Solve the equation.
a/4 − 5/6= −1/2

\(To find the point on the sphere \(x^2 + y^2 + z^2 = 1936\) that is farthest from the point \((-16,5,17)\), we need to follow the given steps.\)

S\(tep 1: Determine the center of the sphere since the equation of the sphere is given as \(x^2 + y^2 + z^2 = 1936\), the center of the sphere is (0, 0, 0).\)

Step 2: Find the equation of the line joining the center of the sphere to the given point

\(The equation of the line joining the center of the sphere to the given point \((-16, 5, 17)\) is given as:\[\frac{x-0}{-16-0}=\frac{y-0}{5-0}=\frac{z-0}{17-0}\]which simplifies to:\[\frac{x}{16}=\frac{y}{5}=\frac{z}{17}=-\lambda\]\)

\(Step 3: Find the point on the sphere at which this line intersects the sphere.

Substitute \(\frac{x}{16}=\frac{y}{5}=\frac{z}{17}=-\lambda\) in the equation of the sphere:\[\left(\frac{-16\lambda}{1}\right)^2+\left(\frac{5\lambda}{1}\right)^2+\left(\frac{17\lambda}{1}\right)^2=1936\]\)

\(Solving this equation, we get:\[\lambda = \pm \frac{44}{\sqrt{1190}}\]So, the two intersection points are:\[\left(\frac{-16\left(\frac{44}{\sqrt{1190}}\right)}{1}, \frac{5\left(\frac{44}{\sqrt{1190}}\right)}{1}, \frac{17\left(\frac{44}{\sqrt{1190}}\right)}{1}\right) \approx (-14.04, 4.34, 14.82)\]and\[\left(\frac{-16\left(-\frac{44}{\sqrt{1190}}\right)}{1}, \frac{5\left(-\frac{44}{\sqrt{1190}}\right)}{1}, \frac{17\left(-\frac{44}{\sqrt{1190}}\right)}{1}\right) \approx (18.04, -5.59, -19.82)\]\)

Step 4: Choose the point which is farthest from the given point of \( (-16,5,17) \).

To determine the point on the sphere that is farthest from the point \((-16, 5, 17)\), we need to find the distance between the two points obtained above and \((-16, 5, 17)\).

\(Using the distance formula, we get the distance between these points and the given point:\[d_1 = \sqrt{(-14.04 + 16)^2 + (4.34 - 5)^2 + (14.82 - 17)^2} \approx 29.52\]and\[d_2 = \sqrt{(18.04 + 16)^2 + (-5.59 - 5)^2 + (-19.82 - 17)^2} \\)\(approx 67.84\]Since \(d_2\) is greater than \(d_1\), the point \((-14.04, 4.34, 14.82)\) on the sphere is farthest from the point \((-16, 5, 17)\).\)

\(Therefore, the point on the sphere \(x^2 + y^2 + z^2 = 1936\) that is farthest from the point \((-16, 5, 17)\) is \((-14.04, 4.34, 14.82)\).\)

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The two points on the sphere that are farthest from ((-16, 5, 17)) are:

\(\((\sqrt{1936 - (44)^2}, 0, 44) \approx (0, 0, 44)\)\) and

\(\((-\sqrt{1936 - (44)^2}, 0, -44) \approx (0, 0, -44)\)\).

To find the point on the sphere (x^2 + y^2 + z^2 = 1936) that is farthest from the point ((-16, 5, 17)), we need to find the point on the sphere that maximizes the distance between the two points.

Let's denote the point on the sphere as ((x, y, z)). The distance between this point and ((-16, 5, 17)) can be calculated using the distance formula:

\(\(d = \sqrt{(x - (-16))^2 + (y - 5)^2 + (z - 17)^2}\)\).

We want to maximize this distance while still satisfying the equation of the sphere, (x^2 + y^2 + z^2 = 1936).

To simplify the problem, we can maximize the square of the distance, \(d^2\), instead of the actual distance. This will give us the same result while avoiding square roots.

