Hey Mom go is climbing to the top of a large cliff. The clip is 50 ft higher than it's starting point. If it takes to go 22 minutes to climb this clip interpret that quoting to describe the rate of change and the coach elevation. Give your answer to the nearest hundredth
The rate of change in this scenario can be interpreted as the climb rate, which is the change in elevation divided by the change in time. In this case, the change in elevation is 50 ft and the change in time is 22 minutes (or 22/60 = 0.37 hours).
So, the climb rate is 50 ft / 0.37 hours ≈ 135.14 ft/hour.
Therefore, the rate of change is approximately 135.14 ft/hour and the coach elevation is increasing at that rate.
To find the rate of change, we need to determine the change in elevation and the time it took to climb the cliff.
Given:
Change in elevation (Δy) = 50 ft (since the cliff is 50 ft higher than the starting point)
Time taken (Δt) = 22 minutes
The rate of change, also known as the average rate of change, is calculated by dividing the change in elevation by the time taken:
Rate of change = Δy / Δt
Plugging in the values, we get:
Rate of change = 50 ft / 22 min
Calculating this, we find:
Rate of change ≈ 2.27 ft/min
Therefore, the rate of change while climbing the cliff is approximately 2.27 feet per minute.
To interpret the result, we can say that on average, the climber is ascending the cliff at a rate of 2.27 feet per minute.
As for the final elevation, since the cliff is 50 ft higher than the starting point, the final elevation can be expressed as:
Final elevation = Starting point + Change in elevation
= Starting point + 50 ft
However, the initial elevation is not given in the question, so we cannot determine the final elevation without that information.
To calculate the rate of change, you'll need to determine the amount of elevation gained per minute.
First, let's define the variables:
- Starting elevation: S
- Cliff elevation: C (which is 50 ft higher than the starting point)
- Time taken to climb: T (22 minutes in this case)
The rate of change is given by dividing the change in elevation by the time taken. In this case, the change in elevation is the height of the cliff, which is C - S.
So, the rate of change is (C - S) / T.
To find the coach elevation, we need to determine the starting elevation (S). Unfortunately, the problem doesn't provide any information about the starting elevation. If you have that information, you can substitute it into the equation. However, if you don't have the starting elevation, we cannot determine the coach elevation accurately.
Therefore, it is not possible to provide an answer to the nearest hundredth without knowing the starting elevation (S).