The equation #P = 1 + d/33# gives the pressure, #P#, in atmospheres (atm) at a depth of #d# feet in the sea. For what depths #d# is the pressure at least 1 atm and at most 7 atm?

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Answer 1 · 2017-01-07T14:21:20

#"1 atm" ≤ P ≤ "7 atm"# when #0 ≤ d ≤ "200 ft"#.

The formula is

#color(blue)(bar(ul(|color(white)(a/a) P = 1 + d/33color(white)(a/a)|)))" "#

We can do some rearranging to get:

#33P = 33 + d#

#d = 33P - 33#

#color(blue)(bar(ul(|color(white)(a/a) d = 33(P - 1)color(white)(a/a)|)))" "#

When #P = "1 atm"#,

#d = 33(1 - 1) = 33×0 = 0#

When #P = "7 atm"#,

#d = 33(7 - 1) = 33×6 = "200 ft"# (2 significant figures)

∴ The pressure is at least 1 atm and at most 7 atm when the depth ranges from 0 ft to 200 ft.