Let R be the relation of the set of all differentiable functions defined f R g iff f and g have the same first derivative; that is f' = g'.

(a) Prove that R is an equivalence relation.

(b) Name three elements in the class 2x^3 + 5

a rectangle cause a can is a cylinder

The equation x^2 + y^2 + 12x + 4y + 15 = 0 represents a circle with center (-6, -2) and radius 5.

To find the center and radius of the circle represented by the equation x^2 + y^2 + 12x + 4y + 15 = 0, we need to complete the square for both x and y terms. First, we will focus on the x terms:

x^2 + 12x = (x + 6)^2 - 36

Next, we will focus on the y terms:

y^2 + 4y = (y + 2)^2 - 4

Substituting these into the original equation, we get:

(x + 6)^2 - 36 + (y + 2)^2 - 4 + 15 = 0

Simplifying, we get:

(x + 6)^2 + (y + 2)^2 = 25

Comparing this to the standard form of the equation of a circle, (x - h)^2 + (y - k)^2 = r^2, we can see that the center of the circle is (-6, -2) and the radius is √25 = 5..

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The pairings for the given arithmetic sequences are:

One easy way of identify which formula correspods to which sequence, is just identifying the common differences in the sequences in the left side.

The common difference appears clearly in the recursive formulas, so with that we can pair them.

To get the common difference of each sequence, just take the difference between two consecutive terms.

For the first one we have:

32 - 35 = -3

For the second sequence:

-23 - (-3) = -20

For the third one:

9 - 7 = 2

For the last one:

14 - 9 = 5

Then the pairings are:

First sequence → fourth formula.

Second sequence → third formula

Third sequence → second formula.

Fourth sequence → first formula.

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The value of t (the duration), we cannot determine the exact total change in elevation.

To determine the total change in the tram's elevation, we need to know the duration or time for which the tram moved upward at a rate of 3 meters per second. Without the time information, we cannot calculate the total change in elevation.

If we assume that the tram moved upward at a rate of 3 meters per second for a certain duration of time, we can use the formula:

Total change in elevation = Rate of change × Time

Let's say the tram moved upward at 3 meters per second for t seconds. The total change in elevation would then be:

Total change in elevation = 3 meters/second × t seconds

However, without knowing the value of t (the duration), we cannot determine the exact total change in elevation.

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The real square roots of 1/100 are ±1/10. To find them, take the square root of both sides of the equation x^2 = 1/100, simplify, and consider the positive values.

To find the real square roots of 1/100, we need to find the values of x that satisfy the equation x^2 = 1/100.

1. Take the square root of both sides of the equation:
√(x^2) = √(1/100)

2. Simplify:
|x| = 1/10

3. Since the square root of a number is always positive, we can conclude that the real square roots of 1/100 are ±1/10.

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Since the null hypothesis was rejected, we can conclude that there is enough evidence to suggest that the mean weight of adult German shepherd dogs is greater than 75 pounds.

However, we cannot conclusively state that the mean weight is exactly 75 pounds, only that it is likely greater than that value. The alternative hypothesis (Hi: μ > 75) supports this conclusion, indicating that the true mean weight is likely higher than the claimed value of 75 pounds.

It is important to note that further research and analysis may be necessary to determine a more precise estimate of the mean weight of adult German shepherds.

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Answer:

60 miles to km would be 0.06 kilometer.

Step-by-step explanation:

The fourth:

The second equation in system 2 is the difference of the equations in system 1. The first equation in system 2 is the first equation in system 1.

Ax + By - (Lx + My) = Ax + By - Lx - My = (A - L)x + (B - M)y

Answer:

The answer is __

because of __

Step-by-step explanation:

Answer:

\(\frac{\sqrt{170} }{7}\)

Step-by-step explanation:

Length = x

Width = 7x

Therefore 7x into x = 170, Rectangle area formula

7x^2=170

7x=root over 170

x = root over 170/ 7

Step-by-step explanation:

There are FOUR queens in a deck of 52 cards

4/52 chance of selecting a queen =  1/13  chance  = .07692 chance

The mean temperature in Cleveland, OH, was 64°F. The accumulated degree days for Cleveland on 6-7 September 2022 were 1. The rest of Ohio accumulated degree days during the same period.

