Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)an =4 + 2n2n + 3n2lim n→[infinity] an =

The fixed point of the function \(f(x) = x.e²-5 is x = 1.2195.\)

Newton's Method is a numerical approximation technique that can be used to find the roots of a given function.

The steps involved in Newton's Method to find the fixed point(s) of the function where \(f(x) = x. e²-5\) are given below:

Step 1: Write the given function as \(f(x) = x.e²-5\)

Step 2: To find the fixed points of the given function, we need to solve f(x) = x.

Therefore, we can rewrite the given function as follows:

\(x = f(x) = x.e²-5 ⇒ x(1 - e²) = 5 ⇒ x = 5/(1 - e²)\)

Step 3: To apply Newton's method, we need to define a function g(x) such that g(x) = x - f(x)/f'(x),

where f'(x) is the first derivative of f(x).

Therefore, \(g(x) = x - (x.e²-5)/(2xe²)\)

Step 4: Iterate the function g(x) until we reach a fixed point.

That is, keep computing g(x) until we obtain g(x) = x.

The iteration formula for Newton's method is given by:

\(xn+1 = xn - f(xn)/f'(xn)\)

For the given function \(f(x) = x.e²-5\), the first derivative is:

f'(x) = e²

Hence, the iteration formula becomes:

\(xn+1 = xn - (xn.e²-5)/(e².xn)\)

\(xn+1 = xn - (xn/e²) + (5/e².xn)\)

\(xn+1 = (2xn + 5/e²xn)/2e²\)

We can use any initial guess x0 to find the fixed point of the given function.

Let's choose x0 = 1.

Then, \(x1 = (2.1 + 5/e²)/2e² ≈ 1.2195x2 = (2.1.2195 + 5/e²1.2195)/2e² ≈ 1.2195\)

After the second iteration, we reach a fixed point.

Hence, the fixed point of the function \(f(x) = x.e²-5 is x = 1.2195.\)

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To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.

To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:

Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).

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Answer:

it is definitely negative, i think it is -3/2

Step-by-step explanation:

is there a better picture of the graph?

A rational function graph crosses its horizontal asymptote when there are two vertical asymptotes because the degree of the numerator is less than the degree of the denominator.

When a rational function has two vertical asymptotes, it means that there are two values of x that make the denominator equal to zero, causing the function to become undefined. As x approaches these values, the function approaches positive or negative infinity.

If the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is a horizontal line y=0. As x approaches infinity or negative infinity, the function approaches this line. However, because the degree of the numerator is less than the degree of the denominator, the function doesn't approach the line fast enough to stay on one side of it. As a result, the graph will cross the horizontal asymptote at some point.

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Parabolas are used to represent quadratic functions. The x-intercepts of the parabola are -1.969 and 6.01. Vertex of the parabola are 2.02 and 78.002.

A quadratic function is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.

The function is given as:

f(x) = \(4.9x^{2} + 19.8x+58\)

Next, we plot the graph of the function f(x)

From the graph (see attachment), we have the following features

Vertex = (2.02, 78.002)

Line of symmetry, x = 2.02

x-intercepts = -1.969 and 6.01

Hence, the x-intercepts of the parabola are -1.969 and 6.01 and Vertex of the parabola are 2.02 and 78.002.

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Answer:

B.

–80, –110

Step-by-step explanation:

-80 and -110

It is an arithmetic sequence. The difference = -30. It is the difference between each number in the sequence: 10-40=-30

-50-30=-80

-80-30 =-110

-80

First Identify the sequence being made here.

10-40 = -30

-20-10 = -30

-50-(-20) = -30

Therefor this pattern is decreasing by a rate of 30 so to continue this, just subtract 30 from -50.

-50-30 = -80

The next term is -80.

Hope I helped!

The prime factorization of the radicand 2 is 9√15.

A number can be expressed as the product of its prime components through the process of prime factorization. A number with precisely two elements, 1 and the number itself, is said to be a prime number.

As an illustration, let's use the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.

Given that,

x= 3√135

Solving the equation further using the rule √A*B = √A*√B

x= 3√9*15

x= 3√9*√15

x=3*3*√15

x= 9√15

Therefore, the prime factorization of the radicand 2 is 9√15.

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The angle shown is less than 90 degrees so it is an acute angle.

answer: acute

The two equations to set up to solve the absolute value equation given are; 3x - 2 = 19 and 3x - 2 = -19.

The solution of the inequality given; -2|2x+3| + 14 ≥ - 16 is; x ≥ 6 OR x ≤ -9.

It follows from absolute value equations that;

| x | = ±x

Hence, | x | = x OR | x | = -x

Ultimately, the two equations to set up are; 3x - 2 = 19 and 3x - 2 = -19.

2. Also, the equation given; -2|2x+3| + 14≥ - 16 can be solved as follows;

-2|2x+3| ≥ - 16 - 14

-2|2x+3| ≥ - 30

|2x+3| ≥ 15

Hence, the equation can be solved as;

2x + 3 ≥ 15 OR 2x + 3 ≤ -15

2x ≥ 12 OR 2x ≤ -18

x ≥ 6 OR x ≤ -9.

