An arc 28 cm is cut from a circle of radius 15 cm. Find the angle of the sector formed by this arc.

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{28}{15}\; \text{radians}[/tex], which is approximately [tex]107^{\circ}[/tex].

Step-by-step explanation:

In a given circle, the angle of a sector is proportional to the length of the corresponding arc:

[tex]\displaystyle \frac{\text{angle of sector $1$}}{\text{angle of sector $2$}} = \frac{\text{length of arc of sector $1$}}{\text{length of arc of sector $2$}}[/tex].

For the circle in this question, [tex]r = 15\; \rm cm[/tex], and the circumference would be:

[tex]2\, \pi \, r = 30\, \pi\; \rm cm[/tex].

The full circle itself is like a sector with an angle of [tex]2\, \pi[/tex], with the arc length equal to the circumference of the circle.

[tex]\displaystyle \frac{\text{angle of sector}}{\text{angle of full circle}} = \frac{\text{length of arc of sector}}{\text{circumference of circle}}[/tex].

[tex]\displaystyle \frac{\text{angle of sector}}{2\,\pi\; \rm rad} = \frac{28\; \rm cm}{30\, \pi\; \rm cm}[/tex].

Rearrange the equation to find the angle of the sector:

[tex]\begin{aligned} & \text{angle of sector} \\ =\; & (2\,\pi\; \rm rad) \cdot \frac{28\; \rm cm}{30\, \pi\; \rm cm} \\ =\; & \frac{28}{15}\; \rm rad\end{aligned}[/tex].

In other words, the angle of this sector would be [tex]\displaystyle \frac{28}{15}\; \rm rad[/tex]. Multiply that measure in radians by [tex]\displaystyle \frac{360^{\circ}}{2\,\pi\; \rm rad}[/tex] to find the value of the angle measured in degrees:

[tex]\begin{aligned} & \frac{28}{15}\; \rm rad \times \frac{360^{\circ}}{2\,\pi\; \rm rad} \approx 107^{\circ}\end{aligned}[/tex].


Related Questions

please please please help!

Answers

Answer:

4

Step-by-step explanation:

The multiplication of both indices gives 4

1/2(f+y)=f-5 as a sentence

Answers

Step-by-step explanation:

½(f + y) = f - 5

(f + y)/2 = f - 5

y + f = 2f - 10

y = f - 10

or

f = y + 10

#mathisfun

Can someone please answer this? Thank you!

Answers

[tex]\\ \sf\longmapsto 1-\left(\dfrac{4}{7}+\dfrac{4}{5}\right)[/tex]

[tex]\\ \sf\longmapsto 1-\left(\dfrac{20+28}{35}\right)[/tex]

[tex]\\ \sf\longmapsto 1-\left(\dfrac{48}{35}\right)[/tex]

[tex]\\ \sf\longmapsto 1-\dfrac{48}{35}[/tex]

[tex]\\ \sf\longmapsto \mid \dfrac{35-48}{35}\mid[/tex]

[tex]\\ \sf\longmapsto \mid \dfrac{-13}{35}\mid[/tex]

[tex]\\ \sf\longmapsto \dfrac{13}{35}[/tex]

Answer:

3/35

Step-by-step explanation:

total bottles 7/7

4/7 are big,

7/7-4/7=3/7 remaining bottles.

4/5×3/7=12/35 are small.

you add the big bottles and small bottles

4/7+12/35=32/35

then you minus from the total which is 7/7

7/7-32/35=3/35 are tiny.

PLZ HELP!! ILL GIVE BRAINLIEST!!!

Answers

the answer is (6,-3)

Answer:

(6, -3)

Step-by-step explanation:

Find the middle of the 2 coordinates.

8 --- 4

7 --- 5

6 --- 6

__________

-7 --- 1

-6 --- 0

-5 --- -1

-4 --- -2

-3 --- -3

Solve for z.

