A wooden beam has a rectangular crosssection of height h in. and width w in. (see the...
Question:
A wooden beam has a rectangular cross-section of height {eq}h\text{ in.} {/eq} and width {eq}w\text{ in.} {/eq} (see the accompanying figure). The strength {eq}S {/eq} of the beam is directly proportional to its width and the square of its height. What are the dimensions of the cross-section of the strongest beam that can be cut from a round log of diameter {eq}d=25\text{ in.} {/eq}?
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Maximum & Minimum:
To find the quantity that is maximum on some value of a variable, we need first to develop a relationship between the variable and that quantity. Then we will use the differentiation technique to get the maximum point.
Answer and Explanation: 1
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The diameter is given as:
{eq}d^2=w^2+h^2 {/eq}
Now, the strength is given as:
{eq}S= w+h^2\\ \Rightarrow S= w+(d^2-w^2)~~~~~~~~~\left [...
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