All categories

2 years ago

A sector with a radius of 6 cm has a central angle measure of 4pi/9 (in radians). What is the area of the sector?

Mathematics

1 answer:

Usimov [2.4K]2 years ago

8 0

Answer:

The area of the sector is 25.1327 cm²

Step-by-step explanation:

The area of a sector of circunference delimited by an angle in radians can be calculated by using the formula below:

area = (angle*r²)/2

area = [(4*pi/9)*(6)²]/2

area = [(4*pi/9)*36]/2

area = (144*pi/9)/2

area = 144*pi/18

area = 8*pi

area = 25.1327 cm²

The area of the sector is 25.1327 cm²

You might be interested in

Without sketching the graph, find the x-intercepts and y-intercepts of the graph of the equation y=x²-x-6 What is/are the x-inte

oksian1 [2.3K]

Given the equation:

$y=x^2-x-6$

Let's find the x-intercepts and the y-intercepts of the graph.

• x-intercept:

The x-intercept are the points where the parabola crosses the x-axis. At x-intercept the y-value is zero.

To find the x-intercepts, substitute 0 for y and solve for x.

We have:

$0=x^2-x-6$

Rewrite the equation:

$x^2-x-6=0$

Factor the left hand side of the equation:

$(x-3)(x+2)=0$

Equate each factor to zero:

x - 3 = 0

Add 3 to both sides:

x - 3 + 3 = 0 + 3

x = 3

x + 2 = 0

Subtract 2 from both sides:

x + 2 - 2 = 0 - 2

x = -2

Therefore, the x-intercepts are:

3, -2

• y-intercept:

The y-intercept is the point where the parabola crosses the y-axis. The x-value at the y-intercept is zero.

To find the y-intercept, substitute 0 for x and solve:

$\begin{gathered} y=0^2-0-6 \\ \\ y=-6 \end{gathered}$

Therefore, the y-intercept is -6.

In point form:

x-intercept: (3, 0), (-2, 0)

y-intercept: (0, -6)

ANSWER:

A. The x-intercepts are (3, 0), (-2, 0)

A. The y-intercept is (0, -6)

5 0

1 year ago

Identify quadrilateral

Sholpan [36]

14. trapezoid

- the bases are parallel

15. rhombus

- if you add 57 and 33 you will get 90 degrees. that means all the other angles the diagonals create intersecting each other are 90 degrees, and one of the properties of a rhombus is they have perpendicular diagonals.

16. kite

- two adjacent sides are congruent, and the two angles drawn are congruent

4 0

2 years ago

2(x - 1) = x + 10<br> x<br> =

aev [14]

In the equation, x = 12

7 0

2 years ago

Read 2 more answers

Can someone help me with this?

defon

Y = 15

Because it’s going to every time by 15

5 0

3 years ago

Vanessa wants to purchase a new cell phone plan. The two plans from which she can choose are shown below. Vanessa used the syste

user100 [1]

Answer:

2. 325 minutes.

Step by step explanation:

We will substitute our given number of minutes in our both equation one by one to find the correct option.

1. Let us substitute m= 775 in both equations.

$CA=22+0.13m$

$CA=22+0.13\cdot 775$

$CA=22+100.75=122.75$

$CB=44+0.09(m-100)$

$CB=44+0.09(775-100)$

$CB=44+0.09\cdot675$

$CB=44+60.75=104.75$

$104.75\neq122.75$

We can see that both plans have different costs , therefore, 1st option is incorrect.

2. Let us substitute m= 325 in both equations.

$CA=22+0.13m$

$CA=22+0.13\cdot 325$

$CA=22+42.25=64.25$

$CB=44+0.09(m-100)$

$CB=44+0.09(325-100)$

$CB=44+0.09\cdot 225$

$CB=44+20.25=64.25$

$64.25=64.25$

When Vanessa has used the phone for 325 minutes, the cost for Plan A and the cost for Plan B will both be $64.25.Therefore, 2nd option is correct choice.

3. Let us substitute m= 32.5 in both equations.

$CA=22+0.13m$

$CA=22+0.13\cdot 32.5$