A scuba diver dove from the surface of the ocean to an elevation of −59
9
10
feet at a rate of −12 feet per minute. After spending 14.5 minutes at that elevation, the diver ascended to an elevation of −8
9
10
feet. The total time for the dive so far was 21
1
8
minutes. What was the rate of change in the diver's elevation during the ascent? Round your answer to the nearest hundredth.
I can't read the elevations.
rate=(finalelevation-initialelevation)/time
To find the rate of change in the diver's elevation during the ascent, we need to calculate the change in elevation and divide it by the time taken. Here's how we can do that:
1. Start by finding the change in elevation during the ascent. The diver started at an elevation of -8
9
10
feet and ended at an elevation of -59
9
10
feet. To find the change, subtract the initial elevation from the final elevation: (-59
9
10
) - (-8
9
10
).
(-59
9
10
) - (-8
9
10
) = -59
9
10
+ 8
9
10
= -59
9
10
+ 8
9
10
= -51
The change in elevation during the ascent is -51 feet.
2. Next, we need to compute the time taken for the ascent. The total time for the dive so far is given as 21
1
8
minutes, and the diver spent 14.5 minutes at an elevation of -59
9
10
feet.
Time taken for the ascent = Total time - Time spent at -59
9
10
feet
= 21
1
8
minutes - 14.5 minutes
= 6
5
8
minutes
The time taken for the ascent is 6
5
8
minutes.
3. Finally, we can find the rate of change in the diver's elevation during the ascent by dividing the change in elevation by the time taken:
Rate of change = Change in elevation / Time taken
= -51 feet / 6
5
8
minutes
Calculate the rate of change using a calculator or by performing the division. Round your answer to the nearest hundredth.
Rate of change ≈ -1.06 feet per minute
Therefore, the rate of change in the diver's elevation during the ascent is approximately -1.06 feet per minute.