Prove that the area of a regular n-gon, with a side of length s, is given by the formula: ns2 Area = 4 tan (15) (Note: when n = 3, we get the familiar formula for the area of an equilateral triangle 2V3 which is .) 4. s3 )

Answers

Answer 1

The area of a regular n-gon with side length s is given by ns2(2 + √3)/4, or ns2tan(π/n)/4 using the trigonometric identity.

Consider a regular n-gon with side length s. We can divide the n-gon into n congruent isosceles triangles, each with base s and equal angles. Let one such triangle be denoted by ABC, where A and B are vertices of the n-gon and C is the midpoint of a side.

The angle at vertex A is equal to 360°/n since the n-gon is regular. The angle at vertex C is equal to half of that angle, or 180°/n, since C is the midpoint of a side. Thus, the angle at vertex B is equal to (360°/n - 180°/n) = 2π/n radians.

We can now use trigonometry to find the area of the triangle ABC: the height of the triangle is given by h = (s/2)tan(π/n), and the area is A = (1/2)sh. Since there are n such triangles in the n-gon, the total area is given by ns2tan(π/n)/4.

Using the fact that tan(π/12) = √6 - √2, we can simplify this expression to ns2(√6 - √2)/4. Multiplying top and bottom by (√6 + √2), we obtain ns2(2 + √3)/4.

For such more questions on Trigonometric identity:

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Related Questions

hi guys..............

please guys answer the correct answer

Answers

Answer:

12) 1.5(m - n)/b13) 2t/(2c + d)

Step-by-step explanation:

Question 12)

Slope between the points:

A(a + b, 4m - n) and B(a - b, m + 2n)

Use slope formula:

Slope = (m + 2n - 4m + n)/(a - b - a - b) = (-3m + 3n)/(-2b) = (-3)(m - n)/(-2)b 1.5(m - n)/bQuestion 13)

Slope between the points:

C(3c - d, s + t) and D(c - 2d, s - t)

Use slope formula:

Slope = (s - t - s - t)/(c - 2d - 3c + d) = (-2t)/(-2c - d) = (-2)t/(-1)(2c + d) 2t/(2c + d)

Find the area of the triangle.

Answers

answer: 28

explanation: a= 8(7)/2 = 28

hope this helps :)

What is the meaning of a sample in mathematics?

Answers

Answer:

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.

Step-by-step explanation:

En un hotel hay 67 habitaciones entre dobles y sencillas, si el número de camas es 92. ¿Cuántas habitaciones hay de cada tipo?

Answers

Answer:

25 dobles y 42 sencillas

Step-by-step explanation:

25 x 2 = 50 camas + 42 = 92

y 25 habitaciones dobles + 42 sencillas = 67

Please answer the photo.

Answers

Answer:

the answer i think is C. AB

Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?

Answers

2(2) + 3(3) =

4 + 9 = 13

I don't know what 90p means but basically, u have to multiply that by 3 and add it to our current total which is 13.

Then, u substract the total cost from the 20 and you should get the change.

The cheerleading squad at Kensington High School had 18 members with the old coach. Now, with the new coach, there are 50% more members on the squad, how many members are on the squad now

Answers

Answer:

27 members

Step-by-step explanation:

So we have 18 members and we see a 50% increase in members.

So:

Now the squad is 150% of 18

We can set up a percent proportion

x/150=18/100

To solve, we do:

(150*18)/100 = x

27 = x

There is an easier way to do this with benchmark fractions.

We find 50% of 18 which is 9

And since it's a 50% increase, we add 9 to 18 and get 27

Let me know if you have any questions

Answer:

B) 8 + J

(It's saying my answer is too short, not too sure why)

The spinner below is divided into five equal-sized sectors. What is the probability that the spinner will stop on a number greater than 3?

Answers

Answer:

40%

Step-by-step explanation: If you have five equal-sized sectors, then the probability that the spinner will stop on 4 and 5 is 40%.

