Problema Solution
Direct Variations
Ata 33 foot depth underwater, the pressure is 29.55 pounds per square inch (psi. At a depth of 66 feet, the pressure reaches 44.4 psi. At what rate is the pressure increasing? (AND, please show me HOW you arrived at the calculation)~ Thanks, Cornelio.
Answer provided by our tutors
the water pressure fromula is
P = (density of liquid)*(gravity at the surface)*(h is height of liquid column)
since the pressure is given in psi we need to convert the ft to inches
1 foot = 12 in
h1 = 33 ft = 33*12 in
P1 = 29.55 psi
h2 = 66 ft = 66*12 in
P2 = 44.4 psi
When two variable quantities have a constant (unchanged) ratio, their relationship is called a direct variation.
P varies directly with h thus we have
P =k*h, where k is a constant or the rate of the variation
in our case we should have
P1/h1 = P2/h2 = k
but since
P1/h1 = 29.55/(33*12) = 0.0746
P2/h2 = 44.4/(66*12) = 0.0506
P1/h1 does not equal P2/h2 so there must be something wrong with the numbers in this problem. Check the numbers and submit the problem again.