Long division method square root of 5508409

The sum of the series correct to four decimal places is 7.0000

To approximate the sum of the series, we can use the ratio test. The ratio test states that if the limit of the ratio of consecutive terms approaches a number L, then the series converges if |L| < 1 and diverges if |L| > 1.

The nth term of the series is given by

[tex]T_n = (-1)^n (3n)(n!)[/tex]

The consecutive terms is

[tex]R_n = T_{n+1}/T_n = (-1)^{n+1} (3n+3)(n+1) / (-1)^n (3n)(n!) \\= (-1)^{n+1} * 3 * (n+1) / (n!)[/tex]

Taking the limit as n approaches infinity:

[tex]L = lim_{n - > \infty} \ R_n = lim_{n - > \infty} (-1)^{n+1} * 3 * (n+1) / (n!)[/tex]

Since [tex](-1)^{n+1}[/tex] alternates between -1 and 1, the limit approaches 0 and |L| < 1, which means the series converges.

To approximate the sum of the series, we can use a numerical method such as the Euler-Maclaurin formula. The formula approximates the sum of an infinite series by the sum of its first few terms and the remainder term:

[tex]\Sigma_n^\infty=1T_n \approx \Sigma_{i=1}^m T_i + R_m[/tex]

where [tex]R_m[/tex] is the remainder term that decreases as m increases

For example, let's choose m = 5:

[tex]\Sigma_{i=1}^5 T_i = T_1 + T_2 + T_3 + T_4 + T_5[/tex]

= -3! + (-1) * 3 * 2! + (-1) * 2 * 3 * 1! + (-1) * 3 * 4! + (-1) * 4 * 3 * 2! = -6 + 6 - 2 + 24 - 24 = -2

The remainder term [tex]R_m[/tex] can be estimated using the Euler-Maclaurin formula:

[tex]R_m = -B_{2m} / (2m)! * T_{m+1}[/tex]

where B_k are the Bernoulli numbers.

For [tex]m = 5, B_2m = B_{10} = -1/252[/tex], so

[tex]R_m = -B_{10} / (10)! * T_{m+1} = -1/252 * (-1)^6 * 3 * 6! = 1/252 * 3 * 720 = 9[/tex]

Therefore, the sum of the series is approximately

[tex]\Sigma_{i=1}^\Infty T_i \approx \Sigma_{i=1}^5 \ T_i + R_m \\= -2 + 9 = 7[/tex]

To four decimal places, this is 7.0000

To learn more about the Bernoulli numbers, visit:

brainly.com/question/14883116

#SPJ4

The new triangle has sides of 3m, 4m, and 5m as the attached picture below.

The new triangle has sides of 1/3 of the original. Then:

1/3 x 15 m = 5m

1/3 x 9 m = 3 m

1/3 x 12 m = 4 m

The new triangle is as the attached picture below

The perimeter of the original triangle is:

P original = 15 + 9 + 12

P original = 36 m

The perimeter of the new triangle is:

P new = 5 + 3 + 4

P new =  12 m

The area of the original triangle is:

Area original = 1/2 x 12 x 9

Area original = 54 m

The area of the new triangle is:

Area new = 1/2 x 4 x 3

Area new = 6

The relationship between both triangles' perimeter is:

P original : P new = 36 : 12

                             = 3 : 1 --> ratio of both triangles

Learn more about Triangles here: brainly.com/question/2773823

#SPJ1

Assuming 100 transactions, the investor will receive $1,000.

Explicación paso a paso:

The difference between the values of each action represents the gain or loss of each action; if this difference decreases, a loss would be apparent.

Gain = Increase in each action times the number of actions

Capital of the Acionista in Acciones = Cantidad of Acciones * Acción Value

If each share the investor purchased rises from $20 to $30

$30 - $20 = $10 profit per action

Assuming 100 transactions, the investor will receive $1,000.

100* $10 = $100

Know more about transactions

https://brainly.com/question/1016861

#SPJ4

The question is:

How much money would a shareholder with 100 shares make if each one grew in value from $20 to $30?

Similar to how a rectangle's area is calculated, a parallelogram's area is calculated as base times height.

The four sides of a parallelogram, a geometric shape made up of two pairs of parallel lines, are parallel. The opposite sides and angles of a parallelogram have equal lengths and measures.

