what is lim x->3 x^2+x-12/x^2-3x

0
7/3
4
DNE

The volume V of solid S is e - 1 cubic unit.

What is Volume?

Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.

To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)

The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)

Therefore, the volume V of solid S can be calculated as:

\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)

To evaluate this integral, we can simplify the expression:

\(V = \int_{e}^{\infty} \ln(x) dx\)

Using integration by parts, we let \(u = \ln(x)\)and dv = dx:

\(du = \frac{1}{x} dx\\v = x\)

Applying the integration by parts formula:

\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)

Evaluating the definite integral:

\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)

Therefore, the volume V of solid S is e - 1 cubic unit.

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Suppose A is a 3×7 matrix. The given 3 x 7 matrix, A, can be written as [a_1, a_2, a_3, a_4, a_5, a_6, a_7], where a_i is the ith column of the matrix. So, A is a 3 x 7 matrix i.e., it has 3 rows and 7 columns.

Thus, the matrix equation is Ax = 0 where x is a 7 x 1 column matrix. Let B be the matrix obtained by augmenting A with the 3 x 1 zero matrix on the right-hand side. Hence, the augmented matrix B would be: B = [A | 0] => [a_1, a_2, a_3, a_4, a_5, a_6, a_7 | 0]We can reduce the matrix B to row echelon form by using elementary row operations on the rows of B. In row echelon form, the matrix B will have leading 1’s on the diagonal elements of the left-most nonzero entries in each row. In addition, all entries below each leading 1 will be zero.Suppose k rows of the matrix B are non-zero. Then, the last three rows of B are all zero.

This implies that there are (3 - k) leading 1’s in the left-most nonzero entries of the first (k - 1) rows of B. Since there are 7 columns in A, and each row can have at most one leading 1 in its left-most nonzero entries, it follows that (k - 1) ≤ 7, or k ≤ 8.This means that the matrix B has at most 8 non-zero rows. If the matrix B has fewer than 8 non-zero rows, then the system Ax = 0 has infinitely many solutions, i.e., a solution space of dimension > 0. If the matrix B has exactly 8 non-zero rows, then it can be transformed into row-reduced echelon form which will have at most 8 leading 1’s. In this case, the system Ax = 0 will have either one unique solution or a solution space of dimension > 0.Thus, there are either an infinite set of solutions or exactly one solution for the homogeneous system Ax = 0.Answer: An infinite set of solutions.

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Answer:

10

Step-by-step explanation:

The sum of the tens would be 6 + 4, or 10; in the actual addition we'd write the "0" and carry the "1" to the hundreds column.

Answer:

Step-by-step explanation:

You want the translation that maps f(x) = x² to g(x) = x² -6x +6.

A graph of the two functions shows g(x) is right 3 units and down 3 units from f(x).

We know the vertex of f(x) = x² is the origin (0, 0). The vertex of g(x) will tell us the translation. Putting that function in vertex form, we have ...

  g(x) = x² -6x +6

  g(x) = (x² -6x) +6

  g(x) = (x² -6x +9) +6 -9 . . . . . add and subtract 9 to complete the square

  g(x) = (x -3)² -3

Compare this to ...

  y = (x -h)² +k . . . . . . has vertex (h, k)

We see that (h, k) = (3, -3).

g(x) is translated right 3 units and down 3 units.

Yes, the slant shear test is a common method used to evaluate the bond strength of resinous repair materials to concrete.

In this test, cylinder specimens are used, which are made by bonding two identical halves at a 30° angle to each other. The specimen is then placed in a testing machine, and a shear force is applied to the bonded area until the specimen fails. The maximum force that the specimen can withstand before failure is recorded, and this value is used to determine the bond strength of the repair material.

The slant shear test is a widely accepted method because it is relatively easy to perform and provides accurate results. It is also useful for determining the effectiveness of different types of repair materials and adhesives, and for evaluating the durability of the bond over time.

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Answer: d. No, because the study was not taken from a random sample of scholarship athletes.

Step-by-step explanation:

Since the study only focuses on basketball players, the sample may not be representative of all scholarship athletes in the university. This can cause bias in the results and make it difficult to generalize the findings to the larger population of scholarship athletes. Therefore, the university administration should not fully trust the results of this study.

Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees

The value of k for the given expression is, 2.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 8 (k + 10) = 48k

Now, We can solve the expression for k as;

⇒ 8 (k + 10) = 48k

Divide by 8,

⇒ k + 10 = 48k/8

⇒ k + 10 = 6k

Subtract k,

⇒ 10 = 6k - k

⇒ 10 = 5k

⇒ 5k = 10

Divide by 5;

⇒ k = 10/5

⇒ k = 2

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The function can be expressed as y = f(g(x)) = (x^2 − 7x + 9)^4, where u = x^2 − 7x + 9 is the inside function and y = u^4 is the outside function.

For the given function y = (x^2 − 7x + 9)^4, the inside function is u = g(x) = x^2 − 7x + 9, and the outside function is y = f(u) = u^4.

