Answer:
12) C) 11π/2 km
13) B) 567π/2 mi²
Explanation:
The arc length and sector area can be found using the appropriate formulas.
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12)
Arc length is given by the formula ...
s = rθ . . . . where r is the radius, and θ is the angle in radians
A 90° angle is π/2 radians, so the arc length is ...
s = (11 km)(π/2)
s = 11π/2 km
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13)
Sector area is given by the formula ...
A = 1/2r²θ . . . . where θ is the central angle in radians
There are 2π radians in 360°, so the angle 315° corresponds to ...
315° = (315/360)×2π = 7/4π radians
Then the sector area is ...
A = 1/2(18 mi)²(7π/4) = 567π/2 mi²