6.6 = 3(z − 16.9) − –0.6

z =

Answers

Answer:

z = 18,9

Step-by-step explanation:

[tex]6.6 = 3(z - 16.9) - - 0.6[/tex]

[tex]6.6 = 3z - 50.7 - ( - 0.6)[/tex]

[tex]6.6 = 3z - 50.7 + 0.6[/tex]

[tex]6.6 = 3z - 50.1[/tex]

[tex]6.6 - 3z = - 50.1[/tex]

[tex] - 3z = - 50.1 - 6.6[/tex]

[tex] - 3z = - 56.7[/tex]

[tex]z = 18.9[/tex]

2. Which number line is correct? Why are the others incorrect? ​

Answers

Answer:

the middle one is correct

Step-by-step explanation:

the first one is incorrect because the way negative numbers are ordered is incorrect it should be "-3, -2, -1"

the middle one is correct because the pattern is consistent and the order of the numbers are correct

the third one is incorrect because the pattern doesn't match "-15" isn't counting by twos 15 isn't an even number

hope I helped ❤

Answer: The 2nd number line is correct

Explanation:

The first number line is incorrect because the -1, -2, -3 should be reversed to get -3, -2, -1. It's reversed because the negatives are a mirror image of the positive counterpart.

The second number line is correct. Each number shown is separated with a gap size of 20. This gap size stays the same throughout the number line.

The third number line is incorrect. The gap from -15 to -12 is 3 units, while the gap from -12 to -10 is 2 units. We see that the gap size isn't the same through the entire number line.

So to summarize: the gap size must be the same and the numbers must be written in the correct order.

5.
For which discriminant is the graph possible?

A. b2 – 4ac = –1
B. b2 – 4ac = 0
C. b2 – 4ac = 4

Answers

C is the only one that will give two real roots (cross the x axis twice)

A has no real roots - the square root of -1 is not real
B has two identical roots - the parabola touches the x axis at one point

Let f(x) = -20x^2 + 14x + 12 and g(x) = 5x - 6. Find f/g and state it’s domain.

Answers

Answer:

-4x - 2 all are real number

HELPP PLSSS!!! When factoring a number, you can use _[blank 1] as a shortcut. For example, you can tell if 5 is a factor of a number if _[blank 21- Match each blank with the option that correctly fills in that blank. blank 2 blank 1 .: it is even .: divisibility rules :: its last digit is 0 or 5 :: the sum of its digits is a multiple of 3 * long division guessing and checking​

Answers

Answer:

blank 1: divisibility rules

blank 2: its last digit is 0 or 5

WILL GIVE BRAINLIEST TO WHOEVER CAN SHOW UR WORK:

89.9cm to m.

Answers

Answer:

give brainliest please I need it to level up

Step-by-step explanation:

divide the value in centimeters by 100 because 1 meter equals 100 centimeters.

So, 89.9 centimeters = 89.9÷ 100 = 0.899 meter.

make a the subject of the formula x²=a²-a²w²​

Answers

Answer:

a = ± [tex]\sqrt{\frac{x^2}{1-w} }[/tex]

Step-by-step explanation:

Given

x² = a² - a²w ← factor out a² from each term on the right side

x² = a²(1 - w) ← divide both sides by (1 - w)

[tex]\frac{x^2}{1-w}[/tex] = a² ( take the square root of both sides )

± [tex]\sqrt{\frac{x^2}{1-w} }[/tex] = a

let h (x)= -x-18 find h (3)

Answers

Answer:

-21

Step-by-step explanation:

h(x) = -x-18

h(3) = -(3)-18 = -21

Answer:

[tex]h(3)=-21[/tex]

Step-by-step explanation:

One is given the following:

[tex]h(x) = -x - 18[/tex]

One is asked to find the value of ([tex]h(3)[/tex]). Substitute ([tex]3[/tex]) in place of ([tex]x[/tex]) and simplify to evaluate,

[tex]h(x)=-x-18\\\\h(3)=-(3)-18\\\\h(3)=-3-18\\\\h(3)=-21[/tex]

Decide!!!!!!!!!!!!!!

