Single Variable Essential Calculus: Early Transcendentals
2nd Edition
ISBN: 9781133112785
Author: James Stewart
Publisher: Cengage Learning
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Chapter B, Problem 6E
Write the sum in expanded form.
6.
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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 B Solutions
Single Variable Essential Calculus: Early Transcendentals
Ch. B - Prob. 1ECh. B - Write the sum in expanded form. 2. i=161i+1Ch. B - Write the sum in expanded form. 3. i=463iCh. B - Write the sum in expanded form. 4. i=46i3Ch. B - Write the sum in expanded form. 5. k=042k12k+1Ch. B - Write the sum in expanded form. 6. k=58xkCh. B - Write the sum in expanded form. 7. i=1ni10Ch. B - Write the sum in expanded form. 8. j=nn+3j2Ch. B - Write the sum in expanded form. 9. j=0n1(1)jCh. B - Write the sum in expanded form. 10. i=1nf(xi)xi
Ch. B - Write the sum in sigma notation. 11. 1 + 2 + 3 + 4...Ch. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Write the sum in sigma notation. 20. 1 x + x2 x3...Ch. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Find the value of the sum. 30. i=1n(25i)Ch. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Find the value of the sum. 35. i=1n(i3i2)Ch. B - Find the number n such that i=1ni=78.Ch. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prove the generalized triangle inequality:...Ch. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50E
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