Answers
Answer:
[tex]\large \boxed{\sf \ \ \pi r^2 \ \ }[/tex]
Step-by-step explanation:
Hello,
We will follow the instructions and then we need first to find the area of any regular n-gon.
I attached one graph so that it is easier to understand.
The n-gon can be divided in n similar isosceles triangles.
So we can find the area of one of these triangles and then multiply by n to get the total area, right?
Let's focus on the triangle OAB then. OA = OB = r, right?
The area of this triangle is the (altitude * AB ) / 2
The angle AOB is [tex]\dfrac{2\pi}{n}[/tex] by construction of the regular n-gon.
So half this angle is [tex]\dfrac{\pi}{n}[/tex] and we can use cosine rule to come up with the altitude:
[tex]\boxed{ altitude = r\cdot cos(\dfrac{\pi}{n}) }[/tex]
Using the sine rule we can write that
[tex]\boxed{ AB=2r\cdot sin{\dfrac{\pi}{n}} }[/tex]
So, the area of the triangle is
[tex]\dfrac{1}{2}\cdot r\cdot cos(\dfrac{\pi}{n}) } \cdot 2r\cdot sin(\dfrac{\pi}{n})\\\\=r^2\cdot cos(\dfrac{\pi}{n})\cdot sin(\dfrac{\pi}{n})[/tex]
Ok, but wait, we know how to simplify. We can use that
[tex]sin(2\theta)=2cos(\theta)sin(\theta)[/tex]
So it gives that the area of one triangle is:
[tex]\dfrac{1}{2}r^2sin(\frac{2\pi}{n})[/tex]
Last step, we need to multiply by n.
[tex]\large \boxed{\sf \ \ A(n)=\dfrac{1}{2}nr^2sin(\dfrac{2\pi}{n}) \ \ }[/tex]
Now, let's use a result from Calculus:
[tex]\displaystyle \lim_{x\rightarrow0} \dfrac{sin(x)}{x}=1[/tex]
How to use it here? Just notice that
[tex]\displaystyle \lim_{n\rightarrow +\infty} \dfrac{sin(\dfrac{2\pi}{n})}{\dfrac{2\pi}{n}}=1\\\\\lim_{n\rightarrow +\infty} \dfrac{n}{2\pi}sin(\dfrac{2\pi}{n})=1\\\\\lim_{n\rightarrow +\infty} nsin(\dfrac{2\pi}{n})=2\pi[/tex]
So, finally
[tex]\Large \boxed{\sf \lim_{n\rightarrow +\infty} A(n)=\dfrac{1}{2}r^22\pi=\pi r^2 }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Related Questions
Un agricultor tiene 140 metros de malla para instalar una cerca en su huerta de hortalizas y esa tiene forma de rectangulo a) encuentra una función que modele el área de la huerta que pueda cercar b)¿Para que valor de la longitud del largo, el area es Maxima?
Answers
Tenemos que sean x e y los lados de la huerta entonces el perímetro sería:
P = 2*x + 2*y
Sabemos que el perimetro es 140, reemplazando:
140 = 2*x + 2*y
x + y = 70
despejamos y, nos queda:
y = 70 - x
Ahora tenemos que el área sería:
A = x*y
reemplazamos y:
A = x*(70 - x)
A = 70*x - x^2
Esta sería la ecuación que modela el área de la huerta.
Derivamos e igualamos a 0:
0 = 70 - 2*x
x = 70/2
x = 35
ahora calculamos y:
y = 70 - 35
y = 35
El área máxima sería:
A = 35*35
A = 1225 m^2
The altitude at which we boil an egg affects how long it takes for the egg to achieve perfect hardness. It takes 198198198 seconds to boil a perfect egg at the lowest place possible, the edge of the Dead Sea, which has an altitude of -418−418minus, 418 meters. The highest place possible is the summit of Mount Everest which has an altitude of 884888488848 meters. It takes 209209209 seconds to boil a perfect egg there. T(a)T(a)T, left parenthesis, a, right parenthesis models the time (in seconds) it takes to boil a perfect egg at an altitude of aaa meters. Which number type is more appropriate for the domain of TTT?
Answers
Answer:
The domain is -418 < a < 8848 where a is an integer.
Step-by-step explanation:
We see from the data given that the domain of T(a) takes both positive and negative integer values ( 8848 meters and -418 meters); T(a) never gets decimal values (and in real life thy won't be of much use because we are not looking for that much accuracy).
