t^2)}, 1 -\sqrt{ (1 - t^2)}, tsin(t)[/tex]

where t varies between -1 and 1.

The resulting curve is a circle with center (0, 1, 0) and radius 1, which lies in the xy-plane and is perpendicular to the z-axis.

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We cannot determine the exact time it takes for the coffee to cool to 45°C without additional information. The value of hA/mC (heat transfer coefficient times surface area over mass times heat capacity) needs to be known to solve for Δt accurately.

The equation describing the cooling of hot coffee is given by:

dT/dt = -h * A * (T - T_room) / (mc)

where T is the temperature of the coffee, T_room is the temperature of the room, h is the heat transfer coefficient, A is the surface area of the cup, m is the mass of the coffee, and c is the heat capacity of the coffee.

We can solve for the time it takes for the coffee to cool from an initial temperature of 80°C to a final temperature of 45°C by integrating both sides of the equation over time, with the initial conditions T(0) = 80°C:

t = (mc / (h * A)) * ln((T_initial - T_room) / (T_final - T_room))

Plugging in the given values, we have:

t = (mc / (h * A)) * ln((80 - 25) / (45 - 25))

Since the units of t are in seconds, we can convert to minutes by dividing by 60:

t = (mc / (h * A)) * ln((80 - 25) / (45 - 25)) / 60

Note that the value of h * A / mc is given as ?, so we cannot determine the exact time it takes for the coffee to cool to 45°C without additional information.

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The cooling of hot coffee can be described by the following equation:

mehA(TT) where 1m is the mass of the coffee (in SI units, kg)

2. c is the heat capacity of the coffee (in SI units, J/kg C)

3. T is the temperature of the coffee (in SI units, C)

4. Tom is the temperature of the room (in SI units, °C)

5. h is the heat transfer coefficient in SI units, W/m O 6. As the surface area of the cup in SI units, m²)

7.ts time (in SI units, s)

#room temperature is 25°C and the coffee is originally at 80 C. how long will it take the coffee to cool to 45 Ct the ratio 10? Provide your answer in minutes.

Answer:

-18 and -27 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

a four-story office building has interior columns spaced 30 ft apart in two perpendicular directions

Determine the service live load for a first floor interior column direction

following ASCE-7  guidelines

Area = 20 * 25 = 500 ft^2 which is > 400 ft^2

Nominal live load on every floor = 80 psf

Hence the reduced service live load ( L )

L = Lo [ 0.25 + 15 / √AI ]  ------ ( 1 )

Lo = unreduced load

AT = Tributary area = 500 * number of floors = 2000 ft^2

AI ( influence area ) = AT * number of floors = 2000 * 4 = 8000 ft^2

Lo = 1.6 * 80 psf * 2000 ft^2 = 256 kips

Input values into equation 1 above

L = 106 kips

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(a) Chebyshev's theorem states that at least 75% of lifespan fall between 748 and 1112 hours.

(b) Chebyshev's theorem states that at least 56% of all lifetimes fall between the average lifespan minus the standard deviation and the average lifetime plus the standard deviation. Additional information, such as the mean and standard deviation of the lifespan, would be required to calculate the exact interval.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

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The volume of the solid obtained by rotating the region in the first quadrant can be found using the method of cylindrical shells.  

The volume of the solid is obtained by rotating the region in the first quadrant bounded by the curves y = tan(x), y = 3, and x = 0 about the line y = 3.

The formula for the volume is:

where a is the value of x such that y = tan(x) intersects y = 3, and y = tan(x) is the equation of the upper boundary of the region being rotated. To find a, we need to solve the equation tan(x) = 3 for x. The exact value of a can then be plugged into the integral.

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The force acting on the adult and the student, both stuck to the wall, is determined by their weight and the centripetal force acting on them.  This means that the net force acting on both of them must be equal to zero.

The quadratic equation in LaTeX:

$ax^2 + bx + c = 0$

The weight of an object is proportional to its mass, and the centripetal force acting on an object is proportional to its mass and the square of its velocity.

Therefore, the ratio of the force acting on the adult to the force acting on the student will be equal to the square of the ratio of their masses and the square of the ratio of their velocities.

Let the mass of the student be 'm' and the mass of the adult be '2m'. Then, the ratio of the forces acting on them will be (2m) / m * (v_adult / v_student)^2, where 'v' represents velocity.

Since the ride remains stationary against the wall for both the student and the adult, this means that the net force acting on both of them must be equal to zero, i.e. their weight must be balanced by the centripetal force acting on them.

Thus, (2m) / m * (v_adult / v_student)^2 = 1.

