Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
15th Edition
ISBN: 9781323047620
Author: Barnett, Ziegler, Byleen
Publisher: Pearson Education
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Textbook Question
Chapter 5.3, Problem 1E
In Problems 1–8, express the relationship between f′(x) and f(x) in words, and write a differential equation that f(x) satisfies. For example, the derivative of f(x) = e3x is 3 times f(x);y′ = 3y. (If necessary, review Section 3.4).
1. f(x) = e5x
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Chapter 5 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
Ch. 5.1 - Matched Problem 1 Note that ddx(x3)=3x2 A. Find...Ch. 5.1 - Find each indefinite integral: (A) 2dx (B) 16etdt...Ch. 5.1 - Matched Problem 3 Find each indefinite integral:...Ch. 5.1 - Matched Problem 4 Find the equation of the curve...Ch. 5.1 - Matched Problem 5 Find the revenue function R(x)...Ch. 5.1 - Matched Problem 6 There are currently 64,000...Ch. 5.1 - Explore and Discuss 1 Formulas 1, 2, and 3 do not...Ch. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - In Problems 18, write each function as a sum of...
Ch. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - Prob. 6ECh. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - Prob. 8ECh. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - In Problems 924, find each indefinite integral....Ch. 5.1 - Is F(x) = (x + 1) (x + 2) an antiderivative of...Ch. 5.1 - Prob. 26ECh. 5.1 - Is F(x) = 1 + x ln x an antiderivative of f(x) = 1...Ch. 5.1 - Is F(x) = x ln x x + e an antiderivative of f(x)...Ch. 5.1 - Is F(x)=(2x+1)33 an antiderivative of f(x) = (2x +...Ch. 5.1 - Is F(x)=(3x2)44 an antiderivative of f(x) = (3x ...Ch. 5.1 - Is F(x)=ex33an antiderivative of f(x)=ex2?...Ch. 5.1 - Is F(x) = (ex 10) (ex + 10) an antiderivative of...Ch. 5.1 - In Problems 3338, discuss the validity of each...Ch. 5.1 - In Problems 3338, discuss the validity of each...Ch. 5.1 - In Problems 3338, discuss the validity of each...Ch. 5.1 - Prob. 36ECh. 5.1 - In Problems 3338, discuss the validity of each...Ch. 5.1 - In Problems 3338, discuss the validity of each...Ch. 5.1 - In Problems 3942, could the three graphs in each...Ch. 5.1 - In Problems 3942, could the three graphs in each...Ch. 5.1 - In Problems 39-42, could the three graphs in each...Ch. 5.1 - In Problems 39-42, could the three graphs in each...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 4354, find each indefinite integral...Ch. 5.1 - In Problems 5562, find the particular...Ch. 5.1 - In Problems 5562, find the particular...Ch. 5.1 - In Problems 5562, find the particular...Ch. 5.1 - In Problems 5562, find the particular...Ch. 5.1 - In Problems 5562, find the particular...Ch. 5.1 - In Problems 5562, find the particular...Ch. 5.1 - In Problems 55-62, find the particular...Ch. 5.1 - In Problems 55-62, find the particular...Ch. 5.1 - Find the equation of the curve that passes through...Ch. 5.1 - Find the equation of the curve that passes through...Ch. 5.1 - In Problems 65-70, find each indefinite integral....Ch. 5.1 - In Problems 6570, find each indefinite integral....Ch. 5.1 - In Problems 6570, find each indefinite integral....Ch. 5.1 - In Problems 6570, find each indefinite integral....Ch. 5.1 - In Problems 6570, find each indefinite integral....Ch. 5.1 - In Problems 6570, find each indefinite integral....Ch. 5.1 - In Problems 7174, find the derivative or...Ch. 5.1 - In Problems 7174, find the derivative or...Ch. 5.1 - In Problems 7174, find the derivative or...Ch. 5.1 - Prob. 74ECh. 5.1 - In Problems 7174, find the derivative or...Ch. 5.1 - Use differentiation to justify the formula...Ch. 5.1 - Assuming that x 0, use differentiation to justify...Ch. 5.1 - Assuming that x 0, use differentiation to justify...Ch. 5.1 - Show that the indefinite integral of the sum of...Ch. 5.1 - Prob. 80ECh. 5.1 - Cost function. 