Which statement describes the sequence defined by a Subscript n Baseline = StartFraction n cubed minus n Over n squared + 5 n EndFraction?

Answers

Answer 1

Answer:

The answer is " The sequence converges to infinity. "

Step-by-step explanation:

Given:

[tex]\to a_n=\frac{n^3-n}{n^2+5n}[/tex]

[tex]\lim_{n \to \infty} a_n= \lim_{n \to \infty} \frac{n^3-n}{n^2+5n}[/tex]

                   [tex]= \lim_{n \to \infty} \frac{n(n^2-1)}{n(n+5)}\\\\= \lim_{n \to \infty} \frac{(n^2-1)}{(n+5)}\\\\= \lim_{n \to \infty} \frac{n(n-\frac{1}{n})}{n(1+\frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n-\frac{1}{n})}{(1+\frac{5}{n})}\\\\[/tex]

Denominator[tex]= \lim_{n \to \infty} 1+\frac{5}{n}=1+\lim_{n\to \infty} \frac{5}{n}=1+0=1[/tex]

Numerator [tex]=\lim_{n\to \infty}n-\frac{1}{n}=\infty[/tex]

[tex]\therefore\\\\\lim_{n\to \infty}a_n=\frac{\infty}{1} =\infty[/tex]


Related Questions

NEED ASAP

What is the product?
а-3
11
5
15а а-3
о
о
Cul —
за
о за
O3

Answers

Answer:

1/3a

Step-by-step explanation:

[tex] \frac{(a - 3)}{15a} \times \frac{5}{(a - 3)} = \frac{5}{15a} = \frac{1}{3a} [/tex]

What is the value of c?
A. 68
B. 71
C. 38
D. 34

Answers

Answer: C

Step-by-step explanation:

See diagram above

Hello, please I bed urgent help with this math problem please

Answers

Answer:

option C

Step-by-step explanation:

[tex]4c^2 + 7c - 5 = 0 , \ where \ a = 4 , \ b = 7 , \ x = - 5[/tex]

[tex]c = \frac{- b \pm \sqrt{b^2 - 4ax }}{2a} \\\\c = \frac{- 7 \pm \sqrt{49 - ( 4 \times 4 \times - 5 )}}{2 \times 4} \\\\c = \frac{- 7 \pm \sqrt{49 + 80}}{8} \\\\c = \frac{- 7 \pm \sqrt{49 + 80}}{8} \\\\c = \frac{- 7 \pm \sqrt{129}}{8} \\\\[/tex]

Answer:

Option C

Step-by-step explanation:

Quadratic formula:

[tex]4c^{2} +7c-5=0[/tex]

[tex]a=4\\b=7\\x=-5[/tex]

[tex]c=\frac{-b\frac{+}{} \sqrt{b^2-4ax}}{2a}[/tex]

[tex]c=\frac{-7\frac{+}{}49-(4*4*-5) }{2*4}[/tex]

[tex]c=\frac{-7\frac{+}{}\sqrt{129} }{8}[/tex]

hope this helps....

'निसंस्मरण' कसको कृति हो​

Answers

Answer:

ok

Step-by-step explanation:

which rule applies to this equation? (6)(3p) = 18p

Answers

Answer:

multiplication rule

Step-by-step explanation:

because 6 * 3p

is equal to 18p

hope this helps you please like and mark as brainliest

Niu earned $312 on an investment of $800. How much would $1100 have earned in the same
investment?

Answers

Answer:

429

Step-by-step explanation:

312/800 = .39

1100 x .39 = 429

Answer:

$429

Step-by-step explanation:

--------------------

[tex]\frac{312}{800} =\frac{x}{100}[/tex]

Cross multiply

[tex]800x=31200[/tex]

Divide both sides by 800

[tex]x=39[/tex]

So, Niu earned 39% on the investment of $800

So, let's find out how much $1,100 would have earned him in the same investment.

--------------->>>>

[tex]\frac{x}{1100}=\frac{39}{100}[/tex]

Cross multiply

[tex]100x=42900[/tex]

Divide both sides by 100

[tex]x=429[/tex]

--------------------

This means that Niu $1,100 would have earned Niu $429 in the same investment.

