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Algebra
Pregunta

A closed box with a square base is required to hav...

A closed box with a square base is required to have a volume of \( 10 \) cubic feet. 

(a) Build a model that expresses the amount \( A \) of material used to make such a box as a function of the length \( x \) of a side of the square base. 

(b) How much material is required for a base \( 1 \) foot by \( 1 \) foot? 

(c) How much material is required for a base \( 2 \) feet by \( 2 \) feet? 

(d) Graph \( A = A ( x ) \) . For what value of \( x \) is \( A \) smallest? 

Answer

 

\(\left. \begin{array} { l } { \text { (a) } A ( x ) = 2 x ^ { 2 } + \frac { 40 } { x } } \\ { \text { (b) } 42 ft ^ { 2 } \text { (c) } 28 ft ^ { 2 } } \\ { \text { (d) } } \\ { A \text { is smallest when } x \approx 2.15 ft . } \end{array} \right.\)

Solución
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