Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137400096
Author: Larry Goldstein, David Lay
Publisher: PEARSON+
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Chapter 7.4, Problem 6E
To determine
The values of
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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 7 Solutions
Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)
Ch. 7.1 - Let f(x,y,z)=x2+y(xz)4. Compute f(3,5,2).Ch. 7.1 - Prob. 2CYUCh. 7.1 - Let f(x,y)=x23xyy2. Compute f(5,0),f(5,2) and...Ch. 7.1 - Prob. 2ECh. 7.1 - Let g(x,y,z)=x/(yz). Compute g(1,1),g(0,1) and...Ch. 7.1 - Let f(x,y,z)=x2ey2+z2. Compute f(1,1,1) and...Ch. 7.1 - Let f(x,y)=xy. Show that f(2+h,3)f(2,3)=3h.Ch. 7.1 - Let f(x,y)=xy. Show that f(2,3+k)f(2,3)=2k.Ch. 7.1 - Cost Find a formula C(x,y,z) that gives the cost...Ch. 7.1 - Cost Find a formula C(x,y,z) that gives the cost...
Ch. 7.1 - Consider the cobb-Douglas production function...Ch. 7.1 - Let f(x,y)=10x25y35. Show that f(3a,3b)=3f(a,b).Ch. 7.1 - Present value The present value of A dollars to be...Ch. 7.1 - Refer to Example 3. If labor costs $100 per unit...Ch. 7.1 - Tax and Homeowner Exemption The value of...Ch. 7.1 - Tax and Homeowner Exemption Let f(r,v,x) be the...Ch. 7.1 - Draw the level curve of height 0,1 and 2 for the...Ch. 7.1 - Draw the level curve of height 0,1 and 2 for the...Ch. 7.1 - Draw the level curve of function f(x,y)=xy...Ch. 7.1 - Draw the level curve of function f(x,y)=xy...Ch. 7.1 - Find the function f(x,y) that has line y=3x4 as a...Ch. 7.1 - Find the function f(x,y) that has the curve y=2x2...Ch. 7.1 - Suppose that a topographic map is viewed as the...Ch. 7.1 - Isocost Lines A certain production process uses...Ch. 7.1 - Match the graphs of the functions in Exercises...Ch. 7.1 - Match the graphs of the functions in Exercises...Ch. 7.1 - Match the graphs of the functions in Exercises...Ch. 7.1 - Match the graphs of the functions in Exercises...Ch. 7.2 - The number of TV sets an appliance store sells per...Ch. 7.2 - The monthly mortgage payment for a house is a...Ch. 7.2 - Find fxandfy for each of the following functions....Ch. 7.2 - Prob. 2ECh. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Prob. 6ECh. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Find fxandfy for each of the following function....Ch. 7.2 - Prob. 13ECh. 7.2 - Let f(p,q)=1p(1+q). Find fq and fp.Ch. 7.2 - Let f(x,y,z)=(1+x2y)/z. fx,fy,andfz.Ch. 7.2 - Prob. 16ECh. 7.2 - Let f(x,y,z)=xzeyz. Find fx,fy,andfz.Ch. 7.2 - Let f(x,y,z)=xyz. Find fx,fz,andfz.Ch. 7.2 - Let f(x,y,z)=x2+2xy+y2+3x+5y. Find...Ch. 7.2 - Prob. 20ECh. 7.2 - Let f(x,y)=xy2+5. Evaluate fy at (x,y)=(2,1) and...Ch. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - ProductivityLabor and Capital The productivity of...Ch. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Let p1 be the average price of MP3 players, p2 the...Ch. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Compute 2fy2, where f(x,y)=60x3/4y1/4, a...Ch. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.3 - Prob. 1CYUCh. 7.3 - Prob. 2CYUCh. 7.3 - Prob. 1ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 17ECh. 7.3 - The function f(x,y)=12x2+2xy+9+3y2x+2y has a...Ch. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 27ECh. 7.3 - Find all points (x,y) where f(x,y) has a possible...Ch. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Find all points f(x,y) has a possible relative...Ch. 7.3 - Prob. 36ECh. 7.3 - Find all points f(x,y) has a possible relative...Ch. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Find all points f(x,y) has a possible relative...Ch. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Find all points f(x,y) has a possible relative...Ch. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Minimizing Surface Area Find the dimensions of the...Ch. 7.3 - Maximizing Profit A company manufactures and sells...Ch. 7.3 - Maximizing Profit A monopolist manufactures and...Ch. 7.3 - Prob. 53ECh. 7.3 - Revenue from Two Products A company manufactures...Ch. 7.4 - Prob. 1CYUCh. 7.4 - Refer to Exercise 29 of Section 7.3. What is the...Ch. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Solve the following exercises by the method of...Ch. 7.4 - Prob. 19ECh. 7.4 - Solve the following exercises by the method of...Ch. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Solve the following exercises by the method of...Ch. 7.4 - Solve the following exercises by the method of...Ch. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Use Lagrange multipliers to find the three...Ch. 7.4 - Minimizing Surface Area Find the dimensions of an...Ch. 7.4 - Maximizing Volume A shelter for use at the beach...Ch. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.5 - Prob. 1CYUCh. 7.5 - Prob. 2CYUCh. 7.5 - Prob. 1ECh. 7.5 - Find the least-squares error E for the...Ch. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - In the remaining exercises, use one or more of the...Ch. 7.5 - In the remaining exercises, use one or more of the...Ch. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.6 - Calculate the iterated integral 02(0x/2e2yxdy)dx.Ch. 7.6 - Prob. 2CYUCh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Calculate the following iterated integrals....Ch. 7.6 - Prob. 5ECh. 7.6 - Calculate the following iterated integrals....Ch. 7.6 - Calculate the following iterated integrals....Ch. 7.6 - Calculate the following iterated integrals....Ch. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Calculate the volumes over the following regions R...Ch. 7 - Give an example of a level curve of a function of...Ch. 7 - Prob. 2CCECh. 7 - Prob. 3CCECh. 7 - Prob. 4CCECh. 7 - Prob. 5CCECh. 7 - Prob. 6CCECh. 7 - Prob. 7CCECh. 7 - State the second derivative test for functions of...Ch. 7 - Prob. 9CCECh. 7 - Prob. 10CCECh. 7 - Prob. 11CCECh. 7 - Give a formula for evaluating a double integral in...Ch. 7 - Let f(x,y)=xy/(1+x). Compute f(2,9),f(5,1), and...Ch. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - In Exercises 1720, find all points (x,y) where...Ch. 7 - Prob. 19RECh. 7 - In Exercises 1720, find all points (x,y) where...Ch. 7 - In Exercises 2123, find all points (x,y) where...Ch. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Find the values of x,y,z at which...Ch. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Use the method of Lagrange multiplier to: A person...Ch. 7 - Use the method of Lagrange multiplier to: The...Ch. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RE
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