(d^2 = (x + 16)^2 + (y - 5)^2 + (z - 17)^2).

To find the farthest point on the sphere, we need to maximize (d^2) subject to the constraint (x^2 + y^2 + z^2 = 1936).

This problem can be solved using Lagrange multipliers. We can define the Lagrangian function:

\(\(L(x, y, z, \lambda) = (x + 16)^2 + (y - 5)^2 + (z - 17)^2 - \lambda(x^2 + y^2 + z^2 - 1936)\).\)

Taking the partial derivatives and setting them to zero

\(\(\frac{\partial L}{\partial x} = 2(x + 16) - 2\lambda x = 0\),\)

\(\(\frac{\partial L}{\partial y} = 2(y - 5) - 2\lambda y = 0\),\)

\(\(\frac{\partial L}{\partial z} = 2(z - 17) - 2\lambda z = 0\),\)

\(\(\frac{\partial L}{\partial \lambda} = -(x^2 + y^2 + z^2 - 1936) = 0\).\)

Simplifying these equations:

\(\(x + 16 - \lambda x = 0\),\)

\(\(y - 5 - \lambda y = 0\),\)

\(\(z - 17 - \lambda z = 0\),\)

\(\(x^2 + y^2 + z^2 = 1936\).\)

From the first three equations, we can factor out \(x\), \(y\), and \(z\):

\(\(x(1 - \lambda) + 16 = 0\),\)

\(\(y(1 - \lambda) - 5 = 0\),\)

\(\(z(1 - \lambda) - 17 = 0\).\)

This implies that either (x = 0), (y = 0), (z = 0), or \(\(\lambda = 1\)\).

If (x = 0), then from the fourth equation (y^2 + z^2 = 1936), we can solve for (y) and (z):

\($\(y = \pm \sqrt{1936 - z^2}\).\)

If (y = 0), then from the fourth equation (x^2 + z^2 = 1936), we can solve for (x) and (z):

\(\(x = \pm \sqrt{1936 - z^2}\)\)

If (z = 0), then from the fourth equation (x^2 + y^2 = 1936), we can solve for (x) and (y):

\(\(x = \pm \sqrt{1936 - y^2}\)\)

If \(\(\lambda = 1\)\), then from the first three equations, we have:

\(\(x + 16 - x = 0 \implies 16 = 0\)\) (which is not possible),

\(\(y - 5 - y = 0 \implies -5 = 0\)\) (which is not possible),

\(\(z - 17 - z = 0 \implies -17 = 0\)\) (which is not possible).

Therefore, we are left with the cases when \($\(x = \pm \sqrt{1936 - z^2}\)\ or\ \(y = \pm \sqrt{1936 - z^2}\)\).

Substituting these values back into the equation of the sphere

(x^2 + y^2 + z^2 = 1936), we can solve for (z).

(x^2 + y^2 + z^2 = 1936) becomes:

\(\(\left(\sqrt{1936 - z^2}\right)^2 + y^2 + z^2 = 1936\)\) or

\(\(\left(-\sqrt{1936 - z^2}\right)^2 + y^2 + z^2 = 1936\)\).

Simplifying:

(1936 - z^2 + y^2 + z^2 = 1936) or

(1936 - z^2 + y^2 + z^2 = 1936).

From these equations, we can conclude that (y^2 = 0). Therefore,

(y = 0).

Now, substituting (y = 0) into the equation \(\(x = \pm \sqrt{1936 - z^2}\)\), we get:

\(\(x = \pm \sqrt{1936 - z^2}\)\)

So, the points on the sphere that are farthest from ((-16, 5, 17)) are given by\(\((x, y, z) = (\pm \sqrt{1936 - z^2}, 0, z)\)\).

To determine the value of (z), we can substitute the equation of the sphere (x^2 + y^2 + z^2 = 1936) into the equation of the farthest point:

\(\((\pm \sqrt{1936 - z^2})^2 + 0 + z^2 = 1936\)\).

