Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Chapter P, Problem 17PSDT
Perform the operation and simplify:
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Question 1:
If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p =
13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the
column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts)
Solution:
A barometer works based on the principle that the pressure exerted by the liquid column
balances atmospheric pressure. The pressure is given by:
P = pgh
Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the
liquid column is inversely proportional to its density:
Step 1: Given Data
PHg
hol=hgx
Poil
• Density of mercury: PHg = 13.6 g/cm³
Density of oil: Poil = 0.92 g/cm³
• Standard height of mercury at 1.00 atm: hμg
Step 2: Compute Height of Oil
= 760 mm = 0.760 m
13.6
hoil
= 0.760 x
0.92
hoil
= 0.760 × 14.78
hoil
= 11.23 m
Step 3: Compare Heights
Since oil is less dense than mercury, the column of oil must be much taller than that of
mercury. The factor by which it is taller is:
Final…
Chapter P Solutions
Calculus For The Life Sciences
Ch. P - What percent of 50 is 10?Ch. P - Simplify 13725.Ch. P - Let x be the number of apples and y be the number...Ch. P - Let s be the number of students and p be the...Ch. P - Solve for k:7k+8=4(3k).Ch. P - Solve for x:58x+116x=1116+x.Ch. P - Write in interval notation: 2x5.Ch. P - Using the variable x, write the following interval...Ch. P - Solve for y:5(y2)+17y+8.Ch. P - Solve for p:23(5p3)34(2p+1).
Ch. P - Carry out the operations and simplify:...Ch. P - Multiply out and simplify (x22x+3)(x+1).Ch. P - Multiply out and simplify (a2b)2.Ch. P - Prob. 14PSDTCh. P - Prob. 15PSDTCh. P - Perform the operation and simplify:a26aa24a2a.Ch. P - Perform the operation and simplify:x+3x21+2x2+x.Ch. P - Solve for x:3x2+4x=1.Ch. P - Solve for z:8zz+32.Ch. P - Simplify 41(x2y3)2x2y5.Ch. P - Prob. 21PSDTCh. P - Simplify as a single term without negative...Ch. P - Factor (x2+1)1/2(x+2)+3(x2+1)1/2.Ch. P - Simplify 64b63.Ch. P - Rationalize the denominator: 2410.Ch. P - Simplify y210y+25.
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