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Butoxors [25]
3 years ago
14

There were 27 bales of hay in the barn. Grant stacked some more bales in the barn.Now there are 76 bales. Let b be the number of

bales Grant stacked in the barn.
Mathematics
1 answer:
lutik1710 [3]3 years ago
4 0

Answer:

b=49

Step-by-step explanation:

27+b=76

76-27= 49

b=49

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The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².

The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines

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Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find

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and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

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Step-by-step explanation:

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