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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:

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When the factors of a trinomial are (x+p) and (x-q) then the coeffcient of the x term in the trinomial is?
Tatiana [17]
The coefficient is:  "1" .
____________________________________________________
          Note:  There is an "<u>implied coefficient</u>" of "1"; since "1",  multiplied by any value, is equal to that exact same value; by convention, we eliminate the "1" as a coefficient.
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Further explanation:
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(x+p)(x−q) = x² − xq + px − pq ;
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<u>F</u>irst:    x*x = x² ;

<u>O</u>uter: x*(-q)= -xq ;

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4 0
3 years ago
17.4 x 1.0 Will the product be less than 17.4, equal to 17.4, or greater than 17.4? 17.4 × 0.98 Less than 17.4 Equal to 17.4 Gre
nikdorinn [45]

Answer:

1) Equal to 17.4

2)Less than 17.4

Step-by-step explanation:

One thing we must always remember that when we have number 0 after the decimal point, it means we do not need to consider that as it will have no effect on product and on the other operations.

So,

1)

17.4 x 1.0 = 17.4 x 1 = 17.4  (Product is equal to 17.4)

2)

Suppose if a number 'A' which is less than 1 is multiplied by any other number 'B', than the multiplication always result in the number less than B.

For example:

1x0.5 = 0.5 which is less than 1

Similarly for

17.4 x 0.98 = Result will be less than 17.4 as the second number is less than 1.

Product is less than 17.4

3 0
3 years ago
1cm 8cm 4cm: surface area
valkas [14]

Answer:

Perimeter of Triangle sum of all sides.

=13 cm

6 0
2 years ago
Read 2 more answers
Note: Figure is not drawn to scale.
zaharov [31]

The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of kite = (product of diagonals)/2

Area of kite = (10 * 14) / 2 = 70 in²

The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².

Find out more on equation at: brainly.com/question/2972832

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6 0
2 years ago
Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one a
BartSMP [9]

Answer: The required conclusion is

"if in triangle ABC, AB ≅ AC, then ∠B and ∠C must be congruent".

Step-by-step explanation:  Given that in triangle ABC,  AB ≅ AC, implies that AB = AC must be true. We are given to assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other.

If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem.

For the same reason, if m∠B < m∠C, then AC < AB.

This is a contradiction to the given information.

We are to state the conclusion.

Since in the beginning, it is given that AB ≅ AC and we have assumed that ∠B and ∠C are not congruent, so

our assumption must be wrong.

That is, ∠B and ∠C must be congruent.

Thus, the required conclusion is

if in triangle ABC, AB ≅ AC, then ∠B and ∠C must be congruent.

5 0
3 years ago
Read 2 more answers
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