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.
Answers
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:
Related Questions
Can someone please help me with this question? Thanks.
Answers
Answer:
f(x) = 3 + 5x
Step-by-step explanation:
For this problem, we can see a simple pattern whereas x increases by 1, y is increasing by 5.
This means that f(0) = 3.
And to create the function, we simply use f(0) summed with the increasing 5 multiplied by the input x.
Hence, we will create the function equation:
f(x) = 3 + 5x
Cheers.
Which represents the equation of the line? *
1 point
у
10
NA 0000
1 (2, 2)
-10-8
-4
12 4 6
8
-20
-2.
10
-4
(0, -4)
-6
10
Answers
Answer:
2
Step-by-step explanation:
A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7.
Suppose you want to scale the copy back to its original size. What scale factor should you use?
Answers
Answer:
1/7.
Step-by-step explanation:
You use the inverse of 7 which is 1/7.
In order to back to its original size, we need to take a scale factor of 1/7.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
For example, 50 meters is very big so we cannot measure it but if we can convert it into 50 mm such that the scale ratio is maintained then it will be easy to draw.
If the rectangle is scaled by scale factor 7 it means it is plotted 7 times big such that a 7:1 scale factor maintain.
Now if we want to see the original rectangle then we need to take 7 times lower than that so a 1/7 scale factor is going to use.
Hence "In order to back to its original size, we need to take a scale factor of 1/7".
To learn more about scale factors,
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A Poker hand consisting of five cards is dealt from a deck of fifty two cards. What is the probability that the Poker hand consists of four spades and one heart?
Answers
Answer: 108336
Step-by-step explanation:
given data:
cards on deck = 52
Since 2 queens are supposed to be in the 5 card hand. Therefore, 2 queens are choosen since we have a total of 4.
Since 2 Queens have been chosen already choosen. we are left with 3cards out of the hand of 5. This cards are to be choosen from the 48 remaining cards. Similarly same process would be used for other combination of playing cards.
(42∗483)+(43∗482)+(44∗481).
= (6 * 17296) + (4 * 1128 ) + (1 * 48)
= 103776 + 4512 + 48
=108336
Use the box-and-whisker plot shown to answer the following question.
What is the interquartile range?
A. 4
B. 6
C. 9
Answers
Answer:
15-9=6 So the answer is B. 6
Simply the exponential expression 5^2
Answers
Answer:
25
Step-by-step explanation:
Please urgent answer needed with steps
Answers
Answer:
43.3
Step-by-step explanation:
Area = Base * Height
Area = 7 * 6.2
Area = 43.3
Given the relation D={(6,4), (8,-1), (x,7), (-3,-6)}. Which of the following values for x will make relation D a function? (A)-3 (B)-6 (C) 8 (D) 6
Answers
Answer:
(B) -6
Step-by-step explanation:
If D is to be a functions, the value of x cannot repeat any of the other values listed first in the ordered pairs. Values of 6, 8, and -3 must be rejected. The only remaining answer choice is -6.
The difference of four times a number and six is two. Find the number
Answers
Step-by-step explanation:
4(x-6)=2
4x-24=2
4x=2+24
4x=28
x=7
If an objects mass is 10kg what is it’s weight?
Answers
Answer:
Weight varies with location depending upon the acceleration due to gravity eg. for a mass m = 10kg on Earth it`s weight is W = mg = 10 x 10 = 100N.
Step-by-step explanation:
The compositions f(g(x)) and g(f(x)) of functions fand g are shown on the graphWhich statements describe the compositions? Check all that apply
Answers
Answer:
a,c,d,f had the same problem just now
Step-by-step explanation:
Answer:
The answers are A, C, D, E !
Step-by-step explanation:
30 Points! will mark brainliest. answer asap Two angles form a linear pair. The measure of one angle is 23 the measure of the other angle. Find the measure of each angle. Smallest angle: Largest angle:
Answers
Answer:
157 degrees
Step-by-step explanation:
the two angles should add up to 180 degrees, so 180 - 23 = 157
answer
smallest 72 and the largest 108
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.α = 0.1 for a two-tailed test.a. ±1.645b. ±2.052c. ±1.4805d. ±2.33
Answers
Answer:
The critical z value used to test a null hypothesis is ±1.645.
