Answers:
- depth after 1 stage is -280 meters
- depth after 2 stages is -220 meters
- depth after 4 stages is -100 meters
- how many stages to return to the surface? 6 stages
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Step-by-step explanation:
After 1 stage, the depth is -340+60*1 = -280 meters. In other words, it's 280 meters below the surface.
After 2 stages, the depth is now -340+60*2 = -220 meters
After 4 stages, the depth is -340+60*4 = -100 meters
After n stages, the depth is -340+60n. Set this equal to zero and solve for n.
-340+60n = 0
60n = 340
n = 340/60
n = 5.667 approximately
This rounds to n = 6
After n = 5 stages, the depth is -340+60n = -340+60*5 = -40 meters
After n = 6 stages, the depth is -340+60n = -340+60*6 = 20 meters, so the submarine is now at the surface. Of course the sub cannot fly to a height of 20 meters above the ocean's surface, so the highest it can go is 0 meters at the surface itself. This means the 6th stage is a movement of 40 meters (instead of 60 meters).
It might help to draw out a vertical number line to visually keep track of everything.