Simplifying:

(1936 - z^2 + z^2 = 1936) or

(1936 - z^2 + z^2 = 1936).

From these equations, we can conclude that \(\(z = \pm 44\)\).

So, the two points on the sphere that are farthest from ((-16, 5, 17)) are:

\(\((\sqrt{1936 - (44)^2}, 0, 44) \approx (0, 0, 44)\)\) and

\(\((-\sqrt{1936 - (44)^2}, 0, -44) \approx (0, 0, -44)\)\).

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Answer:

Choice C: 40 degrees

Explanation:

Because the given figure is a parallelogram, it contains two pairs of equal angles

Answer:

40 degrees

Step-by-step explanation:

Answer: 15.3feet

Step-by-step explanation: Given the scale model of a train as;2cm = 3feet

We are to find the height of real train of height 10.2cm, we can write; 10.2cm = xDivide both expressions

2/10.2 = 3/x2x = 3×10.22x = 30.6x= 15.3

Hence the height if the real train is 15.3feet

The real height of the real train will be;

⇒ 15.3 feet

What is Measurement unit?

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

Jalen has a scale model of a train. 2 centimeters in the represents 3 feet in real train.

Now,

Since, Jalen has a scale model of a train. 2 centimeters in the represents 3 feet in real train.

And, The height of the model train is 10.2 centimeters.

Hence, In the scale model;

1 centimeter = 3/2 feet

Thus, We get;

10.2 centimeters = 10.2 × 3/2 feet

                          = 5.1 × 3 feet

                          = 15.3 feet

Therefore, The real height of the real train will be;

⇒ 15.3 feet

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Answer:

the answer is 81,920 I hope this helps you!!

Answer: The answer is 3

Step-by-step explanation: 1+1+1=3

To solve problems, construct one-variable equations and inequalities.

As opposed to an inequality, which links two different values, an equation declares that two expressions are equal.

Create one-variable equations and inequalities, then utilize them to solve issues.

Include simple rational and exponential equations as well as those resulting from linear and quadratic functions.

In order to answer word problems, students should be able to decipher them and create equations and inequalities.

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The best approximation of the solution to the system is (-2, 7).

Here's how I arrived at the solution using substitution method:

Given the system of linear equations:

3x - 4y = -32

3x + 5y = 24

We'll solve for x in equation 1 and substitute the result into equation 2:

3x - 4y = -32

x = (-32 + 4y) / 3

Substituting this expression of x into equation 2:

3((-32 + 4y) / 3) + 5y = 24

-32 + 4y + 15y = 24 * 3

13y = 24 * 3 + 32

13y = 96

y = 7.38

Rounding the value of y to the nearest integer, we get y = 7.

Substituting y = 7 back into the expression for x:

x = (-32 + 4 * 7) / 3

x = (-32 + 28) / 3

x = -4 / 3

Rounding the value of x to the nearest integer, we get x = -2.

Therefore, the best approximation of the solution to the system of linear equations is (-2, 7).

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Answer:

60 +70+8x+2 = 180 by aum of the angles of triangle is 180 degree

Answer:

gago isipin mo, wag puro brainly hahaha

Answer: 2 pairs of parallel sides!

Step-by-step explanation:

The reciprocal of \(A^m\)  is \(1/A^m.\)

This means that\(A^{-m\) is equivalent to\(1/A^m.\)

The correct answer is\((a) 1/a^m.\)

To understand why, let's break down the expression \(A^{-m}.\)

In mathematics, a negative exponent indicates the reciprocal or inverse of the base raised to the positive exponent.

In this case, \(A^{-m\) can be rewritten as \(1/A^m.\)

The reciprocal of a number is obtained by flipping the fraction or raising it to the power of -1.

So,\(1/A^m\) means the reciprocal of\(A^m.\)

To further simplify, we can rewrite \(A^m\) as \((A^m)^1,\) using the property of raising a power to another power.

Now, by applying the power of a product rule, we have \(A^{(m \times 1)},\) which simplifies to\(A^m\).

