Explanation Formula used: Volume, of the rectangular tank is calculated as, V = l × b × h . Newton’s approximation of x n is given by, x n = x n − 1 − f ( x n ) f ′ ( x n ) . Calculation: Given that, edges of the rectangular tank are 3.00 ft, 5.00 ft and 8.00 ft. Substitute, l = 8 , b = 5 and h = 3 in volume formula. V = l × b × h = 8 × 5 × 3 = 120 Let, x is the increase in each edge to double the volume of tank. Hence, new edges are ( 8 + x ) ft , ( 5 + x ) ft and ( 3 + x ) ft . Substitute, l = 8 + x , b = 5 + x , h = 3 + x and V = 2 V in volume formula. V = l × b × h = ( 8 + x ) × ( 5 + x ) × ( 3 + x ) = ( x 2 + 13 x + 40 ) ( 3 + x ) = x 3 + 16 x 2 + 79 x + 120 For zero deflection, y = 0 . x 4 − 30 x 3 + 1000 x = 0 x ( x 3 − 30 x 2 + 1000 ) = 0 On further simplification, x = 0 or x 3 − 30 x 2 + 1000 = 0 Hence, at x = 0 _ deflection of f ( x ) is zero. Suppose that the given equation of function f ( x ) = x 3 − 30 x 2 + 1000 . Differentiate the function f ( x ) with respect to x. d d x ( f ( x ) ) = d d x ( x 3 − 30 x 2 + 1000 ) f ′ ( x ) = 3 x 2 − 60 x . Substitute x = 6.5 in function f ( x ) . f ( 6.5 ) = ( 6.5 ) 3 − 30 ( 6.5 ) 2 + 1000 = 274.625 − 1267.5 + 1000 = 7.125 Substitute x = 7 in function f ( x ) . f ( 7 ) = ( 7 ) 3 − 30 ( 7 ) 2 + 1000 = 343 − 1470 + 1000 = − 127 Note that, the value of x 1 lies between x = 6.5 and x = 7 hence use the value of x 1 = 6.6 . Substitute x 1 = 6.8 in function f ( x ) . f ( 6.6 ) = ( 6.6 ) 3 − 30 ( 6.6 ) 2 + 1000 = 287.496 − 1306.8 + 1000 = − 19.304 Substitute x 1 = 6.6 in function f ′ ( x ) . f ′ ( 6.6 ) = 3 ( 6.6 ) 2 − 60 ( 6.6 ) = 130.68 − 396 = − 265.32 By Newton’s approximation, x 2 = x 1 − f ( x 1 ) f ′ ( x 1 ) x 2 = 6.6 − − 19.304 − 265.32 = 6.6 − 0.073 = 6.527 Find the third approximation x 3 with x 2 = 6.527 . Substitute x 2 = 6.527 in function f ( x ) . f ( 6.527 ) = ( 6.527 ) 3 − 30 ( 6.527 ) 2 + 1000 = 278.06 − 1278.05 + 1000 = 0.01 Substitute x = 6.527 in function f ′ ( x ) . f ′ ( 6.527 ) = 3 ( 6.527 ) 2 − 60 ( 6.527 ) = 127.805 − 391.62 = − 263.815 From Newton’s method, x 3 = x 2 − f ( x 2 ) f ′ ( x 2 ) x 3 = 6.527 − 0.01 − 263.815 = 6.527 + 0.0004 = 6.5274 Hence, at x = 6.527 _ deflection of function f ( x ) . is zero. Substitute x = − 5.5 in function f ( x ) . f ( − 5.5 ) = ( − 5.5 ) 3 − 30 ( − 5.5 ) 2 + 1000 = − 166.375 − 907.5 + 1000 = − 73.875 Substitute x = − 5 in function f ( x ) . f ( − 5 ) = ( − 5 ) 3 − 30 ( − 5 ) 2 + 1000 = − 125 − 750 + 1000 = − 125 Note that, the value of x 1 lies between x = − 5

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 24, Problem 58RE

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The value of edge should be increased equally to double the volume of the tank by Newton’s method.

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Chapter 24, Problem 57RE

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Chapter 24 Solutions

Basic Technical Mathematics

Ch. 24.1 - For the parabola y = 4 − x2, at the point (3, −5)...Ch. 24.1 - Prob. 2PE Ch. 24.1 - Prob. 1E Ch. 24.1 - Prob. 2E Ch. 24.1 - Prob. 3E Ch. 24.1 - Prob. 4E Ch. 24.1 - Prob. 5E Ch. 24.1 - Prob. 6E Ch. 24.1 - Prob. 7E Ch. 24.1 - Prob. 8E

Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. 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Prob. 20E Ch. 24.4 - Prob. 21E Ch. 24.4 - Prob. 22E Ch. 24.4 - Prob. 23E Ch. 24.4 - Prob. 24E Ch. 24.4 - Prob. 25E Ch. 24.4 - Prob. 26E Ch. 24.4 - Prob. 27E Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - Prob. 31E Ch. 24.4 - Prob. 32E Ch. 24.4 - Prob. 33E Ch. 24.4 - Prob. 34E Ch. 24.4 - Prob. 35E Ch. 24.4 - Prob. 36E Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - Prob. 38E Ch. 24.4 - Prob. 39E Ch. 24.4 - Prob. 40E Ch. 24.4 - Prob. 41E Ch. 24.4 - Prob. 42E Ch. 24.5 - Prob. 1PE Ch. 24.5 - Prob. 2PE Ch. 24.5 - Prob. 1E Ch. 24.5 - Prob. 2E Ch. 24.5 - Prob. 3E Ch. 24.5 - Prob. 4E Ch. 24.5 - Prob. 5E Ch. 24.5 - Prob. 6E Ch. 24.5 - Prob. 7E Ch. 24.5 - Prob. 8E Ch. 24.5 - Prob. 9E Ch. 24.5 - Prob. 10E Ch. 24.5 - Prob. 11E Ch. 24.5 - Prob. 12E Ch. 24.5 - Prob. 13E Ch. 24.5 - Prob. 14E Ch. 24.5 - Prob. 15E Ch. 24.5 - Prob. 16E Ch. 24.5 - 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A microprocessor chip is being designed with a...Ch. 24.7 - Prob. 18E Ch. 24.7 - What are the dimensions of the largest rectangular...Ch. 24.7 - A rectangular storage area is to be constructed...Ch. 24.7 - Prob. 21E Ch. 24.7 - Prob. 22E Ch. 24.7 - Prob. 23E Ch. 24.7 - Prob. 24E Ch. 24.7 - Prob. 25E Ch. 24.7 - Prob. 26E Ch. 24.7 - Prob. 27E Ch. 24.7 - Prob. 28E Ch. 24.7 - Prob. 29E Ch. 24.7 - Prob. 30E Ch. 24.7 - Prob. 31E Ch. 24.7 - Prob. 32E Ch. 24.7 - Prob. 33E Ch. 24.7 - What is the minimum slope of the curve y = x5 −...Ch. 24.7 - Prob. 35E Ch. 24.7 - Prob. 36E Ch. 24.7 - Prob. 37E Ch. 24.7 - Prob. 38E Ch. 24.7 - Prob. 39E Ch. 24.7 - Prob. 40E Ch. 24.7 - Prob. 41E Ch. 24.7 - Computer simulation shows that the drag F (in N)...Ch. 24.7 - Prob. 43E Ch. 24.7 - The potential energy E of an electric charge q due...Ch. 24.7 - An open box is to be made from a square piece of...Ch. 24.7 - Prob. 46E Ch. 24.7 - Prob. 47E Ch. 24.7 - Prob. 48E Ch. 24.7 - An oil pipeline is to be built from a refinery to...Ch. 24.7 - 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Prob. 48RE Ch. 24 - Prob. 49RE Ch. 24 - Prob. 50RE Ch. 24 - Prob. 51RE Ch. 24 - Prob. 52RE Ch. 24 - In Exercises 49–94, solve the given problems. 53....Ch. 24 - Prob. 54RE Ch. 24 - Prob. 55RE Ch. 24 - Prob. 56RE Ch. 24 - The deflection y (in m) of a beam at a horizontal...Ch. 24 - Prob. 58RE Ch. 24 - Prob. 59RE Ch. 24 - Prob. 60RE Ch. 24 - Prob. 61RE Ch. 24 - Prob. 62RE Ch. 24 - In Fig. 24.75, the tension T supports the 40.0-N...Ch. 24 - Prob. 64RE Ch. 24 - Prob. 65RE Ch. 24 - Prob. 66RE Ch. 24 - An analysis of the power output P (in kW/m3) of a...Ch. 24 - The altitude h (in ft) of a certain rocket as a...Ch. 24 - Prob. 69RE Ch. 24 - Prob. 70RE Ch. 24 - Prob. 71RE Ch. 24 - Prob. 72RE Ch. 24 - Prob. 73RE Ch. 24 - A special insulation strip is to be sealed...Ch. 24 - Prob. 75RE Ch. 24 - Prob. 76RE Ch. 24 - Prob. 77RE Ch. 24 - Prob. 78RE Ch. 24 - Prob. 79RE Ch. 24 - Prob. 80RE Ch. 24 - Prob. 81RE Ch. 24 - Prob. 82RE Ch. 24 - Prob. 83RE Ch. 24 - Prob. 84RE Ch. 24 - Prob. 85RE Ch. 24 - Prob. 86RE Ch. 24 - 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