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(A)(2x33)20(6x2)dx...Ch. 5.2 - Matched Problem 2 (A) Find dy for y = f(x) = x3....Ch. 5.2 - Matched Problem 3 Find (x23x+7)4(2x3)dx by...Ch. 5.2 - Matched Problem 4 Use a substitution to find each...Ch. 5.2 - Matched Problem 5 Integrate. 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Find the amount A in...Ch. 5.3 - Prob. 78ECh. 5.3 - Continuous compound interest. Find the amount A in...Ch. 5.3 - Continuous compound interest. Find the amount A in...Ch. 5.3 - Pricedemand. The marginal price dp/dx at x units...Ch. 5.3 - Pricesupply. The marginal price dp/dx at x units...Ch. 5.3 - Advertising. A company is trying to expose a new...Ch. 5.3 - Prob. 84ECh. 5.3 - Biology. For relatively clear bodies of water, the...Ch. 5.3 - Blood pressure. Under certain assumptions, the...Ch. 5.3 - Drug concentration. A single injection of a drug...Ch. 5.3 - Simple epidemic. A community of 10,000 people is...Ch. 5.3 - Prob. 89ECh. 5.3 - Prob. 90ECh. 5.3 - Archaeology. A skull found in an ancient tomb has...Ch. 5.3 - Learning. For a person learning to type, the...Ch. 5.3 - Prob. 93ECh. 5.3 - Perception. The WeberFechner law concerns a...Ch. 5.3 - Prob. 95ECh. 5.3 - Prob. 96ECh. 5.4 - Prob. 1MPCh. 5.4 - Matched Problem 2 Consider the function f(x) = x2 ...Ch. 5.4 - Matched Problem 3 Referring to the figure for...Ch. 5.4 - Matched Problem 4 Using the same integral values...Ch. 5.4 - Prob. 1EDCh. 5.4 - Explore and Discuss 2 If f(x) in Figure 3 were...Ch. 5.4 - In Problems 16, perform a mental calculation to...Ch. 5.4 - In Problems 16, perform a mental calculation to...Ch. 5.4 - In Problems 16, perform a mental calculation to...Ch. 5.4 - Prob. 4ECh. 5.4 - In Problems 16, perform a mental calculation to...Ch. 5.4 - In Problems 16, perform a mental calculation to...Ch. 5.4 - A Problems 710 refer to the rectangles A, B, C, D,...Ch. 5.4 - A Problems 710 refer to the rectangles A, B, C, D,...Ch. 5.4 - A Problems 710 refer to the rectangles A, B, C, D,...Ch. 5.4 - A Problems 710 refer to the rectangles A, B, C, D,...Ch. 5.4 - Prob. 11ECh. 5.4 - Problems 11-14 refer to the rectangles F, G, H, I,...Ch. 5.4 - Prob. 13ECh. 5.4 - Problems 1114 refer to the rectangles F, G, H, I,...Ch. 5.4 - Problems 1522 involve estimating the area under...Ch. 5.4 - Problems 1522 involve estimating the area under...Ch. 5.4 - Problems 1522 involve estimating the area under...Ch. 5.4 - Problems 1522 involve estimating the area under...Ch. 5.4 - Problems 1522 involve estimating the area under...Ch. 5.4 - Problems 1522 involve estimating the area under...Ch. 5.4 - Problems 1522 involve estimating the area under...Ch. 5.4 - Prob. 22ECh. 5.4 - In Problems 2326, calculate the indicated Riemann...Ch. 5.4 - In Problems 2326, calculate the indicated Riemann...Ch. 5.4 - In Problems 2326, calculate the indicated Riemann...Ch. 5.4 - In Problems 2326, calculate the indicated Riemann...Ch. 5.4 - In Problems 2730, calculate the indicated Riemann...Ch. 5.4 - In Problems 2730, calculate the indicated Riemann...Ch. 5.4 - In Problems 2730, calculate the indicated Riemann...Ch. 5.4 - In Problems 2730, calculate the indicated Riemann...