Hope this is helpful

The regular price of color TV is $519.39. During a sale, Hill Tv is selling the Tv is selling the Tv for $421.91. Determine the percent decrease in the price of the Tv

Answers

There is a 18.7% decrease

2 show by calculation of nature of triangle AMK
3 CULCULATE BP MK AK

Answers

Answer:

if he is the to form a 666

Step-by-step explanation:

what

I

I

I

want to

be

a

story

about

I

2

2

please help! (listing BRAINLIST and giving points) ​ :)​

Answers

Answer:

Tan B = 12/5

Sin B = 12/13

Cos B = 5/13

Step-by-step explanation:

sine B =  opposite (12)/hypotenuse (13)

          = 12/13

Cosine B = adjacent/hypotenuse

               = 5/13

Tangent B = opposite/adjacent

                 = 12/5

Here is a picture that can always help you with the three trig ratios.

-2(8-5) Distributive Property

Answers

Answer:

Step-by-step explanation:

- 2 ( 8 - 5 ) = ( - 2 x 8 ) - ( - 2 x 5)

                = - 16 - ( - 10)

                = - 16 + 10

                = - 6

Lines s and t are perpendicular. If the slope of line s is 5, what is the slope of line t

Answers

Slope of line t is -1/5

If two lines are perpendicular, the product of their slopes is -1

For each of the following properties write down a matrix that has this property or explain why there is no such matrix (Hint: Check first whether the dimensions add up)
(a) The column space contains (1,0,0)T, (0,0,1)T while the row space contains (1,1)T and (1, 2)T.
(b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
(c) The column space is R4 and the row space is R3.

Answers

Answer:

a) A =   [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2

b) attached below ( Matrix dose not exist )

c) attached below  ( Matrix does not exist )

Step-by-step explanation:

a) Matrix

A =   [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2

From the matrix ; Column 1 and Column 2 Belong to COL(A)

while : (1,1)^T  =  ( 1,0 )^T +  ( 0,1 )^T  i.e. (1,1)^T  ∈  Row( A )

and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T   i.e. (1, 2)^T  ∈  Row( A )

Hence ; all requirements are fulfilled in Matrix A

b)  The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T

Matrix is Non-existent because condition is not met

attached below

c) Rank | A |

dimension of column space= 4 , dimension of Row space = 3

Given that ; column space ≠ Row space

Hence Matrix does not exist

The Independent party received one-eleventh of the 6,185,894 votes cast. How many votes did the party receive?

Answers

Answer:

562,354 votes

Step-by-step explanation:

1/11 of 6,185,894

=>1/11 x 6,185,894

=>562,354

Write the word sentence as an equation.

The quotient of a number n and 5 is 18.

Answers

Answer:

n/5 = 18

Step-by-step explanation:

Quotient means division.

n/5 = 18

Consider all four-digit numbers that can be made from the digits 0-8 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is less than or equal to 4000

Answers

Answer:

The probability is:

P = 0.375

Step-by-step explanation:

First, we need to find the total number of four-digit numbers that can be made with the digits 0-8, such that the first digit can not be zero.

To do this, we first need to find the number of selections that we have, in this case, there are 4, one for each digit in our 4-digit number.

Now let's count the number of options that we have for each one of these selections:

first digit: we have 8 options (because the 0 can not be here)

second digit: we have 9 options (because now the zero can be taken)

third digit: we have 9 options

fourth digit: we have 9 options.

The total number of combinations is equal to the product of all the numbers of options, this is:

C = 8*9*9*9 = 5,832

Now we need to find how many of these are less or equal than 4000.

So now let's count the options again:

first digit: 3 options {1, 2, 3}

second digit: 9 options

third digit: 9 option

fourth digit: 9 options

Total number of combinations:

C' = 3*9*9*9 = 2,187

Here we should also count the combination for the number 4000 itself, as it was not counted in our previous calculation, then we have:

C' = 2,187 + 1 = 2,188 combinations.

