At a certain factory,the output Q is related to inputs x and y by the expression $Q ( x , y ) = 2 x ^ { 3 } + 2 x ^ { 2 } y ^ { 4 } + 9 y ^ { 5 }$ .If 0 $\leq$ x $\leq$ 8 and 0 $\leq$ y $\leq$ 10,what is the average output of the factory? (Approximate to 2 decimal places.)
A)111,504.00 units
B)235,589.33 units
C)235,590.13 units
D)308,341.33 units

Question

At a certain factory,the output Q is related to inputs x and y by the expression $Q ( x , y ) = 2 x ^ { 3 } + 2 x ^ { 2 } y ^ { 4 } + 9 y ^ { 5 }$ .If 0  $\leq$ x  $\leq$ 8 and 0  $\leq$ y  $\leq$ 10,what is the average output of the factory? (Approximate to 2 decimal places.)
A)111,504.00 units
B)235,589.33 units
C)235,590.13 units
D)308,341.33 units

Quizplus · Accepted Answer

The average output is calculated by integrating the function over the given range for x and y, and then dividing by the area of the range. The correct average output is approximately 235,589.33 units.

At a Certain Factory,the Output Q Is Related to Inputs Q(x,y)=2x3+2x2y4+9y5Q ( x , y ) = 2 x ^ { 3 } + 2 x ^ { 2 } y ^ { 4 } + 9 y ^ { 5 }Q(x,y)=2x3+2x2y4+9y5

At a Certain Factory,the Output Q Is Related to Inputs $Q ( x , y ) = 2 x ^ { 3 } + 2 x ^ { 2 } y ^ { 4 } + 9 y ^ { 5 }$