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Answer:

m = -5

Step-by-step explanation:

I'm not sure of the first part, but this is how to solve the second:

5m > -25

5m/5 > -25/5

m = -5

Answer:

Correct answer should be x= -6

Step-by-step explanation:

prove me wrong

Answer:

Step-by-step explanation:

x represents the numbers of months and y represents the insect

population.

We are told that:

  1) we start with 125 insects, and

 2) the rascals double each month

Lets use m for months they double from the start of 125 insects.).

We can form an equation that will predict the insect population as a function of the numbers of months, m, from the start (125 insects).

Month 0 is 125

Month 1 would be 125*(1+1) or 125*2

 We can rewrite this as 125*2^1

Month 2                 125*2^2  [It dounbes again]

Month 3                  125^3     [It dounbes yet again]

Month 4                  125^4     [And again]

Month 5                  125^5     [And so on to Infinity and Beyond]

The pattern is 125*(2)^m. where m is months since the starting month of 0.

Insect Population(m) = 125*(2)^m

See the attached graph.

The tota number of spaces that should be in the parking lot is 114

From the question, we have the following parameters that can be used in our computation:

Parking ratio = 6 spaces for every 1000 square feet

Also, we have

Floor space = 19000 square feet

using the above as a guide, we have the following:

The number of spaces in the parking lot is

Spaces = Parking ratio * Floor space

So, we have

Spaces = 6/1000 * 19000

Evaluate

Spaces = 114

Hence. there should be 114 parking spaces in the building

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Answer:269.6 square centimeters

Step-by-step explanation:

Answer:

Y=x(600-x)

Step-by-step explanation:

How many trees?

500

Answer: 4,875.05

Step-by-step explanation:

I took the quiz

Answer:

d

Step-by-step explanation:

Answer:

76.275

Step-by-step explanation:

First - the entire circles area is 78.54. \(\pi r^{2}\) with r being 5

6 triangles of that size could fit in that circle.

A=3\(\sqrt{3}\)/(2) * a2

The area of that would equal 64.95

78.54-64.95 = 13.59

then divide that number by 6

which is 2.265.

Take that number from the original 78.54

78.54-2.265 = 76.275

The ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year is 1/6 οr 1:6. Thus, οptiοn D is cοrrect.

The relative size οf twο quantities expressed as the quοtient οf οne divided by the οther; the ratiο οf a tο b is written as a:b οr a/b.

If Sam wοrks fοr his father fοr 2/5 οf the year, then he wοrks fοr his mοther fοr the remaining time, which is 1 - 2/5 = 3/5 οf the year.

Tο find the ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year, we can write:

Sam wοrked fοr his father = 2/3 οf year

Remaining time = 1/3

Sam wοrked fοr his mοther = 1/3(remainder year)=(1/3)*(1/3)

     =1/9

Ratiο οf time spent fοr mοther and father is

= (1/9):(2/3)

=(1/3):2

= 1:6

Sο, οptiοn d) 1/6 is cοrrect answer

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Complete question:

Sam works for his father for 2/3; of the year and works for his mother = of the remainder year. What is the

ratio of the time Sam spends working for his mother to the time he spends working for his father per year?

Number 5

So for the difference of perfect squares factor with the numbers on both factors having to be the same, but one adds and one subtracts.

Answer:

The cost price of the item is $ 3,200, and the marked price of the item is $ 4,000.

Step-by-step explanation:

Since the marked price of an article is 25% above it's cost price, and when it is sold at a discount of 15% there is a gain of $ 200, to find the cost price of the article and the marked price of the article the following calculation must be performed:

X x 1.25 x 0.85 = X + 200

1.0625X = X + 200

6.25 = 200

100 = X

100 x 200 / 6.25 = X

20,000 / 6.25 = X

3,200 = X

3,200 x 1.25 = 4,000

Therefore, the cost price of the item is $ 3,200, and the marked price of the item is $ 4,000.

.

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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Answer:

there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Step-by-step explanation:

To choose three different members from the club to be president, vice president, and treasurer, you can follow these steps:

Step 1: Calculate the number of ways to choose the president:

Since there are 15 club members in total, the number of ways to choose the president is 15.

Step 2: Calculate the number of ways to choose the vice president:

After selecting the president, there are 14 remaining members. The number of ways to choose the vice president from these 14 members is 14.

Step 3: Calculate the number of ways to choose the treasurer:

After selecting the president and vice president, there are 13 remaining members. The number of ways to choose the treasurer from these 13 members is 13.

Step 4: Calculate the total number of ways to choose the president, vice president, and treasurer:

Since each step is independent, you can multiply the number of choices at each step: 15 * 14 * 13 = 2,730.

Therefore, there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

The correct algebraic expressions for the given sequences are: (a) 2x + 1, (b) 3m + 5, and (c) 2y + 4.

(a) The sequence "|---x---|-1--|---x----|" can be represented by the algebraic expression 2x + 1, where 'x' represents the length of the sections. The expression 2x + 1 indicates that each 'x' section has a length of 2x, and the '-1' represents the length of the middle section.