This equation shows that the mass of the rider does not determine if the ride will remain stationary against the wall while rotating. The ride's velocity and the distribution of mass on the ride will determine whether it remains stationary or not, not the mass of the rider.

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The variable y varies directly with x and the equation is y = 1.6x

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

x y

4 6.4

7. 11.2

10 16

13. 20.8

From the table above, we can see that;

The y values is 1.6 multiplied by the x values

This implies that the equation is a direct variation

So, we have the equation to be

y = 1.6x

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Answer:

a. They are proportional

b. 11

Step-by-step explanation: They table is said to be proportional because all their ratios are the same/equal.

b. 5.5 multiplied by 2 is 11.( cross check the other values of wet dog food by multiplying the values by 2)

The problem's matrix representation of linear regression is written as =ε = [ε1 ε2 ε3]'.

A variable's value can be predicted using linear regression analysis depending on the value of some other variable.

Y = Xβ + ε,  where Y is indeed the n x 1 vector of a dependent variable, can be used to describe the linear regression issue as a matrix (Yi),

With n = 3 (observations), k = 2 (independent variables), and a matrix representation of a issue, the following can be written:

Y = Xβ + ε

Y = [0.3 0.8 -0.3]

X = [1 1 1; 1 2 0.1]

β = [β0 β1]'

ε = [ε1 ε2 ε3]'

Thus, the problem's matrix form is written as =ε = [ε1 ε2 ε3]'.

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Answer:

100x+900−900=112x

Step-by-step explanation:

100x+900−900=112x+504−900

The electric field at points on the y-axis above the uppermost charge is given by [tex]E= kq/(a^{2}+y^{2} )^{(3/2)} ,ex=0, ey=kq/(a^{2}+y^{2} )^{(3/2)}[/tex].

The electric field at points on the y-axis above the uppermost charge can be calculated by finding the electric field due to each of the three charges and summing them. This calculation requires the use of Coulomb's law, which states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The electric field due to a single charge is proportional to the charge and inversely proportional to the square of the distance from the charge to the point at which the field is being calculated.

By using the equations for the electric field due to each charge and the vector sum of their electric fields, an expression for the electric field at points on the y-axis above the uppermost charge can be obtained. The final expression would likely be a function of q, a, x, y, and the Coulomb constant k.

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Perimeter of a triangle is the sum of the lengths of it's sides.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Perimeter of a straight sided figure is the total length of it's boundary.

A triangle has three sides.

Length of the boundary of the triangle is the sum of the lengths of it's sides.

If the length of sides of a triangle are a, b and c,

Perimeter = a + b + c

If the triangle is equilateral,

Perimeter = 3a, since all the sides are equal.

Hence the perimeter of the triangle is the sum of the length of the boundary of it.

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The amount of money he will have after paying these bills each month is $2002.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The health insurance plan he selected has an average monthly premium of $297 .

The average monthly cost of his electric bill is $281.

The phone/internet/cable package he wants costs an average of $220 each month.

The monthly salary is $2800.

Now,

Total cost.

= 297 + 281 + 220

= 798

Now,

The amount remaining.

= 2800 - 798

= $2002

Thus,

The amount of money he will have is $2002.

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The solution to the equation [tex] {6}^{(4x - 3)} = - 4[/tex] is x = 0.3019.

To solve the equation [tex]{6}^{(4x - 3)} = - 4[/tex], we need to isolate the variable x. Here are the steps to solve this equation:

First, we need to take the logarithm base 6 of both sides of the equation. This will help us to isolate the exponent.

log6 [tex]{6}^{(4x - 3)}[/tex]= log6 -4

Use the logarithmic property that [tex] log(b) {b}^{x} = x[/tex] to simplify the left-hand side.

4x - 3 = log6 -4

Use a logarithmic table or calculator to find the value of the right-hand side.

4x - 3 = log6 -4

4x - 3 = -1.7924

Finally, we can isolate the variable x by adding 3 to both sides of the equation and then dividing both sides by 4.

4x = 3 - 1.7924

4x = 1.2076

x = 1.2076 ÷ 4

x = 0.3019

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Answer:

yes

Step-by-step explanation:

All the reasoning of the statement is given below.

CA ≅ CB, by the congruent triangles.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given:

CD bisects AB at D.

CD⊥AB

To prove: CA ≅ CB:

Statement 2:

AD ≅ BD

Reason 2:

Definition of segment bisector.

Statement 3:

CD ⊥ AB

Reason 3:

Given.

Statement 6:

CD ≅ CD.

Reason 6:

Reflexive property of congruence.

Statement 7:

ΔCAB ≅ ΔCBD

Reason 7:

Congruent by the criterion SAS.

Therefore, CA ≅ CB.

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