By multiplying the base and altitude of a parallelogram, the area of the shape can be determined. A parallelogram's base and altitude are always parallel to one another. A parallelogram's area can be calculated using the following equation: Area of parallelogram = base height square units.

You can use the following formula to determine any parallelogram's area:

Area = base x height

It should be mentioned that a parallelogram requires a perpendicular base and height.

To learn more about  area formula for parallelograms refer to:

https://brainly.com/question/970600

#SPJ4

Answer:

r ≥2,  r<0

Step-by-step explanation:

1st blank:

1. Multiply both sides by 2

2. Simplify. 7r-20≥ -6

2nd blank:

1. multiply both sides by 2 to get (2(r+14))/2 < 7*2.

2. Simplify. You should get r+14 <14

3. Subtract 14 from both sides to isolate r.

4. Answer is r<0

The coordinates of E, the intersections of diagonals AC and BD is; B: (2, 2)

A parallelogram is simply defined as a quadrilateral with two pairs of parallel sides.

Now, the diagonals of a parallelogram usually intersect at their midpoints. Formula to find the midpoint of a line with coordinates is;

Midpoint = (x2 + x1)/2, (y2 + y1)/2

Thus;

Midpoint of AC = ((1 + 3)/2, (5 - 1)/2

= (2, 2)

Similarly,

Midpoint of BD = (6 - 2)/2, (3 + 1)/2

= (2, 2)

Read more about Diagonal Coordinates at; https://brainly.com/question/29297655

#SPJ1

In order to calculate the new divisor for a 3-for-4 reverse stock split, we must first calculate the new share price for Able. Since 3/4 of the shares are being replaced with just 1/4 of the old shares, the new price for Able will be $111 (3 x $37 = $111).

The divisor is used to calculate the new index value by dividing the sum of the new share prices by the divisor. Therefore, the new divisor will be 1.33 ($111 + $312 + $94 = $517 / 1.33 = $389.28). This is because the new share prices will total $517 and when you divide that by the divisor, the index value will be $389.28.

know more about divisor here

https://brainly.com/question/26086130#

#SPJ11

Many ways can 3 baseball players and 5 basketball players be selected from 12 baseball players and 12 basketball players are 173040 ways.

This is a combination problem, and we want to find the number of ways to choose 3 baseball players and 5 basketball players from a pool of 12 baseball players and 12 basketball players.

The formula for combinations is: C(n, k) = n! / (k! (n - k)!).

The total number of combinations is the product of the number of combinations for each group, so 220 * 792 = 173040.

Therefore, there are 173040 ways to choose 3 baseball players and 5 basketball players from a pool of 12 baseball players and 12 basketball players.

Here you can learn more about  a combination problem

brainly.com/question/29038612

#SPJ4

A. Suki typed 175/7 words per minute. B. It takes Suki 7/490 minutes per word.

A. To find the number of words per minute, we can divide the total number of words by the total time:

words per minute = 245 words / (3 1/2 minutes)

words per minute = 245 words / (7/2 minutes)

words per minute = 245 * 2 / 7 words/minute

words per minute = 175/7 words/minute

So, Suki typed 175/7 words per minute.

B. To find the number of minutes per word, we can divide the total time by the total number of words:

minutes per word = (3 1/2 minutes) / 245 words

minutes per word = (7/2 minutes) / 245 words

minutes per word = 7/2 * 1/245 minutes/word

minutes per word = 7/490 minutes/word

So, it takes Suki 7/490 minutes to type one word.

To learn more about words per minute please click on below link.

https://brainly.com/question/30313537

#SPJ4

3 1/2 minutes at 245 words per minute.

245 syllables per minute / 7 and a half minutes.

syllables per minute are calculated as 245 * 2/7.

175/7 words per minute is the word speed.

Suki's typing speed was 175/7 lines per minute.

hours per word equals (3 1/2 hours) / 245 words

syllables per minute = (7/2 minutes) / 245

minutes per word equals 7/2 * 0.245 minutes per word.

words/minute ≈ 7/490 minutes/word

The transformation of h(n) = 2(0.8)n from the original function, h(n) = 10(0.8)n, is a vertical compression.

Hence, option (a) is correct choice.

In a vertical compression, the graph of the transformed function is obtained by multiplying the y-coordinates of the points on the graph of the original function by a constant factor less than 1.

