A rectangle is bounded by the x-axis and the semicircle $y = \sqrt { 49 - x ^ { 2 } }$ (see figure).Select the area A of the rectangle as a function of x, and determine the domain of the function.
A) $A ( x ) = 2 | x | \sqrt { 49 - x ^ { 2 } }$ , -7 $\le$x $\le$7
B) $A ( x ) = - 2 x \sqrt { 49 - x ^ { 2 } }$ , -7 $\le$ x $\le$7
C) $A ( x ) = x \sqrt { 49 - x ^ { 2 } }$ , x $\ge$ 0
D) $A ( x ) = 2 x \sqrt { 49 - x ^ { 2 } }$ , x $\ge$0
E) $A ( x ) = | x | \sqrt { 49 - x ^ { 2 } }$ , all real numbers

Question

A rectangle is bounded by the x-axis and the semicircle $y = \sqrt { 49 - x ^ { 2 } }$ (see figure).Select the area A of the rectangle as a function of x, and determine the domain of the function.     
A) $A ( x ) = 2 | x | \sqrt { 49 - x ^ { 2 } }$ , -7 $\le$x $\le$7 
B) $A ( x ) = - 2 x \sqrt { 49 - x ^ { 2 } }$ , -7 $\le$ x $\le$7 
C) $A ( x ) = x \sqrt { 49 - x ^ { 2 } }$ , x $\ge$ 0 
D) $A ( x ) = 2 x \sqrt { 49 - x ^ { 2 } }$ , x $\ge$0 
E) $A ( x ) = | x | \sqrt { 49 - x ^ { 2 } }$ , all real numbers

Quizplus · Accepted Answer

The Answer of A rectangle is bounded by the x-axis and the semicircle $y = \sqrt { 49 - x ^ { 2 } }$ (see figure).Select the area A of the rectangle as a function of x, and determine the domain of the function.     
A) $A ( x ) = 2 | x | \sqrt { 49 - x ^ { 2 } }$ , -7 $\le$x $\le$7 
B) $A ( x ) = - 2 x \sqrt { 49 - x ^ { 2 } }$ , -7 $\le$ x $\le$7 
C) $A ( x ) = x \sqrt { 49 - x ^ { 2 } }$ , x $\ge$ 0 
D) $A ( x ) = 2 x \sqrt { 49 - x ^ { 2 } }$ , x $\ge$0 
E) $A ( x ) = | x | \sqrt { 49 - x ^ { 2 } }$ , all real numbers

A Rectangle Is Bounded by the X-Axis and the Semicircle y=49−x2y = \sqrt { 49 - x ^ { 2 } }y=49−x2​

A Rectangle Is Bounded by the X-Axis and the Semicircle $y = \sqrt { 49 - x ^ { 2 } }$