For the problem below, the simple way to get answer would be 10*-12=-120. But how to write it as an Inequality Expression?
---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?
**Write inequality to prove yes or no
THANK YOU!!
To determine whether the submarine can reach the entrance to the cave in less than 10 seconds, we need to write an inequality expression that represents this situation.
Let's define the time it takes for the submarine to descend as "t" (in seconds). Since the submarine is descending, the change in elevation can be expressed as a negative value (-12t). We want to compare this value with the elevation of the cave entrance (-120 feet).
The statement "The rate of change in the submarine's elevation is no greater than -12 feet per second" can be represented as: -12t ≤ -120.
To answer the question, we substitute t = 10 seconds into the inequality and check if it's true or false.
Let's solve the inequality:
-12t ≤ -120
Replace t with 10:
-12(10) ≤ -120
-120 ≤ -120
The inequality is true when -120 is less than or equal to -120. Therefore, the submarine can reach the entrance to the cave in 10 seconds or less.