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Serggg [28]
3 years ago
6

What is the area of the sector with a central angle of 49° and a radius of 11 cm? Use 3.14 for pi and round your final answer to

the nearest hundredth
Mathematics
1 answer:
olga_2 [115]3 years ago
4 0

Answer:

\boxed{\text{51.71 cm}^{2}}

Step-by-step explanation:

If the angle θ is in radians, the formula for the area (A) of a sector of a circle is

A = ½r²θ

If θ is in degrees

A = \dfrac{1}{2}r^{2}\theta \times \dfrac{\pi \text{ rad}}{180^{\circ}}= \pi r^{2}\times\dfrac{\theta }{360}

Data:

θ = 49°

r = 11 cm

Calculation:

\begin{array}{rcl}A& = &3.14\times 11^{2}\times\dfrac{49}{360}\\\\ & = &3.14 \times 121 \times 0.1361\\ & = & \mathbf{51.71}\\\end{array}\\\text{The area of the sector is }\boxed{\textbf{51.71 cm}^{2}}

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Rainbow [258]

By algebra properties we find the following relationships between each pair of algebraic expressions:

  1. First equation: Case 4
  2. Second equation: Case 1
  3. Third equation: Case 2
  4. Fourth equation: Case 5
  5. Fifth equation: Case 3

<h3>How to determine pairs of equivalent equations</h3>

In this we must determine the equivalent algebraic expression related to given expressions, this can be done by applying algebra properties on equations from the second column until equivalent expression is found. Now we proceed to find for each case:

First equation

(7 - 2 · x) + (3 · x - 11)

(7 - 11) + (- 2 · x + 3 · x)

- 4 + (- 2 + 3) · x

- 4 + (1) · x

- 4 + (5 - 4) · x

- 4 - 4 · x + 5 · x

- 4 · (x + 1) + 5 · x → Case 4

Second equation

- 7 + 6 · x - 4 · x + 3

(6 · x - 4 · x) + (- 7 + 3)

(6 - 4) · x - 4

2 · x - 4

2 · (x - 2) → Case 1

Third equation

9 · x - 2 · (3 · x - 3)

9 · x - 6 · x + 6

3 · x + 6

(2 + 1) · x + (14 - 8)

[1 - (- 2)] · x + (14 - 8)

(x + 14) - (8 - 2 · x) → Case 2

Fourth equation

- 3 · x + 6 + 4 · x

x + 6

(5 - 4) · x + (7 - 1)

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Fifth equation

- 2 · x + 9 + 5 · x  + 6

3 · x + 15

3 · (x + 5) → Case 3

To learn more on algebraic equations: brainly.com/question/24875240

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Anna [14]
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Angelina_Jolie [31]
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8 0
3 years ago
Read 2 more answers
Solve: x=4+(4x-4)1/2
Damm [24]

Answer:

x = 10

Step-by-step explanation:

x = 4 + (4x-4) ^ (1/2)

First, we rewrite the expression:

x = 4 + (4x-4) ^ (1/2)

x = 2 (2+ (x-1) ^ (1/2))

x = 4 + 2 (x-1) ^ (1/2)

From here we get a solution for x = 10

To check it we substitute x = 10 in the expression:

10 = 4 + 2 (10-1) ^ (1/2)

10 = 4 + 2 (9) ^ (1/2)

10 = 4 + 2 (3)

10 = 4 + 6

10 = 10

Answer:

The solution is:

x = 10

8 0
2 years ago
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