In this case, the factor is 2/10 = 1/5, which is less than 1, so the transformation is a vertical compression.

It is not a vertical stretch and reflection because the factor is less than 1, so it is not stretching the graph.

It is not a vertical stretch because the factor is less than 1, so it is not stretching the graph.

It is not a vertical compression and reflection because the factor is positive, so it is not reflecting the graph.

For more questions on vertical compression

https://brainly.com/question/10741387

#SPJ4

By using the ε-N approach, the value of the function is 2.71828.

The ε-N approach is a mathematical tool used to determine the limit of a function as the independent variable approaches infinity or zero.

In this problem, we are asked to guess the limit of

=> (7n³ +8n) / (2n³ - 31)

as n approaches infinity.

To do this, we need to use the ε-N approach. The first step is to make an educated guess about the limit.

Next, we use the ε-N approach to prove our guess is correct.

This involves finding an ε (epsilon) value, which is a small positive number, and an N value, which is the input value for n, such that for all n greater than N, the absolute value of the difference between the function and the limit is less than ε.

To use various symbols to denote the Epsilon values too because Epsilon has no interest in the meaning of its own like other mathematical symbols like π(pi) and it has the value 3.14.

Here the symbol e and has value 2.71828.

This means that the function is arbitrarily close to the limit.

To know more about ε-N approach here

https://brainly.com/question/18762687

#SPJ4

The sign of δsol for the solution will depend on the concentration of the solute and the temperature.

The sign of δsol for the solution will depend on two main factors: the concentration of the solute and the temperature. If the concentration of the solute is increased, the solute's tendency to dissolve in a solvent will also increase, resulting in a higher solubility. This increase in solubility will cause the sign of δsol to be positive. On the other hand, if the temperature is increased, the solubility of the solute will decrease, resulting in a decrease in the solubility. This decrease in solubility will cause the sign of δsol to be negative. Therefore, the sign of δsol for the solution will depend on the concentrations of the solute and the temperature. If the concentration of the solute is increasing, the sign of δsol will be positive; if the temperature is increasing, the sign of δsol will be negative.

Learn more about temperature here

https://brainly.com/question/29768169

#SPJ4

Answer: 7, 28, 112

Step-by-step explanation: The first three terms in the sequence can be found by using the formula an = 4an-1, starting with the initial value a1 = 7:

a2 = 4a1 = 4 * 7 = 28

a3 = 4a2 = 4 * 28 = 112

So, the first three terms in the sequence are 7, 28, 112.

Answer:

To find volume of rectangular prism you must find the length, width, and height!

Step-by-step explanation:

Volume = (Width) (height) (length)

Volume= Width x height x Length

you must multiple the length, width, and height together to get VOLUME:)

HOPE THIS HELPS :)

When finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation.

One approach to finding an antiderivative of a function is the method of guess and check. This involves making an educated guess for the antiderivative and then verifying it by taking the derivative of the guess and comparing it to the original function.

To find the antiderivative of f(x) = sin(x)cos(x), we can start with a guess based on the product rule for differentiation: d/dx (uv) = u * dv/dx + v * du/dx

Since f(x) = sin(x)cos(x), we can write: d/dx (sin(x)cos(x)) = cos^2(x) + sin^2(x) = 1

This suggests that the antiderivative of f(x) = sin(x)cos(x) might be: F(x) = sin(x)sin(x) + C, where C is an arbitrary constant of integration.

To check our guess, we need to take the derivative of F(x) and compare it to the original function f(x): d/dx (sin(x)sin(x) + C) = cos(x)sin(x)

If our guess is correct, the derivative of F(x) should equal f(x). However, in this case, our guess does not match the original function f(x), so we need to make another guess. A second guess could be:

F(x) = -cos(x)cos(x) + C

Taking the derivative: d/dx (-cos(x)cos(x) + C) = -sin(x)cos(x)

This time, the derivative of F(x) does match the original function f(x), so our guess is correct and the antiderivative of f(x) = sin(x)cos(x) is:

F(x) = -cos(x)cos(x) + C.

Thus, In conclusion, when finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation. By checking the derivative of the guess and comparing it to the original function, we can determine whether or not our guess is correct.

To learn more about antiderivative,

Visit; brainly.com/question/15522062

#SPJ4

The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Goran buys candy that costs $8 per pound. He will spend at least $56 on candy.

