find the area and perimeter of sector OAB given that angle AOB is 60 degrees and the radius of a circle is 21cm​

Answers

Answer 1

Answer:

Step-by-step explanation:

Perimeter of a sector

The circumference of a circle is 2 pi r.

pi = 3.14

r = 21 cm

The angle of this particular sector is 60 degrees.

So the formula for this sector is P = 2*r + 60/360 * 2* pi * r

Now all you need do is plug the numbers in.

P = 2 * 21 + 1/6 * 2 * 3.14 * 21

P = 42 + 21.98

P = 63.98

Area of the sector

Area of a circle = pi * r^2

Area of a sector = theta / 360 * pi * r^2

theta = 60 degrees

area of this sector = (60/360) * 3.14 * 21^2

Area of this sector = (1/6) * 3.14 * 441

Area of this sector = 230.79

Answer 2

[tex]\bold{\huge{\pink{\underline{ Solution }}}}[/tex]

Given :-

We have given that, Angle AOB is 60° The radius of the circle is 21cm

To Find :-

We have to find the area and perimeter of the sector OAB

Let's Begin :-

We have ,

Two radii of the circle OA and OB = 21 cm each [tex]\bold{\angle{ AOB = 60° }}[/tex]AB is the segment of the circle

We know that,

[ Perimeter of sector = Arc length + radius + radius ]

[tex]\bold{\blue{ Perimeter \: of \: Sector = }}{\bold{\blue{\dfrac{\theta}{360°}}}}{\bold{\blue{× 2πr + r + r }}}[/tex]

Subsitute the required values in the above formula :-

Length of the arc of OAB

[tex]\sf{=}{\sf{\dfrac{ 60°}{360°}}}{\sf{×2πr + 2r }}[/tex]

[tex]\sf{=}{\sf{\dfrac{ 6}{36}}}{\sf{×2×21π + 2 × 21 }}[/tex]

[tex]\sf{= }{\sf{\dfrac{1}{6}}}{\sf{ × }}{\sf{\dfrac{22}{7}}}{\sf{× 42 + 42 }}[/tex]

[tex]\sf{= }{\sf{\dfrac{1}{3}}}{\sf{ × }}{\sf{\dfrac{11}{7}}}{\sf{ × 42 + 42 }}[/tex]

[tex]\sf{= }{\sf{\dfrac{1}{3}}}{\sf{× 11×6 + 42 }}[/tex]

[tex]\sf{ = 11 × 2 + 42 }[/tex]

[tex]\sf{= 22 + 42 }[/tex]

[tex]\bold{\red{= 64 \: cm}}[/tex]

Thus, The perimeter of the sector OAB is 64 cm

Now,

We have to find the area of sector OAB

We know that,

[tex]\bold{\blue{ Area \: of \: sector = }}{\bold{\blue{\dfrac{\theta}{360°}}}}{\bold{\blue{× πr² }}}[/tex]

Subsitute the required values in the above formula :-

Area of sector OAB

[tex]\sf{=}{\sf{\dfrac{60°}{360°}}}{\sf{× πr² }}[/tex]

[tex]\sf{=}{\sf{\dfrac{6}{36}}}{\sf{× π × 21 × 21 }}[/tex]

[tex]\sf{=}{\sf{\dfrac{1}{6}}}{\sf{× π × 21 × 21 }}[/tex]

[tex]\sf{=}{\sf{\dfrac{1 }{6}}}{\sf{× 441π}}[/tex]

[tex]\sf{=}{\sf{\dfrac{1}{6}}}{\sf{× 441 × }}{\sf{\dfrac{22}{7}}}[/tex]

[tex]\sf{=}{\sf{\dfrac{1}{6}}}{\sf{ × 63 × 22}}[/tex]

[tex]\sf{=}{\sf{\dfrac{1}{6}}}{\sf{× 1386 }}[/tex]

[tex]\bold{\red{= 231 \: cm²}}[/tex]

Hence, The area and perimeter of the sector OAB is 64 cm and 231cm²

What is sector?

