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Derive the formula for the area of a sector, and then use it to choose all that are correct.

Marina CMI [18]

Answer:

Part A) $A_s=\frac{\pi r^{2}}{360^o}{\theta}$

Part B) option 1,option 4

Step-by-step explanation:

Part A) Derive the formula for the area of a sector

we know that

The area of circle is equal to

$A=\pi r^{2}$

The area of circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector $A_s$ by a central angle of ∅ degrees

$\frac{\pi r^{2}}{360^o}=\frac{A_s}{\theta}$

$A_s=\frac{\pi r^{2}}{360^o}{\theta}$

Part B) Verify each case

case 1) we have

radius = 5 cm

angle = 120°

area = 26.2 cm 2

Find the area of the sector and then compare with the value of the given area

assume

$\pi=3.14$

substitute the given values

$A_s=\frac{(3.14)(5)^{2}}{360^o}{120^o}$

$A_s=26.2\ cm^2$

so

The given value of area is correct

case 2) we have

radius = 4 cm

angle = 105°

area = 16.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

$\pi=3.14$

substitute the given values

$A_s=\frac{(3.14)(4)^{2}}{360^o}{105^o}$

$A_s=14.7\ cm^2$

so

The given value of area is not correct

case 3) we have

radius = 6 cm

angle = 85°

area = 23.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

$\pi=3.14$

substitute the given values

$A_s=\frac{(3.14)(6)^{2}}{360^o}{85^o}$

$A_s=26.7\ cm^2$

so

The given value of area is not correct

case 4) we have

radius = 7

angle = 75°

area = 32.1 cm 2

Find the area of the sector and then compare with the value of the given area

assume

$\pi=3.14$

substitute the given values

$A_s=\frac{(3.14)(7)^{2}}{360^o}{75^o}$

$A_s=32.1\ cm^2$

so

The given value of area is correct

5 0

3 years ago

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life ( 150,000 miles of driv

fgiga [73]

Answer:

Mg/mi. A Company Has 16 Cars Of This Model In Its Fleet. ... The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in d ... organic gas (NMOG) in the exhaust over the useful life (150,000 miles of driving) of cars of a particular model varies Normally with mean 85 mg/mi and standard deviation 6 mg/mi.

Step-by-step explanation:

7 0

2 years ago

What is the solution to this system of linear equations?

tigry1 [53]

Answer:

(3,-1)

Hope this helps! :)

3 0

3 years ago

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What is the value of x?<br> 5x+11°<br> 119°

frutty [35]

Answer:

21.6

Step-by-step explanation:

119 = 5x + 11

119 - 11 = 5x

108 = 5x

108÷5 = x

21.6 = x

hope this helped you.

please give me brainliest.

thank you and have a great day ahead :D

8 0

3 years ago

Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).

AVprozaik [17]

Answer:

458435464546484845kdnh

7 0

3 years ago

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