The probability of randomly choosing a number that is smaller than or equal to 4000 will be equal to the quotient between the number of combinations that are smaller than or equal to 4000 (2,188 combinations) and the total number of combinations (5,832)

this is:

P = 2,188/5,832 = 0.375

Is there a local minimum at x= -4?

Answers

9514 1404 393

Answer:

  yes

Step-by-step explanation:

Yes, the turning point at (-4, -16) is a local minimum. It is a minimum because the curve goes upward either side of it. It is local (not global) because the curve has values that are lower than -16 at other values of x.

__

Similarly, the point (4, 16) is a local maximum.

3x – 4(x - 4) + 4 = 13
Solve for x step by step
Please answer quickly

Answers

Answer:

7

Step-by-step explanation:

3x – 4(x - 4) + 4 = 13

=> 3x - 4x + 16 + 4 = 13

=> - x + 20 = 13

=> - x = 13 - 20

=> - x = - 7

=> x = 7

Answer:

x = 7

Step-by-step explanation:

3x – 4(x - 4) + 4 = 13

3x - 4x + 16 + 4 = 13

-x + 20 = 13

-x + 20 - 20 = 13 - 20

-x = -7

(-x = -7)/-1

x = 7

Hope this helps.

What is the range of this function?

Answers

Answer:

D. {-8, -5, 3, 7}

Step-by-step explanation:

__________

The amount of time needed to complete a job, t, varies inversely with the number of workers, w. If 10 workers can complete a job in 20 minutes, how many minutes would it take 5 workers?

Answers

it would take 40 minutes for 5 workers

The amount of time needed to complete a job by 5 workers is

40 minutes.

What is a unit rate?

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

The amount of time needed to complete a job, t, varies inversely with the number of workers.

Number of workers = W

Time to complete 1 work  = T

This means,

T = 1 / W

W = 1 / T

10 workers can complete a job in 20 minutes.

This can be written as:

10 W = 1 / 20

Divide 10 on both sides.

1 W = 1 / 200

This means,

1 worker can complete a job in 200 minutes.

Now,

1 W = 1/ 200

Multiply 5 on both sides.

5 W = 5/200

5 W = 1 / 40

This means 5 workers will take 40 minutes to complete the work.

Thus,

The amount of time needed to complete a job by 5 workers is

40 minutes.

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Can anyone help me? Find the value of x

Answers

Answer:

x = 7

Step-by-step explanation:    6  25  13  55

since these are similiar triangles the sides of one triangle are equal to the other triangle by the same ratio

The ratio of 90/27  is the same as the (9x-13)/15  ratio

(9x-13)/15 = 90/27

9x - 13  = 15 × 90/27

9x - 13  = 15 × 3 1/3

9x - 13 =   50

9x  =  63

 x = 7

Can :) mean happily taken on a bio? Alex got it on his?
Answer ASAPPPP
Someone

Answers

Answer:

Yes,

Step-by-step explanation:

When " :) " is used in a bio it means the person is happy

The heights of students in a class are normally distributed with mean 63 inches and standard deviation 4 inches. Use the Empirical Rule to determine the interval that contains the middle 68% of the heights.

Answers

Answer:

The interval that contains the middle 68% of the heights is between 59 and 67 inches.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 63, standard deviation of 4.

The interval that contains the middle 68% of the heights.

By the Empirical rule, within 1 standard deviation of the mean. So

63 - 4 = 59

63 + 4 = 67

The interval that contains the middle 68% of the heights is between 59 and 67 inches.

Plz help with this question I don’t get it is an image

Answers

Answer:

D

Step-by-step explanation:

For this question, we know that x represents the thousands of square feet in the stadium. We also know that the stadium is 18 thousand square feet. Therefore, the amount of thousands of square feet, or x, is 18. We can then plug 18 in for x in the equation, getting

[tex]C(x) = \frac{7250000}{18+60} \\= \frac{7250000}{78}\\= 92948[/tex]

as our cost

The price of a 5-minute phone call is $1.75. What is the price of a 19-minute phone call?

Answers

Answer:

$6.65

Step-by-step explanation:

You could start by seeing the price of a 1 minute phone call. if you divide 1.75 by 5 it is 0.35. that means 1 minute costs $0.35. so the equation would be 0.35 times 19. which is 6.65 dollars.

