The diagram shows a vector of a circle centre O and radius 6 cm. Mn is a chord of the circle. Angle MON is 50degrees. Calculate the area of the shaded segment. Give your answer to three significant figures

The Diagram Shows A Vector Of A Circle Centre O And Radius 6 Cm. Mn Is A Chord Of The Circle. Angle MON

Answers

Answer 1

Answer:

Area of the shaded region = 1.92 cm²

Step-by-step explanation:

Area of the shaded region = Area of sector OMN - Area of isosceles triangle OMN

Drop a perpendicular OP from vertex O to opposite side MN.

Perpendicular OP will bisect angle MON.

m∠MOP = 25°

By cosine ratio in triangle OPN,

cos(25°) = [tex]\frac{OP}{ON}[/tex]

OP = ON.cos(25°)  

OP = 6cos(25°)

OP = 5.438 cm

By sine ratio of angle PON,

sin(25) = [tex]\frac{PN}{ON}[/tex]

PN = ON.sin(25)

     = 6sin(25°)

     = 2.536 cm

Since, MN = 2(PN)

MN = 5.071 cm

Area of ΔOMN = [tex]\frac{1}{2}(OP)(MN)[/tex]

                         = [tex]\frac{1}{2}(5.438)(5.071)[/tex]

                         = 13.788 cm²

Area of sector OMN = [tex]\frac{\theta}{360}(\pi r^{2})[/tex]

Here 'θ' is the angle subtended by the arc MN at the center.

Area of sector OMN = [tex]\frac{50}{360}(\pi )(6^{2})[/tex]

                                  = 15.708 cm²

Area of the shaded region = 15.708 - 13.788

                                             = 1.92

                                             ≈ 1.92 cm²

The Diagram Shows A Vector Of A Circle Centre O And Radius 6 Cm. Mn Is A Chord Of The Circle. Angle MON
Answer 2

Answer:

Area of the shaded region = Area of sector OMN - Area of isosceles triangle OMN

Drop a perpendicular OP from vertex O to opposite side MN.

Perpendicular OP will bisect angle MON.

m∠MOP = 25°

By cosine ratio in triangle OPN,

cos(25°) = \frac{OP}{ON}ONOP

OP = ON.cos(25°)  

OP = 6cos(25°)

OP = 5.438 cm

By sine ratio of angle PON,

sin(25) = \frac{PN}{ON}ONPN

PN = ON.sin(25)

     = 6sin(25°)

     = 2.536 cm

Since, MN = 2(PN)

MN = 5.071 cm

Area of ΔOMN = \frac{1}{2}(OP)(MN)21(OP)(MN)

                         = \frac{1}{2}(5.438)(5.071)21(5.438)(5.071)

                         = 13.788 cm²

Area of sector OMN = \frac{\theta}{360}(\pi r^{2})360θ(πr2)

Here 'θ' is the angle subtended by the arc MN at the center.

Area of sector OMN = \frac{50}{360}(\pi )(6^{2})36050(π)(62)

                                  = 15.708 cm²

Area of the shaded region = 15.708 - 13.788

                                             = 1.92

                                             ≈ 1.92 cm²


Related Questions

please help! (URGENT)

Answers

It’s 180-135 which equals 45 so it is 45 degrees for X

CAN SOMEONE HELP ME PLEASEEE

Answers

Answer:

a. 45 degrees

b. 315 degrees

c. 8π

d. π

e. 7π

f. 16π

g. 2π

PLEASE HELP ME ASAP?!?
Find the length of the missing side. Simplify all radicals.

Answers

Answer:

22.47

22.5 (simplified)

Step-by-step explanation:

22.47 = √(8^2 + 21^2)

Can you help me find the value of x is.

a. 132
b. 200
c. 228
d. 256​

Answers

Answer:

C

Step-by-step explanation:

C

6x -4=-4+6x
can i get some help with this question​

Answers

Answer:

infinite solutions

Step-by-step explanation:

At first, we try to isolate the x, but adding 4 to  -4 on both sides. Both sides have a -4 so it cancels out on both sides of the equation. Similarly, both sides also have a positve 6x, so when we subtract 6x from 6x we get 0. After simplification, we get x = x; x can be any number [ex. 1=1, 2=2, 3=3,etc.], therefore any number can fit into this equation

6x - 4 = -4 + 6x

6x - 4 + 4 = -4 + 4 +6x

6x = 6x

x = x

Answer:

infinite solutions

Step-by-step explanation:

Need help please!!!!!!

