How do you do this question?

Exact value:  [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]

Approximate value:    c = 0.08387

Round the approximate value however you need to

==============================================

Work Shown:

Let x = 1+c

[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]

We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.

Each new term is found by multiplying the previous term by 1/x.

Assuming -1 < r < 1 is true, the infinite geometric sum is

[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]

Plug in S = 11 and solve for x

[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]

Use the quadratic formula to find the two solutions

[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]

Using these x values, we find that the corresponding r values are

r = 1/x = 1/(1.08387) = 0.92262

r = 1/x = 1/(-0.08387) = -11.92321

The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387

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

Using the solution that corresponds to x = 1.08387, we find the value of c is

[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]

prin ce insusiri se remarca sfantul si dreptul simeon

The area of a square sports arena is 10,000 m² what are the dimensions of the sports arena on the map.

Help please!!
Find the equation of a line perpendicular to 5x - 3y = - 2 that contains the point (-4,5). Write the equation in slope
intercept form

11. Mark builds 3 Lego towers. Each tower is made of 5 square layers
which have a width and length of 5 Lego pieces. Suddenly, Mark's little
brother breaks one and runs off with 45 pieces. Use the expression to show
how many pieces Mark is left with.

A bakery sells, on average, 100 special breads per day and collects with these sales, on average, R $ 300.00. It was found that the quantity of special breads sold daily increases if the price is reduced, according to the equation q = 400 - 100p, in which q represents the quantity of special breads sold daily and p, its price in reais. In order to increase the flow of customers, the bakery manager decided to run a promotion. To do so, it will modify the price of special bread so that the quantity to be sold daily is as large as possible, without decreasing the average daily collection on the sale of this product. The price p, in reais, of the special bread in this promotion should be in the range

a) R $ 0.50 p b) R $ 1.50 p c) R $ 2.50 p d) R $ 3.50 p e) R $ 4.50 p

5.) You are working for a car dealership. You are doing an inventory of the lot. You counted 34
trucks. 15 cars, and 8 SUVs. What is the ratio of SUVs to total vehicles on the lot?

If three times a number is at least four or more than eight times the number, which of the following is true? A-The number is at least negative four-fifths.

B- the number is at most four-fifths.

C-The number is at least four-fifths.

D-The number is at most negative four-fifths .

(Graph attached)
Please show work
What is the average speed of the runner at 4 seconds
​

Give brainliest answer

(3.1 · 10² ) (2 · 10³) Write in Scientific Notation.

t Park Junior High, 10%, or 160, of the students, play a musical instrument. How many students attend the school?

A tape diagram. StartFraction part Over whole EndFraction = StartFraction 10 Over 100 EndFraction = StartFraction 160 Over question mark EndFraction

Which statements are correct? Check all that apply.
The total number of students is 160.
The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.
The percent as a part-to-whole ratio is StartFraction 160 Over 100 EndFraction
There are 1,600 students in the school.
There are 250 students in the school.

Simplify the expressions by distributing and combining like terms 5/8x-2(7-1/4x)

Solve for x in the equation x squared minus 10 x + 25 = 35

A well is 20ft deep. A snail at the bottom of the well climbs upto 4ft each day and slips back 2ft every night.how many days the snail to reach the too

If he drank 80% of his water on his entire hike, how much did he drink?

find the value of x.
(6x+8)
(7x-7)

have a random argument with yourselves

Mrs. Balcon owes the dentist $342. She wants to have her payments taken from her checking account over the next 7 1/2 months. By what amount will her account change each month for the first 7 months?

The houses on a city block were thought to be valued at $175,000, $163,000,
$142,000, $135,000, $191,000, $122,000, and $147,000, respectively. But a
public assessor has determined that the value of each house is actually
$20,000 higher than previously thought. According to the public assessor,
what is the median value of the houses?
O A. $162,000
O B. $167,000
O c. $155,000
O D. $147,000
SUBMIT

Given the linear function 2x - y= 5 what is the slope? And As x increase does y increase or decrease and as x decreases does y increase or decrease

use a number line to solve the sum
2+5

in the real world humans hear sound as an analog signal. this means the signal is a continuous waveform which is completely processable by human ears. however machines 'hear' sound a little differently as they process sound digitally which is a discrete waveform. when sound is recorded or transmitted electronically the continuous (analog) waveform is sampled to convert it to a discrete (digital) sequence. sampling is the process of reducing a continuous time signal to a discrete-time signal. as the sampling rate increases the sound quality of the recording or transmission will improve. the graphs below represent two different samples of pure tone. sample one is taken 8 times per unit of time. sample two is taken 16 times per unit of time. a) why would sample 2 reproduce a better replication of the pure signal? b) write a sinusoid model for sample 2

Please help what is -0.5 divided by -1/5

A couch and coffee table cost a total of $1156. The cost of the couch is three times the cost of the coffee table find the cost of each item.

In an experiment, college students were given four quarters

John's sister is twice his age. In 5 years the sum of their ages will be 31. How old are John and his sister now? Briefly explain how you arrived at your answer.

Think about the proportion and the cross products for this problem:

Shelley sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20.

A hotel manager is buying wallpaper for the rooms in his
hotel. Each roll of wallpaper costs $48. If he spent $5,568,
how many rolls of wallpaper did the hotel manager buy?
1,017
106
1,016
116

The two triangles shown are similar. Find the value of a/b

3. What is the set of ordered pairs such that no twvo
ordered pairs have the same x-value but different y-
values?
A. Function
C. Relation
B. Theorem
D. None of these​