Step-by-step explanation:
We are given that the data has a normal distribution and the number of observations is greater than fifty.
And we have to find the critical z value used to test a null hypothesis at α = 0.1 for a two-tailed test.
Firstly, as we know that to find the critical z value we need only the level of significance to be known.
Here, the level of significance is given = [tex]\alpha[/tex] = 0.10
But for the two-tailed test, the level of significance to be considered is given by = [tex]\frac{\alpha }{2}[/tex] = [tex]\frac{0.10}{2}[/tex] = 0.05 or 5%.
Now, in the z table; we can see that the critical z value at a 5% level of significance (for the two-tailed test) is given as 1.645.
Hence, the critical z value used to test a null hypothesis at α = 0.1 for a two-tailed test is ±1.645.
According to the z-distribution, the critical value is given by:
a. ±1.645
The critical value for a two-tailed test with a significance level of [tex]\alpha[/tex] is |z| such that -z has a p-value of [tex]\frac{\alpha}{2}[/tex].
In this problem, [tex]\alpha = 0.1[/tex], then [tex]\frac{\alpha}{2} = 0.05[/tex].
Looking at the z-table, z has a p-value of 0.05 for z = -1.645, hence the critical value is ±1.645A similar problem is given at https://brainly.com/question/18306091
A space for storing boxes is 36 inches high. Each box is 6 inches high. A space of 9 inches must be left at the top. what is the maximum number of boxes that can be stacked in this space?
Answers
Answer:
Step-by-step explanation: 36-9 equals 27. You can only fit 4 evenly so thats the answer
The maximum number of boxes that can be stacked in the space of 36 inches keeping 9 inches on the top empty is 4.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that the height of the space in which boxes are needed to be stored is 36 inches high. Also, the height of the box is 6 inches.
But a space of 9 inches must be left at the top. Therefore, the space left to keep the boxes is,
Space left to keep the boxes = 36 inches - 9 inches
= 27 inches
Now, the number of boxes that can be put in the leftover space is,
Number of boxes = 27 inches / 6 inches
= 4.5
Since a half box can be placed in the space, therefore, the number of boxes that can be in the space is 4.
Hence, the maximum number of boxes that can be stacked in the space of 36 inches keeping 9 inches on the top empty is 4.
Learn more about Division here:
https://brainly.com/question/369266
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Solve the equation: q – 17 = 23
Answers
Answer:
Hey there!
q-17=23
+17=+17
q=40
Let me know if this helps :)
Explanation:
q - 17 = 23
q = 23 + 17
q = 40
1/2 (b - 10) + 2b = 25
Answers
Answer:
the answer is 12
Step-by-step explanation:
Simplify both sides of the equation.
12(b−10)+2b=25
(12)(b)+(12)(−10)+2b=25(Distribute)
12b+−5+2b=25
(12b+2b)+(−5)=25 (Combine Like Terms)
52b+−5=25
52b−5=25
add 5 to both sides.
52b−5+5=25+5
52b=30
multiply both sides by 2/5.
(25)*(52b)=(25)*(30)
b=12
Answer:
b=12
Step-by-step explanation:
1/2 (b - 10) + 2b = 25
Multiply each side by 2 to get rid of the fractions
2*1/2 (b - 10) +2* 2b = 25*2
b-10 +4b = 50
Combine like terms
5b -10 = 50
Add 10 to each side
5b -10+10 = 50+10
5b = 60
Divide by 5
5b/5 = 60/5
b = 12
The water level at the Dead Sea dropped from 390 meters below sea level in 1930 to 423 meters below sea level in 2010. By how much did the water level drop from 1930 to 2010?
