A scuba diver dove from the surface of the ocean to an elevation of −59

9/10
feet at a rate of −15 feet per minute. After spending 12 minutes at that elevation, the diver ascended to an elevation of −38
9/10
feet. The total time for the dive so far was 19
1/8 minutes. What was the rate of change in the diver's elevation during the ascent? Round your answer to the nearest hundredth.

rate of change = distance.time

time descending is 59.9/15 = 4 min
The diver rose 21 ft, so
21ft/(19 1/8 - 4 - 12) = 6.72 ft/min

To find the rate of change in the diver's elevation during the ascent, we first need to find the total change in elevation during the ascent.

Given:
Initial elevation: -59 9/10 feet
Final elevation: -38 9/10 feet

To find the change in elevation, we subtract the initial elevation from the final elevation:

Change in elevation = Final elevation - Initial elevation
= (-38 9/10) - (-59 9/10)

To subtract the mixed numbers, we need to convert them to improper fractions:

Change in elevation = (-388/10) - (-599/10)
= (-388 + 599)/10
= 211/10
= 21.1 feet

Now, we need to find the time taken for the ascent. We are given that the total dive time so far was 19 1/8 minutes, and the diver spent 12 minutes at the elevation of -59 9/10 feet.

Time for ascent = Total dive time - Time spent at -59 9/10 feet
= (19 1/8) - 12

To subtract mixed numbers, we need to convert them to improper fractions:

Time for ascent = (154/8) - (96/8)
= (154 - 96)/8
= 58/8
= 7.25 minutes

Finally, to find the rate of change in the diver's elevation during the ascent, we divide the change in elevation by the time taken:

Rate of change = Change in elevation / Time for ascent
= 21.1 feet / 7.25 minutes
≈ 2.91 feet per minute

Therefore, the rate of change in the diver's elevation during the ascent is approximately 2.91 feet per minute.

To find the rate of change in the diver's elevation during the ascent, we need to calculate the change in elevation divided by the time taken for the ascent.

Step 1: Calculate the change in elevation:
Change in elevation = Final elevation - Initial elevation
Change in elevation = (-38 9/10) - (-59 9/10)

To perform the subtraction, we need to convert the mixed numbers to improper fractions:
-38 9/10 = -38 + 9/10 = -380/10 + 9/10 = -389/10
-59 9/10 = -59 + 9/10 = -590/10 + 9/10 = -599/10

Change in elevation = (-389/10) - (-599/10)

To subtract fractions, we need a common denominator, which in this case is 10.
Change in elevation = (-389 - (-599))/10
Change in elevation = (-389 + 599)/10
Change in elevation = 210/10
Change in elevation = 21

Step 2: Calculate the time taken for the ascent:
Time taken for the ascent = Total time - Time spent at the initial elevation
Time spent at the initial elevation = 12 minutes
Total time = 19 1/8 minutes = 19 + 1/8 = 19 + 1/8 = 152/8 + 1/8 = 153/8

Time taken for the ascent = (153/8) - 12

To subtract fractions, we need a common denominator, which in this case is 8.
Time taken for the ascent = (153 - 96)/8
Time taken for the ascent = 57/8

Step 3: Calculate the rate of change in elevation during the ascent:
Rate of change = Change in elevation / Time taken for the ascent
Rate of change = 21 / (57/8)
Rate of change = 21 * (8/57)
Rate of change = 336/57
Rate of change ≈ 5.89 feet per minute (rounded to the nearest hundredth)

Therefore, the rate of change in the diver's elevation during the ascent is approximately 5.89 feet per minute.