Answer :
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!
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!