Therefore, the reciprocal of \(A^m\) is \(1/A^m\).

This means that \(A^{-m }\) is equivalent to \(1/A^m.\)

The correct answer is (a) \(1/a^m.\)

In summary, the correct answer is (a)\(1/a^m\)for \(A^{-m}.\)  

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the area of the surface that corresponds to the part of the plane 13x + 5y + z = 65 lying in the first octant is 32.5 square units.

To find the area of the surface that corresponds to the part of the plane 13x + 5y + z = 65 lying in the first octant, we need to find the equation of the portion of the plane that lies in the first octant and then calculate the surface area of that portion.

First, we need to find the intercepts of the plane with the x, y, and z-axes. Setting x = 0, we get:

5y + z = 65

Setting y = 0, we get:

13x + z = 65

Setting z = 0, we get:

13x + 5y = 65

Solving these three equations simultaneously, we get:

x = 5, y = 13, z = 0

So the plane intersects the x-axis at (5,0,0), the y-axis at (0,13,0), and the z-axis at (0,0,65).

The part of the plane that lies in the first octant is bounded by the x-axis, the y-axis, and the line connecting (5,0,0) and (0,13,0). This triangular region has a base of length 5 and a height of 13, so its area is (1/2)513 = 32.5.

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A string of length 6 can be formed using the symbols from the alphabet {A,B,C,D,E,F}, such that the string begins with either A, E, or F and ends in D in the following ways: There are 3 ways to select the first symbol (A, E, or F) of the string.

There are 6 ways to select the second symbol of the string (since any of the six symbols can be chosen at this point). There are 6 ways to select the third symbol of the string (since any of the six symbols can be chosen at this point). There are 6 ways to select the fourth symbol of the string (since any of the six symbols can be chosen at this point). There are 6 ways to select the fifth symbol of the string (since any of the six symbols can be chosen at this point).

There is only 1 way to select the sixth symbol (since it has to be D).Hence, the total number of ways to form the string of length 6 using the symbols from the alphabet {A,B,C,D,E,F}, such that the string begins with either A, E, or F and ends in \(D is 3⋅6⋅6⋅6⋅6⋅1 = 3⋅6⁴ = 3⋅1296 = 3888.\) , the correct option is (a) 3⋅6⁴.

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If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find (f/g)(x), we need to divide f(x) by g(x) as follows:

f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2

f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)

To simplify this expression, we can factor the numerator and denominator:

f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]

Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:

f(x) / g(x) = (x - 3) / (x + 2)

Therefore, (f/g)(x) = (x - 3) / (x + 2).

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The increasing the difference between sample means will result in a larger t statistic. This means that the difference between the two sample means is more likely to be statistically significant and less likely to be due to chance.

the t statistic is calculated by taking the difference between the sample means and dividing it by the standard error of the difference. When the difference between sample means increases, the numerator of the t statistic increases, while the denominator (the standard error) remains relatively constant. This leads to a larger t statistic and a smaller p-value, indicating stronger evidence against the null hypothesis.

increasing the difference between sample means has a significant effect on the independent-measures t statistic. It increases the strength of the evidence against the null hypothesis, making it more likely that the difference between the two groups is real and not due to chance.

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Step-by-step explanation:

Given -:

One number is 25% more than another number

Sum of the two number = 135

Explanation -:

Let us assume the first number as x

Then,

Second number = x + 0.25

A. T. Q

x + x + 0.25 = 135

✎ 2x + 0.25 = 135

✎ 2x = 135 - 0.25

✎2x = 135 - 0.25

✎ 2x = 134.75

\( \small{✎x = \frac{134.75}{2} = 67.375} \)

First number = 67.375

Second number = x + 0.25

= 67.375 + 0.25

= 67.625

Check

67.375 + 67.625 = 135

Hence, verified

Answer:

d =90 e=52 f=52

Step-by-step explanation:

The angle that are crosppsinding have equal angle.

like f=e.