Answers

Answer:

x = 13.75

Step-by-step explanation:

(4x + 5) - 10 = 50

4x + 5 - 10 = 50

4x - 5 = 50

4x = 50 + 5

4x = 55

x = 55/4

x = 13.75

will give brainlist

the question is: the endpoints of line segment AR are A(8,-2) and R(-4,1)? round your answer to the nearest tenth​

Answers

Answer:

The answer is 12.4.

Step-by-step explanation:

The exact distance would be 3 rooted to 17 but the decimal is 12.4.

I used my graphing calculator so i can't explain much :))

Hope this helps:))

PLEASE HELP! WILL MARK BRANLIEST
A university has 34,590 students. In a random sample of 165 students, 11 speak three or more languages. Predict the number of students at the university who speak three or more languages.



The expected number of students at the university who speak three or more languages is____

Answers

11/165 = x/34590
165x = 380490
x=2306
The expected number of students at the university who speak three or more languages is 2,306.

If M, N, and O are midpoints of JKL, find LJ.

Answers

Answer:

the answer is 12

Step-by-step explanation:

edg 2021

The length of the side LJ of triangle ΔJKL can be obtained as 12 units. The correct option is (C).

What is a triangle?

A triangle is a two dimensional shape bound by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.

As per the given question, O is the midpoint of LK.

Then, LO = OK.

The equation can be written as,

⇒ 2x = x + 8

⇒ x = 8

Then, NJ = 8 - 2 = 6

Since, N is also the midpoint of LJ.

LJ = 2 × NJ

⇒ LJ = 2 × 6 = 12.

Hence, the length of the side LJ can be found as 12 units.

To know more about triangle click on,

https://brainly.com/question/2773823

#SPJ2

Sandra is buying new carpet for the floors of her house. The cost depends on the area of the floors. Which is the dependent variable, and which is the independent variable?

A. The dependent variable is the cost, and the independent variable is the area of the floors.
B. The dependent variable is the number of walls in the house, and the independent variable is the cost.
C. The dependent variable is the cost, and the independent variable is the number of walls in the house.
D. The dependent variable is the area of the floors, and the independent variable is the cost.​

Answers

Answer:

A.The dependent variable is the cost, and the independent variable is the area of the floors.

Step-by-step explanation:

Because I had a quiz with the same question and got it right, and because the paragraph says "The cost depends on the area of the floors."

Answer:

A.

Step-by-step explanation:

"The cost depends on the area of the floors"

The independent variable is the cause and the dependent variable is the effect. Took the test.

What is the area of this parallelogram?
28 m²
56 m²
84 m²
120 m²

Answers

Answer:

84 m squared

Step-by-step explanation:

Answer:

84 m²

Step-by-step explanation:

Area of parallelogram = (4 + 8)* 7 = 12*7 = 84 Sq m

hello please anyone answer that 9/20=.......%​

Answers

THATS A DIFFICULT QUESTION SIR

Question/Equation:

9/20=__%

Answer/Steps to answer:

1. For the denominator, recognize that 20×5=100.

Multiple = 55

2. Multiply both the numerator and denominator by the multiple 5.

9×5/20×5

3. Simplify.

45/100

4. Simplify.

45% (0.45 Is Decimal Form)

Done by NeighborhoodDealer

Find the slope and y-intercept of the line.
4)
m=
b=

Answers

Answer:

m=y = 2x + 4.

y intercept is 4

Step-by-step explanation:

Ben buys packs of golf balls with his new golf club. Write an expression for this
situation if the golf club is $45 and the packs of golf balls are $4 per pack.
Remember, we do not know how many packs of golf balls he purchased.
Expression:

Answers

Answer:

4x + 45

______

Solve this quadratic equation using the quadratic formula.
(3- y)(y + 4) =3y -5

Answers

Answer:

y=-(2±√21)

Step-by-step explanation:

Answer:

y=-6.5

Step-by-step explanation:

the ratio is 3:1 how many parts are there​

Answers

I think it will be 6:2

Solve Using Substitution
-9x + 6y = 18
y = -6​

Answers

Answer:

the answer should be x = -6

Step-by-step explanation:

-9x + 6y = 18

-9x + 6(-6) = 18

-9x - 36 = 18

-9x - 36 + 36 = 18 + 36

-9x = 54

-9x ÷ -9 = 54 ÷ -9

x = -6

A bag is filled with green and blue marbles. There are 43 marbles in the bag. If there are 7 more green
marbles than blue marbles, find the number of green marbles and the number of blue marbles in the bag.
Equation (use x as your variable):
The number of blue marbles is:____
The number of green marbles is:____

Answers

Answer:

Blue marbles: 18

Green marbles: 25

Step-by-step explanation:

First off, we have to define our variables.

g = # of green marbles

b = # of blue marbles

We know two equations:

g + b = 43 and g = b + 7

If you're wondering how I got the first equation, it was because the number of green and blue marbles is 43. For the second equation, we know that there are 7 more green marbles than blue marbles.

Now, we have an equation for the number of green marbles. We can plug that equation into the equation g + b = 43.

So, (b + 7) + b = 43.

When we simplify it, we get 2b + 7 = 43.

We subtract 7 from both sides, which gets us 2b = 36.

Now, b = 36/2.

b = 18.

So, we found out the number of blue marbles that we have. We know that g + b = 43. Now, all we have to do is plug in the number of blue marbles into that equation to find out the number of green marbles.

g + 18 = 43.

g = 43 - 18.

g = 25.

Thus, the number of green marbles we have is 25 and the number of blue marbles is 18.

help me please I am very confused T-T

Answers

i believe you do 180 - 149 because it's a linear pair, it makes a t shape!!

Answer:

x=31

Step-by-step explanation:

that is an example of suplementary angles meaning that they will add up to equal 180

180-149=31

x=31

pLz, help I really don't understand these problems at all.
Click here to see the screenshot

Answers

Answer:

1. You should use subtraction (20-12.68=7.32)

2. You should use multiplication

3. You need to know 5 boxes and $5.29

4. You need to know 10 packages and 2 cases

Step-by-step explanation:

I hope this helpss!!

what is the value of y?

Answers

The value of Y is h:8.

Answer:

g. 8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

since it's a 45 45 90 triangle, both the legs are the same (8) and the hypotenuse(y) would be 8 rad 2 :)

Given that ABCD is a parallelogram with diagonals intersecting at M. Segment PQ is drawn such that P lies on AB and Q lies on DC and it passes through M. Prove that PM is congruent to QM.​

Answers

Answer:

we thus have enough informnation to prove that the two triangles are congruent. Because of thism, one side of the triangles, Pm which is the congruent side to that of PQ must be equal as well and

PM = QM

Step-by-step explanation:

because it's a parrallelogram, Ad = BC and AB = DC.

P passes through both  AB and DC on a diagonal, angles created by P have oppoiste exterior angles of eachother.

the diagonals of AC create congruent angles at DMC and AMB and because P is cutting through them, the angles P cuts at DMQ and QMC are equal to that of AMP and PMB

that being said, we now see that the angles of APM triangle and AMC triangol are equal and because the diagonal of BD is is being cut by AC, which AD is parralel to BC  and AB to Dc, we know now that lines AM and MC are congruent

we thus have enough informnation to prove that the two triangles are congruent. Because of thism, one side of the triangles, Pm which is the congruent side to that of PQ must be equal as well and

thus PM = QM

The alternate interior angles formed by the parallel sides and a common

transversal are equal, such that ΔPBM and ΔQDM are congruent.