Based on the given information, the maximum temperature in Cleveland was 70°F and the minimum temperature was 58°F. To find the mean temperature, we add the maximum and minimum temperatures and divide by 2: (70°F + 58°F) / 2 = 128°F / 2 = 64°F.

Degree days are a measure of heating or cooling requirements. In this case, since the mean temperature in Cleveland was lower than a certain base temperature, degree days were accumulated. The base temperature is typically set at 65°F for cooling and 55°F for heating. Since the mean temperature in Cleveland was below the base temperature, the accumulated degree days are heating degree days (HDD).

For the specific date of 6-7 September 2022, Cleveland accumulated 1 heating degree day (HDD). This means that the average temperature for that period was 1 degree below the base temperature of 55°F.

The remaining stations in Ohio also accumulated heating degree days (HDD) on 6-7 September 2022. This indicates that the temperatures across the rest of Ohio were below the base temperature during that period.

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Answer:

A)

Step-by-step explanation:

Answer:

I love your profile picture

The critical point (0,0) is A. asymptotically stable and is a C. center.

To solve the given system of differential equations, we can write it in matrix form:

X' = AX,

where X = [x, y] is the vector of unknowns, and A = [[-6, -5], [-5, -6]] is the coefficient matrix.

To find the particular solution satisfying the initial condition x(0) = 2, y(0) = -2, we can use the general solution:

X(t) = e^(At) * X(0),

where e^(At) represents the matrix exponential.

Calculating the matrix exponential for A, we find:

e^(At) = [[e^(-11t), -5e^(-11t)], [-5e^(-11t), e^(-11t)]].

Substituting t = 0 and X(0) = [2, -2], we get:

X(t) = e^(A*0) * [2, -2] = I * [2, -2] = [2, -2],

where I is the identity matrix.

Therefore, the particular solution is x = 2 and y = -2.

Based on the general solution, we can conclude the following statements:

The critical point (0,0) is A. asymptotically stable and is a C. center.

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\(\displaystyle\bf 4x^2+3=-7x\\\\4x^2+7x+3=0 \\D=49-48=1 \\\\x_{1;2}=\frac{-7\pm1}{8} => x_1=-1\quad ; \quad x_2=-\frac{3}{4} \\\\\\Answer:\boxed{x_1=-1\quad ; \quad x_2=-\frac{3}{4} }\)

Answer:

y=2x-8

Step-by-step explanation:

y=Mx+k

Plug in(3,-2)(6,4)

3m+k=-2

6m+k=4

First function multiply by 2,we got:

6m+2k=-4

6m+k=4

k=-8

Y=Mx-8

Plug in any points that is in the question, I use(6,4)

4=6m-8

m=2

Y=2x-8

Answer:

y = 2x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, - 2) and (x₂, y₂ ) = (6, 4)

m = \(\frac{4+2}{6-3}\) = \(\frac{6}{3}\) = 2, then

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (6, 4 ), then

4 = 12 + c ⇒ c = 4 - 12 = - 8

y = 2x - 8 ← equation of line

With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

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Answer:

20 inches

Step-by-step explanation:

A rectangular object can instead be thought about as two right triangles with the hypotenuse being the diagonal we are solving for.

With this in mind the Pythagorean Theorem can be used to solve for c

c^2=a^2+b^2

A=16 inches

B= 12 inches

C= hypotenuse

C^2=16^2+12^2

C^2=256+144

C^2=400

Take the square root of both sides: C = 20 inches

The eigenvector corresponding to the eigenvalue λ3 = -3 is:

v3 = [1 1 0] + (m + 3)(-2 -2 1) where m can take any real value.

To obtain the eigenvector corresponding to the eigenvalue λ3 = -3, we can use the fact that the matrix M is symmetric.

Let's denote the eigenvector corresponding to λ3 = -3 as v3 = [x y z].

To obtain v3, we can use the following equation:

M * v3 = λ3 * v3

Multiplying the matrix M with the vector v3, we have:

| a b c |   | x |   | -3x |

| b d e | * | y | = | -3y |

| c e f |   | z |   | -3z |

From the equation above, we can write a system of equations:

ax + by + cz = -3x

bx + dy + ez = -3y

cx + ey + fz = -3z

Since M is symmetric, we know that a = d, b = e, and c = f.

