Supplementary angles measure ____

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

Elina [12.6K]

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.

4 0

7 months ago

HELP ASAP,, WILL GIVE BRAINLIEST

madreJ [45]

Answer:

a = 50°, b = 130°, c = 20°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles in the right triangle

a + 40° + 90° = 180°

a + 130° = 180° ( subtract 130° from both sides )

a = 50°

a and b are adjacent angles and sum to 180° , so

a + b = 180°

50° + b = 180° ( subtract 50° from both sides )

b = 130°

Then sum the angles in the top triangle, that is

30° + 130° + c = 180°

160° + c = 180° ( subtract 160° from both sides )

c = 20°

8 0

3 years ago

Select the values that make the inequality h < 2 true.

weqwewe [10]

Given:

The inequality is:

$h\leq 2$

To find:

The values that make the given inequality true.

Solution:

We have,

$h\leq 2$

It means the value of h must be less than or equal to 2.

In the given options, the list of numbers which are less than or equal to 2 is

-6, -3, -1, 1, 1.9, 1.99, 1.999, 2

The list of numbers which are greater than 2 is

2.001, 2.01, 2.1, 3, 5, 7, 10

Therefore, the first 8 options are correct and the required values are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.

3 0

2 years ago

How to solve and graph the problem

zhenek [66]

The answer is m>−3 but i can't show the graph

4 0

2 years ago

A stadium has 53,000. Seats sell for $ 42 in Section A, $ 36 in Section B, and $ 30 in Section C. The number of seats in Se

il63 [147K]

A = B + C = 53,000 / 2 = 26,500

section A: 26,500 (seats) x 42 = $1,113,000
$1,996,800 - $1,113,000 = $883,800

So now
B + C = 26,500 so B = 26,500 - C
36B + 30C = $883,800

substitute B = 26,500 - C into 36B + 30C = $883,800

36B + 30C = $883,800
36(26,500 - C) + 30C = $883,800
954,000 - 36C + 30C = $883,800
-6C = -70,200
C =11,700

B = 26,500 - C
B = 26,500 - 11,700
B = 14,800

Answer
A: 26,500 seats
B: 14,800 seats
C: 11,700 seats

3 0

2 years ago

Supplementary angles measure _____ degrees?​

Supplementary angles measure _____ degrees?