Therefore, we have:

u = x^2 − 7x + 9

y = u^4

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Answer:

The sum has to be 180°, so: 2x-9+2x-6+x=180

you can solve it: 5x-15=180

x-3=36

x=36+3

x=39

so the angles are:

x=39

2x-9=2*39-9=69

2x-6=2*39-6=72

Answer:

Either circle will do since they are the same size. If you already know the radius, you can move on. If you don't know the radius, then you can use a ruler to measure the widest part of the circle and then divide it by 2. This will be more accurate than trying to measure half of the diameter. Let's say that the radius of this cylinder is 1 inch (2.5 cm). Write it down.

Step-by-step explanation:

The relationship would be the volume of a cylinder is 3 times the volume of a refraction cup.

A cylindrical shape is a three-dimensional geometrical shape consisting of two parallel circular bases which are connected by some height h.

Part A: To find the volume of a cylinder, we need the dimensions of the cylinder such as the radius of the base of the cylinder and the height of the cylinder.

Part B: We have given the base of the refraction cup as a half-circle, we can calculate the radius of the base.

The diameter is given as 8 cm so, the radius would be half of the diameter.

r = 4cm

Part C:  If you put two refraction cups together, we get the full three-dimensional shape that is a circle.

Part D: The formula for the volume of a cylinder is V=pi r^2 h.

\(V=\pi r^2 h\\V=3.14\times4^2\times 2\\V = 100.48\)

Part E: The volume of a refraction cup = \(4/3\pi r^{3}\)

= 4/3 (3.14)(8)

= 33.49

Part F: The relationship between the value D and the value from Part D is as follows

The volume of a cylinder = 3 times the volume of a refraction cup

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Between Method A with a MAD(Mean Absolute Deviation) of 1.4 and Method B with a MAD (Mean Absolute Deviation) of 1.8, Method A performed better as it has a smaller MAD value.

To decide which estimating strategy performed the leading, we got to compare their Mean Absolute Deviation (Mad) values. Mad may be a degree of the average outright contrast between the genuine values and the forecasted values.

A little Mad esteem shows distant better; a much better; a higher; stronger; an improved" an improved forecasting accuracy, because it implies the forecasted values are closer to the real values.

Hence, between Strategy A with a Mad of 1.4 and Strategy B with a Mad of 1.8, Strategy A performed way better because it incorporates littler Mad esteem.

Be that as it may, it's vital to note that Mad alone does not allow a total picture of the determining execution. Other measurements, such as Mean Squared Blunder (MSE) or Mean Supreme Rate Blunder (MAPE) ought to too be considered to assess the exactness of the estimating strategies.

Furthermore, the setting and reason for the determining ought to too be taken under consideration when choosing the fitting estimating strategy. 

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Graphs can be used to represent functions, and vice verse

(a) The values of f(-7), f(0), f(4) and f(9)

Hence, the values of f(-7), f(0), f(4) and f(9) are -6, 3, 1 and -4, respectively.

(b) The number of values of the x at f(x) = 5

At f(x) =5, the values of x are -10, 1 and 3.

Hence, f(x) = 5 illustrate three values of x

(c) The y-intercept

This is the point where the graph crosses the y-axis, i.e. when x = 0.

Hence, the y-intercept is 3

(d) The maximum and the minimum values of the graph

The highest point on the graph is (2.5,5.5), while the least point is (-7,-6)

Hence, the maximum and the minimum values of the graph are 5.5 and 6, respectively.

(e) Why the graph represents a function

It represents a function because it passes the vertical line test.

This in other words means that, each x value has exactly one y value

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The Least Common Multiplier of \($q(2-4), r(-6-8), s(-102), t(-26)$\) is \($-9282 q r s t$\).

What is Least Common Multiplier ?

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

Lowest Common Multiplier (LCM)

The LCM of a, b is the smallest multiplier that is divisible by both a and b

Factor \($q(2-4): \quad-2 q$\)

Factor \($r(-6-8): \quad-2 \cdot 7 r$\)

Factor \($s(-102): \quad-17 \cdot 2 \cdot 3 s$\)

Factor \($t(-26): \quad-13 \cdot 2 t$\)

Multiply each factor with the highest power:

\($$-13 \cdot 17 \cdot 2 \cdot 3 \cdot 7 \cdot q \cdot r \cdot s \cdot t$$\)

Simplify

\($-9282 q r s t$\)

Complete question: Find the Least Common Multiplier  of Q(2, -4), R(-6, -8), S(-10, 2), T(-2, 6) is:

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Answer:

308

Step-by-step explanation:

this is the answer right

The correct inequality to find the value of t is: 15 x 3t > 3000.

Let the number of days it takes for the number of people who have liked the video to reach more than 3,000 be t. According to the given statement, The number of people who like a particular video online triples every day after the day the video is posted.

If 15 people like the video on the day it is posted, then the total number of likes the next day is 3 x 15, i.e. 45 (3 times the number of people who like the video).

Therefore, the number of likes increases exponentially by a factor of 3 every day. So, we can write the number of likes in t days as 15 x 3t

To find t such that the number of people who have liked the video reaches more than 3,000, we can use the following inequality: 15 x 3t > 3000

We can simplify the above inequality as follows: 15 x 3t > 3000⇒ 3t > 200⇒ t > log3 200⇒ t > 5.7 (approx)

Therefore, it takes 6 days for the number of people who have liked the video to reach more than 3,000.

