When 4/5 is written as a decimal, how many digits are in the smallest sequence of repeating digits?
1 answer:
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One complete revolution of the minute hand sweeps a central angle of 360° which is equivalent to 60 minutes.
That is, the minute hand creates
(360°/(60 min) = 6 degrees/min.
From 3:35 to 3:55 is 20 minutes.
It sweeps a central angle of
(20 min)*(6 deg/min) = 120°
Because 360° = 2π radians,
120° = (120/360)*2π = (2π)/3 radians
Answer:
In decimals, this is 2.1 radians (nearest tenth)
Part 2:
Because the minute hand is 4 inches long, the length of the arc swept is
(4 in)*(2π/3 radians) = 8π/3 inches
Answer:
In decimals, this is 8.4 inches (nearest tenth).
That is, the minute hand creates
(360°/(60 min) = 6 degrees/min.
From 3:35 to 3:55 is 20 minutes.
It sweeps a central angle of
(20 min)*(6 deg/min) = 120°
Because 360° = 2π radians,
120° = (120/360)*2π = (2π)/3 radians
Answer:
In decimals, this is 2.1 radians (nearest tenth)
Part 2:
Because the minute hand is 4 inches long, the length of the arc swept is
(4 in)*(2π/3 radians) = 8π/3 inches
Answer:
In decimals, this is 8.4 inches (nearest tenth).