Final answer:
The shark initially at 24.6 meters below sea level, after a series of rises and dives, is subsequently at a depth of 9.8 meters below sea level.
Step-by-step explanation:
When calculating the final depth of the shark after multiple movements, we can treat rises in depth as negative values and dives as positive values since a dive increases the shark's depth below sea level.
To determine the depth the shark is at now, we need to add up the distances it has moved up and down from its original depth.
The shark initially swims at a depth of 24.6 meters below sea level. It then rises 7 1/3 meters, ascends another 14.3 meters, and then dives back down 6 5/6 meters.
Therefore, the depth the shark is at now can be calculated as follows: 24.6 + (7 1/3) + 14.3 - (6 5/6).
This can be simplified as: 24.6 + 22/3 + 14.3 - 41/6.
Converting the mixed fractions to improper fractions and finding a common denominator, we get: 24.6 + 22/3 + 14.3 - 41/6 = 24.6 + 66/6 + 14.3 - 41/6 = 24.6 + 66/6 + 14.3 - 41/6 = 24.6 + 25/6 + 14.3 - 41/6 = 24.6 + (25 + 14.3 - 41)/6 = 24.6 + (-1.7)/6 = 24.6 - 0.2833 = 24.3167 meters below sea level.Starting at 24.6 meters below sea level, the shark rises by 7 1/3 meters (which can be written as 7.333 meters for convenience) and then ascends another 14.3 meters, followed by a dive of 6 5/6 meters (or 6.833 meters). The total change in depth can be calculated as a sum of these movements:
Starting depth: 24.6 meters
Rise: -7.333 meters
Ascend: -14.3 meters
Dive: +6.833 meters
Adding these values together:
24.6 - 7.333 - 14.3 + 6.833 = 9.8 meters below sea level
Therefore, after all the movements, the shark is at a depth of 9.8 meters below sea level.