(b) The sequence "|-----m-----|-----m----|-----m----|----5----|" can be represented by the algebraic expression 3m + 5, where 'm' represents the length of the sections. The expression 3m + 5 indicates that each 'm' section has a length of 3m, and the '+5' represents the length of the final section.

(c) The sequence "|-----y----|----2----|-----y----|----2---|" can be represented by the algebraic expression 2y + 4, where 'y' represents the length of the sections. The expression 2y + 4 indicates that each 'y' section has a length of 2y, and the '+4' represents the length of the middle and final sections.

In these expressions, the variable represents the length of the corresponding section, and the coefficients and constants represent the specific lengths of the sections in the sequence.

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Complete Question

Use an algebraic expression to represent each sequence of lengths shown below.

(a) |---x---|-1--|---x----|  

(b)  |-----m-----|-----m----|-----m----|----5----|

 (c) |-----y----|----2----|-----y----|----2---|    

Answer:

(-x+z)/4

Step-by-step explanation:

Evaluate the $\heartsuit$ operation to simplify.

\begin{align*}

H(x,y,z) &= \left(x \heartsuit y\right) \heartsuit z - x \heartsuit \left(y \heartsuit z\right) \\

&= \left(\dfrac{x+y}{2}\right) \heartsuit z - x \heartsuit \left(\dfrac{y+z} 2\right) \\

&= \dfrac{\dfrac{x+y}{2} + z}{2}  - \dfrac{x + \dfrac{y+z}{2}}{2}

\end{align*}This looks ugly, but it works out! Continue by multiplying each fraction's numerator and denominator by $2$, in order to eliminate the complex fractions.

\begin{align*}

H(x,y,z) &= \dfrac{\dfrac{x+y}{2} + z}{2}  - \dfrac{x + \dfrac{y+z}{2}}{2} \\

&= \dfrac{x + y + 2z}{4} - \dfrac{2x + y + z}{4} \\

&= \dfrac{(x+y+2z) - (2x + y + z)}{4}

&= \dfrac{-x+z}{4}

\end{align*}Surprisingly it simplifies all the way down to $H(x,y,z) = \boxed{\dfrac{-x + z}{4}}$. The value of $y$ is not even used!

Answer:

x=15 y=12 z=2

Step-by-step explanation:

4x=60 x=15

5y=60 y=12

2z=4 z=2

Answer:

x= 1

if thats not what u trien find lmk and ill fix it n give correct answer

Step-by-step explanation:

Consequently, m less than or equivalent to 19 is the answer to the discrepancy. If Mercedes uses her entire $25 gift card on music, she can buy a maximum of 19 tracks.

According to experts, inequality promotes political instability and slows down economic development. Because wealthy families typically spend a smaller percentage of their money than do poorer households, concentrated wealth and income lower the amount of economic demand. The business may suffer if low-income households have fewer options.

The amount of money Mercedes can spend on songs is equal to the value of the gift card, which is $25. Since each song costs $1.29, the number of songs she can purchase must satisfy the inequality:

1.29m ≤ 25

where m is the number of songs she can purchase.

To solve for m, we can divide both sides by 1.29:

m ≤ 25/1.29

m ≤ 19.38

When we round to the closest whole integer, we obtain:

m ≤ 19

Therefore, the solution to the inequality is m less-than-or-equal-to 19. Mercedes can purchase at most 19 songs with her $25 gift card, assuming she spends all of it on songs.

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Answer: 12.04 feet

Hope this helped.

Answer:

12.04 feet is the approximate answer.

There are 5 choices left), and 5 ways to choose the remaining element of Y. This gives us a total of 7 × 5 × 5 = 175 ordered pairs (X,Y).

Let's first consider the possible values of |X ∪ Y|.

If |X ∪ Y| = 1, it means that X and Y have no elements in common, and each set has only one element. There are 7 such sets: {1},{2},{3},{4},{5},{6},{7}.

If |X ∪ Y| = 2, it means that X and Y have one element in common. There are 7 ways to choose the common element, and 6 ways to choose the remaining element of X (it cannot be the same as the common element, so there are only 6 choices left), and 6 ways to choose the remaining element of Y (again, it cannot be the same as the common element or the element of X, so there are only 6 choices left). This gives us a total of 7 × 6 × 6 = 252 ordered pairs (X,Y).

If |X ∪ Y| = 3, it means that X and Y have two elements in common. There are 7 ways to choose the common elements, and 5 ways to choose the remaining element of X (it cannot be any of the common elements, so there are 5 choices left), and 5 ways to choose the remaining element of Y. This gives us a total of 7 × 5 × 5 = 175 ordered pairs (X,Y).

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Answer:

Perimeter of the rectangle = 14n + 6 units

Step-by-step explanation:

Perimeter of a rectangle = (2 * length) + (2 * width)

Perimeter of a rectangle = 2(length + width)

Length of the rectangle = 4n + 3 units

Width of the rectangle = 3n units

Perimeter of the rectangle = 2(length + width)

= 2{(4n + 3) + 3n}

= 2(4n + 3 + 3n)

= 2(7n + 3)

= 14n + 6

Perimeter of the rectangle = 14n + 6 units