1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elza [17]
2 years ago
6

The value of

Mathematics
1 answer:
marusya05 [52]2 years ago
4 0

\large\underline{\sf{Solution-}}

We have to find out the value of the fraction.

<u>Let us assume that:</u>

\sf \longmapsto x =2 +   \dfrac{1}{2 +  \dfrac{1}{2 +  \dfrac{1}{2 + ... \infty} } }

<u>We can also write it as:</u>

\sf \longmapsto x =2 + \dfrac{1}{x}

\sf \longmapsto x =\dfrac{2x + 1}{x}

\sf \longmapsto  {x}^{2}  =2x + 1

\sf \longmapsto {x}^{2}  - 2x - 1 = 0

<u>Comparing </u>the given <u>equation</u> with <u>ax² + bx + c = 0,</u> we get:

\sf \longmapsto\begin{cases} \sf a =1 \\ \sf b =  - 2 \\ \sf c =  - 1 \end{cases}

<u>By quadratic formula:</u>

\sf \longmapsto x =  \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{8} }{2}

\sf \longmapsto x =  \dfrac{2 \pm2 \sqrt{2} }{2}

\sf \longmapsto x = 1 \pm\sqrt{2}

\sf \longmapsto x = \begin{cases} \sf 1  + \sqrt{2} \\ \sf 1 -  \sqrt{2}  \end{cases}

<u>But </u><u>"</u><u>x"</u><u> cannot be negative. Therefore:</u>

\sf :\implies x = 1 + \sqrt{2}

So, the value of the fraction is 1 + √2.

You might be interested in
How do you solve <br>|3x|=18
Oduvanchick [21]

We can get two different equations from this:

3x = 18

and

3x = -18

So:

x = 6, x = -6

x = {6, -6}

6 0
3 years ago
Read 2 more answers
Solve for x:<br> Зах + b = с
Brrunno [24]
X= c/3a - b/3a if I’m right.
6 0
2 years ago
Read 2 more answers
1. The point (1,-7) is on a circle k, which has its<br> centre at 0(0,0)<br> Sketch the circle k.
maria [59]

Answer:

answered with a diagram

6 0
3 years ago
U GET BRAINLIEST IF ANSWER CORRECTLY
tangare [24]
1)5/24
2)1 and 1/3 im not sure 
3)1 and 1/3
4)1/7
7 0
3 years ago
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distribu
Elodia [21]

Answer:

a) Standard error = 0.5

b) 99% Confidence interval:  (19.2125,21.7875)

Step-by-step explanation:

We are given the following in the question:

Population mean =  20.50 mpg

Sample standard deviation = 3.00 mpg

Sample size , n = 36

Standard Error =

=\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{3}{\sqrt{36}} = 0.5

99% Confidence interval:

\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}

Putting the values, we get,

z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.575

20.50 \pm 2.575(\displaystyle\frac{3}{\sqrt{36}})= 20.50 \pm 1.2875 = (19.2125,21.7875)

4 0
3 years ago
Other questions:
  • How to solve 8340divided by 1.2
    7·1 answer
  • Find the missing measure for a right circular cone given the following information. Find V if r = 2 and L.A. = 12pie
    14·1 answer
  • A Web music store offers two versions of a popular song. The size of the standard version is 2.2
    7·1 answer
  • Calculate 5% of 800. Please show working out with steps
    15·2 answers
  • Determine whether each pair of actions results in independent or dependent events.
    10·1 answer
  • an island has three towns located at points with the coordinates a (15,3) b (25,10) and c (0,20) where the coordinates have unit
    12·1 answer
  • Nick rolls a fair dice 126 times.
    9·2 answers
  • 15/23 - 5/23<br>lets see who can solve​
    13·2 answers
  • 6 x 2 7 x 2 8 x 2 3 x 3
    14·1 answer
  • Pasadena Candle Inc. projected sales of 58,000 candles for January. The estimated January 1 inventory is 2,900 units, and the de
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!