Sure, let's work through this step-by-step to fully understand the problem and the solution.
1. Understand the Given Information:
- The highway has a grade value of 1190.
- The grade indicates the steepness of the slope in percentage. Here the grade value corresponds to a slope calculation provided as [tex]\(-\frac{11}{100}\)[/tex].
2. Grade and Slope Relationship:
- The given grade of [tex]\(-\frac{11}{100}\)[/tex] translates to the slope of the highway in fractional form. This means for every 100 units of horizontal distance, the highway drops 11 units of vertical distance (since it's a descent, the slope is negative).
3. Convert Slope to Percentage:
- The next step is to convert the slope [tex]\(-\frac{11}{100}\)[/tex] into a percentage to understand the steepness as commonly expressed in road grades.
- The slope [tex]\(-\frac{11}{100}\)[/tex] is equivalent to multiplying by 100 to obtain the percentage.
- Therefore, [tex]\(-\frac{11}{100} \times 100 = -11\%\)[/tex].
4. Discuss the Interpretation:
- The highway's grade of 1190 corresponds to a slope of [tex]\(-11\%\)[/tex].
- This suggests that the highway descends 11 meters vertically for every 100 meters horizontally. The negative sign is indicative of a downward slope.
Summary:
- The highway with a 1190 grade has a slope of [tex]\(-0.11\)[/tex].
- This slope converts to a grade percentage of [tex]\(-11\%\)[/tex].
I hope this detailed explanation clarifies the relationship between the given grade and the corresponding slope and grade percentage. Please feel free to ask if you have any further questions!