Answer:

Step-by-step explanation:

Remark

This is a regular pentagon. The information given is enough the find the area of 1 triangle. There are 5 such triangles. So find the area of 1 of the triangles. The answer will be 5 times as much.

Givens

b = 18.3

h = 12.6

Formula

1 triangle = 1/2 * b * h

5 such triangles = 5 times as much

Solution

Area(1_triangle) = 1/2 * 18.3 * 12.6

Area (1_triangle) = 115.29

Answer: 5 * 115.29

Answer: 576.45

Answer:

Step-by-step explanation:

-3x – 10 = 32 Help me I need the answer

-3x – 10 = 32

-3x = 32 + 10

-3x = 42

x = 42 :(-3)

x = - 14

-----------------

check

-3 × (-14) - 10 = 32                      (remember pemdas)

42 - 10 = 32

32 = 32

the answer is good

Answer:

k+15

Step-by-step explanation:

The word "increased" indicates that there will be addition and the word "product" indicates there will be multiplication. Since it's asking for the product of 5 and 3, we can solve by multiplying those two numbers to get 15. Our variable k will then add 15. So, the final answer we get is: k+15

False. let a be a real square matrix. if a is diagonalizable then a is symmetric

Explanation: Diagonalizability and symmetry are two different properties of a square matrix. A real square matrix A is diagonalizable if it can be transformed into a diagonal matrix D through a similarity transformation with an invertible matrix P, i.e., A = PDP^(-1). A matrix is symmetric if A = A^T, where A^T is the transpose of A.

While it is true that every symmetric matrix is diagonalizable, the converse is not necessarily true. In other words, not every diagonalizable matrix has to be symmetric.

Conclusion: The statement "if A is diagonalizable then A is symmetric" is false because diagonalizability does not guarantee symmetry.

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Answer:

Lines r and s are at an angle if you change the degrees a little bit like 2x 1.5o

Step-by-step explanation:

I dont rlly know im giving it a go!

Answer: 30

Step-by-step explanation:

100-70=30

Answer:

The correct graph is graph B.

Answer:

y = -16/7 x + 13/7

Step-by-step explanation:

The question asks to rewrite 16x + 7y = 13 into slope intercept form.

Slope intercept form is:

y = mx+b

M is the slope, b is the intercept.

We can first rearrange the equation:

Inital equation: 16x+7y = 13

Rearranged: 7y = -16x+13

Now we just have to divide 7 to both sides:

Therefore, the correct answer is y = -16/7 + 13/7

Answer:

35 seconds

Step-by-step explanation:

At negative values he is inside the volcano,  when he reaches 0 he will be at the top of the volcano

At 35 seconds, the elevation is 0, so he is at the top of the volcano

The Taylor series for f(x) = 1/x, centered at c=1, is:
1/(x-1) = Σ[n=0 to infinity] (-1)ⁿ * (x-1)ⁿ

The Taylor series for the function f(x) = 1/x centered at c = 1 using the definition of Taylor series. The Taylor series for a function f(x) is given by:

f(x) ≈ f(c) + f'(c)(x-c) + f''(c)(x-c)^2/2! + f'''(c)(x-c)^3/3! + ...

For f(x) = 1/x and c = 1, let's find the first few derivatives and their values at c = 1:

f(x) = 1/x
f'(x) = -1/x^2
f''(x) = 2/x^3
f'''(x) = -6/x^4

Now, evaluate them at c = 1:

f(1) = 1
f'(1) = -1
f''(1) = 2
f'''(1) = -6

Now we can plug these values into the Taylor series formula:

f(x) ≈ 1 - (x-1) + 2(x-1)^2/2! - 6(x-1)^3/3! + ...

Simplifying the expression, we get:

f(x) ≈ 1 - (x-1) + (x-1)^2 - (x-1)^3 + ...

This is the Taylor series for the function f(x) = 1/x centered at c = 1.

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A: (a) A = [0 1; -1 0]. This matrix has only real entries and when we square it, we get A² = [-1 0; 0 -1], which is equal to -I.