The correct inequality to find the value of t is: 15 x 3t > 3000.

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The given position vectors u, v, and w are coplanar. The equation of the plane containing them is -5x - 10y + 5z = 0.



To determine coplanarity, we need to check if the three vectors u, v, and w lie on the same plane. We can do this by computing the scalar triple product. If it equals zero, the vectors are coplanar.

[u, v, w] = u · (v x w) = (2i - j - k) · ((4i + 3j + 2k) x (6i + 7j + 5k)) = 0.

Since the scalar triple product is zero, the vectors u, v, and w are coplanar. To find the equation of the plane, we use two of the vectors (let's use u and v) as direction vectors, and their cross product as the normal vector.

Normal vector n = u x v = (2i - j - k) x (4i + 3j + 2k) = -5i - 10j + 5k.

Therefore, the equation of the plane containing the vectors is -5x - 10y + 5z + d = 0. To find d, we substitute a point on the plane (such as the origin) and solve for d. The equation of the plane is -5x - 10y + 5z + 0 = 0, which simplifies to -5x - 10y + 5z = 0.

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Answer:

There are no solutions

Step-by-step explanation:

We are given the system of inequalities:

y ≥ 3x + 1

y ≤ 3x - 3

The regions of each inequality are shown in the graph. The blue-shaded region is the solution to the first inequality and the red-shaded region is the solution to the second inequality.

If a solution for the system existed, it should be a common region of both individual solutions. Since both lines have the same slope (3) and the solutions have no intersection, the system of inequalities has no solution.

Answer: There are no solutions

Answer:

yv1dzybazu ai zai is zie

Step-by-step explanation:

side zue auebaiw ai was wiz

Answer:

below

Step-by-step explanation:

a. A mile is approximately 1.609 kilometers

b. There are aproximately 0.621 miles in a kilometer

Answer:

2,8 and -2,-8 this us answer maybe

Answer:

B

Step-by-step explanation:

8 = 1/2x2
16 = x2

4 = x (square root)
-4=x

To find the mean and standard deviation of the corrected pH measurements, we can use the following formulas:

Corrected Mean = (Original Mean + Correction Factor) * Multiplication Factor

Corrected Standard Deviation = Original Standard Deviation * Multiplication Factor

The correction factor is 0.3 and the multiplication factor is 1.4. Therefore, the corrected mean is:

Corrected Mean = (4.8 + 0.3) * 1.4 = 7.14

And the corrected standard deviation is:

Corrected Standard Deviation = 1.2 * 1.4 = 1.68

Therefore, the mean of the corrected pH measurements is 7.14 and the standard deviation is 1.68.

In summary, to find the corrected mean and standard deviation of the pH measurements, we need to add the correction factor (0.3) to the original mean, multiply the result by the multiplication factor (1.4), and multiply the original standard deviation by the multiplication factor. The corrected mean is 7.14 and the corrected standard deviation is 1.68.

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Answer:

15 x 8 x 11 x 17 = 22440

We have a segment AB, of which we know the coordinates of one endpoint A=(-2,-8) and the midpoint M=(2,-7).

We can relate the x and y coordinates of the endpoints and the midpoints as:

The coordinates of the midpoints are the average of the coordinates of the endpoints.

As we know the coordinates of A and M, we can calculate the coordinates of B as:

Answer: the coordinates of B are (6, -6)

Step-by-step explanation:

step 1. slope intercept form: y = mx + b

step 2. m (slope) = (4 - 5)/(3 - 0) = -1/3.

step 3. Pick one of the points: (0, 5).

step 4. b is 5, the y intercept.

step 5. y = (-1/3)x + 5.

Answer:

1166.4

Step-by-step explanation:

Assuming this is the whole question, you multiply the weight of a single box by the amount in a case to find the weight of a case, hence 24.3*48 =1166.4

1 box of cereal = 24.3

48 boxes of cereal = 24.3 × 48

48 boxes of cereal:-

=> 24.3 × 48

=> 1166.4

Therefore, 48 boxes of cereal weighs 1166.4

The cost price of the furniture is 2400 Ghana cedis, representing the original price before the 25% profit was added.

To find the cost price of the furniture, we need to work backward from the selling price. The selling price is given as 3000 Ghana cedis, which includes a 25% profit.

Let's assume the cost price is represented by 'x'. Adding a 25% profit to the cost price gives us 1.25x.

We know that the selling price is 3000 Ghana cedis, so we can set up the equation 1.25x = 3000 and solve for x.

Dividing both sides of the equation by 1.25, we find x = 3000 / 1.25 = 2400.

Therefore, the cost price of the furniture is 2400 Ghana cedis. This means that the furniture was originally purchased for 2400 cedis before the 25% profit was added.

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Answer:

(8+8)=16 + (5x3)=15

Step-by-step explanation:

so 16+15=31 all you have to do is parenthesis first then do whatever is in the middle last