In (x-1)² = 3
This is a natural logarithm please help !

The integral ∫x/√(x²+1) dx is equal to  √(x² + 1) + C where c is the constant of integration.

To evaluate the integral ∫x/√(x²+1) dx, we can use a substitution.

Let's let u = x² + 1.

Then, differentiating both sides with respect to x:

we have du = 2x dx, which implies that dx = du/(2x).

Substituting these values into the integral, we get:

∫x/√(x²+1) dx = ∫(x/(2x)) × (1/√(x²+1)) du

= (1/2) ∫(1/√u) du

= u^(1/2) + C.

Finally, substituting back u = x² + 1, we obtain:

∫x/√(x²+1) dx = √(x² + 1) + C,

where C represents the constant of integration.

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The expanded form of (x + 2)⁷ is x⁷ + 14x⁶ + 84x⁵+ 280x⁴ + 560x³ + 672x² + 448x + 128 by binomial theorem.

To expand the expression (x + 2)⁷ using the binomial theorem, you can follow these steps:

Determine the coefficients of the terms in the expansion.

The coefficients can be found using the binomial coefficient formula:

nCr = n! / (r! × (n-r)!), where n is the exponent of the binomial and r is the power of the variable in each term.

In this case, n = 7, and the terms will range from x⁷ to 2⁷.

(x + 2)⁷ = 1x⁷ + 7x⁶2¹+ 21x⁵2² + 35x⁴2³ + 35x³2⁴ + 21x²2⁵ + 7x¹2⁶ + 12⁷

(x + 2)⁷ = x⁷ + 14x⁶ + 84x⁵+ 280x⁴ + 560x³ + 672x² + 448x + 128

Therefore, the expanded form of (x + 2)⁷ is x⁷ + 14x⁶ + 84x⁵+ 280x⁴ + 560x³ + 672x² + 448x + 128

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Collective security is a system formed to maintain peace among nations in which participant members agree that a military attack on one is an attack on all and will result in a united response by all members.

option A.

Collective security can be understood as a security arrangement, political, regional, or global, in which each state in the system accepts that the security of one is the concern of all, and therefore commits to a collective response to threats to, and breaches of peace.

So the concept of collective security replaces the one of military alliances between States, which prevailed until World War II, to ensure the collective defense of a State by its allies in case of aggression by another State.

Thus, Collective security is a system formed to maintain peace among nations in which participant members agree that a military attack on one is an attack on all and will result in a united response by all members.

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Answer:

to compare -2.3 and -8/3, we need to put them in the same form. We can convert -8/3 to a decimal by dividing -8 by 3, which gives us -2.66667.

Now we can see that -2.3 is greater than -2.66667, so we can write -2.3 > -8/3.

Step-by-step explanation:

Don't worry I can help.

Mathmetics isn't easy. so study

Answer:

160

Step-by-step explanation:

We Know

200 is added to 5 times a certain number the result is 1000

Find the number.

Let x represent the unknown number; we have the equation

200 + 5x = 1000

5x = 800

x = 160

So, the unknown number is 160

The weight of 200 ceramic ball bearings is approximately 26 ounces.

To calculate the weight of 200 ceramic ball bearings, we need to find the weight of a single ball bearing and then multiply it by the number of ball bearings.

The volume of a single ball bearing can be calculated using the formula for the volume of a sphere: V = (4/3) * π * r^3, where r is the radius.

For a ball bearing with a radius of 0.25 inch, the volume is V = (4/3) * 3.14 * (0.25)^3 = 0.0654 cubic inches.

Since 1 cubic inch of ceramic weighs 2 ounces, the weight of a single ball bearing is 0.0654 * 2 = 0.1308 ounces.

To find the weight of 200 ball bearings, we multiply the weight of a single bearing by the number of ball bearings: 0.1308 * 200 = 26.16 ounces.

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Answer:

y = 7

Step-by-step explanation:

The tiny marks on all three sides show that all three sides of the triangle are the same. This means also that all three angles of the triangle are also equal to each other. The triangle is equilateral as well as equiangular.