Sector is nothing but the portion covered by the two radii of the circle For example, In the given circle OAB is sector as it is enclosed by two radii OA and OB.
Find The Area And Perimeter Of Sector OAB Given That Angle AOB Is 60 Degrees And The Radius Of A Circle

Related Questions

sketch the graph of f(x)=-3^x and describe the end behavior of the graph.

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Answer: 3-

Step-by-step explanation:

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Answer:

1.5

Step-by-step explanation:

because if u divide 6 by 4 that will equal 1.5

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Answers

Answer:

1a. 58/99

1b. 53/90

1c. 29/50

Step-by-step explanation:

let's start with the easiest one

1.(c)

0.58 = 58/100 = 29/50

that is the simplest possible form, as 29 is a prime number and not a factor of 50.

1.(a)

0.585858585858... = 58×0.0101010101010101...

now, we know that 1/"double digit" (like 1/22) mostly produces a repeating pattern with a period length of 2 after the decimal point.

and we find

1/99 = 0.01010101010101...

so, our solution is

58 × 1/99 = 58/99

that is the simplest possible form, as 58 and 99 do not share any factors.

1.(b)

0.5888888888888... = 0.5 + 0.0888888888888... =

= 0.5 + 8×0.01111111111111... = 0.5 + 8×1/10 × 0.1111111111...

we know how to create 0.11111111111... :

1/9 = 0.111111111111111...

so, our solution is

0.5 + 8 × 1/10 × 1/9 = 0.5 + 8/90 = 5/10 + 8/90 =

= 45/90 + 8/90 = 53/90

this is the simplest possible form, as 53 is already a prime number and not a factor of 90.

lolololololololololollolool

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lolo lol is the answer because it is

How I find a area of a trapezoid

Answers

The answer is - The formula for the area of a trapezoid is area equals 1/2 times parentheses base 1+ base two times height where the bases are the parallel sides

using the distance formula d=√(x2- x1)^2 +(y2-y^1, what is the distance between point (-3,1) and point (-2,4) rounded to the nearest tenth

Answers

Answer:

[tex]d = \sqrt{(x2 - x1) + (y2 - y1)} \\ d = \sqrt{ (- 3 + 2) + (1 + - 4)} \\ d = \sqrt{ - 1 + - 3 } \\ d = \sqrt{ - 4 } \\ d = - 2[/tex]

Step-by-step explanation:

hope it helps you<3

yall HELP PLEASE What is the slope of the line segment?

Answers

Answer:

a. 5

Step-by-step explanation:

Taking two points, (0,0) and (1,5), find the slope using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Plugging the two points in, we have [tex]\frac{5-0}{1-0}=5[/tex] as the slope.

Answer:

Slope = 5

Step-by-step explanation:

We will use 2 points on the line.

(1 , 5) and (2 , 10)

formula for slope = y2 - y1/x2 - x1

10 - 5/2 - 1

= 5/1

= 5

The slope is 5.

please help it would really help alot

Answers

Step-by-step explanation:

An appropriate estimation would be to the ones place.

[tex] \frac{36 \div 4}{40 \div 4} = \frac{9}{10} [/tex]

9/10 (90%) is closer to 1 than to 0.

The estimation for 36/40 is 1.

1/3 (33%) is closer to 0 than to 1.

The estimation for 1/3 is 0.

[tex] \frac{70 \div 10}{100 \div 10} = \frac{7}{10} [/tex]

7/10 (70%) is closer to 1 than to 0.

The estimation for 7/10 is 1.

1/8 (12.5%) is closer to 0 than to 1.

The estimation for 1/8 is 0.

