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Draw a diagram to illustrate the problem as shown below.
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations
For this case, we perform the conversions:
First roll:
We make a rule of three to determine the number of "c" boxes that can be packed with 300 meters of adhesive tape.
1 -----------> 4.2
c -----------> 300
You can pack 71 boxes.
Second roll:
We make a rule of three to determine the number of "c" boxes that can be packed with 70 meters of adhesive tape.
1 -----------> 4.2
c -----------> 70
You can pack 16 boxes.
Third roll:
1 -----------> 4.2
c -----------> 50
You can pack 11 boxes.
Thus, in total you can pack
Answer:
98 boxes