Answers

A third alternative to the formulas I suggested in a comment is to use the vector cross product. Recast the three given points as points in 3D space with 0 z-coordinate:

A(20, 21, 0), B(8, 29, 0), and C(13, 1, 0)

Now consider two vectors,

u = B - A = 〈8, 29, 0〉 - 〈20, 21, 0〉 = 〈-12, 8, 0〉

v = C - A = 〈13, 1, 0〉 - 〈20, 21, 0〉 = 〈-7, -20, 0〉

Then recall the cross product identity,

||u × v|| = ||u|| ||v|| |sin(θ)|

where θ is the angle between the two vectors. The magnitude of u × v is equal to the area of the parallelogram spanned by u and v, and hence twice the area of the triangle of interest.

So we have

area = ||1/2 〈-12, 8, 0〉 × 〈-7, -20, 0〉||

area = 1/2 ||〈-12, 8, 0〉 × 〈-7, -20, 0〉||

area = 1/2 ||〈0, 0, 296〉||

area = 296/2

area = 148

Katie and mina both commute to work. Katie's commute on train takes 10 minutes more then 1/2 as may minutes as Mina’s commute by car. It takes Katie 30 minutes to get to work which equation determines how many minutes it takes Mina to get to work. (9th grade Algebra 1)

Answers

Answer:

It’s A.

Step-by-step explanation:

Took the test and got it right

1 months salary 1000 rupees. How many salary in 1 day.​

Answers

Step-by-step explanation:

1 month has 30 days

so 100 ÷ 30

so ans is 33.3 rupees for one day

MARK AS BRAINLIST IF IT IS USEFUL

Year8 Maths(Angles)

Help me plz!!

Answers

Step-by-step explanation:

a 360/9 = 40

b 2/9 × 360 = 80

c similarly 160

d 400

What is the greatest common factor of 39 and 3?

Answers

Answer:

The GCF of 39 and 3 is 3

Step-by-step explanation:

3/3= 1

39/3= 13

Write an equivalent expression by distributing the "−" sign outside the parentheses:

−(−6.8k+8)

Answers

Answer:

[tex] - ( - 6.8k + 8) \\ = + 6.8k - 8 \\ thank \: you[/tex]

please help me-- financial math!!
The balance on Taylor's credit card is $2000. It has an interest rate of 12.5%. She wants to compare the difference between paying $75 and $100 of the monthly balance. How much does she save in interest and fees if she pays $100 instead of $75?

Answers

Answer:

Step-by-step explanation:

2000 * .125/12 = $20.83

at $100 remaining balance = $1920.81

at $75 remaining balance   = $1945.81

M decreased by 1??????

Answers

Answer:

Step-by-step explanation:

Ssssyiijnbrr

Please help I’m failing math

Answers

I’ve attached my answer
Hope it helps and always willing to help!!
Have a nice day :)

What expression is equivalent to 9-(-12)

Answers

Answer:

9 + 12

Step-by-step explanation:

9 - (-12)

Subtracting a negative is like adding

9 + 12

21

9-(-12) [ - and - became + ]

9 + 12

9 + 12 = 21

write 15009 in expanded notation

Answers

Answer:

the answer is 10000+5000+9

Answer:

10,000+5,000+9

Step-by-step explanation:

that is the answer

Why might you need to use the addition or subtraction property of equality more than once after you have used the distributive property and combined like terms? Explain. Sample Response: If there is a variable term and a constant on each side of the equation, then you will need to use the addition or subtraction property of equality once to isolate the variable term and once to isolate the constant. Which did you include in your response? Check all that apply. Use the addition or subtraction property of equality once to isolate the variable term. Use the addition or subtraction property of equality once to isolate the constant.

Answers

Answer:

We have to use addition or subtraction property of equality to determine the value of variable involve.

Step-by-step explanation:

Example with variable term:

3x=4-x

Add x on both sides of equation:

3x+x=4-x+x

4x=4

x=1

Example with contact involve:

5y+7=12

Subtract 7 from both sides

5x+7-7=12-7

5x=5

x=5/5

x=1

Find the distance between the two points in simplest radical form (-8,-4) (0,-8).

Answers

Answer: Distance = 4√5

Concept:

Here, we need to know the concept of the distance formula.    

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Given information

(x₁, y₁) = (-8, -4)

(x₂, y₂) = (0, -8)

Given equation

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute values into the equation

[tex]Distance=\sqrt{(0+8)^2+(-8+4)^2}[/tex]

Simplify values in the parentheses through addition

[tex]Distance=\sqrt{(8)^2+(-4)^2}[/tex]

Simplify exponents

[tex]Distance=\sqrt{64+16}[/tex]

Simplify by addition

[tex]Distance=\sqrt{80}[/tex]

Simplify the radical value into the simplest form

[tex]Distance=4\sqrt{5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

how to do you divide? ​

Answers

Answer:

I HOPE IT WILL HELP YOU A LOT.

please help this 2 sums

Answers

Answer:

Step-by-step explanation:

Sin (A +  B) = Sin A *Cos B + Cos A *Sin B

Sin 75 = Sin (30 + 45)

           = Sin 30 * Cos 45 + Cos 30 * Sin 45

           [tex]= \dfrac{1}{2}*\dfrac{1}{\sqrt{2}}+\dfrac{\sqrt{3}}{2}*\dfrac{1}{\sqrt{2}}\\\\\\= \dfrac{1}{2\sqrt{2}}+\dfrac{\sqrt{3}}{2\sqrt{2}}\\\\= \dfrac{1+\sqrt{3}}{2\sqrt{2}}[/tex]

f(x) = roots 3x + 7

if f^-1 (x) is the invers of f(x), then determine the result of f^-1(2)!​

Answers

[tex]f(x) = \sqrt{3x} + 7 \\ \\ f ^{ - 1} (x) = ( \sqrt{3x} + 7) ^{ - 1} \\ \\ f ^{ - 1} (x) = \frac{1}{ \sqrt{3x} + 7} \\ \\ \\ f ^{ - 1} (2) = \frac{1}{ \sqrt{3(2)} + 7} \\ \\f ^{ - 1} (2) = \frac{1}{ \sqrt{6} + 7} \\ \\ f ^{ - 1} (2) = \frac{1}{ \sqrt{6} + 7} \times \frac{ \sqrt{6} - 7 }{ \sqrt{6} - 7 } \\ \\ f ^{ - 1} (2) = \frac{ \sqrt{6} - 7 }{(6 - 49)} = \frac{ \sqrt{6} - 7 }{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ \sqrt{6} - 7 }{ - 43} = \frac{2.449 - 7}{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ - 4.551}{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ 4.551}{ 43} =0.10584[/tex]

I hope I helped you^_^

John sold a car for 60,000 dollars and made a profit of 20%.what is the cost price of the car​

Answers

Answer:

72,000

Step-by-step explanation:

20% of 60,000 = 12,000

60,000 + 12,000 = 72,000

Chow,...!

Please explain how you got the answers also please. Thank you :)

Answers

Answer:

x = -2 —> y = 4

x= 0 —> y = 1

x= 3 —> y = 1/8

Step-by-step explanation:

X= –2

[tex]y = ( \frac{1}{2} ) ^{x} \\ y = ( \frac{1}{2} ) ^{ - 2} =( \frac{2}{1} ) ^{2} = {2}^{2} = 4[/tex]

X= 0

[tex]y = ( \frac{1}{2} ) ^{x} \\ y = ( \frac{1}{2} ) ^{ 0} =1[/tex]

X= 3

[tex]y = ( \frac{1}{2} ) ^{x} \\ y = ( \frac{1}{2} ) ^{ 3} = \frac{ {1}^{3} }{ {2}^{3} } = \frac{1}{8} [/tex]

I hope I helped you^_^

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