So the appropriate number type for the domain of T(a) would be integers. And if you are interested, the domain is -418 < a < 8848.
A length is stated as 4 m correct to the nearest m. What is the lower bound?
Answers
The lower bound is the smallest value that rounds up to the given value.
Given value = 4m
The lower bound would be 3.5m
Any number less than .5 rounds down, any number greater to or equal to 0.5 rounds up, so if you have 3.5 or higher it rounds to 4
Evaluate 5(x-1)-2 when x=3
Answers
Answer:
8
Step-by-step explanation:
5(x-1)-2
Put x as 3 and evaluate.
5(3-1)-2
5(2)-2
10-2
= 8
Answer:
8solution,
X=3
[tex]5(x - 1) - 2 \\ putting \: the \: value \: of \: x \\ = 5(3 - 1) - 2 \\ = 5 \times 2 - 2 \\ = 10 - 2 \\ = 8[/tex]
1. The ratios of the side lengths of triangle ABC are 7:9:12 and the perimeter is 168 m. Find the lengths of each side.
Answers
Answer:
d
Step-by-step explanation:
What is the area of a circle whose diameter is 64
Answers
Answer:
A ≈ 3215.36
Step-by-step explanation:
A = πr²
Radius - D/2
Radius - 64/2 → 32
A = 3.14(32)²
A = 3215.36
Hope this helps! :)
Answer:
3215.36 um²
Step-by-step explanation:
d = 2r => r = d/2 = 64/2 = 32 um
A = π·r²
= 3.14·32²
= 3.14·1024
≈ 3215.36 um²
I need help with this question!
Answers
Answer:
A = 0 -7 b= 0 -7
3 2d 3 2d
Let's calculate A and B:
A= 0*2d- 3*(-7) = -3*(-7) = 21B= 0.2d- 3*(-7) = -3*(-7) = 21Calculte (AB)^(-1):
(AB)^(-1) = (21*21)^(-1) = (21²)^(-1) = 21^(-2)Calculte B^(-1) and A^(-1):
B^(-1) * A^(-1) = 21^(-1) * 21^(-1)= 21^(-1-1) = 21^(-2)so:
(AB)^(-1) = B^(-1) * A^(-1)
Working out simultaneous equations.
Answers
Answer:
x = 6/5
y = 8/5
Step-by-step explanation:
3x - y = 2
2x + y = 4
Add the equations, cancelling y.
5x = 6
x = 6/5
Put x as 6/5 in the second equation and solve for y.
2(6/5) + y = 4
12/5 + y = 4
y = 4 - 12/5
y = 8/5
A pairing of numbers from domain to range is called as...?
Answers
Answer:
A relation
Step-by-step explanation:
A relation can be defined as a pairing of numbers in a data set. The pairing of numbers are the domain and the range.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
8x – 2 – 5x + 7 = one solution
Answers
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▹ Answer
3x + 5
▹ Step-by-Step Explanation
8x - 2 - 5x + 7
= 3x - 2 + 7
= 3x + 5
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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Answer: For the equation to have one solution, use any number that does not contain 3x.
Step-by-step explanation:
8x - 2 - 5x + 7
Combine like terms
3x + 5
someone help asap math 10
Answers
Answer:
Required angle measures 39°
Step-by-step explanation:
Let's say, x measures the angle between the hypotenuse and the common base of two triangles.
Sin(x) = 5/8
x = 39°
This angle is complementary to the angle other than theta (let's say y) in the required triangle.
90 - x = y and 90 - theta = y
>>> Theta = x
Best Regards!
Can someone help me I really need to finish this quick? Can someone tell me how to get 14.50?
Answers
Answer:
Please see details below
Step-by-step explanation:
Notice that since you have drawn mid-segments for all sides of the triangles, the three smaller triangles generated at the vertices, are all similar triangles to the large one (XYW).
Let's look at what happens with the smaller triangles:
Triangle QXR is similar to XYW, since the side QR has to be parallel to the big side WY. By construction, the side XQ is half of the side XW, therefore all sides of the smaller triangle *QXR formed must maintain the same proportion. Then side QR is half of side WY which makes side WY = 2 (2.93 cm) = 5.86 cm.
