To determine the width of the driveway and the height of the carport, we need to use the given expressions for area, length, volume, and area beneath the carport.
### Step-by-Step Solution:
1. Given Information:
- Area of the driveway: [tex]\( 55x^2 + 43x - 18 \)[/tex]
- Length of the driveway: [tex]\( x + 9 \)[/tex]
2. To Find: Width of the driveway
- The width of a rectangle is found by dividing its area by its length.
[tex]\[
\text{Width of the driveway} = \frac{\text{Area of the driveway}}{\text{Length of the driveway}}
\][/tex]
[tex]\[
\text{Width of the driveway} = \frac{55x^2 + 43x - 18}{x + 9}
\][/tex]
3. Given Information:
- Volume of the carport: [tex]\( 48x^3 + 68x^2 - 8x - 3 \)[/tex]
- Area of the driveway beneath the carport: [tex]\( 8x^2 + 10x - 3 \)[/tex]
4. To Find: Height of the carport
- The height of a 3-dimensional rectangular space (like the carport) can be found by dividing its volume by the area of its base.
[tex]\[
\text{Height of the carport} = \frac{\text{Volume of the carport}}{\text{Area of the driveway beneath the carport}}
\][/tex]
[tex]\[
\text{Height of the carport} = \frac{48x^3 + 68x^2 - 8x - 3}{8x^2 + 10x - 3}
\][/tex]
Upon simplifying these expressions, we get the following results.
- The width of the driveway:
[tex]\[
\frac{55x^2 + 43x - 18}{x + 9}
\][/tex]
- The height of the carport:
[tex]\[
6x + 1
\][/tex]
### Final Answer:
Width of the driveway:
[tex]\[ \text{Width of the driveway} = \frac{55x^2 + 43x - 18}{x + 9} \][/tex]
Height of the carport:
[tex]\[ \text{Height of the carport} = 6x + 1 \][/tex]
Replace the values into the expressions:
- Width of driveway (first line):
[tex]\[
\frac{55x^2 + 43x - 18}{x + 9}
\][/tex]
- Height of carport (second line):
[tex]\[
6x + 1
\][/tex]