Let's denote these common values as m:

mx + by + cz = -3x

bx + my + bz = -3y

cx + by + mz = -3z

Now, we can substitute the values provided for v1 and v2:

m * 1 + b * (-1) + c * 0 = -3 * 1

b * 1 + m * (-1) + b * 0 = -3 * (-1)

c * 1 + b * (-1) + m * 0 = -3 * 0

Simplifying these equations:

m - b = -3

b - m = 3

c - b = 0

From the second equation, we can rewrite it as b = m + 3 and substitute it into the first equation:

m - (m + 3) = -3

m - m - 3 = -3

-3 = -3

The third equation shows that c = b, and since we found b = m + 3, we have c = m + 3.

Now, we can express the eigenvector v3 in terms of m:

v3 = [x y z] = [1 -1 0] = [1 1 0] + [-2 -2 0] = [1 1 0] + (m + 3)(-2 -2 1)

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Answer:

\(m=\frac{8}{5}\)

Step-by-step explanation:

Considering the vertices of quadrilateral ABCD following the Translation (x,y)→(x+4,y−2) and Translation: (x,y)→(x−1,y−4), the new points are

preimage        image           Image

A(2,3)                (6,1)             (5,-3)

B(6,−2)              (10,0)          (9,-4)

C(10,−1)             (14,-1)           (13,-3)

D(11,6)               (15,4)            (14,0)

Translation is a straight line movement as shown by the rule which is applied to determine the final position of the image

information from the question

Translation: (x,y) → (x+4,y−2)

Translation: (x,y) → (x−1,y−4)

Applying the rule

preimage   (x,y)→(x+4,y−2)     image     (x,y)→(x−1,y−4)   Image

A(2,3)        → (2+4,3−2)           (6,1)           →(6−1,1−4)        (5,-3)

B(6,−2)      →(6+4,-2−2)           (10,0)        →(10−1,0−4)      (9,-4)

C(10,−1)     →(10+4,-1−2)           (14,-1)        →(14−1,-1−4)      (13,-3)

D(11,6)       →(11+4,6−2)            (15,4)         →(15−1,4−4)      (14,0)

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Answer:

I believe the answer is 5c + 4.

Step-by-step explanation:

The first step in simplifying expressions like this is to combine the values with the same coefficient and rearrange them so that they are next to each other in the expression. When you do this, you also have to keep the operation that comes before it if possible. 8c + 6 -3c - 2 will be turned into 8c - 3c + 6 - 2. Now you can simplify the expression in different parts. 8c - 3c = 5c, and 6 - 2 = 4. Keep the addition operation in the middle and combine the numbers:

5c + 4.

A line is defined as the set of points that extends infinitely in both directions and has no thickness or width.

It can be represented by two points, and in three dimensions, it will have the values of x, y, and z, which are all non-zero.

However, a line in two dimensions will have the z value set to zero. In geometry, a line is described as a straight path that extends indefinitely in both directions without any width or thickness. It can be drawn between two points and is said to have length but not width or thickness.

Two points are sufficient to determine a line in a two-dimensional plane. However, in a three-dimensional space, a line will have three values, x, y, and z, which are all non-zero.

When we talk about a line in two dimensions, we refer to a line that is drawn on a plane. It is a straight path that extends infinitely in both directions and has no thickness.

A line in two dimensions has only two values, x and y, and the z value is set to zero.

This means that the line only exists on the plane and has no depth. A line in three dimensions has three values, x, y, and z.

These values represent the position of the line in space. The line extends infinitely in both directions and has no thickness. Because it exists in three dimensions, it has depth as well as length and width.

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Step-by-step explanation:

Answer:

Step-by-step explanation:

>> ▪︎ 3x-ax=2x+5 ▪︎<<

>> ▪︎ 3x-ax-2x=5 ▪︎<<

>> ▪︎x(3-2-a)=5 ▪︎<<

>> ▪︎x=5/1-a ▪︎<<

Using Mathematica, we can find the roots of the function y = x^3 Exp[-x] Sin[2x] by substituting x = 3t and evaluating the expression for t in the range [0,1]. The roots correspond to the values of t where the function crosses the x-axis.