Correct response;

PM is congruent to QM  by CPCTC

How is the congruency of the segments determined?

The two column proof is presented as follows;

Statement [tex]{}[/tex]                                          Reason

ABCD is a parallelogram [tex]{}[/tex]                         Given

AC and DB are diagonals of ABCD [tex]{}[/tex]        Given[tex]{}[/tex]

M is the point of intersection of the diagonals [tex]{}[/tex] Given

MB ≅ DM, and AM ≅ CM;[tex]{}[/tex]  Properties of the diagonals of a parallelogram

∠PMB ≅ ∠DMQ [tex]{}[/tex]                                Vertical angles theorem

∠PBM ≅ ∠QDM [tex]{}[/tex]                                Alternate interior angles theorem

ΔPBM ≅ ΔQDM  [tex]{}[/tex]                               Angle-Side-Angle Congruency post.

PM ≅ QM [tex]{}[/tex]                                          CPCTC

ΔPBM is congruent to ΔQDM by Angle-Side-Angle congruency

postulate, given that they have two angles and an included side that are

congruent.

Therefore;

PM is congruent to QM by Corresponding Parts of Congruent Triangles are Congruent, CPCTC.

Learn more about congruency postulates here:

https://brainly.com/question/17003791

Sixteen plus five times a number is more than the number plus 32. Write an inequality and solve it.

Answers

Answer:

x>4

Step-by-step explanation:

16+5x>x+32

5x>x+16

4x>16

x>4

Answer: answer my question

Step-by-step explanation:

pls help it’s 30 points :)

Which mathematical sentence matches the story?
A school is holding a cake sale to raise money. They are selling cakes for $1 each and soft
drinks for $.50 (50 cents) each. How many cakes and drinks do they have to sell to make
at least $100?

Answers

Answer: they will need to sell 1,000 soft  drinks and 50 cakes

Step-by-step explanation:

10pts
Cierra had $18 to spend on 6 pencils for school. After
buying the pencils she had $7.50 left. How much did
she spend on each pencil? Write an equation to represent your problem

Answers

Answer:

Step-by-step explanation:

$18-$7.50= $10.50

Answer:

f(x)=3x

f(x)=x+2

f(x)=3√3+x2

Step-by-step explanation:

Alexa is making a bracelet using beads. She uses 1 red bead for every 5 silver beads. If she uses a total of 20 silver beads, how many red beads does she use? Tingsug can you please answer this for me? pls

Answers

Answer:

4 red beads

Step-by-step explanation:

Help I will be marking brainliest!

A. 48
B. 124.8
C. 135.2
D. 115.2

Answers

Answer:

B.  124.8

Step-by-step explanation:

ΔBDS ~ ΔBZD

BD = 52BZ = 20BS = ?

Use ratios of similar triangles:

BS/BD = DZ/BZBS = BD*DZ/BZ

DZ = √(52²-20²) = 48

BS = 52*48/20 = 124.8

Correct choice is B

I WILL GIVE BRAINLIEST! I NEED IT ASAP!!!
Which lateral face has the largest area, the bottom one, left one, or diagonal one? What is its area?

Answers

Answer:

LSA of a cube = 100 in²

Explanation:

Let the area of the cube be a.

Given the following data;

a = 5 in²

To find the lateral surface area;

We know that a cube has four faces and as such the lateral surface area would be the area of the four faces.

Lateral surface area (LSA) of a cube = 4a²

Substituting into the equation, we have;

LSA of a cube = 4*5²

LSA of a cube = 4*25

LSA of a cube = 100 in²

Therefore, the lateral surface area of the package is 100 square inches.

THe Left one

The bottom and the left lateral face have the largest area.

The area of the prism is 96 cm³.

What is a prism?

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The bottom one:

Lateral area.

= 12 x 4

= 48 cm²

The left one:

Lateral area.

= 12 x 4

= 48 cm²

The diagonal one:

Lateral area.

= 1/2 x 4 x 4

= 8 cm²

Now,

Area.