5 minutes call = $1.75

1 minute call = $1.75/5 = $0.35

19 minutes call = $0.35 × 19 = $6.65

What is the answer to this question

Answers

Answer:

its b because when subtract 30-24=6

petrol cost 99p per litre. How much would 47 cost?​

Answers

Answer:

4653

Step-by-step explanation:

I am not sure if that 47 in also in litres but if yes then

step 1

1litre=99p

47litre=?

step2

cross multiply such that

47litre × 99p

step3

devide by by 1litre

47litre ×99p

------------------

1litre

so litre counsels litre then your answer will be in pounds so 47×97p÷1=4653

I can not seee the answers

Answers

Answer:

What do you mean

Step-by-step explanation:

PLEASE HELP!!!

WILL MARK BRAINLIEST

WORTH A LOT OF POINTS!!!!!!!
In circle P, m WPX = 28 degrees, m ZPY = 38 degrees. ZW and VX are diameters. Find each angle measure.

Answers

Answer:

2.28°

3.28°

4.28°

5.114°

6.180°

7.114°

8.332°

9.322°

10.152°

Step-by-step explanation:

The required measure of the angles are given as,
2] 28°       3]  28°     4]  28°      5]  114°   6]  180°   7]  114°   8] 332°   9]  322° and   10]  152°.

Given that,
In circle P, m WPX = 28 degrees, m ZPY = 38 degrees. ZW and VX are diameters. Find each angle measure.

What is the angle?

orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,

The diameter of the circle has a measure of angle 180°,
So, mVXZ = 180°,
Since,
mVZ = mWX
mVZ = 28°
Similarly, all the angles can be evaluated,

Thus, the required measure of the angles are given as,
2] 28°       3]  28°     4]  28°      5]  114°   6]  180°   7]  114°   8] 332°   9]  322° and   10]  152°.

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Heyy!! Can someone help me please!!

3 (5x + 2) - 2 (4x -4)

I don’t know what to doooo!!

Answers

Answer:

7x + 14

Step-by-step explanation:

the first thing to do is expand the parentheses/brackets.

3(5x + 2) -2(4x - 4) will be

3(5x) + 3(2) -2(4x) -2(-4)

= 15x + 6 - 8x + 8

collect like terms

15x - 8x + 6 + 8 = 7x + 14

the answer is 7x + 14

Answer:

3(5x+2)-2(4x-4)

15x+6-8x+8

15x-8x+6+8

7x+14

3 16. If 270º < AS 360° and cos(A)= 3/4 then determine the exact values of sin (A) and tan ( A)​

Answers

Answer:

[tex]{ \boxed{ \tt{trig \: identity : { \bf{ { \cos}^{2} A + { \sin }^{2} A = 1}}}}} \\ \therefore \: { \green{ \tt{ \sin A = \sqrt{1 - { \cos }^{2}A } }}} \\ \sin A = \sqrt{1 - {( \frac{3}{4}) }^{2} } \\ \sin A = \frac{ \sqrt{7} }{4} = 0.661 \\ \\ { \green{ \tt{ \tan A = \frac{ \sin A }{ \cos A} }}} \\ \tan(A ) = \frac{ \frac{ \sqrt{7} }{4} }{ \frac{3}{4} } = \frac{ \sqrt{7} }{3} = 0.882 \\ \\ { \underline{ \blue{ \tt{ becker \: jnr}}}}[/tex]

The exact values of sin (A) and tan ( A)​ are 0.661 and 0.882 respectively.

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given that 270º < AS 360° and cos(A)= 3/4.

We are required the exact values of sin (A) and tan ( A)​

Since, cos(A)= 3/4.

cos ²A + sin² A = 1

sin A = √ 1- cos ²A

sin A = √ 1-  (3/4) ²

Sin A = 0.661

Tan A = sin A / Cos A

Tan A = 0.661/ 3/4 = 0.882

Hence, the exact values of sin (A) and tan ( A)​ are 0.661 and 0.882 respectively.

Learn more about trigonometric;

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