Answers
Answer:
33ft below sea level
Step-by-step explanation:
423-390=33ft
Which polynomials can be factored using the binomial theorem? Check all that apply. x2 + 20x + 400 x2 + 40x + 400 x3 – 3x2 + 9x – 27 x3 – 9x2 – 27x – 27 256x4 – 64x3 + 16x2 – 4x + 1 256x4 – 256x3 + 96x2 – 16x + 1
Answers
Answer:
(x2 - 5x + 7) • (x - 4)
Step-by-step explanation:
Answer:
SECOND AND LAST ONE
x2 + 40x + 400
256x4 – 256x3 + 96x2 – 16x + 1
Step-by-step explanation:
Graph the function and select the y-intercept
y = 2 • 3^x
a. 1
b. 2
c. 3
d. 4
Answers
Answer:
For the graph see attached image.
The y-intercept is 2
Step-by-step explanation:
The requested graph of the function is included in the attached image.
The y-intercept can be seen from the image, but also from finding the y-value when x= 0 (zero):
[tex]y=2\,\,\,3^x\\y=2\,\,\,3^0\\y = 2 \,\,\,(1)\\y = 2[/tex]
Answer:
To graph the function y = 2 • 3^x, we can start by identifying the y-intercept. The y-intercept is the point where the graph intersects the y-axis, which occurs when x = 0.
To find the y-intercept, we substitute x = 0 into the equation y = 2 • 3^x:
y = 2 • 3^0 = 2 • 1 = 2
Therefore, the y-intercept is 2, which corresponds to option (B).
A father earns a $2000 dividend from an oil investment and
distributes it equally amongst his children.
Answers
Answer:
To divide the money evenly, without him taking any, use the formula in which x is the amount of children.
2000/x
It's that simple!
2000 dollars divided by x children.
I'm sorry if I misunderstood.
Good luck mate! :)
Please add Brainliest if you'd like, not that it matters.
Remember to try your best every day!
sketch and label the figures described. Use dashes for hidden parts.
Answers
Answer:
this means that the figures given to you , sketch and label the ones described and use dashes for hidden one
Step-by-step explanation:
If the correlation coefficient has a negative value, then the coefficient of determination:_________.a. can take on either a negative or positive value.b. must be positive.c. will also have a negative value.d. will equal zero.
Answers
Answer:
Step-by-step explanation:
The sign of r depends on the sign of the estimated slope coefficient b1:
If b1 is negative, then r takes a negative sign.
If b1 is positive, then r takes a positive sign.
That is, the estimated slope and the correlation coefficient r always share the same sign. Furthermore, because r2 is always a number between 0 and 1, the correlation coefficient r is always a number between -1 and 1.
One advantage of r is that it is unitless, allowing researchers to make sense of correlation coefficients calculated on different data sets with different units. The "unitless-ness" of the measure can be seen from an alternative formula for r, namely:
r=∑ni=1(xi−x¯)(yi−y¯)∑ni=1(xi−x¯)2∑ni=1(yi−y¯)2−−−−−−−−−−−−−−−−−−−−−−−√
If x is the height of an individual measured in inches and y is the weight of the individual measured in pounds, then the units for the numerator is inches × pounds. Similarly, the units for the denominator is inches × pounds. Because they are the same, the units in the numerator and denominator cancel each other out, yielding a "unitless" measure.
Another formula for r that you might see in the regression literature is one that illustrates how the correlation coefficient r is a function of the estimated slope coefficient b1:
r=∑ni=1(xi−x¯)2−−−−−−−−−−−−√∑ni=1(yi−y¯)2−−−−−−−−−−−√×b1
Which of these is a factor in this expression- 7z^4-5+10(y^3+2). Choices- A- 7z^4-5, B- 10(y^3+2) C = -5+10(y^3+2) D= (y^3+2)
Answers
Answer:
D. ([tex]y^{3}[/tex] + 2)
Step-by-step explanation:
A factor of an expression can either be in the form of an algebraic expression, alphabet or number. In the question, the given expression can be written as;
7[tex]z^{4}[/tex] - 5 + 10[tex]y^{3}[/tex] + 20
Factorizing the expression gives;
7[tex]z^{4}[/tex] - 5 + 10([tex]y^{3}[/tex] + 2)
Therefore, it would be observed that the factor in the expression is;
([tex]y^{3}[/tex] + 2)
A number divided by eleven.