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 3142, calculate the definite integral...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - In Problems 4354, calculate the definite integral,...Ch. 5.4 - B In Problems 5560, discuss the validity of each...Ch. 5.4 - B In Problems 5560, discuss the validity of each...Ch. 5.4 - B In Problems 5560, discuss the validity of each...Ch. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - B In Problems 5560, discuss the validity of each...Ch. 5.4 - Problems 61 and 62 refer to the following figure...Ch. 5.4 - Prob. 62ECh. 5.4 - C Problems 63 and 64 refer to the following...Ch. 5.4 - C Problems 63 and 64 refer to the following...Ch. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - For Problems 6568, use derivatives to determine...Ch. 5.4 - For Problems 6568, use derivatives to determine...Ch. 5.4 - In Problems 6972, the left sum Ln or the right sum...Ch. 5.4 - In Problems 6972, the left sum Ln or the right sum...Ch. 5.4 - In Problems 6972, the left sum Ln or the right sum...Ch. 5.4 - In Problems 6972, the left sum Ln or the right sum...Ch. 5.4 - Prob. 73ECh. 5.4 - Prob. 74ECh. 5.4 - Medicine. The rate of healing, A(t) (in square...Ch. 5.4 - Prob. 76ECh. 5.4 - Learning. A psychologist found that, on average,...Ch. 5.4 - Prob. 78ECh. 5.5 - Matched Problem 1 Repeat Example 1 for the daily...Ch. 5.5 - Matched Problem 2 Evaluated 13(4x2ex+5x)dx.Ch. 5.5 - Matched Problem 3 Use both methods described in...Ch. 5.5 - Matched Problem 4 Use both method 2 described in...Ch. 5.5 - Matched Problem 5 Repeat Example 5 if...Ch. 5.5 - Matched Problem 6 Repeat Example 6 if C(t) = 1 and...Ch. 5.5 - c 1.54.3xlnxdx to three decimal places.Ch. 5.5 - Matched Problem 8 Find the average value of g(t) =...Ch. 5.5 - Matched Problem 9 Given the supply equation...Ch. 5.5 - Prob. 1EDCh. 5.5 - In Problems 18, use geometric formulas to find the...Ch. 5.5 - In Problems 18, use geometric formulas to find the...Ch. 5.5 - In Problems 18, use geometric formulas to find the...Ch. 5.5 - In Problems 18, use geometric formulas to find the...Ch. 5.5 - In Problems 18, use geometric formulas to find the...Ch. 5.5 - In Problems 18, use geometric formulas to find the...Ch. 5.5 - In Problems 18, use geometric formulas to find the...Ch. 5.5 - In Problems 18, use geometric formulas to find the...Ch. 5.5 - A In Problems 912, (A) Calculate the change in...Ch. 5.5 - A In Problems 912, (A) Calculate the change in...Ch. 5.5 - Prob. 11ECh. 5.5 - A In Problems 912, (A) Calculate the change in...Ch. 5.5 - Evaluate the integrals in Problems 1332. 13. 057dxCh. 5.5 - Evaluate the integrals in Problems 1332. 14....Ch. 5.5 - Evaluate the integrals in Problems 1332. 15....Ch. 5.5 - Evaluate the integrals in Problems 1332. 16. 035dxCh. 5.5 - Evaluate the integrals in Problems 1332. 17....Ch. 5.5 - Prob. 18ECh. 5.5 - Evaluate the integrals in Problems 1332. 19....Ch. 5.5 - Evaluate the integrals in Problems 1332. 20....Ch. 5.5 - Evaluate the integrals in Problems 1332. 21....Ch. 5.5 - Prob. 22ECh. 5.5 - Evaluate the integrals in Problems 1332. 23....Ch. 5.5 - Evaluate the integrals in Problems 1332. 24....Ch. 5.5 - Evaluate the integrals in Problems 1332. 25....Ch. 5.5 - Prob. 26ECh. 5.5 - Evaluate the integrals in Problems 1332. 27....Ch. 5.5 - Evaluate the integrals in Problems 1332. 28....Ch. 5.5 - Evaluate the integrals in Problems 1332. 