The same reasoning is valid when we compare triangle RYS with the larger triangle XYW: side RS of the small triangle is half of side XW of the large triangle, That is: XW = 2 (2.04 cm) = 4.08 cm
Similarly, small triangle SWQ is similar to XYW, and the side QS has to be half of side XY, therefore side XY = 2 (2.28 cm) = 4.56 cm
Then, the perimeter of triangle XYW is:
XY + YW + XW= 4.56 cm + 5.86 cm + 4.08 cm = 14.5 cm
a person earns $25,100 one year and gets a 5% raise in salary. what is the new salary?
Answers
Answer:
A 5% raise can be written as 1.05 so the new salary is 25100 * 1.05 = $26355.
Which situations would be represented with a positive number? Check all that apply.
The temperature outside is 34°F.
The Dead Sea is 1,349 feet below sea level.
Nicole lost 2 pounds last month.
Sebastian owes his friend $4
A football team gains 11 yards on a play.
Long Island Sound is at sea level.
Answers
Answer:
A and e
Step-by-step explanation:
Pls help? This is confusing
Answers
Answer:
8.1 metresStep-by-step explanation:
[tex]sin \: 54 = \frac{opposite \: side}{hypotenuse} [/tex]
[tex]sin \: 54 = \frac{h}{10} [/tex]
[tex]0.8090 = \frac{h}{10} [/tex]
[tex]h = 10 \times 0.8090[/tex]
[tex]h = 8.09[/tex]
[tex]h = 8.1[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
h = 8.1 m
Step-by-step explanation:
Sin 54 = [tex]\frac{opposite }{hypotenuse}[/tex]
Where opposite = h, hypotenuse = 10 m
0.809 * 10 = h
=> h = 8.1 m
Solve the triangle. Round your answers to the nearest tenth.
Answers
Answer:
<B = 47°
<C = 28°
b = AC = 28.0
Step-by-step explanation:
Given:
∆ABC
AB = c = 18
BC = a = 37
<A = 105°
Required:
Length of AC = b
measure of angle B and angle C
SOLUTION:
==>Use the sine rule, sin A/a = sinC/c to find the angle of C:
SinA = sin(105) = 0.9659
a = 37
sinC = ?
c = 18
0.9659/37 = sinC/18
Cross multiply
0.9659*18 = 37*sinC
17.3862 = 37*sinC
Divide both sides by 37
17.3862/37 = sinC
0.4699 = sinC
sinC = 0.4699
C = Sin-¹(0.4699)
C = 28.0° (nearest tenth)
==>Find angle B using sum of angles in a triangle:
Angle B = 180 - (105+28)
Angle B = 180 - 133
Angle B = 47°
==>Find length of b using sine rule, b/sinB = c/sinC:
SinC = sin(28) = 0.4695
SinB = sin(47) = 0.7314
c = 18
b = ?
b/0.7314 = 18/0.4695
Cross multiply
b*0.4695 = 18*0.7314
b*0.4695 = 13.1652
Divide both sides by 0.4695
b = 13.1652/0.4695
b = 28.0 (nearest tenth)
Which relation is a function of x?
Answers
Answer: The bottom option, the graph.
Step-by-step explanation:
A relation is something that gets input from a set, called domain (usually the x) and "transforms" them into an output, from a set called the range.
Now, a relation is only a function if, for all the elements x in the domain, each one of them has only one element y in the range associated to it.
For example, in the first set we can see that the value x = 1 appears two times, it is related to different values in the range, then this is not a function.
The second relation is not a function.
the third relation is:
x = 3*y^2 - 7
This is a function, but in this relation x is the output and y the input, so this is a function of y.
In the fourth relation we can see a graph, this is a function (each value in the domain is related to only one in the range), and in the horizontal axis we can see a x, so this is a function of x.
Answer:
D
Step-by-step explanation:
the sum of the first 6 terms of a geometric series is 15624 and the common ratio is 5. what is the first term of the series?
Answers
Answer:
first term a=4
Step-by-step explanation:
Sum of the first 6 terms S6 = 15624
common ratio r= 5
n= 6
first term a=?
Formula: S6= a(r^n-1)/r-1
15624 = a( 5^6-1)/5-1
15624 = a(15625-1)/4
15624= a( 15624)÷4
15624= 15624a÷4
Cross multiply
15624×4 = 15624a
62496 = 15624a
divide both sides by 15624
62496÷15624 = 15624a÷15624
4 = a
a= 4
two angles of a triangle measure 58 degrees and 104 degrees what is the measure of the third angle? A) 18 degrees B) 28 degrees C) 152 degrees D) 162 degrees
Answers
Answer:
a) 18
Step-by-step explanation:
you first add the 58 and 104 degrees,
=162
then you subtract,
=180-162
=18
hope this helps!