Answers
Answer:
Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number. So, for instance, 2728 has alternating sum of digits 2 – 7 + 2 – 8 = -11. Since -11 is divisible by 11, so is 2728.
Refer to the following distribution of commissions:______. Monthly Commissions Class Frequencies $600 up to $800 3 $800 up to 1,000 7 $1,000 up to $1,200 11 $1,200 up to $1,400 22 $1,400 up to $1,600 40 $1,600 up to $1,800 24 $1,800 up to $2,000 9 $2,000 up to $2,200 4 For the preceding distribution, what is the midpoint of the class with the greatest frequency?
Answers
Answer:
the midpoint of the class with the greatest frequency 1500
Step-by-step explanation:
The illustration of the dataset given can be well represented in a table format as shown below.
Class Frequency Relative Frequency
$600 - $800 3 [tex]\mathbf{ \dfrac{3}{120} = 0.025}[/tex]
$800 - $1000 7 [tex]\mathbf{ \dfrac{7}{120} = 0.059}[/tex]
$1000 - $1200 11 [tex]\mathbf{ \dfrac{11}{120} = 0.092}[/tex]
$1200 - $1400 22 [tex]\mathbf{ \dfrac{22}{120} = 0.183}[/tex]
$1400 - $1600 40 [tex]\mathbf{ \dfrac{40}{120} = 0.333}[/tex]
$1600 - $1800 24 [tex]\mathbf{ \dfrac{24}{120} = 0.2}[/tex]
$1800 - $2000 9 [tex]\mathbf{ \dfrac{9}{120} = 0.075}[/tex]
$2000 - $2200 4 [tex]\mathbf{ \dfrac{4}{120} = 0.033}[/tex]
Total 120 1
Therefore, the midpoint of the class with the greatest frequency is between $1400 - $1600 since the frequency 40 happens to be the greatest frequency
The midpoint =[tex]\dfrac{upper \ limit + \ lower \ limit}{2}[/tex]
The midpoint =[tex]\dfrac{1400+1600}{2}[/tex]
= 1500
Simplify 4(x + 40) +2(x -3) plsss help
Answers
Answer:
6x + 154
Step-by-step explanation:
4(x + 40) +2(x -3) =
4x + 160 + 2x - 6 =
6x + 154
Answer:
2(3x + 77)
Step-by-step explanation:
4(x+40)+2(x-3)
4x+160+2x-6
6x+154
=2(3x+77)
PLEASE ANSWER QUICK!Kierran is trying to find the circumference of a circle. He knows that the radius (r) of the circle is 6 feet and that the diameter, d=2r. Which formula should he use?
A) A=3.14(2r)^2
B) C=3.14(2r)
C) A=3.14d^3
D) C=3.14(2D)
Answers
Answer:
B.Step-by-step explanation:
The formula for the circumference is of a circle is: C = 2πr. ___________________________________________________________
I AM ALWAYS HAPPY TO HELP :)PLEASE HELP I WANNA Sleep BC it's midnight
Please answer both A and B
For Brainliest
Answers
Pick any of the two sides and set them equal to one another. So we'll have three different equations
4(x-1) = x+8
or
x+8 = 2x+4
or
4(x-1) = 2x+4
This works because in any equilateral triangle, the three sides are the same length.
--------------------------
If you're curious about the value of x, then we could do the following steps.
x+8 = 2x+4
2x+4 = x+8
2x-x = 8-4
x = 4
If x = 4, then
4(x-1) = 4(4-1) = 12x+8 = 4+8 = 122x+4 = 2*4+4 = 12Each side is 12 units long
Answer:
5-x=40+29 (x=69)
Step-by-step explanation:
Wich compound inequality is graphed below?
Answers
Answer:
the third one: -15 <= 4x-3 < 5
You buy a container of cat litter for $12.25 in a bag of cat food for X dollars the total purchase is $19.08 which includes 6% sales tax right and solve equation to find the cost of the cat food
Answers
Answer:
List Price = $ 20.30
Discount Amount = $ 1.22