Anyway, all the angles are the same so we can write an equation.

8y+4+8y+4+8y+4=180

see end of explanation for solving this equation (or not)

OR since all the angles are the same each one is 60° (bc 60+60+60=180)

So 8y + 4 = 60

this equation is easier to solve.

8y + 4 = 60

subtract 4

8y = 56

divide by 8

y = 7

8y+4+8y+4+8y+4 =180

combine like terms

24y + 12 = 180

subtract 12

24y = 168

divide by 24

y = 7

To the nearest tenth of a foot, the base of the pole is approximately 9.2 feet from the house, corresponding to option 9.2 feet.

To find the distance from the base of the pole to the house, we can use the trigonometric function sine (sin). Since we know the angle between the pole and the ground is 50 degrees, we can use the formula:

sin(∠) = opposite/hypotenuse

In this case, the opposite side is the distance we are trying to find (base of the pole from the house) and the hypotenuse is the length of the pole, which is given as 12 feet.

sin(50°) = opposite/12

We can rearrange the equation to solve for the opposite side:

opposite = 12 * sin(50°)Using a calculator to evaluate the sine of 50 degrees, we find:

opposite ≈ 9.162 feet

Among the given options, the measurement closest to the value of the opposite side is 9.2 feet. Option 9.2 feet is the closest value.

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The simplified expression is: -2x - 4x^2 + 2.

simplify the given expression, 3(x-2x^2) + (x-2)(2x-1).

First, let's distribute the 3 into the first set of parentheses: 3x - 6x^2. Now, let's apply the distributive property to the second set of parentheses: (x-2)(2x-1) becomes 2x^2 - x - 4x + 2, which simplifies to 2x^2 - 5x + 2.

Now, combine the simplified expressions: (3x - 6x^2) + (2x^2 - 5x + 2). Add the corresponding terms: (3x - 5x) + (-6x^2 + 2x^2) + 2. This results in -2x - 4x^2 + 2.
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Answer:

  B  (see below)

Step-by-step explanation:

You want the graph that shows the system of equations ...

All of the graph choices correctly show the first equation.

Perhaps the graph is most easily chosen by rewriting the second equation to slope-intercept form. We can do that by adding (y-2) to both sides of the equation:

  y = 4x -2

This tells us the graph of 4x -y = 2 will have a positive slope and a y-intercept of -2. The attached graph meets those requirements.

__

Additional comment

The correct graph is the second from the left in this problem statement. We know that sometimes attachments submitted to Brainly are presented right to left, so we cannot say for certain it is selection B. We expect you will match the appearance, and not go by the letter alone.

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Answer: I'm sure its  A.=60 B=15 and C=i dont really know sorry

Step-by-step explanation:A - 6x10 B - 5x3 C - ?

PLEASE GIVE BRAINLIEST <33

Answers:

1: 245.04

A=2πrh+2πr2=2·π·3·10+2·π·32≈245.04423

2: 150.8

Formula: 2r² + 2rh

2 x 3 x 3 + 2 + 3 x 5 = 150.796447372

Rounded: 150.8

3: 892

Sides(Front & Back) #1: 17 x 4 x 2 = 136

Sides(Side) #2: 18 x 4 x 2 = 144

Bases(Bottom & Top): 17 x 18 x 2 = 612

The speed of the spaceship is 62.8 meters per second.

We can define speed as the quotient between distance and time.

Remember that the length of an arc of an angle x, in a circle of radius R is:

L = (x/360°)*2*π*R²

Where π = 3.14

Here we know that the time is 5 seconds, and the distance is the lengt of an arc of 90° in a circle of 200 meters, the length of that arc is:

L = (90°/360°)*2*3.14*200m = 314 meters.

Then the speed of the spaceship is given by:

S = 314m/5s = 62.8 meters per second.

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The vertex of the graph is (0,-2); minimum value.

Given that;

The graph of the quadratic function.

Now, We need to determine the vertex of the graph and also determine whether it is a minimum or maximum value.

Vertex:

The vertex of the parabola is the point at which the parabola makes a turn to form a U - shaped graph.

