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Math Calculus Calculus & Its Applications

37. Level of Water from Melting Snow Melting snow causes a river to overflow its banks. Let h ( t ) denotes the number of inches of water on Main Street t hours after the melting begins. If h ' ( 100 ) = 1 3 , by approximately how much water level change during the next half hour ? Which of the following two conditions is the better news? i) h ( 100 ) = 3 , h ' ( 100 ) = 2 , h ' ' ( 100 ) = − 5 ii) h ( 100 ) = 3 , h ' ( 100 ) = − 2 , h ' ' ( 100 ) = 5

37. Level of Water from Melting Snow Melting snow causes a river to overflow its banks. Let h ( t ) denotes the number of inches of water on Main Street t hours after the melting begins. If h ' ( 100 ) = 1 3 , by approximately how much water level change during the next half hour ? Which of the following two conditions is the better news? i) h ( 100 ) = 3 , h ' ( 100 ) = 2 , h ' ' ( 100 ) = − 5 ii) h ( 100 ) = 3 , h ' ( 100 ) = − 2 , h ' ' ( 100 ) = 5

Solution Summary: The author explains how to determine the change in water level from melting snow during the next half hour.

Calculus & Its Applications

Calculus & Its Applications

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 2.2, Problem 37E

37.

Level of Water from Melting Snow Melting snow causes a river to overflow its banks. Let h ( t ) denotes the number of inches of water on Main Street t hours after the melting begins.

If h ' ( 100 ) = 1 3 , by approximately how much water level change during the next half hour ?

Which of the following two conditions is the better news?

i) h ( 100 ) = 3 , h ' ( 100 ) = 2 , h ' ' ( 100 ) = − 5 ii) h ( 100 ) = 3 , h ' ( 100 ) = − 2 , h ' ' ( 100 ) = 5

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Chapter 2.2, Problem 36E

Chapter 2.2, Problem 38E

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Calculus & Its Applications

Ch. 2.1 - Does the slope of the curve in Fig. 17 increases...Ch. 2.1 - At which labelled point on the graph in Fig. 18 is...Ch. 2.1 - Exercises 1-4 refer to graphs (a)-(f) in Fig.19...Ch. 2.1 - Exercises 1-4 refer to graphs (a)-(f) in Fig.19...Ch. 2.1 - Exercises 1-4 refer to graphs (a)-(f) in Fig.19...Ch. 2.1 - Exercises 1-4 refer to graphs (a)-(f) in Fig.19...Ch. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Describe each of the following graphs. Your...

