30,000,000÷2000 how many zeros are cancelled from each number in this equation?

Answer: −200y−125

Step-by-step explanation:

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

Learn more about integrations here:

https://brainly.com/question/30217024

#SPJ1

Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

The transformations that maps Figure Y onto Figure Z are given by:

A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

Another example of a transformation is a dilation, when the coordinates of the function are all multiplied by a constant, called scale factor. Due to the multiplication, after a dilation, the dilated figure is not congruent to the original figure, as they will have different side lengths.

For the dashed figure, we have that the coordinates of Y were all multiplied by 1/3, hence the first transformation is:

Dilation with a scale factor of 1/3.

Then for the dashed figure into Figure Z, the following rule is applied to each vertex:

(x,y) -> (x,-y).

Hence the second transformation is:

Reflection over the x-axis.

Due to the dilation, Figures Y and Z are not congruent.

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

360 - 169 equals 191

Step-by-step explanation:

191

Answer:

A = 92°

B = 100°

C = 88°

D = 80°

Step-by-step explanation:

Cyclic quadrilateral : a quadrilateral drawn inside (inscribed) a circle.

The opposite angles in a cyclic quadrilateral add up to 180°.

Therefore, A + C = 180° and B + D = 180°

If A + C = 180° , then

⇒ (x + 2) + (x - 2) = 180

⇒ x + 2 + x - 2 = 180

⇒ 2x = 180

⇒ x = 90°

Therefore,

A = x + 2 = 90 + 2 = 92°

C = x - 2 = 90 - 2 = 88°

D = x - 10 = 90 - 10 = 80°

B = 180 - D = 180 - 80 = 100°

Step-by-step explanation:

One possible equivalent equation to the given formula is:

uppercase B = 3 uppercase V ÷ h

To see why this equation is equivalent, we can isolate uppercase B in the original formula by multiplying both sides by 3/h:

3/h * uppercase V = 3/h * (one-third uppercase B h)

Simplifying the right-hand side:

3/h * (one-third uppercase B h) = uppercase B

Substituting back in the original formula gives:

uppercase B = 3/h * uppercase V

-4 is the value for s

Answer:

3.725 x 10^6 is the scientific notation

Answer:

There are many formations a group of 5 can make. Examples could be STS (Shoulder To Shoulder), single file, and double column with one leader. There are many more formations that could be made but these three would be the most acceptable line formations in a school environment.

Answer:

I think the ans is option 'a'

Final Answer:

Corresponding Angles Theorum; ∠AGF and ∠EHD are congruent

Answer:

translation

Step-by-step explanation:

To map Triangle DEF onto Triangle GHJ, a transformation is needed to be done.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent. Hence all the three sides and three angles are congruent.

Triangle D E F is shifted down and to the right to form triangle G H J.  Hence to map Triangle DEF onto Triangle GHJ, a transformation is needed to be done.

Find out more on Congruent triangles at: https://brainly.com/question/1675117

Answer:

haha same

Step-by-step explanation:

i think the answer is B

Answer:

hmm not so difficult

Step-by-step explanation:

I think it's B

Answer:

f^(-1)(x) = ±√(x - 5).

Step-by-step explanation:

Replace f(x) with y: y = x^2 + 5.

Swap the x and y variables: x = y^2 + 5.

Solve the equation for y. To do this, we'll rearrange the equation:

x - 5 = y^2.

Take the square root of both sides (considering both positive and negative square roots):

±√(x - 5) = y.

Swap y and x again to express the inverse function:

f^(-1)(x) = ±√(x - 5).

Answer: 207936 millimeters squared

Step-by-step explanation:

57 * 57 = 3249

3249 * 64 = 207936

Answer: 207936 millimeters^2

Step-by-step explanation: 57*57=3249

3249 64 times is 207936.

Answer:

21.5

Step-by-step explanation:

Answer:

2n - 7

Step-by-step explanation:

To get the sum you would combine like terms.

So:

n + n= 2n

7 + -14 = 7 - 14 = -7

Put it together:

2n - 7

Answer:

40+20=72-12

60=60

Step-by-step explanation:

4*10+4*5=6*12-6*2

40+20=72-12

60+60

The required vertex of the curve in the graph is (-3, 8).

A graph of a parabola is shown, and from the graph vertex of the curve is to be determined.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate the y is called ordinate.

here,
The peak of the graph is at the location of the ordered pair (-3, 8),
So, the vertex of the graph is also (-3, 8).

Thus, the required vertex of the curve in the graph is (-3, 8).

Learn more about coordinate here:

brainly.com/question/13498438

#SPJ1

Answer:

269.75

Hope this helps:)

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf r = 5}\)

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

\(\rule[225]{225}{2}\)

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

Answer:

Option 4

Step-by-step explanation:

Let any two real number a and b (no matter +ve, -ve or 0). a ≥ b

The average of them will always lie in between them or be equal(if 0).

Let's prove : According to the statement,

a ≥ (a + b)/2 ≥ b

2a ≥ a + b ≥ 2b

2a ≥ a + b and a + b ≥ 2b

a ≥ b and a ≥ b, as we assumed.

Moreover, as the average exists in between a and b, we have the average (a + b)/2. Similarly, there exists one more average of (a + b)/2 and a or b, which definitely lie between a and b as (a + b)/2 lies there and smaller than a and b.

In the same order, we can have many average and the process would stop. This leads to infinite number between a and b.

Notice that we talked about all the numbers moreover there are many irrational(non-terminating like 9.898989.... etc numbers as well.

Option (4), infinite solutions.

Note: we solved for all the number (not specifically odd, even, natural, whole, integer, etc).

Answer:

4x^2 - 12x + 9

Explanation:

(2x - 3)^2

(2x - 3)(2x - 3)

2x(2x - 3) -3 (2x - 3)

4x^2 - 6x - 3 (2x - 3)

4x^2 - 6x - 6x + 9

4x^2 - 12x + 9

Answer:

Write in standard form.

(x−6)2+(y−5)2=49

Answer:

Step-by-step explanation:

Answer: y = 3b

Step-by-step explanation:

Equation of given relationship model is y = 3b.

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Given,

∵ each blanket requires 3 skeins of yarn

∴ b blanket requires 3b skeins of yarn

Total number of skeins = y = 3b

Hence, y = 3b

Learn more about equation here:

brainly.com/question/10413253

#SPJ5

Answer:

Step-by-step explanation:

3:7 = ___: 49

3 : 7 = x : 49

x = 3 × 49 ÷ 7

x = 147 ÷ 7

x = 21

3 : 7 = 21 : 49  (your answer)

Answer:

first term (a)=-2

common difference (d)=8

Now,

87th term=a+(n-1)d

=-2+(87-1)×8

=-2+86×8

=-2+688

=686