CALCULUS+ITS APPLICATIONS
CALCULUS+ITS APPLICATIONS
12th Edition
ISBN: 9780135164884
Author: BITTINGER
Publisher: PEARSON
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 6.1, Problem 23E

Baseball: total bases. A batter’s total bases is a statistic given by

B s , d , t , h = s + 2 d + 3 t + 4 h ,

where s is the number of singles, d the number of doubles, t the number of triples, and h the number of home runs hit by the batter. During the 2017 season, Arizona’s Paul Goldschmidt hit 93 singles, 34 doubles, 3 triples, and 36 home runs. (Source: retrosheet.org.)

a) Find B(93, 34, 3, 36).

b) Interpret the meaning of this number.

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Chapter 6 Solutions

CALCULUS+ITS APPLICATIONS

Ch. 6.1 - 2. . Ch. 6.1 - Forf(x,y)=x23xy,find(0,2),f(2,3),andf(10,5).Ch. 6.1 - Prob. 3ECh. 6.1 - 3. . Ch. 6.1 - 6. . Ch. 6.1 - Forf(x,y)=Inx+y3,findf(e,2),f(e2,4),andf(e3,5).Ch. 6.1 - 8. . Ch. 6.1 - Forf(x,y,z)=x2y2+z2,findf(1,2,3)andf(2,1,3).Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...
Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - Yield. The yield of a stock is given by YD,P=DP,...Ch. 6.1 - Prob. 14ECh. 6.1 - 17. Cost of storage equipment. Consider the cost...Ch. 6.1 - Savings and interest. A sum of $1000 is deposited...Ch. 6.1 - Monthly car payments. Ashley wants to buy a 2019...Ch. 6.1 - Monthly car payments. Kim is shopping for a car....Ch. 6.1 - 21. Poiseuille’s Law. The speed of blood in a...Ch. 6.1 - Body surface area. The Haycock formula for...Ch. 6.1 - 23. Body surface area. The Mosteller formula for...Ch. 6.1 - Prob. 22ECh. 6.1 - Baseball: total bases. A batters total bases is a...Ch. 6.1 - Soccer: point system. A point system is used to...Ch. 6.1 - 26. Dewpoint. The dewpoint is the temperature at...Ch. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Explain the difference between a function of two...Ch. 6.1 - 30. Find some examples of function of several...Ch. 6.1 - Wind Chill Temperature. Because wind speed...Ch. 6.1 - Wind Chill Temperature. Because wind speed...Ch. 6.1 - Prob. 33ECh. 6.1 - Wind Chill Temperature. Because wind speed...Ch. 6.1 - Use a graphics program such as Maple or...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Prob. 40ECh. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=2z3yCh. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=7x5yCh. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=2x3+3xyxCh. 6.2 - Prob. 4ECh. 6.2 - . 6. Ch. 6.2 - . 5. Ch. 6.2 - Find. 7. Ch. 6.2 - Find fx,fy,fz(2,1),andfy(3,2). f(x,y)=x2y2Ch. 6.2 - Prob. 9ECh. 6.2 - Find 9. Ch. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Find fxandfy f(x,y)=xy+y5xCh. 6.2 - Find 20. Ch. 6.2 - Prob. 20ECh. 6.2 - Find fbandfm f(b,m)=5m2mb23b+(2m+b8)2+(3m+b9)2Ch. 6.2 - Find fbandfm f(b,m)=m3+4m2bb2+(2m+b5)2+(3m+b6)2Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Find (The symbol is the Greek letter...Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Find the four second-order partial derivatives....Ch. 6.2 - Find the four second-order partial derivatives....Ch. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find fxy,fxy,fyx,andfyy. (Remember, fyx means to...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find fxy,fxy,fyx,andfyy. (Remember, fyx means to...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Prob. 37ECh. 6.2 - Let z=fx,y=xy. Use differentials to estimate...Ch. 6.2 - Let z=fx,y=2x+y2. Use differentials to estimate...Ch. 6.2 - Let z=fx,y=exy. Use differentials to estimate...Ch. 6.2 - The Cobb-Douglas model. Lincolnville Sporting...Ch. 6.2 - The Cobb-Douglas model. Riverside Appliances has...Ch. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Nursing facilities. A study of Texas nursing homes...Ch. 6.2 - Temperaturehumidity Heat Index. In summer, higher...Ch. 6.2 - Prob. 48ECh. 6.2 - Use the equation for Th given above for Exercises...Ch. 6.2 - Use the equation for Th given above for Exercises...Ch. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Reading Ease The following formula is used by...Ch. 6.2 - Reading Ease The following formula is used by...Ch. 6.2 - Prob. 55ECh. 6.2 - Reading Ease The following formula is used by...Ch. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Find fxandft. f(x,t)=(x2+t2x2t2)5Ch. 6.2 - In Exercises 63 and 64, find fxx,fxy,fyx,andfyy...Ch. 6.2 - In Exercises 63 and 64, find fxx,fxy,fyx,andfyy...Ch. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Do some research on the Cobb-Douglas production...Ch. 6.2 - Considerf(x,y)=In(x2+y2). Show that f is a...Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum or minimum value. 15....Ch. 6.3 - Find the relative maximum or minimum value. 16....Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - Explain the difference between a relative minimum...