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The short hand and long hand clock are 4cmand6cm long respectively find the distance traveled by their tips in two days?
Every day, the hour hand makes 2 complete revolutions and the minute hand makes 24 revolutions (one per hour). So we have 4 complete revolutions on the hour hand and 48 on the minute hand.
First, let us find out the distance per revolution these make. If you noticed on a clock, these would be considered radii, the minute hand makes:
C = 2πr
==> C = 2π(4)
==> C = 8π
==> C ≈ 25.133 cm/revolution
and the hour hand makes:
C = 2πr
==> C = 2π(6)
==> C = 12π
==> C ≈ 37.699 cm/revolution
So the sums are:
48(8π cm) + 4(12π cm)
= 384π cm + 48π cm
= 432π cm
≈ 1,357.168 cm
Therefore, the sum of the distances traveled is about 1,357 cm.
What else can I help you with?
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