283 is the same as the quotient of 97 and u

Answers

Answer:

283=97/u U=2.917

Step-by-step explanation:

if you have choices and more information, it would be helpful when answering questions

A balloon containing 0. 040 mol of a gas with a volume of 5. 0 mL was expanded to 1. 0 L. Which equation should you use to find the amount of gas added? V subscript 2 equals StartFraction V subscript 1 n subscript 2 over n subscript 1 EndFraction. N subscript 2 equals StartFraction V subscript 2 n subscript 1 over V subscript 1 EndFraction. N subscript 2 equals StartFraction V subscript 1 n subscript 1 over V subscript 2 EndFraction.

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Answer:

n2=v2n1/v1

Or B

Step-by-step explanation:

P, R, and T are constant, then the volume is directly proportional to the mole. Then the correct option is A.

What is an ideal gas equation?

An ideal gas is a theoretical composed of a set of randomly moving gas particles that interacts only through elastic collision.

Given

A balloon containing 0.040 mol of a gas with a volume of 5.0 mL was expanded to 1.0 L.

[tex] \rm V_1 = 5 \ mL\\ V_2 = 1000 \ mL\\ n_1 = 0.040 \ mol [/tex]

We know the equation of the ideal gas.

[tex] \rm PV = nRT [/tex]

where P, R, and T are the constant, then

[tex] P \propto n[/tex]

Then we have

[tex] \rm \dfrac{V_2}{V_1} = \dfrac{n_2}{n_1} \\\\ V_2 = n_2 *\dfrac{V_1}{n_1} [/tex]

Thus, the correct option is A.

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Factor this trinomial: 6x^2 +19x+3

Please show all work, I give Brainliest.

Answers

Step-by-step explanation:

[tex]\implies \: {6x}^{2} + 19x + 3 \\ \implies {6x}^{2} + (18 + 1)x + 3 \\ \implies {6x}^{2} + 18x + x + 3 \\ \implies6x(x + 3) + 1(x + 3) \\ \implies(x + 3)(6x + 1)[/tex]

Raheel is comparing the cost of two parking garages. Garage A charges a flat fee of $6 per car plus $0.50 per hour. Garage B charges a flat fee of $2 per car plus $1 per hour.

Answers

Answer:

$6 + .50x = $2 + $1.00x

4 = .50x

8hr = x, the number of hours when both garages cost the same amount

$6 + .50 x 8 =

$10 would be the cost a both garages after 8 hours

Step-by-step explanation:

#A

Flat fee=6Rate of change=0.5

Equation in slope intercept form

y=mx+by=0.5x+6

#B

Flat fee=2$Rate of change=1

Equation in slope intercept form

y=x+2

Now for compare take any no

Let's take 10

For garage A

y=0.5(10)+6=5+6=11$

For garage B

y=10+2=12$

Hence Garage B is charging more

Sue Ellen owns 2/7 of a business. What percent of the partnership does she own?

Answers

Answer:

20%?

Step-by-step explanation:

I think im wrong but what u can do is u can convert the fraction into a decimal then get ur answer from there.

Layla read 6 books in the first two months she was a member of a book club. Which equation best represents y, the total number of books read in x number of months?
A. y = 6x
B. y = 2x
C. y = 3x
D. Not Here

Answers

Answer:

C

Step-by-step explanation:

So if we look at the information that we already know, Layla's reading to months ratio is, 6:2. But to find out the equation we want to find out how many books she reads in ONE month instead of two.

Divide 2/2, and for ratios if you divide one side you have to do the same thing to the other side, so we get, 3:1. Where Layla reads 3 books per 1 month.

Therefore the answer is C.

If we wanted to double check our answer we could substitute our information back in:

6=3×2

6=6

Since the equations equal each other, we know we got it correct.

find the value of x in the equation below.
PLEASE SHOW ALL YOUR WORK
-3x-5=-17

Answers

Answer: x=4

Step-by-step explanation:

-3x-5=-17

    +5   +5

-3x=-12

/-3   /-3

x=4    

1. What are the vertices of △′′′white up pointing triangle . e prime , f prime , g prime for each translation? a. ⟨,−⟩(△)=△′′′

Answers

Answer:

The coordinates of the vertices are ′(,−), e prime . open 1 comma negative 3 close comma ′(,−), f prime . open 5 comma negative 2 close comma and ′(,−). g prime . open 4 comma negative 8 close .

