I posted this question earlier but I think I asked for too much so I am trying again and giving the answer I have, If you could tell me if it is correct, I would appreciate it.

A sub is 7500 meters below sea level surfaces at rate of 80 meters per min. the depth of sub after m minutes is given by d(m) = -7500 +80m. give range and calculate domain.
80m = -7500
M = 90.3 domain
d = 80(0) -7500 = -7500 range
thanks for your help

The range is d = -7500 to 0 meters, since it cannot go higher than sea level, and cannot be lower than it started out, while rising.

The domain is m = 0 to 93.75 minutes.

d = 7500 - 80 t

domain = 0 to 7500/80 or 0 to 93.75

range = -7500 to 0

thank you drwls and damon, i really appreciate you help. ann

The equation you provided, d(m) = -7500 + 80m, is correct and represents the depth of the submarine after m minutes.

To find the domain of this function, you need to consider the possible values for the independent variable m. In this case, since m represents the time in minutes, it cannot be negative (as time cannot be negative in real-world scenarios). Therefore, the domain is all non-negative real numbers: m ≥ 0.

To calculate the range of the function, which represents the possible values for the depths of the submarine, you can substitute different values of m into the equation.

For the initial depth, when m = 0, we have:
d(0) = -7500 + 80(0) = -7500

So the submarine is initially at a depth of -7500 meters below sea level.

For the rate of descent, every minute the submarine surfaces 80 meters, so the depth increases by 80 meters per minute.

Now let's consider a specific time, for example, after 10 minutes:
d(10) = -7500 + 80(10) = -7500 + 800 = -6700

After 10 minutes, the submarine is at a depth of -6700 meters below sea level.

Based on these calculations, we can see that the range of the function is all real numbers less than or equal to -7500. Or in other words, the range is d ≤ -7500.

So, the answer you provided for the range (-7500) is correct.

Additionally, you correctly calculated the value of m that satisfies the equation 80m = -7500 as m = 90.3.

In summary:
- The domain is m ≥ 0 (all non-negative real numbers).
- The range is d ≤ -7500 (all real numbers less than or equal to -7500).
- The value of m that satisfies 80m = -7500 is m = 90.3.