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andrew-mc [135]
2 years ago
14

Prove that every bounded increasing sequence is convergent

Mathematics
1 answer:
aleksklad [387]2 years ago
4 0
The proof of this can be get with a slight modification. It can be prove that every bounded is convergent, If (an) is an increasing and bounded sequence, then limn → ∞an = sup{an:n∈N} and if (an) is a decreasing and bounded sequence, then limn→∞an = inf{an:n∈N}.
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A regular decagon has sides that are 8 cm long. What is the area of the figure? Round to the nearest whole number.
blsea [12.9K]

<u>Given</u>:

Given that the regular decagon has sides that are 8 cm long.

We need to determine the area of the regular decagon.

<u>Area of the regular decagon:</u>

The area of the regular decagon can be determined using the formula,

A=\frac{s^{2} n}{4 \tan \left(\frac{180}{n}\right)}

where s is the length of the side and n is the number of sides.

Substituting s = 8 and n = 10, we get;

A=\frac{8^{2} \times 10}{4 \tan \left(\frac{180}{10}\right)}

Simplifying, we get;

A=\frac{64 \times 10}{4 (\tan \ 18)}

A=\frac{640}{4 (0.325)}

A=\frac{640}{1.3}

A=642.3

Rounding off to the nearest whole number, we get;

A=642 \ cm^2

Thus, the area of the regular decagon is 642 cm²

Hence, Option B is the correct answer.

5 0
2 years ago
What is this problem -12=4(x-7)-8x
Fofino [41]

-12=4(x-7)-8x

One solution was found :

                  x = -4

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :


                    -12-(4*(x-7)-8*x)=0


Step by step solution :

Step  1  :

Equation at the end of step  1  :

 -12 -  (4 • (x - 7) -  8x)  = 0

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :


  4x + 16  =   4 • (x + 4)


Equation at the end of step  3  :

 4 • (x + 4)  = 0

Step  4  :

Equations which are never true :

4.1      Solve :    4   =  0

Hope this helps you, Have a nice day.

4 0
3 years ago
Write <br> 23/25 as a percent
Firdavs [7]
3 / 25 = x / 100 

<span>23/25 = 0.92 = 92/100 </span>

<span>x = 92%</span>
8 0
3 years ago
Read 2 more answers
What is the y-intercept of the exponential function? y=2(3)^x
ValentinkaMS [17]

Answer:

( 0 , 2 )

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y .

x-intercept(s): None

y-intercept(s): ( 0 , 2 )

3 0
3 years ago
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vlabodo [156]
The 3 it is the one the bottom left corner
5 0
3 years ago
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