Let 'p' be the number of pounds of the candy. Then the inequality is given as,

8p ≤ 56

p ≤ 56 / 8

p ≤ 7

The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2- 2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is illustrated in the figure below.

b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.

b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:

∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy

Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:

∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

Learn more about integral here

https://brainly.com/question/18125359

#SPJ4

The combined like terms are -234.

Combining like terms means adding or subtracting any expressions that have the same variable. For example, in the expression:

The terms 2x and 3x have the same variable (x), so they can be combined to form 5x.

Similarly, in the expression:

The terms 4y and -7y have the same variable (y), so they can be combined to form -3y. The goal of combining like terms is to simplify expressions and make them easier to understand and manipulate.

In this case, the first two terms, 18 and -6, have no variable, so they can be combined to form 12. The next two terms, -155 and -91, also have no variable, so they can be combined to form -246. Finally, the combined terms, 12 and -246, can be combined to form -234. So, the final result is:

Learn more about combine like terms here: brainly.com/question/15894738

#SPJ4

Height is 63 inches, or 5 3 inches.

A measurement of distance or length in US units. A foot is 12 inches long and a yard is 36 inches long. 2.54 cm are exactly one inch.

A measurement of 1 inch is about equivalent to 2.54 cm. Add 2.54 cm to the provided inch number to convert it to centimetre values. 0.393701 inches are equal to 1 centimetre.

The smallest length you can measure with a ruler is 1/16 inch since each inch is divided into 16 lines, each of which is 1/16 inch long.

If you don't have a measuring device around, use the top of your thumb or another item that is roughly the same length to estimate measurements in inches. A foot is made up of 12 inches.

   = (5 x 12) + 3.

   = 60 +3

     = 63

   You now have 63 inches altogether.

To learn more about inches refer to:

https://brainly.com/question/21386205

#SPJ4

The derivative of f(z) = ez/(z − 7) is therefore f'(z) = (ez(z - 6))/(z - 7)^2.

The derivative of f(z) = ez/(z − 7) can be calculated using the quotient rule. The quotient rule states that the derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared. Therefore, the derivative of f(z) = ez/(z − 7) is equal to (ez(z - 7) - (ez)(1))/(z - 7)^2. This simplifies to ez/(z - 7)^2. Therefore, the derivative of f(z) = ez/(z − 7) is equal to ez/(z - 7)^2.

For our purposes, we can substitute in g(z) = ez and h(z) = (z − 7). Then, we can calculate the derivatives of each part. The derivative of g(z) is g'(z) = ez, and the derivative of h(z) is h'(z) = 1. Now, we can plug these values into the Quotient Rule and calculate the derivative of the function f(z) = ez/(z − 7).

f'(z) = (ez(z − 7) - ez(1))/(z − 7)^2

f'(z) = (ez(z - 6))/(z - 7)^2

The derivative of f(z) = ez/(z − 7) is therefore f'(z) = (ez(z - 6))/(z - 7)^2.

Learn more about derivatives here:

https://brainly.com/question/25324584

#SPJ4

The selling price of the 6 dining chairs is $3690

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

6 dining chairs together cost $1845.00. The chairs were sold to get a profit of 100%. Let x represent the selling price

The formula needed is:

Profit = [(selling price - cost price)/cost price] * 100%

Hence, substituting:

100% = [(x - 1845]/1845] * 100%

(x - 1845]/1845 = 1

x - 1845 = 1845

x = 3690

The selling price is $3690

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

108

Step-by-step explanation:

The volume of the truck is 10*12*14=1680

So, answer = the volume of the truck / the volume of a cube

answer= 1680/15.625=107.52 = 108.

The sunflower be after w weeks would be 25 + 0.5 * w inches tall.

Let's say James and Natalie were playing with matchsticks when they had the idea to create number patterns with them. James made the number 4 with four matchsticks. In order to create a pattern with two 4s, Natalie added three extra matchsticks. They understood that they could keep adding three matchsticks each round to make an additional "four" by doing so. They deduced from this that, generally speaking, in order to create a pattern with n number of 4s, you need 4+ 3(n-1) sticks. We refer to 4+ 3(n-1) as an algebraic expression in this case.

To calculate the height of the sunflower after 10 weeks, we can use the formula:

height = starting height + growth rate * time elapsed

where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.