Step-by-step explanation:

What is the conversion factor for the relationship between millimeters and centimeters?.

Answers

Answer:

  10 mm = 1 cm

Step-by-step explanation:

10 mm = 1 cm

__

The SI prefix "milli-" means 1/1000. The prefix "centi-" means 1/100. Consequently 1 cm = 0.010 m and 1 mm = 0.001 m.

There are 10 mm in 1 cm.

What is the 4th equivalent fraction to
5/6

Answers

Answer:

20/24

Step-by-step explanation: Hope this helps

Review the equation below. 2KClO3 Right arrow. 2KCl + 3O2 How many moles of oxygen are produced when 2 mol of potassium chlorate (KClO3) decompose? 1 2 3 6

Answers

Answer:   3 mol of O₂

Solution:

The Balance chemical equation is as follow,

                               2 KClO₃    →    2 KCl  +  3 O₂

According to this equation on decomposition 2 moles of Potassium chlorate (KClO₃) produces 2 moles of Poatassium chloride (KCl) and 3 moles of oxygen gas (O₂).

Therefore, when,

                    2 moles of KClO₃ produces  =  3 moles of O₂

So,

                 2 moles of KClO₃ will produce  =  X moles of O₂

Solving for X,

                    X =  (2 mol × 3 mol) ÷ 2 mol

                   X  =  3 mol of O₂

Using above method you can calculate any amount of O₂ or KCl produced by decomposing any amount of KClO₃.

Answer:

3 mol of O₂

Step-by-step explanation:

i got a hundred on Edge

Bryant types 1400 words in 25 minutes. How many words does he type per minute?

Answers

Answer:

56 words per minute

Step-by-step explanation:

1400÷25=56

Answer:

56 wpm

Step-by-step explanation:

need help please this is due very soon

Answers

So focus. On that stop playing on your phone

what's this....?
5(x+9)=60

Answers

x=3

Steps:
I used a calculator.

Answer:

Raquel has gross pay of $732 and federal tax withholdings of $62. Determine Raquel’s net pay if she has the additional items withheld: Social Security tax that is 6. 2% of her gross pay Medicare tax that is 1. 45% of her gross pay state tax that is 21% of her federal tax a. $600. 99 b. $610. 54 c. $641. 83 d. $662. 99.

Step-by-step explanation:

hello ur intro

A veterinarian divided 4/5 of a bottle of medicine equally among 4 sick cats. How much did she give each sick cat?

Answers

I think it’s 1/5 or 3 1/5

Select all the expressions that are equivalent to 4-3.
A) -12
B) (-4) - (-4).(-4)
C) 2-6
D (1/4) • (1/4) • (1/4)
E) (1) · (1). (1)
F) 8-1/ 2 to the power of 2
G) 12

Answers

Answer:

See below.

Step-by-step explanation:

4*-3

A) -12

C) 2*-6

-hope it helps

The expressions that are equivalent to 4 × -3 are A) -12 and C) 2 × -6.

What is the expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Option A is a straightforward multiplication of 4 and -3, which gives -12.

Option C (2 × -6) is equal to -12.

Option B can be simplified as follows: (-4) - (-4) · (-4) = (-4) - 16 = -20.

Therefore, option B is not equivalent to 4 × -3.

Option D is equal to 1/64.

Option E is equal to 1.

Option F is equal to 2, and option G is equal to 12.

Options B, D, E, F, and G are not equivalent to 4 × -3.

