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2 years ago

A sector of a circle has an arc length of pi cm and a central angle of pi over 6 radians. What is the area of the sector?

Mathematics

1 answer:

liberstina [14]2 years ago

4 0

Answer:

Area of sector is 6pi cm^2

Step-by-step explanation:

Mathematically pi radians is 180 degrees

thus pi/6 radians is 180/6 = 30 degrees

The formula for the length of an arc is;

theta/360 * 2 * pi * r

where theta in this case is 30 degrees

And the arc length is pi

so we have

30/360 * 2 * pi * r = pi

30/360 * 2 * r = 1

60r = 360

r = 360/60

r = 6 cm

Now the area of a sector is;

theta/360 * pi * r^2

30/360 * pi * 36

= 6pi cm^2

You might be interested in

List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was ca

Yanka [14]

Answer:

a. P(X = 0)= 0.001

b. P(X = 1)= 0.001

c. P(X=2)= 0.044

d. P(X=3)= 0.117

e. P(X=4)= 0.205

f. P(X=5)= 0.246

g. P(X=6)= 0.205

h. P(X=7)= 0.117

i. P(X=8)= 0.044

j. P(X=9)= 0.001

k. P(X=10)= 0.001

Step-by-step explanation:

Hello!

You have the variable X with binomial distribution, the probability of success is 0.5 and the sample size is n= 10 (I suppose)

If the probability of success p=0.5 then the probability of failure is q= 1 - p= 1 - 0.5 ⇒ q= 0.5

You are asked to calculate the probabilities for each observed value of the variable. In this case is a discrete variable with definition between 0 and 10.

You have two ways of solving this excersice

1) Using the formula

$P(X)= \frac{n!}{(n-X)!X!} * (p)^X * (q)^{n-X}$

2) Using a table of cummulative probabilities of the binomial distribution.

a. P(X = 0)

Formula:

$P(X=0)= \frac{10!}{(10-0)!0!} * (0.5)^0 * (0.5)^{10-0}$

P(X = 0) = 0.00097 ≅ 0.001

Using the table:

P(X = 0) = P(X ≤ 0) = 0.0010

b. P(X = 1)

Formula

$P(X=1)= \frac{10!}{(10-1)!1!} * (0.5)^1 * (0.5)^{10-1}$

P(X = 1) = 0.0097 ≅ 0.001

Using table:

P(X = 1) = P(X ≤ 1) - P(X ≤ 0) = 0.0107-0.0010= 0.0097 ≅ 0.001

c. P(X=2)

Formula

$P(X=2)= \frac{10!}{(10-2)!2!} * (0.5)^2 * (0.5)^{10-2}$

P(X = 2) = 0.0439 ≅ 0.044

Using table:

P(X = 2) = P(X ≤ 2) - P(X ≤ 1) = 0.0547 - 0.0107= 0.044

d. P(X = 3)

Formula

$P(X = 3)= \frac{10!}{(10-3)!3!} * (0.5)^3 * (0.5)^{10-3}$

P(X = 3)= 0.11718 ≅ 0.1172

Using table:

P(X = 3) = P(X ≤ 3) - P(X ≤ 2) = 0.1719 - 0.0547= 0.1172

e. P(X = 4)

Formula

$P(X = 4)= \frac{10!}{(10-4)!4!} * (0.5)^4 * (0.5)^{10-4}$

P(X = 4)= 0.2051

Using table:

P(X = 4) = P(X ≤ 4) - P(X ≤ 3) = 0.3770 - 0.1719= 0.2051

f. P(X = 5)

Formula

$P(X = 5)= \frac{10!}{(10-5)!5!} * (0.5)^5 * (0.5)^{10-5}$

P(X = 5)= 0.2461 ≅ 0.246

Using table:

P(X = 5) = P(X ≤ 5) - P(X ≤ 4) = 0.6230 - 0.3770= 0.246

g. P(X = 6)

Formula

$P(X = 6)= \frac{10!}{(10-6)!6!} * (0.5)^6 * (0.5)^{10-6}$

P(X = 6)= 0.2051

Using table:

P(X = 6) = P(X ≤ 6) - P(X ≤ 5) = 0.8281 - 0.6230 = 0.2051

h. P(X = 7)

Formula

$P(X = 7)= \frac{10!}{(10-7)!7!} * (0.5)^7 * (0.5)^{10-7}$

P(X = 7)= 0.11718 ≅ 0.1172

Using table:

P(X = 7) = P(X ≤ 7) - P(X ≤ 6) = 0.9453 - 0.8281= 0.1172

i. P(X = 8)

Formula

$P(X = 8)= \frac{10!}{(10-8)!8!} * (0.5)^8 * (0.5)^{10-8}$

P(X = 8)= 0.0437 ≅ 0.044

Using table:

P(X = 8) = P(X ≤ 8) - P(X ≤ 7) = 0.9893 - 0.9453= 0.044

j. P(X = 9)

Formula

$P(X = 9)= \frac{10!}{(10-9)!9!} * (0.5)^9 * (0.5)^{10-9}$

P(X = 9)=0.0097 ≅ 0.001

Using table:

P(X = 9) = P(X ≤ 9) - P(X ≤ 8) = 0.999 - 0.9893= 0.001

k. P(X = 10)

Formula

$P(X = 10)= \frac{10!}{(10-10)!10!} * (0.5)^{10} * (0.5)^{10-10}$

P(X = 10)= 0.00097 ≅ 0.001

Using table:

P(X = 10) = P(X ≤ 10) - P(X ≤ 9) = 1 - 0.9990= 0.001

Note: since 10 is the max number this variable can take, the cummulated probability until it is 1.

I hope it helps!

4 0

3 years ago

Solve for m p=3rmv^2

juin [17]

Let’s Solve for m

p=3rmv^2

Step 1 Flip the equation

3mrv^2=p

Step 2 Divde Both Sides by 3rv^2

3mrv^2/3rv^2=p/3rv^2

m=p/3rv^2

ANSWER

m=p/3rv^2

7 0

3 years ago

I will give you the brainlessest if you awnser the following plz and thank you so much

kirill115 [55]

2. x + y = 82
x - y = 24
---------------add
2x = 106
x = 53

x + y = 82
53 + y = 82
y = 82 - 53
y = 29

solution is : (53,29)
=======================
3. y = 2x
y = 4x + 6

2x = 4x + 6
2x - 4x = 6
-2x = 6
x = -3

y = 2x
y = 2(-3)
y = -6

solution is (-3,-6)
========================
4. 5x + 8y = -29
7x - 2y = -67...multiply by 4
----------------
5x + 8y = -29
28x - 8y = - 268 ..result of multiplying by 4
-----------------add
33x = - 297
x = - 9

5x + 8y = -29
5(-9) + 8y = -29
-45 + 8y = -29
8y = -29 + 45
8y = 16
y = 2

solution is : (-9,2)
=======================
5. y = -4x + 6
y = -5x - 4

-4x + 6 = -5x - 4
-4x + 5x = -4 - 6
x = -10

y = -4x + 6
y = -4(-10) + 6
y = 40 + 6
y = 46

solution is (-10,46)
=========================
6. H(m) = 2m + 12
H(m) = 3m + 10
=========================
7. -8x + 4y > -52
4y > 8x - 52
y > 2x - 13 <==
=========================
8. 3x - y = 28
3x + y = 14
---------------add
6x = 42
x = 7

3x - y = 28
3(7) - y = 28
21 - y = 28
-y = 28 - 21
-y = 7
y = -7

solution is (7,-7)
=====================
10. 5x - 5y > 70
-5y > -5x + 70
y < x - 14 <==
=====================
11. sorry...dont know
=====================
12. y = 4x + 4
y = -3x - 3

4x + 4 = -3x - 3
4x + 3x = -3 - 4
7x = -7
x = -1

y = 4x + 4
y = 4(-1) + 4
y = 0

solution is (-1,0)
=======================
13. -12x - 2y > - 42
-2y > 12x - 42
y < -6x + 21 <==
=======================
14. -5x + 2y = 9
3x + 5y = 7

solution is (-1,2)
========================
15. 3x + 6y = -2
15x + 30y = -10....divide by 5 to reduce = 3x + 6y = -2
is the same line....infinite solutions
========================
1. (the graph).....y < = 3x - 4....3rd one
========================
9. (2nd graph)....y < = -3x + 4....last one

8 0

3 years ago

3x + 4y=17<br>- 4x – 3y = - 18

OleMash [197]

Answer:

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Which fraction is not in simplest form? Explain. <br> : 9/21 , 7/18, 3/25, 12/31

Slav-nsk [51]

9/21 because it can still be reduced to 3/7