The probability that the spinner will stop on a number greater than 3 will be 0.4 or 40%.

What is probability?

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

The spinner below is divided into five equal-sized sectors.

The probability of it stopping more than 3 = probability of stops at 4 + probability of stops at 5.

⇒ 1/5 + 1/5

⇒ 2/5 = 0.4

So, 0.4 x 100 = 40%

Hence "The probability that the spinner will stop on a number greater than 3 will be 0.4 or 40%".

For more information about the probability,

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The angle of depression from a window 10 m above the ground to a coin on the ground is
15°. Find the distance of the coin from the base of the building.

Answers

Answer:

37.3 m

Step-by-step explanation:

Let the distance of the coin to the base of the building be represented by x. Applying the required trigonometric function, we have:

Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]

Tan 15 = [tex]\frac{10}{x}[/tex]

0.2680 = [tex]\frac{10}{x}[/tex]

x = [tex]\frac{10}{0.2680}[/tex]

= 37.3134

x = 37.3 m

The distance of the coin from the base of the building is 37.3 m.

Help pls ^picture^

I really need this quick

Answers

Answer:

[tex]4.4*10^9[/tex]

Step-by-step explanation:

[tex]8.8(10^6)(5(10^2))\\=8800000*500\\=8.8*1000000*5*100\\=(8.8*5)*(1000000*100)\\=44*100000000\\=4400000000\\4400000000=4.4*10^9[/tex]

Rafael and his sister bought snacks for movie night.

Rafael got 3 boxed candies and 1 bag of chips for $6.99.

His sister got 2 bags of chips and 1 boxed candy for $5.98.

Find the cost for 1 of each of these items in dollars.

Answers

Answer:

1. $2.33

2. $2.99

Step-by-step explanation:

$6.99/3

$5.98/2

Answer:

bag of chips is 2.19

boxed candy is 1.60

Step-by-step explanation:

Desmos Calcuator

Solve for x : 80 + x = 100 - 14

Answers

Answer:

x=6

Step-by-step explanation:

100-14=86

86-80=6

8(8p+8)=640 solve
Answer ASAP please

Answers

Answer:

p = 9

Step-by-step explanation:

8(8p + 8) = 640

use the dist property

64p + 64 = 640

-64 -64

64p = 576

divide by 64

p = 9

Answer:

Step-by-step explanation:

What are the 2 roots of the equation 2x^2-5x-3=0

Answers

Answer:

Hence, 3/2 and 1 are the roots of the equation.

The slope of a line passing through the point (5.-6) is 0.4.
Drag the proper numbers and signs to obtain the equation of the line in slope-intercept form.

Answers

Answer:

using formula y2-y1/x2-x1, x1= -6,x2= o, y1= 5,y2= 4

Step-by-step explanation:

4-5/0-(-6)

-1/0+6

-1/6

is your answer

Help ASAP I’ll give you brainlest

Answers

Answer:

5.33 OR 5 1/3

Step-by-step explanation:

3 x 2³ ÷ 2 x 4 -1 +2

3 x 8 ÷ 2 x 4 -1 + 2

24 ÷ 8 +1

24 ÷ 9

2.66 OR 2 2/3

Our teacher hasn’t explained the concept yet but class was canceled today

Answers

Answer:

What grade is this?

Step-by-step explanation:

Which equation is the result of adding theses two equations -2x+4y=17 3x-10y=-3

Answers

Answer:

x=-79/4, y=-45/8. (-79/4, -45/8).

Step-by-step explanation:

-2x+4y=17

3x-10y=-3

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

3(-2x+4y)=3(17)

2(3x-10y)=2(-3)

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

-6x+12y=51

6x-20y=-6

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

-8y=45

y=45/-8=-45/8

3x-10(-45/8)=-3

3x+450/8=-3

3x+225/4=-3

3x=-3-225/4

3x=-12/4-225/4

3x=-237/4

x=(-237/4)/3

x=(-237/4)(1/3)

x=-237/12=-79/4

Please help.
Algebra.

