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
OlgaM077 [116]
3 years ago
13

Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Mathematics
1 answer:
Vaselesa [24]3 years ago
8 0

Answer:

\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: }  \frac{3\pi}{2}\text{ mi}

Step-by-step explanation:

The circumference of a circle with radius r is given by C=2\pi r. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle \theta^{\circ} is equal to 2\pi r\cdot \frac{\theta}{360}.

Formulas at a glance:

  • Circumference of a circle with radius r: C=2\pi r
  • Length of an arc with central angle \theta^{\circ}: \ell_{arc}=2\pi r\cdot \frac{\theta}{360}

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting r=2 into our circumference formula, we get:

C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}

You might be interested in
Emma earns 120 frequent flyer miles for every $40 of merchandise she buys with her credit card. Which of the following equations
Stells [14]
120 divided by 40 = 3

That’s the equation
7 0
3 years ago
Read 2 more answers
Find the equation of a line that contains the points (3,7) and (-6, 4). Write the equation in slope-intercept form, using
NikAS [45]

Answer:

y=\frac{1}{3} x+6

Step-by-step explanation:

(3,7)(-6,4)

Step 1. Find the slope (by using the slope-formula)

m = slope

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{4-7}{-6-3}

m=\frac{-3}{-9}

m=\frac{3}{9}

m=\frac{1}{3}

Step 2. Write the equation (using the slope and the points)

Here's how to do it:

Slope-intercept Formula y=mx+b whrere m = slope and b = y-intercept

Plug in the slope into the Slope-intercept Formula

y=\frac{1}{3} x+b

Find the y-intercept (b) by using a point and substituting their x and y values

y=\frac{1}{3} x+b

Point: (3, 7)

7=\frac{1}{3} (3)+b

7=1+b

b=7-1

b=6

Step 3. Write the equation in Slope-intercept form

y=mx+b

y=\frac{1}{3} x+6

3 0
2 years ago
How do simplify 4(x-3)+5(x-3)
vesna_86 [32]

Answer:

9x-27

Step-by-step explanation:

4(x-3)+5(x-3)=4x-12+5x-15=4x+5x-12-15=9x-27

4 0
3 years ago
Which formula(s) can be used to find the nth partial sum of a geometric sequence or the sum of the first n terms of a geometric
ivolga24 [154]

Step-by-step explanation:

An=A1. R raised to the power n-1

6 0
3 years ago
Micheala drives 825 miles to Cali the trip takes her 17 hours she uses 38 gallons of gas on the trip which costs her $125 find h
In-s [12.5K]
48.53 mph
21.71 MPG
$3.29 per gallon
8 0
3 years ago
Other questions:
  • Grade 7 : Help, anyone? Urgent!!!!!!!!
    13·1 answer
  • How do I find the length of the third side of the triangle
    6·1 answer
  • There are 15 girls and 12 boys in Ms. Grady's 6th period class. Ms. Grady
    8·1 answer
  • 6378 scientific notation
    10·1 answer
  • Which numbers are solutions of the inequality x&gt;-12 ? check all that apply.
    6·2 answers
  • 12. Elly's credit card record for the last 7 months is below. Based on the information from the table, what will be her new bala
    6·2 answers
  • 1) Write 5 consecutive whole numbers preceding 25002
    15·1 answer
  • Acellus
    6·1 answer
  • What do you know abou the graph of y=5 ?​
    6·1 answer
  • Express as a product:<br> <img src="https://tex.z-dn.net/?f=1-4sin%5E2%5Calpha" id="TexFormula1" title="1-4sin^2\alpha" alt="1-4
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!