Answer:
18 is the third angle
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
58+104 +x = 180
Combine like terms
162+x = 180
Subtract 162
x = 180-162
x =18
Please help! Rhombus LMNO is shown with its diagonals. The length of LN is 30 centimeters. What is the length of LP? A.) 14 B.) 15 C.) 20 D.) 30
Answers
Answer:
B
Step-by-step explanation:
Since the diagonals of a rhombus bisect each other, that means P is the midpoint of LN. Therefore, LP = 1/2 * LN = 1/2 * 30 = 15.
Which of the following polynomials has a remainder of -7 when divided by x – 2?
A. 4x3 + 2x2 + 5
B. x3 - 2x2 - 4x + 1
c. 3x² + 6x - 2
D.-2x3 + 4x2 + 3x - 2
Answers
Answer:
[tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]
Step-by-step explanation:
Given
Polynomials A to D
Divisor: x - 2
Required
Which of polynomial A - D has a remainder of -7
We start by equating the divisor to 0
[tex]x - 2 = 0[/tex]
Make x the subject of formula
[tex]x = 2[/tex]
Next is to substitute 2 for x in the polynomials to get the remainder;
[tex]A.\ 4x^3 + 2x^2 + 5[/tex]
[tex]4(2)^3 + 2(2)^2 + 5[/tex]
Open Brackets
[tex]4 * 8 + 2 * 4 + 5[/tex]
[tex]32 + 8 + 5[/tex]
[tex]Remainder = 45[/tex]
[tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]
[tex](2)^3 - 2(2)^2 - 4(2) + 1[/tex]
Open Brackets
[tex]8 - 2 * 4 - 4 * 2 + 1[/tex]
[tex]8 - 8 - 8 + 1[/tex]
[tex]Remainder = -7[/tex]
[tex]C.\ 3x^2 + 6x - 2[/tex]
[tex]3(2)^2 + 6(2) - 2[/tex]
Open Brackets
[tex]3 * 4 + 6 * 2 - 2[/tex]
[tex]12 + 12 - 2[/tex]
[tex]Remainder = -2[/tex]
[tex]D.\ -2x^3 + 4x^2 + 3x - 2[/tex]
[tex]-2(2)^3 + 4(2)^2 + 3(2) - 2[/tex]
Open Brackets
[tex]-2 * 8 + 4 * 4 + 3 * 2 - 2[/tex]
[tex]-16 + 16 + 6 - 2[/tex]
[tex]Remainder = 4[/tex]
From the calculations above, the polynomial with a remainder of -7 when divided by [tex]x - 2[/tex] is [tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]
The value of the polynomial [tex]x^3-2x^2-4x+1[/tex] is -7 at x = 2. So, option B is correct.
Important information:
Remainder is -7.Divisor is [tex]x-2[/tex].Remainder Theorem:According to the Remainder Theorem, if a polynomial is p(x) is divided by (x-c), then the remainder is p(c).
If polynomials have a remainder of -7 when divided by x – 2. So, the value of the polynomial must be -7 at x = 2.
Substitute x = 2 in the first polynomial.
[tex]4(2)^3+2(2)^2+5=45\neq -7[/tex]
Substitute x = 2 in the second polynomial.
[tex](2)^3-2(2)^2-4(2)+1=-7[/tex]
Substitute x = 2 in the third polynomial.
[tex]3(2)^2+6(2)-2=22\neq -7[/tex]
Substitute x = 2 in the fourth polynomial.
[tex]-2(2)^3+4(2)^2+3(2)-2=4\neq -7[/tex]
Only the value of the second polynomial is -7 at x = 2. Therefore, the correct option is B.
Find out more about 'Remainder Theorem' here:
https://brainly.com/question/4515216
Cuanto mide el Tigre y cuanto pesa
Answers
Answer:
Pesa 320 kilogramos y su cola mide un metro.
ayuda porfavor :b lo nesesito para hoy por fa
Answers
Answer:
a) x = 10
Step-by-step explanation:
En este romboide, el angulo A es igual a el angulo C, y el angulo ABC es igual a el angulo CDA.
Entonces, el angulo C es 7x.
