To solve this problem step-by-step, follow the instructions below:
a) You are given that 38 degrees is taken from 100%. You need to determine the remainder in degree measure.
1. Start with the full measure, which is 100%.
2. Subtract the portion that is taken, which is 38 degrees.
[tex]\[ 100\% - 38° = 62° \][/tex]
Thus, the remainder in degree measure is 62 degrees.
Additionally, you asked about 10% and 15° in grade measure. Let's clarify this based on the specific context:
Degree Measure and Grade Measure
1. Degree Measure: Degrees are typically used in circular measurements, with a full circle being 360 degrees.
2. Grade Measure (also called Gradian Measure): This is another unit of angular measure where a full circle is divided into 400 grades (or gradians).
To convert between degrees and grades:
- 1 degree = 400/360 grades
- 1 grade = 360/400 degrees
Now, let's perform each specific conversion:
10% conversion:
3. To determine what 10% corresponds to in degrees (if considering a full circle):
- 10% of 360° = 0.10 * 360° = 36°
4. To convert 36 degrees into grades:
- [tex]\( 36° \times \frac{400}{360} = 40 \text{ grades} \)[/tex]
15° conversion:
5. To convert 15 degrees into grades, use the conversion factor:
- [tex]\( 15° \times \frac{400}{360} = 16.67 \text{ grades} \)[/tex]
In summary:
- The remainder in degree measure after taking 38 degrees out of 100% is 62 degrees.
- 10% corresponds to 36 degrees, which is equivalent to 40 grades.
- 15 degrees is equivalent to approximately 16.67 grades.