29....Ch. 5.5 - Evaluate the integrals in Problems 1332. 30....Ch. 5.5 - Evaluate the integrals in Problems 1332. 31....Ch. 5.5 - Evaluate the integrals in Problems 1332. 32....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 33....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 34....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 35....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 36....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 37....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 38....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 39....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 40....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 41....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 42....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 43....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 44....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 45....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 46....Ch. 5.5 - B Evaluate the integrals in Problems 3348. 47....Ch. 5.5 - Prob. 48ECh. 5.5 - In Problems 4956, (A)Find the average value of...Ch. 5.5 - Prob. 50ECh. 5.5 - In Problems 4956, (A)Find the average value of...Ch. 5.5 - In Problems 4956, (A)Find the average value of...Ch. 5.5 - In Problems 4956, (A)Find the average value of...Ch. 5.5 - Prob. 54ECh. 5.5 - In Problems 4956, (A)Find the average value of...Ch. 5.5 - In Problems 4956, (A)Find the average value of...Ch. 5.5 - C Evaluate the integrals in Problems 5762. 57....Ch. 5.5 - C Evaluate the integrals in Problems 5762. 58....Ch. 5.5 - C Evaluate the integrals in Problems 5762. 59....Ch. 5.5 - C Evaluate the integrals in Problems 5762. 60....Ch. 5.5 - C Evaluate the integrals in Problems 5762. 61....Ch. 5.5 - C Evaluate the integrals in Problems 5762. 62....Ch. 5.5 - Prob. 63ECh. 5.5 - Use a numerical integration routine to evaluate...Ch. 5.5 - Use a numerical integration routine to evaluate...Ch. 5.5 - Use a numerical integration routine to evaluate...Ch. 5.5 - The mean value theorem states that if F(x) is a...Ch. 5.5 - Prob. 68ECh. 5.5 - Cost. A company manufactures mountain bikes. The...Ch. 5.5 - Cost. Referring to Problem 69, compute the...Ch. 5.5 - Salvage value. A new piece of industrial equipment...Ch. 5.5 - Maintenance costs. Maintenance costs for an...Ch. 5.5 - 73. Employee training. A company producing...Ch. 5.5 - Prob. 74ECh. 5.5 - Useful life. The total accumulated costs C(t) and...Ch. 5.5 - Useful life. The total accumulated costs C(t) and...Ch. 5.5 - Average cost. The total cost (in dollars) of...Ch. 5.5 - Average cost. The total cost (in dollars) of...Ch. 5.5 - Sales. The rate at which the total number of sales...Ch. 5.5 - Prob. 80ECh. 5.5 - Supply function. Given the supply function...Ch. 5.5 - Demand function. Given the demand function...Ch. 5.5 - Labor costs and learning. A defense contractor is...Ch. 5.5 - Labor costs and learning. If the rate of labor use...Ch. 5.5 - Prob. 85ECh. 5.5 - Repeat Problem 85 with an order of 1.200 units...Ch. 5.5 - Oil production. Using production and geological...Ch. 5.5 - Prob. 88ECh. 5.5 - Biology. A yeast culture weighing 2 grams is...Ch. 5.5 - Medicine. The rate at which the area of a skin...Ch. 5.5 - Temperature. If the temperature in an aquarium (in...Ch. 5.5 - Medicine. A drug is injected into the bloodstream...Ch. 5.5 - Politics. Public awareness of a congressional...Ch. 5.5 - Population composition. The number of children in...Ch. 5 - Find each integral in Problems 16. 