Answers

1. 5

2. 3

This is the answer

Answer:

question 1 should be 5 and question 2 should be 3

Step-by-step explanation:

Probably of Carl solving the 10 problems if there's 20 to study and he knows 15 and ten of the 20 are on the test.

Answers

Answer:

1/3

Step-by-step explanation:

Probability of solving ten problems by Carl

Given

Total number of problems = 20

Number of problems studied by Carl = 15

Number of problems out of the 20 set of problem coming in test is 10

Case I - All ten problems come from the set of known 15 question

10/15 * 10/20 = 1/3

Adrianna is two years older than Fernando, while Lucy is triple Fernando's age. If the sum of their ages is eighty-two, how old is Adrianna?

HELPPPP MEEEEE!!!!!!

Answers

27 i think lol :) x byeeeee

Answer:

Step-by-step explanation:

x + (2+x)+ (3x) =82

x+x+3x= 82-2

5x=80

x= 16

Fernando is 16

Adrianna is 2 years older so she is 18

And Lucy is 3x 16=48

together 82

Is my answer right? I don’t really know this subject very well

Answers

First let's review how to find the surface area of a rectangular prism. Since the opposite faces have the same area, we just need to find one of each pair of faces and multiply the result by 2.

One face in each pairs adds up to 6*4+2*4+2*6=24+8+12=44

Now we just need to multiply this by 2!

44*2=88 cm^2

I really hope my explanation helped, if there are any more question about this please ask me in the comments I will answer them.

Select the correct answer.

What are the factors of the function represented by this graph?

A. (x − 4) and (x − 8)
B. (x − 4) and (x + 8)
C. (x + 4) and (x − 8)
D. (x + 4) and (x + 8)

Answers

The factors of the function represented by the graph are (x + 4) and (x - 8)

How to determine the factors of the function represented by the graph?

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that:

The graph intersects with the x-axis at x = -4 and x = 8

So, we have

x = -4 and x = 8

Set the equations to 0

So, we have

x + 4 = 0 and x - 8 = 0

This means that the factors of the function represented by the graph are (x + 4) and (x - 8)

Answers

Answer:

Step-by-step explanation:

you take 7/5 and turn it into an improper fraction

you then have 1 2/5

1 2/5 is smaller then 11

HELPPPPP HELLPPPPPP Plsss

Answers

Answer:

1) -5

2) 21

3) 60

4) -52

5) -12

6) 31

7) -16

8) -27

9) 5

10) -11

11) 16

12) -24

13) 11

14) -36

15) 2

16) 36

17) -31

18) -48

19) -24

20) -21

need help in this show working please

Answers

this is what i got hope it helps

Please help due today

Answers

(-2, 4) area is 10 units

Help Please

Acellus:
Find the value of Y in angle measures and segment lengths

Answers

Did you try to do the math photo part of this app but i think it’s 6cm

Answer:

4.3

Step-by-step explanation:

I hope this helps!

Andre says that 534+ 214= 712 because 748= 712. Identify his mistake.

Answers

Step-by-step explanation:

748 ≠ 712 so 534 + 214 only = 748 not 712

He is wrong because it equals it equals 748 and 712 has nothing to do with it

Solve for value the two angles in the triangle and classify the triangle using the sides and angles

Answers

Step-by-step explanation:

x + 15 +2x + 66 = 180

3x + 81 = 180

3x = 99

x = 99/3 = 33

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.

Answer:

The angles are 66, 66, and 48 degrees

The triangle is isosceles because 2 angles are equal, thus two leg lengths are equal

Step-by-step explanation:

the sum of all three angles in a triangle = 180 degrees

66 + 2x + (x+15) = 180

simplify

66 +3x + 15 = 180

reduce

81 + 3x = 180

subtract 81 from each side

81 - 81 + 3x = 180 - 81

3x = 99

divide both sides by 3

3x/3 = 99/3

x = 33

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