Question

Create a table showing how long the air will last at 0 ft, 33 ft, 66 ft, and 99 ft. Construct your table to include three columns. The first column should be the depth in feet, the second the pressure in atm, the third the time in minutes

Answer 1

this goes with it as well The rate at which a scuba diver uses air in the tank depends on many factors, such as the diver's age and lung capacity. Another important factor is the depth of the dive. A scuba diver continues to breathe normally while descending. Every time the diver inhales, the tank delivers enough air to inflate the diver's lungs. This means that the amount of air delivered by the tank must increase with the depth in order to withstand the increasing pressure. At greater depths, the diver uses the air in the tank more quickly. The amount of time the air will last is inversely proportional to the pressure at the depth of the dive.
9) The amount of time (t) the air will last is inversely proportional to the pressure (P) at its depth.

a) Write an inverse variation that models the relationship between t and P.
t = k/p
b) Suppose a tank has enough air to last 60 minutes at the surface. The pressure is 1 atm at the surface. Solve for k.
when t = 60 and p = 1
60 = k/1
60 x 1= 60
k = 60
c) The pressure is 4 atm at a depth of 99 ft. How long will it last at a pressure of 4 atm?

when p = 4
t = k/p
t = 60 mins atm / 4 atm
t = 15 mins

Answer 2

@zepdrix

Answer 3

@TheSmartOne

Answer 4

@sshayer

Answer 5

also this
2) Write an equation that represents Boyle’s law (the volume of air varies inversely with the pressure). Use k for the variation constant.

y=k/x
v=k/p
4=k/3

3) Solve for k utilizing the fact that you have 4 quarts of air in your lungs when the pressure is 3 atm and 6 quarts of air in your lungs when the pressure is 2 atm. Rewrite your inverse variation equation from Question #2 using your new value for k.
4=k/3
k=4(3)
k=12
v=12/3
V=12/P


4) Using your equation from Question #3, construct a table relating the volume of air in your lungs to the pressure. The values for the pressures are 1 atm, 2 atm, and 3 atm.
P | V
1 | 12
2 | 6
3 | 4


5) Write an equation relating volume to depth. (Hint: Replace P in your equation from Question #3 with an expression in terms of d. You do not need to simplify your equation.)
P =( d/33 ) + 1 (relationship between depth and pressure
V = 12/P
 = 12/((d/33) + 1)
 = 12/((d + 33)/33)
 = 396/(d + 33)


6) Using your new equation, make a table to show how the volume of air in your lungs varies with the depth. Set up your table as you would an x/y chart. Let d, the depth, be the independent variable and V, the volume, be the dependent variable. Use these values for d: 99, 66, 33, and 0 (you would be at the water’s surface when d = 0).



D | V
99| 3
66| 4
33| 6
0 | 12

Answer 6

Just use the inverse variation equation you came up with (t = k/p). You already know how long the tank will last at 0 ft and 99 ft and what pressure they undergo. From there, look at your incomplete table and see what patterns you can find so you can complete the table.

Answer 7

this is what i got @Oops

Answer 8

is it right?

Answer 9

@Oops

Answer 10

@18jonea check your third column