Log3+log9+log27+log81+...... Question: how many terms of the section log2187?

The midsegment is equal to the average of the lengths of the bases, so:

Where:

and

Therefore:

Answer:

x+1/3

Step-by-step explanation:

Add the terms together (3x+1), then divide by how many terms there are (3), to get the average of the expressions

Answer:

a real number is a value of a continuous quantity that can represent a distance along a line

Step-by-step explanation:

Answer:  6

Step-by-step explanation:

You can find the scale factor by comparing a side that is similar from each

AB is similar to PQ

2.4/2 = 1.2

Your scale factor is 1.2.  So each of the sides was multiplied by 1.2

EDx1.2 = x

x= 5(1.2)

x= 6

To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

to know more about  magnitude and direction here:

brainly.com/question/1447482

#SPJ11

Answer:

729 : 9 = 80 +1 is correct

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

For such more question on variable

https://brainly.com/question/28248724

#SPJ8

Hello

See attachment.

CB² = AC² + AB²

CB² = 6² + 5²

CB² = 61

CB = √61ù

CB = DE = √61

CE² = CD² + DE²

DC² = CE² - DE²

DC² = 8² - (√61)²

DC² = 64 - 61

DC² = 3

DC = √3

x = √3

Answer:

x=5

Step-by-step explanation:

2x−7=−3x+18

Step 1: Add 3x to both sides.

2x−7+3x=−3x+18+3x

5x−7=18

Step 2: Add 7 to both sides.

5x−7+7=18+7

5x=25

Step 3: Divide both sides by 5.

5x

5

=

25

5

x=5

Answer:

x = 5

Step-by-step explanation:

2x - 7 = -3x + 18

2x - 7 + 7 = -3x  + 18 + 7

2x = -3x + 25

2x + 3x = -3x + 25 + 3x

5x = 25

x = 5

The required measures of the angles of parallelogram ABCD as are follows m∠A = 66°,  m∠B = 114°, and m∠C = 66°.

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given parallelogram ABCD,

m∠D = 114°

In a parallelogram, the opposite angles are congruent, so m∠A is congruent to m∠C. This means that m∠A and m∠C have the same measure.

If m∠D = 114°, then m∠A must be equal to 180° - 114° = 66°, since the measures of the adjacent angles of a parallelogram add up to 180°.

So, m∠A = m∠C = 66°

So, m∠B = 114°

Learn more about parallelograms here:

brainly.com/question/11220936

#SPJ1

Answer:25. Do better bro that’s sad

Step-by-step explanation:

Answer:

One ticket is 25 dollars

Step-by-step explanation:

Let T be tickets

$100 = 4T

\(\frac{100}{4} = \frac{4}{4}T\)

$25 = T

Therefore, one ticket is equal to 25 dollars

Using the Fundamental Counting Theorem, the number of possible sequences of eight coin faces is of 256.

It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

In this problem, there are 8 events, each with 2 possible outcomes, hence:

\(n_1 = n_2 = \cdots = n_8 = 2\)

Hence, the total number of sequences is given by:

\(N = 2^8 = 256\).

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

#SPJ1

Answer:

C) 256

Step-by-step explanation:

Essentially, each coin flip is a decision, and heads or tails is the choice offered. Therefore, we calculate that there are 28 possible sequences, or 256.

Took the quiz ;)

Answer:

900 ft

Step-by-step explanation:

I if 1 centimeter equals 3 ft and the dimensions are 10 cm by 10 cm then the real dimensions are 30 ft by 30 ft and that is 900 ft.

55/63 is already in its simplified form.

To simplify 55/63, we can divide both the numerator and denominator by their greatest common factor (GCF). To find the GCF of 55 and 63, we can use prime factorization:

55 = 5 × 11

63 = 3 × 3 × 7

The common factors of 55 and 63 are 1, so the GCF is 1. We can divide both the numerator and denominator by 1:

55/1/63/1

Therefore, 55/63 in simplest form is 55/63.

Learn more about Simplification here:

https://brainly.com/question/28996879

#SPJ

The angle of depression of the power line making with ground and  connected to the top of building is 48.18°.

Given, A power line is connecting the top of a building to the ground 160 meters away from the base of the building.

we are asked to determine at what angle is the wire connected at the building (building and wire angle), if the wire is 240 meters long.

The length of the wire connected to the top of building = h = 240 meters

The distance of the power line away from base of building = x = 160 meters

Let The angle of depression = Ф

now, cos angle = base/hypotenuse

cosФ = OA/Ob

or cosФ = x/h

or cosФ = 160/240

or cosФ = 2/3

therefore, Ф = cos⁻¹(2/3)

so, Ф = 48.18°

So the angle of depression from the ground = Ф = 48.18°

Learn more about Angle of depression here:

brainly.com/question/17193804

#SPJ9

Answer:

k = 0

k = - \(\frac{9}{7}\)

Step-by-step Explanation

Quadratic Equation​:

7\(k^{2}\)=9k = 0

a = 7

b = 9

c = 0

k =  \(\frac{-9+-\sqrt{9^{2}-4x7x0 } }{2x7}\)

Simplify:

k = \(\frac{-9+-9}{14}\)

Separate Equations:

k = \(\frac{-9+9}{14}\)

k = \(\frac{-9-9}{14}\)

Solve:

k = 0

k = - \(\frac{9}{7}\)

Answer:Para preparar la tabla de frecuencia para un histograma, es necesario primero establecer el número de intervalos que se desea tener.