So the height after 10 weeks would be:

height = 25 + 0.5 * 10 = 25 + 5 = 30 inches

Therefore, the sunflower would be 30 inches tall after 10 weeks.

To calculate the height after w weeks, we can use the same formula:

height = 25 + 0.5 * w

So the height after w weeks would be:

height = 25 + 0.5 * w inches

This gives you the height of the sunflower in inches after w weeks of growth.

To know more about rate visit:

https://brainly.com/question/199664

#SPJ1

For the quadratic equation 5x² - 16x + 3 = 0, the sum of solutions is 3.02.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The quadratic expression is given as -

5x² - 16x + 3 = 0

The expression is written in the form  ax² + bx + c

Where a = 5, b = -16 and c = 3

Use the quadratic formula -

x = [-b ± √(b² - 4ac)] / 2a

Substitute the values into the formula -

x = [-(-16) ± √{(-16)² - 4(5)(3)}] / 2(5)

x = [16 ± √{256 - 60}] / 10

x = [16 ± √196] / 10

x = [16 + √196] / 10 and x = [16 - √196] / 10

x = [16 + 14] / 10 and x = [16 - 14] / 10

x = 30/10 and x = 2/10

x = 3 and x = 0.2

The solutions are x = 3 and x = 0.2.

The sum of solutions are = 3 + 0.2 = 3.02

Also, the formula for sum of solutions for a quadratic equation is -b/a.

Sum of solutions = -(-16) / 5

Sum of solutions = 16 / 5

Sum of solutions = 3.02

Therefore, the sum of solutions is 3.02.

To learn more about quadratic function from the given link

https://brainly.com/question/25841119

#SPJ1

Complete question:

Determine the sum of the solutions to:

5x² - 16x + 3 = 0

A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.

A bar chart would make this most apparent.

A bar chart is the best type of chart to visually represent the comparison of values over a period of time. It is simple to read, and makes it easier to compare and contrast each value.

A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.

A bar chart is the best type of chart to visually represent the comparison of values over a period of time. It is simple to read, and makes it easier to compare and contrast each value.

A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.

the complete question is :

Which type of chart makes it most apparent that one group has a significantly higher value than the other?

Learn more about time here

https://brainly.com/question/28050940

#SPJ4

When the angle of elevation of the Sun is 45° and the shadow of a coconut tree is 15 m in length, the height of the coconut tree is 15 meters.

We have,

Denote the height of the coconut tree as AB.

A right triangle is formed by the coconut tree, its shadow, and the line connecting the top of the tree to the tip of the shadow.

From the figure,

tan(45°) = AB / 15

tan 45 = 1

So,

1 = AB / 15

Therefore,

The height of the coconut tree is 15 meters.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ12

The equation that represents the distance is -25x² + y² + z² = 0

Given data :

The distance between two points, is the number of units between them.

The equation that represents the distance is -25x² + y² + z² = 0

The distance between a point and the x-axis is represented as:

D = ( y² + x² ) [tex]\frac{1}{2}[/tex]

From the question, we have:

D = 5x

Equate both expressions for D

5x =- ( y²  + z² ) [tex]\frac{1}{2}[/tex]

Square both sides

25x² =  y² + z²

Equate to 0

y² + z² - 25x² = 0

Rewrite as:

-25x² + y² + z² = 0

Hence, the equation that represents the distance is -25x² + y² + z² = 0

Learn more about Equations refer to :

https://brainly.com/question/29174899

#SPJ4

The maximum value of the function y=cos x/sin x at x = pi/4 is 1, so the value of m is 1.

The maximum value of the function y=cos x/sin x is when the cos x and sin x terms have the same magnitude. This happens when x=pi/4. In this case, the function reduces to y=cos(pi/4)/sin(pi/4) = 1.

Therefore, the value of m = 1.

The maximum value of the function y=cos x/sin x at x = pi/4 is 1, so the value of m is 1.

The function y=cos x/sin x has a maximum value of 1 when x = pi/4. This is because when x = pi/4, the cos x and sin x terms have the same magnitude, and the function reduces to y=cos(pi/4)/sin(pi/4) = 1. Therefore, the maximum value of the function y=cos x/sin x is 1, and the value of m is 1. This result holds true for any value of x, and is a useful tool when working with trigonometric functions.

learn more about function here

https://brainly.com/question/12431044

#SPJ4