a.
To find: To find the dimensions of the width and depth.
a.
Answer to Problem 37E
The width are
Explanation of Solution
Given:
The strength S of a rectangle wooden beam is proportional to its width times the square of its depth.
Where S,w,d,k are the strength, width, depth and a constant respectively.
Concept Used: Pythagoras Thoerem.
Calculation:
Considering the figure, by Pythagoras theorem
The square of the hypotenuse is equal to the sum of square of adjacent side and opposite side.
Substituting
For any function
Substituting
Since
The critical points occurs at
For maximum strength, the dimensions are width is
b.
To find: To find the dimensions of the width.
b.
Answer to Problem 37E
The width are
Explanation of Solution
Given:
The strength S of a rectangle wooden beam is proportional to its width times the square of its depth.
Where S,w,d,k are the strength, width, depth and a constant respectively.
Calculation:
Plotting the graph between S and w
For maximum strength, the dimensions are width is
It is same as obtained in a.
b.
To find: To find the dimensions of the depth.
b.
Answer to Problem 37E
The depth is
Explanation of Solution
Given:
The strength S of a rectangle wooden beam is proportional to its width times the square of its depth.
Where S,w,d,k are the strength, width, depth and a constant respectively.
Calculation:
Plotting the graph between S and d.
For maximum strength, the dimensions are depth is
It is same as obtained in a.
The change in the value of k, will change the maximum strength but it will not change the dimension of the strongest beam, since dimensions are independent of k. For different values of k, the graph will be same expect that the vertical scale will be different.
Chapter 4 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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