Solve the problem.
-A farmer has 1,600 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width $x$ of the rectangle. What is the domain of $A$ ?
A) $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 1,600 \mathrm { x } ; \quad \{ \mathrm { x } \mid 0

Question

Solve the problem.
-A farmer has 1,600 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width $x$ of the rectangle. What is the domain of $A$ ?
A) $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 1,600 \mathrm { x } ; \quad \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}$
B) $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}$
C) $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 800 \}$
D) $A ( x ) = x ^ { 2 } + 800 x ; \{ x \mid 0 < x < 800 \}$

Quizplus · Accepted Answer

The perimeter of the rectangle is given as $2x + 2y = 1,600$, where $x$ is the width and $y$ is the length. Solving for $y$, we get $y = 800 - x$. The area $A$ of the rectangle is $xy$, substituting $y$ gives $A(x) = x(800 - x) = 800x - x^2$, which matches choice C. The domain of $A$ is $0 < x < 800$ because the width $x$ must be positive and less than half the total fencing to form a rectangle.

Solve the Problem xxx Of the Rectangle AAA ? A) A(x)=−x2+1,600x;{x∣0<x<1,600}\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 1,600 \mathrm { x } ; \quad \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}A(x)=−x2+1,600x;{x∣0<x<1,600}

Solve the Problem $x$ Of the Rectangle $A$ ?
A) $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 1,600 \mathrm { x } ; \quad \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}$