Ch. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Prob. 10E Ch. 2.1 - Describe each of the following graphs. 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Fill in each box of...Ch. 2.2 - The first and second derivatives of the function...Ch. 2.2 - Suppose that Fig. 20 contains the graph of y=s(t),...Ch. 2.2 - Suppose that Fig. 20 contains the graph of y=v(t),...Ch. 2.2 - 23. Refer to figure 21, Looking at the graph f(x),...Ch. 2.2 - In figure 22, the t axis represent the time in...Ch. 2.2 - 25. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 26. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 27. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 28. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 29. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 30. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 31. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - Prob. 32E Ch. 2.2 - 33. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 34. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 35. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - Prob. 36E Ch. 2.2 - 37. Level of Water from Melting Snow Melting snow...Ch. 2.2 - 38. Changes in Temperature T(t) is the temperature...Ch. 2.2 - Prob. 39E Ch. 2.2 - Prob. 40E Ch. 2.2 - Prob. 41E Ch. 2.2 - 42. Match each observation (a)(e) with a...Ch. 2.2 - Prob. 43E Ch. 2.2 - Drug Diffusion in the Bloodstream After a drug is...Ch. 2.2 - Prob. 45E Ch. 2.2 - Prob. 46E Ch. 2.3 - Which of the curves in Fig.15 could possibly be...Ch. 2.3 - Which of the curves in Fig.16 could be the graph...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Prob. 14E Ch. 2.3 - Prob. 15E Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Prob. 24E Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Prob. 31E Ch. 2.3 - Prob. 32E Ch. 2.3 - Prob. 33E Ch. 2.3 - Let a,b,c,d be fixed numbers with a0, and let...Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - Prob. 36E Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - In Exercises 41 and 42, determine which function...Ch. 2.3 - In Exercises 41 and 42, determine which function...Ch. 2.3 - Consider the graph of g(x) in Fig. 17. a. If g(x)...Ch. 2.3 - U. S. Population The population (in millions) of...Ch. 2.3 - Index-Fund Fees When a mutual fund company charges...Ch. 2.3 - Prob. 46E Ch. 2.3 - Technology Exercises Draw the graph of...Ch. 2.3 - Technology Exercises Draw the graph of...Ch. 2.3 - Technology Exercises Draw the graph of...Ch. 2.3 - Technology Exercises Draw the graph of...Ch. 2.4 - Determine whether each of the following functions...Ch. 2.4 - Prob. 2CYU Ch. 2.4 - Prob. 3CYU Ch. 2.4 - Find the x intercepts of the given function....Ch. 2.4 - Prob. 2E Ch. 2.4 - Find the x intercepts of the given function....Ch. 2.4 - Prob. 4E Ch. 2.4 - Find the x intercepts of the given function....Ch. 2.4 - Find the x intercepts of the given function....Ch. 2.4 - Show that the function f(x)=13x32x2+5x has no...Ch. 2.4 - Prob. 8E Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Prob. 14E Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Prob. 16E Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Prob. 18E Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Prob. 21E Ch. 2.4 - Prob. 22E Ch. 2.4 - Sketch the graphs of the following functions for...Ch. 2.4 - Prob. 24E Ch. 2.4 - Sketch the graphs of the following functions for...Ch. 2.4 - Prob. 26E Ch. 2.4 - Sketch the graphs of the following functions for...Ch. 2.4 - Prob. 28E Ch. 2.4 - Prob. 29E Ch. 2.4 - Prob. 30E Ch. 2.4 - Prob. 31E Ch. 2.4 - Prob. 32E Ch. 2.4 - Find the quadratic function f(x)=ax2+bx+c that...Ch. 2.4 - Prob. 34E Ch. 2.4 - Prob. 35E Ch. 2.4 - Prob. 36E Ch. 2.4 - Prob. 37E Ch. 2.4 - Technology Exercises Height of Tropical Grass The...Ch. 2.5 - Volume A canvas wind shelter for the beach has a...Ch. 2.5 - Prob. 2CYU Ch. 2.5 - For what x does the function g(x)=10+40xx2 have...Ch. 2.5 - Find the maximum value of the function f(x)=12xx2,...Ch. 2.5 - Find the minimum value of f(t)=t36t2+40, t0 and...Ch. 2.5 - For what t does the function f(t)=t2-24t have its...Ch. 2.5 - Optimization with Constraint Find the maximum of...Ch. 2.5 - Optimization with Constraint Find two positive...Ch. 2.5 - Optimization with Constraint Find the minimum of...Ch. 2.5 - In Exercise 7, can there be a maximum for Q=x2+y2...Ch. 2.5 - Minimizing a Sum Find the positive values of x and...Ch. 2.5 - Maximizing a Product Find the positive values of...Ch. 2.5 - Area There are 320 available to fence in a...Ch. 2.5 - Volume Figure 12 (b) shows an open rectangular box...Ch. 2.5 - Volume Postal requirements specify that parcels...Ch. 2.5 - Perimeter Consider the problem of finding the...Ch. 2.5 - Cost A rectangular garden of area 75 square feet...Ch. 2.5 - Cost A closed rectangular box with a square base...Ch. 2.5 - Surface Area Find the dimensions of the closed...Ch. 2.5 - Volume A canvas wind shelter for the beach has a...Ch. 2.5 - Area A farmer has 1500 available to build an...Ch. 2.5 - Area Find the dimensions of the rectangular garden...Ch. 2.5 - Maximizing a Product Find two positive numbers,...Ch. 2.5 - Minimizing a Sum Find two positive numbers, xandy,...Ch. 2.5 - Area Figure 140 (a) shows a Norman window, which...Ch. 2.5 - Surface Area A large soup can is to be designed so...Ch. 2.5 - In Example 3 we can solve the constraint equation...Ch. 2.5 - Cost A ship uses 5x2 dollars of fuel per hour when...Ch. 2.5 - Cost A cable is to be installed from one corner,...Ch. 2.5 - Area A rectangular page is to contain 50 square...Ch. 2.5 - Distance Find the point on the graph of y=x that...Ch. 2.5 - Prob. 30E Ch. 2.5 - Distance Find the point on the line y=2x+5 that is...Ch. 2.5 - Technology Exercise Inscribed Rectangle of Maximum...Ch. 2.6 - In the inventory problem of Example 2, suppose...Ch. 2.6 - In the inventory problem Example 2, Suppose that...Ch. 2.6 - Inventory Problem Figure 6 shows the inventory...Ch. 2.6 - Refer to Fig. 6. 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List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Prob. 20RE Ch. 2 - In Fig. 4 (a) and 4 (b), the t axis represents...Ch. 2 - U.S. Electric Energy United States electrical...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. 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