Will give brainilest!

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

Vaselesa [24]

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 $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

Question 1:

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:

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

Question 2:

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:

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

8 0

2 years ago

Select all values of x that make the inequality true -x+6> 10 true .

Rufina [12.5K]

Answer:

C. -4.01

H. -7

Step-by-step explanation:

Solving inequalities:

We have a set of numbers to verify which ones of them make the below inequality true

$-x+6>10$

Rearrange

$-10+6>x$

Operating

$-4>x$

Flipping

$x$

The set of solutions contains every number less than -4

There are only two numbers less than -4 in the set of options:

C. -4.01

H. -7

4 0

2 years ago

Read 2 more answers

What is the common factor of 9 and 12

Lelu [443]

3

We found the factors and prime factorization of 9 and 12. The biggest common factor number is the GCF number. So the greatest common factor 9 and 12 is 3.

7 0

2 years ago

Read 2 more answers

BRAINLIEST!!

tekilochka [14]

Answer:

$\frac{1}{20}$