3. In the fairy tale Cinderella, Cinderella was told by the fairy to leave the royal ball before the first stroke of midnight, otherwise she would return to her original ragged look. Suppose the fairy loosened her restriction and only required Cinderella to leave the ball before the time when the hours hand and minutes hand first form a straight line after midnight. Before which time should Cinderella leave the ball?
Please provide your answer with detailed explanation.
Thank you!
Maths problem (F.3 Inequality)
2009-11-27 5:28 am
回答 (1)
2009-11-27 5:55 am
✔ 最佳答案
x^o means x degreesa \< b means a is smaller or equal to b
b>/ a means b is larger or equal to a
. : means therefore
*.* means because
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In a minute, the angle that minute-hand rotate about
=360^o/60
=6^o
In a minute, the angle that hour-hand rotate about
=360^o/(12*60)
=0.5^o
Let x min after midnight be the time Cinderella should leave the ball.
6^o x \< 0.5^o x +180^o
11x \< 360
x \< 360 /11
.: Cinderella should leave the ball 360/11 min after midnight.
Explanation:
6^o x : the angle marked by the min-arms at midnight and at the time Cinderela should leave the ball. (for simplicity: min-arm-angle)
0.5^o x : the angle marked by the hr-arms at midnight and at the time Cinderela should leave the ball. (for simplicity: hr-arm-angle)
When the hr-arm and the min-arm form a st line, the hr-arm-angle +180^o = min-arm-angle
.: before the hr-arm and the min-arm form a st line, the hr-arm-angle +180^o >/ min-arm-angle.
(*.* the min-arm has not reached the st line extended from the hr-arm)
(eg 00:30
the hr-arm and the min-arm DOES NOT (not yet) form a st line
hr-arm-angle=15^o
min-arm-angle=180^o
hr-arm-angle+180^o >/ min-arm-angle)
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