1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PtichkaEL [24]
11 months ago
11

Find the length of the arc and express your answer as a fraction times pie

Mathematics
1 answer:
Elina [12.6K]11 months ago
4 0

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}

To find the length of the arc, s, the formula is

\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}

Substitute the variables into the formula to find the length of an arc, s above

\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}

Hence, the length of the arc, s, is 3π units.

You might be interested in
Find the measure of the missing angle <br> Answer: a=
statuscvo [17]

Answer:

C + 88 = 180

-88         -88

C and B = 92

Since C is vertical to B that means both values are the same. Therefore the values of c and b is 92 degrees.

6 0
3 years ago
20 % of 2 is equal to <br><br> A. 20 <br> B. 4 <br> C. 0.4 <br> D. 0.04
ExtremeBDS [4]
I think the answer is 0.4

4 0
3 years ago
Which fraction is between 2/3 and 6/7
MrRa [10]

Answer:

For example, 16/21

Step-by-step explanation:

Are there choices?

There is an infinite number of numbers between any two numbers.

2/3 = 14/21

6/7 = 18/21

One example of a fraction between 2/3 and 6/7 is 16/21

16/21 is between 2/3 and 6/7.

5 0
2 years ago
When f(x) = -3, what is x?
julia-pushkina [17]

Answer:

not enough info

Step-by-step explanation:

f times x equals -3 there could be many answers like f is 1 x is -3 or f is -3 x is 1 and more

3 0
2 years ago
What are the possible values of x for the following functions? f(x)=2-x/x(x-1)
nevsk [136]

The possible values of x for the following functions are values on real number except 0 and 1

<h3>Domain of a function</h3>

The domain of a function are the values of the independent variable for which it exists.

Given the function below

f(x)=2-x/x(x-1)

The function does not exist at the. point where the denominator is zero. From the function given, the function does not exist when;

x(x -1) = 0

x = 0 and x = 1

Hence the possible values of x for the following functions are values on real number except 0 and 1

Learn more on domain of a function here; brainly.com/question/1770447

#SPJ1

5 0
1 year ago
Other questions:
  • In the morning, Marco sold 12 cups of lemonade for $3. By the end of the day, he had earned $9. How many cups of lemonade did he
    5·2 answers
  • Chissy had 4 gallons of gas in her tank when she arrived at the gas station. She pumped gas into her car at a rate of 3/10 gallo
    12·1 answer
  • Evaluate and answer in standard form:<br><br>(3^2)^2​
    10·1 answer
  • What is the first step in simplifying the expression 11x-2-3(1-7x)^2\(x+1)
    8·2 answers
  • Find the values of a given that AGHJ ZAMNP.<br> G<br> N<br> (2x<br> 50°<br> 142<br> M<br> H
    9·1 answer
  • 15)
    5·1 answer
  • Please help I might fail!!
    10·2 answers
  • Which expressions is not equivalent 2x^2+10x+12?
    10·1 answer
  • 4·(4+32+42) please help fast
    5·2 answers
  • A Man borrowed Rs 500 for 3 years at the rate of 5% find his interest and amount​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!