A rectangular beam is cut from a cylindrical log of radius 50 cm. A cross-section of the log is shown below. (b) Find S'(w) The strength, S, of a beam of width w and height h is proportional to wh². (a) Express the strength of the beam as a function of w only. Use k as the proportionality constant and lower case w S(w) = k(1000w - w³) = Height = h || W X 50 (c) Find the exact width and height of the beam of maximum strength. Width =

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
icon
Related questions
Question
A rectangular beam is cut from a cylindrical log of radius 50 cm. A cross-section of the log is shown below.
(b) Find S'(w) =
The strength, S, of a beam of width w and height h is proportional to wh².
(a) Express the strength of the beam as a function of w only. Use k as the proportionality constant and lower case w.
s(w) = k(1000w - w³)
W
Width =
h
Height
1
=
W
50
X
(c) Find the exact width and height of the beam of maximum strength.
Transcribed Image Text:A rectangular beam is cut from a cylindrical log of radius 50 cm. A cross-section of the log is shown below. (b) Find S'(w) = The strength, S, of a beam of width w and height h is proportional to wh². (a) Express the strength of the beam as a function of w only. Use k as the proportionality constant and lower case w. s(w) = k(1000w - w³) W Width = h Height 1 = W 50 X (c) Find the exact width and height of the beam of maximum strength.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

Blurred answer
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage