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vazorg [7]
3 years ago
10

Find the area of the crescent-shaped region (called a lune) bounded by arcs of circles with radii r = 2 and r = 14

Mathematics
1 answer:
Liula [17]3 years ago
3 0

the complete question in the attached figure 

Let 

A1-------> half of the area of the blue circle
A2-------> area of the circular segment formed by the diameter of the blue circle treated as a chord of the red circle

A3---------- > area of the crescent-shaped region

A3=A1-A2

A1=pi*2²/2=6.28

Area of ​​the circular sector

if 360 º corresponds to an area of pi*14²

2*arc sin(2/14)------------------- X

X=16.43*pi*14²/360---------- > X=28.10

Triangle area:

------- >(4/2)*√(14²-2²=27.72 

Area of ​​the circular segment A2=Area of ​​the circular sector-Triangle area

A2=28.10-27.72=0.38

A3=  A1-A2=6.28-0.38=5.90 units²

the answer is 5.90 units²

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2x^2+5x+3=0

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2*3=6

Find which two numbers add up to 5 and multiply into 6:

3+2=5\\3*2=6\\3,2

Split 5x as the sum of 3x and 2x:

2x^2+3x+2x+3

Now factor out a common term for the first 2 terms:

2x^2+3x\\x(2x+3)

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2x+3\\1(2x+3)

Re-insert:

x(2x+3)+1(2x+3)=0

Factor out the common term 2x+3 and insert the values in front of the parentheses (x and 1):

(2x+3)(x+1)=0

Separate the parentheses and equal them to 0. Solve for x:

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and

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