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 themaximum strength of the beam.23 The number of salmon swimming upstream in a river to spawn is approximated bys(x) = -x³ + 3x² + 360x + 5000, with x representing the temperature of the water indegrees (°C). (This model is valid only if 6 ≤ x ≤ 20.) Find the water temperature thatresults 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 forwhich 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, isgiven by V = 180x² - 6x³.b Find the domain, S, of the function V: S→ R, V(x) = 180x2 - 6x³ which describesthe situation.c Sketch the graph of the function with rule y = V(x).dFind 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.

Given information Length of wire = 360 cm Also, given that the length of rectangular box is twice…

Answered: Question 24 a

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Question 24 a

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 39CT: The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model...

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Question

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.

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