Hence, from the figure, the parabola turns at the point (- 1, 1) to form a U - shaped graph.

Therefore, the vertex of the graph is (- 1, 1)

Minimum or maximum value:

When the parabola is open upwards, then the vertex is the lowest point on the graph which is the minimum value on the graph.

Thus, the graph has a minimum value.

Hence, the vertex of the graph is (0,-2); minimum value.

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The values for P and a that will cause the function f(x) = Pa^x to be an exponential growth function are:

C. P = 4; a = 5

D. P = 1; a = 4

An exponential growth function is characterized by the property that the base (a) of the exponential term is greater than 1 (a > 1). This is because the exponentiation of a number greater than 1 by increasing values of x leads to exponential growth.

Therefore, the values for P and a that will cause the function f(x) = Pa^x to be an exponential growth function are:

C. P = 4; a = 5

D. P = 1; a = 4

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The BR is the perpendicular bisector of AC by CPCTC (corresponding parts of congruent triangles are congruent).

Based on the given information that angles ABR and ACR are right angles, and AB = AC, we can conclude that triangles ABR and ACR are right triangles.

Using the shared hypotenuse AR and the reflexive property, we can determine that side AB is congruent to side AC.

With this information, the transitive property allows us to conclude that angle BAR is congruent to angle CAR. Next, using the HL congruence postulate, we can prove that triangle ABR is congruent to triangle ACR.

This means that side BR is congruent to side CR, and angle BAC is bisected by line segment BR by the definition of bisector.

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The measure of angle ∠4 in the parallelogram is 33.5°.

Since, A parallelogram is a four-sided flat shape with opposite sides that are parallel and equal in length. This means that the opposite sides run parallel to each other, and the opposite angles are equal in measure.

Parallelograms can have various shapes and sizes, but they all share the same properties of having parallel opposite sides and angles. Some examples of parallelograms include rectangles, squares, and rhombuses.

We knw that,

The sum of the two adjacent angles of the parallelogram is 180°.

Hence, The measure of an angle ∠4 is,

∠4 = (180 - 113 ) / 2

∠4 = 33.5°

Therefore, the angle will be 33.5°.

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The equation of the line passing through the points (-4, 2) and (-2, 1) is y = (-1/2)x.

To find the equation of a line passing through two points, we can use the point-slope form of a linear equation, which is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

Given the points (-4, 2) and (-2, 1), we can calculate the slope (m) using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the values:

m = (1 - 2) / (-2 - (-4))

= (-1) / (2)

= -1/2

Now, we can choose one of the points, let's say (-4, 2), and substitute its coordinates along with the slope into the point-slope form:

y - 2 = (-1/2)(x - (-4))

Simplifying further:

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

Distributing (-1/2) to (x + 4):

y - 2 = (-1/2)x - 2

Adding 2 to both sides to isolate y:

y = (-1/2)x

Therefore, the equation of the line passing through the points (-4, 2) and (-2, 1) is y = (-1/2)x.

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It will take 20 weeks for Raymond and Beth's libraries to have the same number of books.

To determine the number of weeks it will take for Raymond and Beth's libraries to contain the same number of books, we need to set up an equation based on their book acquisition rates.

Let's assume the number of weeks it takes for their libraries to have the same number of books is 'x'. Raymond starts with 10 books and adds 2 books per week, so his total number of books after 'x' weeks is 10 + 2x. Similarly, Beth starts with 30 books and adds 1 book per week, resulting in a total of 30 + x books after 'x' weeks.

Since we want their libraries to contain the same number of books, we can set up the equation: 10 + 2x = 30 + x.

Simplifying the equation, we subtract 'x' from both sides: x = 30 - 10.

Therefore, x = 20.

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Make sure your formatting is clear and easy to understand. Remember, it’s all about helping others understand the answer.

nation:

In a given year, for each oil change the owner gets, the amount spent on repairs. decreases by 99 dollars Option B

To complete the statement about the slope of the line of best fit, we need to examine the coefficient of the x-term in the equation y = -99x + 725. The coefficient of x, which is -99, represents the slope of the line.