(b) B = [0 1; 0 0]. This matrix is not 0, but when we square it, we get B² = [0 0; 0 0], which is equal to 0.

(c) C = [0 1; -1 0] and D = [1 0; 0 -1]. When we multiply these two matrices, we get CD = [-1 0; 0 1] and DC = [0 -1; 1 0], which are opposite matrices.

(d) E = [1 1; 1 1] and F = [-1 1; 1 -1]. When we multiply these two matrices, we get EF = [0 0; 0 0], which is equal to 0, although no entries of E or F are zero.

Here is explanation -

(a) A = [[0, -1], [1, 0]] is a 2x2 matrix with real entries that satisfies A^2 = -I. To see this, we can simply calculate the square of the matrix A:

A^2 = [[0, -1], [1, 0]] * [[0, -1], [1, 0]]

= [[00 + -11, 0*-1 + -10], [10 + 01, 1-1 + 0*0]]

= [[-1, 0], [0, -1]]

As we can see, A^2 = -I, where I is the 2x2 identity matrix.

(b) B = [[0, 1], [0, 0]] is a 2x2 matrix with real entries that satisfies B^2 = 0, although B ≠ 0. To see this, we can calculate the square of the matrix B:

B^2 = [[0, 1], [0, 0]] * [[0, 1], [0, 0]]

= [[00 + 10, 01 + 10], [00 + 00, 01 + 00]]

= [[0, 0], [0, 0]]

As we can see, B^2 = 0, although B ≠ 0.

(c) C = [[0, 1], [-1, 0]] and D = [[0, -1], [1, 0]] are 2x2 matrices with real entries that satisfy CD = -DC. To see this, we can calculate the product of matrices C and D:

CD = [[0, 1], [-1, 0]] * [[0, -1], [1, 0]]

= [[00 + 10, 0*-1 + 11], [-10 + 01, -1-1 + 0*0]]

= [[0, 1], [1, 1]]

DC = [[0, -1], [1, 0]] * [[0, 1], [-1, 0]]

= [[00 - 11, 01 + -10], [10 - 0-1, 11 + 00]]

= [[-1, 0], [1, 1]]

As we can see, CD ≠ -DC, so C and D do not satisfy the condition CD = -DC, not allowing the case CD = 0.

(d) E = [[1, 1], [0, 1]] and F = [[1, 0], [1, 1]] are 2x2 matrices with real entries that satisfy EF = 0, although no entries of E or F are zero. To see this, we can calculate the product of matrices E and F:

EF = [[1, 1], [0, 1]] * [[1, 0], [1, 1]]

= [[11 + 10, 11 + 11], [01 + 10, 01 + 11]]

= [[1, 2], [0, 1]]

As we can see, EF = 0, although no entries of E or F are zero.

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The radius of convergence is 7 and the interval does not include x = -7, the interval of convergence is [ -7, 7 ).

The radius of convergence of the series ∑[infinity]n=1(−1)nxn7√n is R = 7.

To find the radius of convergence, we can use the ratio test:

lim[n→∞] |(−1)^(n+1) * x^(n+1)/(7√(n+1))| / |(−1)^n * x^n/(7√n)|

= lim[n→∞] |x/(7√(n+1))|

= 0 for any finite x.

Therefore, the series converges for all x within a distance of 7 from 0. In other words, the radius of convergence is 7.

To find the interval of convergence, I, we need to check the endpoints x = -7 and x = 7 separately.

When x = -7, the series becomes ∑[infinity]n=1 (1/n)^(1/2), which is a harmonic series that diverges. Therefore, x = -7 is not in the interval of convergence.

When x = 7, the series becomes ∑[infinity]n=1 (-1)^n / n^(1/2), which converges by the alternating series test. Therefore, x = 7 is included in the interval of convergence.

Since the radius of convergence is 7 and the interval does not include x = -7, the interval of convergence is [ -7, 7 ).

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