To find the volume of a stall in terms of its width [tex]\( x \)[/tex] feet, you need to consider the given equation:
[tex]\[ 9x^2 + 1080x \][/tex]
1. Start by recognizing the volume expression in terms of width [tex]\( x \)[/tex]:
[tex]\[ V = 9x^2 + 1080x \][/tex]
2. Next, determine if it is possible for the width of the stall to be 10 feet by substituting [tex]\( x = 10 \)[/tex] into the volume expression:
[tex]\[ V = 9(10^2) + 1080(10) \][/tex]
3. Calculate each term in the equation:
[tex]\[ 9(10^2) = 9(100) = 900 \][/tex]
[tex]\[ 1080(10) = 10800 \][/tex]
4. Add the two results together to find the volume:
[tex]\[ V = 900 + 10800 = 11700 \][/tex]
So, the volume of the stall when the width is 10 feet is 11700 cubic feet.
Thus, the completed equation is:
[tex]\[ 9x^2 + 1080x = 11700 \][/tex]
Yes, it is indeed possible for the width of the stall to be 10 feet, as it results in a meaningful volume calculation.
[tex]\[ \boxed{11700} \][/tex]
Is it possible for the width of a stall to be 10 feet?
[tex]\[ \boxed{\text{Yes}} \][/tex]