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.4 - In Exercises 1 – 4, find the regression line for...Ch. 6.4 - In Exercises 1 4, find the regression line for...Ch. 6.4 - In Exercises 1 – 4, find the regression line for...Ch. 6.4 - In Exercises 1 4, find the regression line for...Ch. 6.4 - Prob. 5ECh. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - Prob. 18ECh. 6.5 - Prob. 1ECh. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of subject to given constraint,...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of subject to given constraint,...Ch. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - 19. Maximizing typing area. A standard piece of...Ch. 6.5 - 20. Maximizing room area. A carpenter is building...Ch. 6.5 - 21. Minimizing surface area. An oil drum of...Ch. 6.5 - Juice-can problem. A large juice can has a volume...Ch. 6.5 - Maximizing total sales. Total sales, S, of...Ch. 6.5 - Maximizing total sales. Total sales, S, of Sea...Ch. 6.5 - 25. Minimizing construction costs. Denney...Ch. 6.5 - Minimizing the costs of container construction....Ch. 6.5 - Minimizing total cost. Each unit of a product can...Ch. 6.5 - 28. Minimizing distance and cost. A highway passes...Ch. 6.5 - 29. Minimizing distance and cost. From the center...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - Business: maximizing profits with constraints. A...Ch. 6.5 - Business: minimizing costs with constraints....Ch. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Prob. 46ECh. 6.5 - Economics: the Law of Equimarginal Productivity....Ch. 6.5 - 44. Business: maximizing production. A computer...Ch. 6.5 - 45. Discuss the difference between solving...Ch. 6.5 - Prob. 59ECh. 6.6 - Prob. 1ECh. 6.6 - Prob. 2ECh. 6.6 - In Exercises 1–16, evaluate the double integral....Ch. 6.6 - In Exercises 1–16, evaluate the double integral....Ch. 6.6 - In Exercises 1–16, evaluate the double integral....Ch. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Prob. 8ECh. 6.6 - Prob. 9ECh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - In Exercises 1–16, evaluate the double integral....Ch. 6.6 - In Exercises 1–16, evaluate the double integral....Ch. 6.6 - In Exercises 1–16, evaluate the double integral....Ch. 6.6 - Prob. 15ECh. 6.6 - Prob. 16ECh. 6.6 - Prob. 17ECh. 6.6 - Prob. 18ECh. 6.6 - Prob. 19ECh. 6.6 - 17–32. For each double integral in Exercises...Ch. 6.6 - 17–32. For each double integral in Exercises...Ch. 6.6 - 17–32. For each double integral in Exercises...Ch. 6.6 - Prob. 23ECh. 6.6 - Prob. 24ECh. 6.6 - Prob. 25ECh. 6.6 - 17–32. For each double integral in Exercises...Ch. 6.6 - 17–32. For each double integral in Exercises...Ch. 6.6 - Prob. 28ECh. 6.6 - Prob. 29ECh. 6.6 - Prob. 30ECh. 6.6 - Prob. 31ECh. 6.6 - Prob. 32ECh. 6.6 - Find the volume of the solid capped by the surface...Ch. 6.6 - 16. Find the volume of the solid capped by the...Ch. 6.6 - 17. Find the average value of. Ch. 6.6 - 18. Find the average value of. Ch. 6.6 - 19. Find the average value of, where the region of...Ch. 6.6 - Prob. 38ECh. 6.6 - 21. Life sciences: population. The population...Ch. 6.6 - 22. Life sciences: population. The population...Ch. 6.6 - Prob. 41ECh. 6.6 - Prob. 42ECh. 6.6 - Prob. 43ECh. 6.6 - Is evaluated in much the same way as a double...Ch. 6 - Match each expression in column A with an...Ch. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following 10. Ch. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following 12. Ch. 6 - Given, find each of the following 13. Ch. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following 15. Ch. 6 - 16. State the domain of Ch. 6 - Given, find each of the following 17. Ch. 6 - Given z=2x3Iny+xy2, find each of the following...Ch. 6 - Given, find each of the following 19. Ch. 6 - Given, find each of the following 20. Ch. 6 - Given, find each of the following 21. Ch. 6 - Given, find each of the following 22. Ch. 6 - Find the relative maximum and minimum values [6.3]...Ch. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 29RECh. 6 - Find the extremum of f(x,y)=6xy subject to the...Ch. 6 - Prob. 31RECh. 6 - Find the absolute maximum and minimum values of...Ch. 6 - Evaluate [6.6] 0112x2y3dydxCh. 6 - Evaluate [6.6] 33. Ch. 6 - Business: demographics. The density of students...Ch. 6 - 35. Evaluate . Ch. 6 - Prob. 37RECh. 6 - Prob. 39RECh. 6 - Prob. 1TCh. 6 - Prob. 2TCh. 6 - Prob. 3TCh. 6 - Given fx,y=2x3y+y, find each of the following. 4....Ch. 6 - Given fx,y=2x3y+y, find each of the following. 5....Ch. 6 - Given fx,y=2x3y+y, find each of the following. 6....Ch. 6 - Prob. 7TCh. 6 - Prob. 8TCh. 6 - Prob. 9TCh. 6 - Prob. 10TCh. 6 - Prob. 11TCh. 6 - Prob. 12TCh. 6 - Prob. 13TCh. 6 - 14. Business: maximizing production. Southwest...Ch. 6 - Find the largest possible volume of a rectangular...Ch. 6 - Find the average value of fx,y=x+2y over the...
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