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
Natali5045456 [20]
3 years ago
15

Suppose a regular n-gon is inscribed in a circle of radius r. Diagrams are shown for n=6, n=8, and n = 12. n = 6 n=8 n = 12 a a

VT a Imagine how the relationship between the n-gon and the circle changes as n increases. 1. Describe the relationship between the area of the n-gon and the area of the circle as n increases.​

Mathematics
1 answer:
m_a_m_a [10]3 years ago
6 0

Answer:If an N-gon (polygon with N sides) has perimeter P, then each of the  

N sides has length P/N.  If we connect two adjacent vertices to the  

center, the angle between these two lines is 360/N degrees, or 2*pi/N  

radians.  (Do you understand radian measure well enough to follow me  

this far?)

The two lines I just drew, plus the side of the polygon between them,  

form an isosceles triangle.  Adding the altitude of the isosceles  

triangle makes two right triangles, and we can use one of them to  

derive the equation

 sin(theta/2) =  s/(2R)

where theta is the apex angle (which I said is 2*pi/N radians), R is  

the length of the lines to the center (the radius of the circumscribed  

circle), and s is the length of the side (which I said is P/N).

Putting those values into the equation, we have

 sin(pi/N) = P/(2NR)

so that

 P = 2NR sin(pi/N)

gives the perimeter of the N-gon with circumradius R.

Can we see a connection between this formula and the perimeter of a  

circle?  The perimeter of the circumcircle is 2*pi*R.  As we increase  

N, the perimeter of the polygon should get closer and closer to this  

value.  Comparing the two, we see

 2NR*sin(pi/N) approaches 2*pi*R

 N*sin(pi/N)   approaches pi

You can check this out with a calculator, using big numbers for N such  

as your teacher's N=1000.  If you calculate the sine of an angle in  

degrees rather than radians, the formula will look like

 N*sin(180/N) --> pi

Step-by-step explanation:

You might be interested in
Does a function have to be linear
Mkey [24]

Answer:

Hi there

Step-by-step explanation:

A linear function is a type of function and so must follow certain rules to be classified as a “function”. For example, functions can only have one output for each input. On the other hand, equations are just statements that make two things equal, like x = y or 52x = 100.

<em>~Your Welcome! :)</em>

6 0
3 years ago
8r+9r-11r+7r what is the answer I have to turn it in today!!
Drupady [299]

Answer:

13r

Step-by-step explanation:

8+9=17-11=6+7=13

7 0
2 years ago
Read 2 more answers
Mrs. Spring left half of her estate to her son Sam. She left half of the remaining half to her cousin Fred. She left half of the
FinnZ [79.3K]

The total amount of Mrs. Spring's estate is $200,000

<h3>What is a fraction?</h3>

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Let the total estate = 100x

Share left with Sam = 50x

Remaining share = 50x

Now,

Share left with cousin Fred = 1/2 of 50x = 25x

Remaining  share = 25x

Share left with nephew Bill = 1/2 x (25x) = 12.5x

Remaining share = 12.5x

Share left with the care of the cat Chester = 12.5x

12.5x = $25,000

Now,

12.5x = $25,000

Multiply with 100/12.5 on both sides.

100/12.5 x 12.5x = 100/12.5 x $25,000

100x = $200,000

Thus,

The total amount of Mrs. Spring's estate is $200,000

Learn more about fractions here:

brainly.com/question/24370499

#SPJ1

5 0
1 year ago
Solve 9x-10÷2=x+9<br>explain how​
Mariulka [41]

Answer:

x = 4

Step-by-step explanation:

7 0
3 years ago
Hi please help me ill give you uh brainlest
alina1380 [7]

Answer:

<h2>1.1</h2>

is answer

plz mark as brainliest plz

6 0
2 years ago
Read 2 more answers
Other questions:
  • I'm smart just giving point...whats 9 time 3
    13·2 answers
  • A circular pizza that is 18 inches in diameter is cut into 8 equal slices. What is the area of a single slice?
    8·1 answer
  • Which equation represents the graph?
    10·1 answer
  • How much do you have to add to 1,750 m to get 4 m?
    13·1 answer
  • What is the constant of proportionality y=4.75x
    7·1 answer
  • What percent of 25 is 20?<br> A) 40%<br> B) 50%<br> C) 60%<br> D) 80%
    10·2 answers
  • Please answer need help
    13·1 answer
  • jim is selling greeting cards at a booth at a folk fair. he will be paid $12 plus $2 for each box that he sells how many boxes m
    12·1 answer
  • For your speech to be effective, you must carefully consider what your specific _____________ is. a. purpose b. audience c. thes
    13·1 answer
  • I will award brainliest to whoever correctly answers this!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!