To find the roots of the given function, we substitute x = 3t into the expression y = x^3 Exp[-x] Sin[2x]. This gives us y = (3t)^3 Exp[-3t] Sin[2(3t)]. Simplifying further, we have y = 27t^3 Exp[-3t] Sin[6t].

Using Mathematica, we can evaluate this expression for t values ranging from 0 to 1. The roots of the function correspond to the values of t where y equals zero, indicating that the function crosses the x-axis. By plotting the function or using numerical methods such as FindRoot or NSolve in Mathematica, we can determine the values of t where y = 0, thus finding the roots of the function.

In summary, by substituting x = 3t and evaluating the expression y = x^3 Exp[-x] Sin[2x] for t in the range [0,1] using Mathematica, we can find the roots of the function, which represent the values of t where the function crosses the x-axis.

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Answer:

\(f(t) = 7.23( {1.0114}^{t} )\)

t = 0 represents January 1, 2014

(a)

\(f(6) = 7.23( {1.0114}^{6} ) = 7.739\)

The population of the world is expected to be about 7.739 billion people on January 1, 2020.

(b)

\(7.23( {1.0114}^{t} ) = 10\)

\(t = about \: 28.61 \: years\)

The population of the world is expected to be 10 billion people in about 28.61 years after January 1, 2014 (sometime in August 2042).

The variation constant is y = 5/x.

When a variable y varies inversely as another variable x, the relationship can be expressed as y = k/x, where k is the variation constant.

In this case, we are given that y varies inversely as x, and y = 45 when x = 1/9. We can use this information to find the value of the variation constant k.

Substituting the given values into the equation, we have:

45 = k / (1/9).

To solve for k, we can multiply both sides of the equation by (1/9):

45 * (1/9) = k.

Simplifying the expression:

k = 5.

Therefore, the variation constant in this situation is k = 5.

To find the equation of variation, we substitute the value of k into the equation y = k/x:

y = 5/x.

Thus, the equation of variation for this situation is y = 5/x.

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The correct answer is D. Normal, with a center at mu and a standard deviation of sigma/√n. The correct answer is A. The standard deviation will be smaller, but the center will remain the same.

a) When the sample is randomly selected from a population that has a Normal distribution, the sampling distribution of the sample mean will also have a roughly Normal shape.

The population mean (mu) will serve as the sampling distribution's center, and the sampling distribution's standard deviation (sometimes referred to as the standard error) will be equal to the population standard deviation (sigma) divided by the square root of the sample size (n). The correct answer is D.

b) The sampling distribution's standard deviation (or standard error) diminishes as the sample size increases. This is so that the population mean can be estimated with more accuracy, which reduces the variability in the sample means. As long as the population as a whole doesn't change, the sample distribution's center (the population mean) will, however, stay the same. The correct answer is A.

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The complete question is:

A sample is chosen randomly from a population that can be described by a Normal model. Complete parts a and b below.

a) What's the sampling distribution model for the sample mean? Describe shape, center, and spread.

Choose the correct answer below.

A. Normal, with a center at a and a standard deviation of mu/root n.

B. Normal, with a center at sigma/ root n and a standard deviation of mu.

C. Normal, with a center at mu/ root n and a standard deviation of sigma.

D. Normal, with a center at mu and a standard deviation of sigma/ root n.

b) If a larger sample is chosen, what's the effect on this sampling distribution model?

A. The standard deviation will be smaller, but the center will remain the same.

B. The center will be smaller, but the standard deviation will remain the same.

C. The standard deviation will be larger, but the center will remain the same.

D. The center will be larger, but the standard deviation will remain the same.

Answer: 36.95

Step-by-step explanation:

Because its an equilateral triangle, each side is equal. We can split the equilateral into a 30-60-90 triangle. The base is x, the height is x\(\sqrt{3}\) and the hypotenuse is 2x.

32/\(\sqrt{3}\) = 18.4752086

So the height is equal to:

x = 18.4752086

18.4752086\(\sqrt{3}\)

Since the hypotenuse is 2x, we can calculate that with:

2x

= 2(18.4752086)

= 36.9504172

The length of each side is 36.95