1. (6x+3)dxCh. 5 - Find each integral in Problems 16. 2. 10205dxCh. 5 - Find each integral in Problems 16. 3. 09(4t2)dtCh. 5 - Prob. 4RECh. 5 - Find each integral in Problems 16. 5. 1+u4uduCh. 5 - Find each integral in Problems 16. 6. 01xe2x2dxCh. 5 - Is F(x) = ln x2 an antiderivative of f(x) = ln...Ch. 5 - Is F(x) = ln x2 an antiderivative of f(x)=2x?...Ch. 5 - Is F(x) = (ln x)2 an antiderivative of f(x) =2 ln...Ch. 5 - Is F(x) = (ln x)2 an antiderivative of f(x)=2lnxx?...Ch. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - In Problems 13 and 14, find the derivative or...Ch. 5 - In Problems 13 and 14, find the derivative or...Ch. 5 - Find a function y = f(x) that satisfies both...Ch. 5 - Find all antiderivatives of (A)dydx=8x34x1...Ch. 5 - Approximate 15(x2+1) dx, using a right sum with n...Ch. 5 - Prob. 18RECh. 5 - Use the following table of values and a left sum...Ch. 5 - Find the average value of f(x) = 6x2 + 2x over the...Ch. 5 - Describe a rectangle that has the same area as the...Ch. 5 - In Problems 22 and 23, calculate the indicated...Ch. 5 - In Problems 22 and 23, calculate the indicated...Ch. 5 - Use the graph and actual areas of the indicated...Ch. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Use the graph and actual areas of the indicated...Ch. 5 - Use the graph and actual areas of the indicated...Ch. 5 - Prob. 29RECh. 5 - Use the graph and actual areas of the indicated...Ch. 5 - Prob. 31RECh. 5 - Problems 3237 refer to the slope field shown in...Ch. 5 - Problems 3237 refer to the slope field shown in...Ch. 5 - Problems 3237 refer to the slope field shown in...Ch. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Find each integral in Problems 3848. 38.111+xdxCh. 5 - Find each integral in Problems 3848....Ch. 5 - Find each integral in Problems 3848. 40.5etdtCh. 5 - Find each integral in Problems 3848. 41.1e1+t2tdtCh. 5 - Find each integral in Problems 3848. 42.xe3x2dxCh. 5 - Find each integral in Problems 3848. 43.3112xdxCh. 5 - Prob. 44RECh. 5 - Find each integral in Problems 3848....Ch. 5 - Prob. 46RECh. 5 - Find each integral in Problems 3848. 47.exex+3dxCh. 5 - Prob. 48RECh. 5 - Find a function y = f(x) that satisfies both...Ch. 5 - Find the equation of the curve that passes through...Ch. 5 - (A)Find the average value off(x)=3x over the...Ch. 5 - Prob. 52RECh. 5 - Find each integral in Problems 5256 53.x(x31)2dxCh. 5 - Prob. 54RECh. 5 - Find each integral in Problems 5256. 55.07x16xdxCh. 5 - Prob. 56RECh. 5 - Find a function y = f(x) that satisfies both...Ch. 5 - Prob. 58RECh. 5 - Graph Problems 5962 on a graphing calculator, and...Ch. 5 - Prob. 60RECh. 5 - Graph Problems 59-62 on a graphing calculator, and...Ch. 5 - Prob. 62RECh. 5 - Prob. 63RECh. 5 - Use a numerical integration routine to evaluate...Ch. 5 - Use a numerical integration routine to evaluate...Ch. 5 - Prob. 66RECh. 5 - Prob. 67RECh. 5 - Prob. 68RECh. 5 - Profit function. If the marginal profit for...Ch. 5 - Prob. 70RECh. 5 - Inventory. Suppose that the inventory of a certain...Ch. 5 - Price-supply. Given the price-supply function...Ch. 5 - Prob. 73RECh. 5 - Prob. 74RECh. 5 - Prob. 75RECh. 5 - Pollution. An environmental protection agency...Ch. 5 - Population. The population of Mexico was 116...Ch. 5 - Archaeology. The continuous compound rate of decay...Ch. 5 - Learning. An average student enrolled in a typing...
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