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

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Answer 1 · 2017-01-07T14:21:20

$1 atm \leq P \leq 7 atm$ $"1 atm" ≤ P ≤ "7 atm"$ when $0 \leq d \leq 200 ft$ $0 ≤ d ≤ "200 ft"$ .

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.

The equation P = 1 + d/33P=1+d33P = 1 + d/33 gives the pressure, PPP, in atmospheres (atm) at a depth of ddd feet in the sea. For what depths ddd is the pressure at least 1 atm and at most 7 atm?