A submarine descends from sea level to the entrance of an underwater cave. The elevation of the entrance is -120 feet. The rate of change in the submarine's elevation is no greater than -12 feet per second. Can the submarine reach the entrance to the cave in less than 10 seconds? Explain the inequality
THANK YOU!!
10 * -12 = -120
I did see this answer, but how is this written as an inequality type of expression?
Thank you!
To determine if the submarine can reach the entrance of the underwater cave in less than 10 seconds, we need to consider the rate of change in elevation.
Let's assume the initial elevation of the submarine at sea level is 0 feet. The elevation of the entrance of the cave is -120 feet, indicating that the submarine needs to descend by 120 feet.
We are given that the rate of change in the submarine's elevation is no greater than -12 feet per second. This means that the submarine is descending at a maximum rate of 12 feet per second.
Let's set up an inequality to represent this situation:
-12t ≤ -120
Here, t represents the time (in seconds) it takes for the submarine to reach the entrance.
To solve this inequality, we divide both sides by -12 (keeping in mind that dividing by a negative number reverses the inequality):
t ≥ -120 / -12
Simplifying the inequality, we have:
t ≥ 10
This means that the submarine needs at least 10 seconds to descend to the entrance of the cave. Since we're asked if the submarine can reach the entrance in less than 10 seconds, the answer is no, it cannot.
Therefore, the submarine cannot reach the entrance to the cave in less than 10 seconds.
To determine if the submarine can reach the entrance of the underwater cave in less than 10 seconds, we need to examine the relationship between the depth of the entrance, the rate of change in elevation, and the time it takes for the submarine to descend.
Let's assume that the time it takes for the submarine to reach the entrance of the cave is denoted by t (in seconds).
The elevation of the entrance is -120 feet, which means it is 120 feet below sea level. Since the submarine is descending, the change in elevation can be represented by a negative value.
The rate of change in elevation, or the speed at which the submarine descends, is given as no greater than -12 feet per second. Again, the negative sign indicates descent.
Let's break down the given information:
- Elevation of the entrance: -120 feet
- Rate of change of elevation: no greater than -12 feet per second
- Time it takes to reach the entrance: t seconds
The inequality that represents the situation can be written as:
Rate of change of elevation * Time ≤ Change in elevation
-12 * t ≤ -120
To check if the submarine can reach the entrance in less than 10 seconds, we substitute t = 10 into the inequality:
-12 * 10 ≤ -120
-120 ≤ -120
In this case, the inequality holds true, indicating that the submarine can reach the entrance in less than 10 seconds.
Therefore, the submarine can indeed reach the entrance of the underwater cave in less than 10 seconds based on the given conditions.