Luego, se debe determinar el ancho común de los intervalos (interval width). Para esto, se calcula la diferencia del dato mayor y el dato menor, y se divide entre el número de intervalos deseados. Este resultado se redondea al entero mayor más cercano.

Por ejemplo, si se desea tener 10 intervalos y encontramos que el dato mayor es 35 y el menor es 12,

Step-by-step explanation:

Answer:

Mexico's total score was 49

The overall average was 7

Step-by-step explanation:

7.5+6.4+9.1+5.4+5.4+6.2+9.0=49

49/7=7

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

To know more about Maclaurin series:

https://brainly.com/question/31745715

#SPJ4

Answer:

Step-by-step explanation:

12C = 36

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

We have: SM = TM ( because M is the midpoint )

So: x + 12 = 8x - 2

=> x - 8x = -2 - 12

=> -7x = -14

=> x = (-14) / (-7) = 2

Answer: x = 2

Ok done. Thank to me :>

Answer:

Always in the range zero to one

Step-by-step explanation:

Option c is the answer

The tangent point of line 2x+3y=-20 is (-7, -1).

To find the point of tangency, determine the intersection point of the line 2x + 3y = -20 and the circle centered at (-3, 4).

The point of tangency will lie on the line that is perpendicular to the tangent line and passes through the center of the circle.

The slope of the given line is -2/3, so the slope of the line that is perpendicular to it is 3/2:

y - 4 = (3/2)(x + 3)

y - 4 = (3/2)x + 9/2

y = (3/2)x + 17/2

Substitute this expression for y into the equation of the tangent line and solve for x:

2x + 3y = -20

2x + 3[(3/2)x + 17/2] = -20

2x + (9/2)x + 51/2 = -20

(13/2)x = -91/2

x = -7

Substituting this value of x into the equation of the line:

y = (3/2)x + 17/2 = (3/2)(-7) + 17/2 = -1

Therefore, the point of tangency is (-7, -1).

Find out more on tangent point here: https://brainly.com/question/4470346

#SPJ1

Using the laws of logarithms, we can write:

ln[(x – 4)^38 (3x – 8)^34] = 38 ln(x – 4) + 34 ln(3x – 8)

This expression is now a sum of two logarithmic expressions which do not contain the logarithms of products, quotients, or powers.

To evaluate the derivative of ln[(x – 4)^38 (3x – 8)^34], we can use the chain rule and the fact that the derivative of ln(u) is du/u. Therefore:

d/dx ln[(x – 4)^38 (3x – 8)^34]

= d/dx [38 ln(x – 4) + 34 ln(3x – 8)]

= 38 d/dx ln(x – 4) + 34 d/dx ln(3x – 8)

= 38 * 1/(x - 4) + 34 * 3/(3x - 8)

= 38/(x - 4) + 102/(3x - 8)

= 100(3x - 32)/(x - 4)(3x - 8)

Therefore, the derivative of ln[(x – 4)^38 (3x – 8)^34] is 100(3x - 32)/(x - 4)(3x - 8).

For more questions like logarithms, visit the link below:

https://brainly.com/question/29087402

#SPJ11

When the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.

The rate at which the area of a triangle changes can be found by multiplying the rate at which the base is shrinking by the rate at which the height is increasing.

Given:

Rate of shrinking of the base = -2 cm/min

Rate of increasing of the height = 3 cm/min

Height of the triangle = 38 cm

Base of the triangle = 32 cm

To find the rate at which the area of the triangle changes, we use the formula for the area of a triangle:

Area = (1/2) * base * height

Differentiating the area formula with respect to time gives us:

dA/dt = (1/2) * (db/dt) * height + (1/2) * base * (dh/dt)

Substituting the given values, we have:

dA/dt = (1/2) * (-2) * 38 + (1/2) * 32 * 3

Simplifying, we get:

dA/dt = -38 + 48

dA/dt = 10 cm²/min

Therefore, when the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.

To know more about triangle refer here:

https://brainly.com/question/2773823

#SPJ11

The percent notation is 55%.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentage is %. In order to convert a fraction to percentage notation, multiply by 100.

Percent notation = fraction that attended the wedding x 100

= 11/20 x 100 = 55%

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.

To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example

If x = 0, then y = 0/2 = 0, so the first point is (0,0).

If x = 2, then y = 2/2 = 1, so the second point is (2,1).

If x = 4, then y = 4/2 = 2, so the third point is (4,2).

If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).

We can plot these points on a coordinate plane

As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.

Learn more about coordinates plane here

brainly.com/question/24134413

#SPJ4

Answer: A

Step-by-step explanation:

If he increases the amount then the less time it will take to pay the loan

Answer:

I think the answer is option d