En un triangulo, los angulos se suman para ser 180 degrados. En el triangulo BCE, hay un angulo recto.
7x + 2x + 90 = 180
7x + 2x = 90
9x = 90
x = 10
Espero que este te ayude!
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 8x+ 16 = 5
A. *= V11+ 4
)
B. x= -15+4
O C. x= -15-4
D. x= V5 + 4
E. x= -111-4
OF. x= V5 - 4
Answers
Answer:
x² - 8x+ 16 = 5
x² - 8x + 16 - 5 = 0
x² - 8x + 11 = 0
Using the quadratic formula
x = -b±√b² - 4ac / 2a
a = 1 , b = - 8 c = 11
x = --8±√(-8)² - 4(1)(11) / 2(1)
x = 8 ± √ 64 - 44 / 2
x = 8±√20 / 2
x = 8 - √ 20 / 2 or x = 8 + √ 20 / 2
x = - √ 5 + 4 or x = √5 + 4
Hope this helps
three coins are flipped
what is the probability of getting no heads ?
What is the probability of getting at least two tails
PLEASE HELP
Answers
Answer:
probability of getting no heads: 1/ 8
probability of at least two tails: 1/4
Step-by-step explanation:
To calculate the probability of getting no heads, multiply the probability of not getting heads for each coin. A coin has two sides: heads and tails; the probability of not getting heads would be 1/2.
1. Multiply the probabilities for each coin
1/2 · 1/2 · 1/2 = 1/8
To calculate the probability of getting at least two tails, multiply the probability of getting tails for two coins and the probability of flipping either heads or tails for the remaining coin. Because it is at least two tails, the remaining coin can flip to either heads or tails.
1. Multiply the probabilities for each coin
1/2 · 1/2 · 2/2 = 1/4
Elena’s aunt bought her a $150 savings bond when she was born. When Elena is 20 years old, the bond will have earned 105% in interest. How much will the bond be worth when Elena is 20 years old?
Answers
The correct answer is $307.5
Explanation:
The total of the bond after 20 years is $150 plus the interests during this time (105% of $150). This last value can be calculated by multiplying the percentage (105) by the total ($150) and dividing it into 100% (total percent represented by $150. The process is shown below:
[tex]150 = 100[/tex]%
[tex]x = 105[/tex]%
[tex]x = \frac{150 x 105}{100}[/tex]
[tex]x = 157.5[/tex]
This means the total money in interest is $157.5 and this added to $150 is equivalent to $307.5
The y-intercept of the graph of a line is located at (0, –2). The line also passes through the point (5, 1).
Answers
Answer:
y - 1 = (3/5)x
Step-by-step explanation:
First find the slope of this line. As we move from (0, -2) to (5, 1), x (the 'run') increases by 5 and y (the 'rise') increases by 3. Thus, the slope of this line is m = rise / run = 3/5.
Using the point-slope formula for the equation of a straight line:
y - 1 = (3/5)(x - 5), or
y - 1 = (3/5)x This can also be written as 5y - 5 = 3x, or
y = (3/5)x + 1
Please help!! Maths question I don't understand!
Answers
Answer:
see explanation
Step-by-step explanation:
The statements tells us that w is inversely proportional to v and the equation relating them is
v = [tex]\frac{k}{w}[/tex] ← k is the constant of proportion
To find k use the condition v = 9, w = 5, that is
9 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )
45 = k
v = [tex]\frac{45}{w}[/tex] ← equation of proportion
When w = 4 , then
v = [tex]\frac{45}{4}[/tex] = 11.25
Hour many hours are in 7 days?
Answers
Answer: 168 hours
Step-by-step explanation:
There are 24 hours in a day. Thus, simply multiply 7*24 to get 168.
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------------
Answer: There are 168 hours in 7 days.
Since there 24 hours in a day, Multiply 24 times 7 and you get 168.
Example : 24 x 7 = 168.
Use the number to find 1/4 +-21/8
Answers
Answer:
-2 3/8
Step-by-step explanation:
1/4 +-21/8
Get a common denominator
1/4 * 2/2 + -21/8
2/8 - 21/8
-19/8
-16/8 - 3/8
-2 -3/8
-2 3/8
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▹ Answer
-19/8 → -2 3/8 → -2.375
▹ Step-by-Step Explanation
1/4 + -21/8
1/4 - 21/8
2 - 21/8
-19/8
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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