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which of the following polynomials has a graph with odd symmetry? a. 7x^4+13x^3-11 b. 5x^7+4x^6+3x^5+x c.13x^5 -1/2x^3+7x+3 d. 8x^5+7x^3-5x

Answers

Answer:

D) [tex]f(x)=8x^5+7x^3-5x[/tex]

Step-by-step explanation:

A function is odd if its graph is symmetric to the origin, which we can check this if [tex]f(-x)=-f(x)[/tex] is true:

Option A

[tex]f(x)=7x^4+13x^3-11\\\\f(-x)=7(-x)^4+13(-x)^3-11\\\\f(-x)=7x^4-13x^3-11[/tex]

Since [tex]f(-x)\neq-f(x)[/tex], then the function does not have odd symmetry

Option B

[tex]f(x)=5x^7+4x^6+3x^5+x\\\\f(-x)=5(-x)^7+4(-x)^6+3(-x)^5+x\\\\f(-x)=-5x^7+4x^6-3x^5+x[/tex]

Since [tex]f(-x)\neq-f(x)[/tex], then the function does not have odd symmetry

Option C

[tex]f(x)=13x^5-\frac{1}{2}x^3+7x+3\\\\f(-x)=13(-x)^5-\frac{1}{2}(-x)^4+7(-x)+3\\ \\f(-x)=-13x^5-\frac{1}{2}x^4-7x+3[/tex]

Since [tex]f(-x)\neq-f(x)[/tex], then the function does not have odd symmetry

Option D

[tex]f(x)=8x^5+7x^3-5x\\\\f(-x)=8(-x)^5+7(-x)^3-5(-x)\\\\f(-x)=-8x^5-7x^3+5x[/tex]

Since [tex]f(-x)=-f(x)[/tex], then the function DOES have odd symmetry. You can also see that the function is odd because every term has an odd exponent.

Find the three consecutive square numbers whose sum is 149.

Answers

Answer:

36 + 49 + 64 = 149

6^+7^2+8^2

Hope This Helps!!!

Classify each pair of numbered angles. Drag and drop the descriptions into the boxes to correctly classify each pair of numbered angles. Each description may be used more than once. Two lines intersect. The largest angle has the equation (3x minus 52) degrees to define it and the second to largest angle has the equation (2x plus 2) degrees to define it. A straight line with another line coming out of it at an angle. The largest angle has the equation (10x minus 20) degrees to define it and the smaller angle has the equation (6x plus 8) degrees to define it.

Answers

(i) Pairs of neighboring angles are supplementary and opposite angles have the same measure.

(ii) The two angles formed by a line coming out of another line are supplementary.

How to analyze pairs of angles

(i) When two straight lines pass through each other, then two pairs of opposite angles are constructed. A pair with angles of [tex](3\cdot x + 52)^{\circ}[/tex] and another pair with angles of [tex](2\cdot x + 2)^{\circ}[/tex], each pair of angles with different measures are supplementary.[tex]\blacksquare[/tex]

(ii) When a straight line comes out of another straight line, from a point distinct to any endpoint of the former, then we construct two supplementary angles. The largest angle has a value of [tex](10\cdot x + 20)^{\circ}[/tex], whereas the smaller one has a value of [tex](6\cdot x + 8)^{\circ}[/tex]. [tex]\blacksquare[/tex]

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Adrian wants to buy a skateboard that costs $85 After 1 month, he has $4 in savings and plans to quadruple the amount he has saved each month for 4 months Will Adrian have enough money to buy the skateboard in 4 months?

Answers

Adrien will not have enough money in 4 months.
Answer: $64
4 x4=16
16x4=64
64≠85

Find the coordinates of point C on AB that is = of the distance from A to B.

Answers

Answer:

We need to see the graph can u show me the graph

Step-by-step explanation:

?

Help! it's giving me a headache and I will be very thankful

Answers

Answer:

Hey, I'm not sure if this will help but by just looking at it I would say C.

Explanation:

This is because it looks like the parallelogram can be adjusted to be a rectangle which would give you the answer of 77.

I hope that makes sense!


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