= ( 1/2 x 4 x 4 ) x 12

= 8 x 12

= 96 cm³

Thus,

The bottom and the left lateral face have the largest area.

The area of the prism is 96 cm³.

Learn more about prism here:

https://brainly.com/question/12649592

#SPJ3

If m = 36 degrees, then find the
m

Answers

Answer:

probablt m= 0.628

Step-by-step explanation:

complete the equation of the line whose y-intercept is (0, -1) and the slope is 4

Answers

Answer:

y=4x-1

Step-by-step explanation:

We know that the slope equation is y=mx+b. M is the slope and B is the y-intercept. M is provided to be 4 and B is provided to be -1, so all we have to do is plug them in to get the answer.

Answer:

y = 4x - 1

Step-by-step explanation:

Slope-intercept form:

y = mx + b

So, input all the values...

y = 4x - 1

Hope this helps :)

Let me know if there are any mistakes!!

Other Questions
PLZ HELP RN I WILL GIVE YOU BRAINIEST!!! Roman was studying the life of fish, frogs, and turtles inDoyle Park. In two hours, he counted 4 more frogs thanturtles. The number of fish he counted was twice thenumber of turtles. In total, he counted 68 animals. Howmany fish were there? how many frogs were there? how many turtles were there? In 2021, Holyoak Inc. offers a coupon for $20 off qualifying purchases of its new line of products. Holyoak sold 11,400 of these products during the year. By year-end of 2021, 8,500 coupons had been redeemed and the $20 reduction of purchase price provided to customers. Holyoak's historical experience with such coupons indicates that 85% of customers use the coupon. Holyoak recognizes coupon expense in the period coupons are issued. What is the expense that Holyoak should report for its promotional coupons in its 2021 income statement Which city is closest to the equator?Nairobi KenyaBogota ColombiaPhoenix ArizonaSeattle Washington Eugene had $57.93 to spend when he went to Staples. He bought 4 notebooks for $7.99 each and some pens for $2.49 each. After paying for his supplies he had $18.50 left. How much did each pens cost? use the distributive property to find two expressions that are equivalent to 7(3x - 4)please help me i cant do this anymore, i'm having a panic attack and this is all due in 4 hours Can someone help me with this question if a + b + c is equals to 270 then prove that sin a cos b sin c + cos a sin b sin c + sin a sin b cos c = cos a cos b cos c Why does Egypt care if a country south of them is building a dam?The river flows south, so it could back up tradeEgypt always worries about anything to do with the NileThe river flows north, so it could lower their water level.They do not really care; they just think it is not needed. Gems are minerals used in jewelry their beauty determines their value.1) No change2) jewelry , 3) jewelry ;4) jewelry, however, their The ABC box company makes square puzzle cubes that measure 4 inches along each edge. They shipped the cubes in a box 8 in x 12 in x 16 in. How many cubes can they ship in the box? To the nearest tenth, find the area of a circle with adiameter of 8 meters. Use 3.14 Paraphrase: And while we respect their right to advocate for reform, What was the mistrust between the Henrietta Lacks and the tuskegee pls help this is really complicated for my brain so if anyone knows how to do backtracking and undoing any help is accepted!!! Lisez la question. Puis, choisissez le bon pronom complment d'objet indirect pour complter la rponse. ric, me donnes-tu les fleurs ? Oui, je ______ donne les fleurs. identify the relationship between angles f, b, and a in the above diagram. PLEASE HELP WILL GIVE BRAINLIEST 7TH GRADE MATH Select ALL the correct answers.What were two weakness of American government under the Articles of Confederation did the Philadelphia Mutiny highlightA.) States could not coin their own money.B.) States did not have to comply with requests from CongressC.) Congress could not appoint federal judges.D.) Congress could not raise any money to pay militias. Factor completely and then place the factors in the proper location on the grid.36 x2 + 60 x + 25 How did rising tensions between the North and the South lead to Southern secession? (Lesson 1.3)3-4 sentences Use the drop-down menus to select the bestanswers.v is a life-sustaining, odorlessgas in the air.is a waste product ofrespiration