3. (3 points (bonus)) in seawater, the pressu...
3. (3 points (bonus)) in seawater, the pressure p is related to depth d according to 33p - 18d = 495, where d is in feet and p is in pounds per square inch. (a) (2 point) solve this equation for p in terms of d. 33p - 18d = 495 15 -15 = 30 (b) (1 points) the titanic was discovered at a depth of 12,460 ft. find the pressure at this depth. 12,460 - 30 = 12,430
Answer
# Explanation:
## Step1: Isolate the term with p
Add 18d to both sides of the equation $33p - 18d=495$.
$33p=495 + 18d$
## Step2: Solve for p
Divide both sides of the equation by 33.
$p=\frac{495 + 18d}{33}=\frac{495}{33}+\frac{18d}{33}=15+\frac{6d}{11}$
## Step3: Find the pressure at a given depth
Substitute $d = 12460$ into the equation for p.
$p=15+\frac{6\times12460}{11}=15+\frac{74760}{11}=15 + 6796.36\approx6811.36$
# Answer:
(a) $p = 15+\frac{6d}{11}$
(b) Approximately 6811.36 pounds per square inch