The equation P = 1 + d/33 gives the pressure, P, in atmospheres (atm) at a depth of d feet below sea level. For what depths d is the pressure at least 1 atm and at most 2 atm?
1 Answer
Explanation:
For starters, you can find the value of
As you know, the atmosphere is a unit of pressure defined as the pressure exerted by the Earth's atmosphere at sea level.
Since at sea level basically means a depth of
d = "0 feet"
Now, you know that you must have
P_1 = 1 + d_1/33 >= "1 atm" The depth
d_1 corresponds to a pressure of at least"1 atm"
and also
P_2 = 1 + d_2/33 <= "2 atm" The depth
d_2 corresponds to a pressure of at most"2 atm"
From the first inequality, you get that
1 + d_1/33 = 1
d_1/33 = 0 implies d_1 = "0 feet" -> matches what we got by using the definition of an atmosphere!
For the second inequality, you get that
1 + d_2/33 <= 2
d_2/33 <= 1 implies d_2 <= "33 feet"
Therefore, you can say that the pressure is at least
Notice that you can also set up this as a compound inequality
1 <= 1 + d/33 <= 2
Solve this to get
0 <= d/33 <= 1
o<= d <= 33
Once again, you get