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Question 24 a

Question 24 a

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 24 a
d Sketch the graph of S against x. Bfx and y which give the strongest beam. f If the cross-sectional depth of the beam must be less than or equal to 19 cm, find the maximum strength of the beam. 23 The number of salmon swimming upstream in a river to spawn is approximated by s(x) = -x³ + 3x² + 360x + 5000, with x representing the temperature of the water in degrees (°C). (This model is valid only if 6 ≤ x ≤ 20.) Find the water temperature that results in the maximum number of salmon swimming upstream. 24 A piece of wire 360 cm long is used to make the twelve edges of a rectangular box for which the length is twice the breadth. a Denoting the breadth of the box by x cm, show that the volume of the box, V cm³, is given by V = 180x² - 6x³. b Find the domain, S, of the function V: S→ R, V(x) = 180x2 - 6x³ which describes the situation. c Sketch the graph of the function with rule y = V(x). d Find the dimensions of the box that has the greatest volume. e Find the values of x (correct to two decimal places) for which V = 20 000.
Transcribed Image Text:d Sketch the graph of S against x. Bfx and y which give the strongest beam. f If the cross-sectional depth of the beam must be less than or equal to 19 cm, find the maximum strength of the beam. 23 The number of salmon swimming upstream in a river to spawn is approximated by s(x) = -x³ + 3x² + 360x + 5000, with x representing the temperature of the water in degrees (°C). (This model is valid only if 6 ≤ x ≤ 20.) Find the water temperature that results in the maximum number of salmon swimming upstream. 24 A piece of wire 360 cm long is used to make the twelve edges of a rectangular box for which the length is twice the breadth. a Denoting the breadth of the box by x cm, show that the volume of the box, V cm³, is given by V = 180x² - 6x³. b Find the domain, S, of the function V: S→ R, V(x) = 180x2 - 6x³ which describes the situation. c Sketch the graph of the function with rule y = V(x). d Find the dimensions of the box that has the greatest volume. e Find the values of x (correct to two decimal places) for which V = 20 000.
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