In general, the slope of a line indicates the rate of change between two variables. In this case, the x-axis represents the number of oil changes per year, and the y-axis represents the cost of repairs per year. The slope of -99 tells us how the cost of repairs changes with respect to the number of oil changes.

The negative sign in front of the slope (-99) indicates that there is a negative relationship between the number of oil changes and the cost of repairs. This means that as the number of oil changes per year increases, the cost of repairs decreases.

So, to complete the statement, we can say that in a given year, for each oil change the owner gets, the amount spent on repairs decreases by $99.

Therefore, the correct response is B) decreases by 99 dollars.

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The value of the missing length is 5.3

To determine the missing sides, we need to know the Pythagorean theorem, we have;

The Pythagorean theorem states that the square of the longest side of a triangle is equal to the sum of the squares of the other two sides of the triangle.

From the information given, we have that;

1.

8² = 6² + x²

find the squares, we have;

64 = 36 + x²

collect like terms

x² = 28

x = 5. 3 units

2. 8² = 6² + y²

find the squares

y² = 28

y = √28

find the square root

y = 5.3 units

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The diameter of the washing machine which is equivalent to the wavelength using the graph above would be = 2.5in.

To calculate the diameter of the washing machine drum, the formula that should be used is given below as follows;

V = fλ

where

V = displacement/time

F = 1/T

But;

Displacement = 10 in

Time = 2 seconds

V = 10/2 = 5 in/s

F = 1/2 = 0.5

λ = 5/0.5 = 2.5in

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Answer:

[tex]\frac{4}{5}[/tex]

0.8

Step-by-step explanation:

Happy to help:)

The electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

In the analogy of a circuit with resistance, we can compare it to an obstacle race. Here's how we can relate the different elements:

Circuit: The entire obstacle race course represents the circuit itself. It includes all the components and paths that the participants will go through.

Obstacles: The obstacles in the race represent the resistors in the circuit. Just like resistors impede the flow of electrical current in a circuit, obstacles in the race impede the progress of the participants.

People/Participants: The people participating in the race represent the flow of electric current in the circuit. They are the "charge" moving through the circuit, encountering and overcoming obstacles (resistors) to reach the finish line.

The goal of the participants (people) is to navigate through the obstacles (resistors) and complete the race (circuit) by reaching the finish line.

Similarly, in an electrical circuit, the goal is for the electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

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The difference between the sprinting and jogging of Carla is 3 1/6 laps.

The difference between the sprinting and jogging of Carla is calculated as follows;

The total distance sprinted = 9 1/6 laps

The total distance jogged = 6 laps

To find the difference between the sprinting and jogging, we will convert the mixed fraction into improper fraction as follows;

9 1/6 laps = 55/6 laps = 9.167 laps

The difference between the sprinting and jogging of Carla is;

= 9.167 laps - 6 laps

= 3.167 laps = 3 1/6 laps

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The initial Value of the function is 332.The rate of change of the function is -5%.

In the given function f(x) = 332(0.95)^t, where t represents time, we can determine the initial value and the rate of change as a percent.

1. Initial Value:

The initial value refers to the value of the function when the independent variable (t) is equal to zero. In this case, when t = 0, the function becomes:

f(0) = 332(0.95)^0

f(0) = 332(1)

f(0) = 332

Therefore, the initial value of the function is 332.

2. Rate of Change as a Percent:

The rate of change represents how the function changes over time. In this case, the function is an exponential decay function because the base (0.95) is less than 1.

To determine the rate of change as a percent, we can look at the exponent of the base (0.95). In the given function, the exponent is represented by the variable t. The base (0.95) is multiplied by itself t times.

The rate of change is calculated by subtracting 1 from the base and multiplying by 100% to express it as a percentage. In this case:

Rate of Change = (0.95 - 1) * 100%

Rate of Change = (-0.05) * 100%

Rate of Change = -5%

Therefore, the rate of change of the function is -5% (exponential decay).

- The initial value of the function is 332.

- The rate of change of the function is -5% (exponential decay).

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