Problem
A piece of rectangular sheet metal is 20 inches wide. It is to be made into a drain gutter by turning up the edges to form parallel sides. Let $x$ represent the length of each of the parallel sides.
Give the restrictions on $x$.
$0
Solution
Step 1 ：The restrictions on $x$ are $0
Step 2 ：The function that gives the area of a cross-section of the gutter is $A(x)=x(20-2x)$.
Step 3 ：The value of $x$ that maximizes the area of the cross-section is \(\boxed{5}\).
Step 4 ：The maximum area of the cross-section is \(\boxed{50}\) square inches.
Step 5 ：The values of $x$ for which the area of a cross-section will be less than 30 square inches are between $0$ and $5 - \sqrt{10}$ or between $\sqrt{10} + 5$ and $10$.
From Solvely APP
Solution
Step 1 ：The restrictions on $x$ are $0 Step 2 ：The function that gives the area of a cross-section of the gutter is $A(x)=x(20-2x)$. Step 3 ：The value of $x$ that maximizes the area of the cross-section is \(\boxed{5}\). Step 4 ：The maximum area of the cross-section is \(\boxed{50}\) square inches. Step 5 ：The values of $x$ for which the area of a cross-section will be less than 30 square inches are between $0$ and $5 - \sqrt{10}$ or between $\sqrt{10} + 5$ and $10$.
